ON THE ELECTRON AFFINITIES OF PERFLUOROALKANES: A SYSTEMATIC

DENSITY FUNCTIONAL STUDY

by

ANKAN PAUL

(Under the Direction of Henry F. Schaefer)

ABSTRACT

The electron affinities of several perfluorolalkane (PFA) molecules have been

investigated employing hybrid and pure density functional methods. The optimum structures of

the neutral PFAs and their corresponding radical anions have been predicted employing pure and

hybrid density functionals in conjunction with a double zeta basis set augmented with

polarization and diffuse functions (DZP++). Electron affinities, structural features of neutrals and

anions of (a) linear chain PFAs (n-PFAs) and branched chain PFAs with tertiary C-F bonds, (b)

mono-cyclic PFAs (c-PFAs) and CF3- substituted c-PFAs, and (c) perfluoro-bicyclo[n, n,

0]alkanes (n,n,-BCPFAS), have been explored. Adiabatic electron affinity (AEA) trends for n-

PFAs (general formula, n-CnF2n+2, with “n” corresponding to the carbon chain length) reveal that

AEAs show a drastic enhancement moving from n=2 to n=3, beyond that they exhibit a slow

increase with increments falling of steadily with extending chain length, terminating at n=7. The

radical anions of n-PFAs show a characteristic structural feature, an exceptionally long C-F bond

in the middle carbon of the chain. Branched PFAs with a tertiary C-F bond are found to possess

higher AEA than the linear chain PFAs. Mono-cyclic PFAs (general formula of c-PFA, c-CnF2n,

and “n” corresponds to the carbon ring size) exhibit a peculiar trend of AEAs with increasing

ring size. The AEAs of c-CnF2n increase from n=3 to n=5 but then dramatically fall off for both

n=6 and n=7. It was noted that there is a change in the mode of binding the “extra electron”

beyond the 5-memebred ring. CF3- substituted c-PFAs display enhanced adiabatic electron

affinity due to the presence of tertiary C-F bonds. Adiabatic and vertical electron affinities were

computed for perfluoro-bicyclo[n, n, 0]alkanes, with “n” ranging from 1 to 4. All the n.n-

BCPFAs have tertiary C-F bonds. However, the mode of binding the “unpaired electron”

changes significantly over the different ring sizes for these bicyclic radical anions. The highly

strained 1, 1-BCPFA is predicted to have the highest AEA among the family of BCPFA

molecules that were examined.

INDEX WORDS: Perfluoroalkanes, Tertiary C-F bonds, Density Functional Theory,

Electron Affinity, and Spin Density.

ON THE ELECTRON AFFINITIES OF PERFLUOROALKANES: A SYSTEMATIC

DENSITY FUNCTIONAL STUDY

by

ANKAN PAUL

Bachelor of Science, Presidency College, University of Calcutta, India (1998)

Master of Science, Indian Institute of Science, India (2001)

A Thesis Submitted to the Graduate Faculty of The University of Georgia in Partial Fulfillment

of the Requirements for the Degree

DOCTOR OF PHILOSOPHY

ATHENS, GEORGIA

2005

© 2005

Ankan Paul

All Rights Reserved

ON THE ELECTRON AFFINITIES OF PERFLUOROALKANES: A SYSTEMATIC

DENSITY FUNCTIONAL STUDY

by

ANKAN PAUL

Major Professor: Henry F Schaefer

Committee: Nigel Adams Henning Meyer

Electronic Version Approved: Maureen Grasso Dean of the Graduate School The University of Georgia May 2005

iv

DEDICATION

To my parents

v

ACKNOWLEDGEMENTS

“The woods are lovely dark and deep.

But I have promises to keep.

And miles to go before I sleep

And miles to go before I sleep”.

(Robert Frost, Stopping by Woods on a Snowy evening)

These immortal lines by Robert Frost nicely parallel the journey of my academic life, my

thoughts and feelings on reaching a certain coveted destination. My academic pilgrimage was not

filled with solitude but marked by the auspicious presence of many people who had inspired and

helped me in several ways to reach my goal. On this occasion, I will like to take a sojourn and

express gratitude to those people who inhabit the “woods” of my memories.

I will go back to my school days where for the first time the seed of curiosity was

implanted in me. I will like to thank all my school teachers who through their lectures, guidance,

and disciplining had instilled in me the respect for the culture of learning. I will never forget my

English tutor Mr. Kusum Kumar Roy, who during my high school days initiated the thought

process related to politics. Incessant discussions regarding political situations in the world gave

birth to the critic and skeptic in me. .

My college days are replete with fond memories of many people who affected me in

different ways. My teachers at Presidency College taught me how to appreciate chemistry and

chemical bonding. Especially, I will like to acknowledge Prof. Dipak Mandal, Prof. Achintya

Kumar Sen, Prof. Sanjeeb Ghosh and Prof. Sailen Jha who molded my understanding of

vi

chemical principles. They were instrumental in building up my foundation of chemical

knowledge. During my college years I came across many friends who have shared with me their

vivacity and thoughts and have always stood beside during my bad times. I thank them all.

Especially Rajarshi, Anupam, Rhitoban, Debopam and others who joined with me the Indian

Institute of Science, Bangalore for their Masters study. I cannot forget the College canteen where

we spent hours discussing science, politics and music.

As for the teachers at IISC, Prof. Jayaraman Chandrasekhar and Prof. D. D. Sarma

introduced me to the domain of theoretical chemistry. Prof. Chandrasekhar and Prof. Uday

Maitra opened up the wonders of physical organic chemistry, molecular orbital theory and

symmetry rules. I will like to express my gratitude to Prof. Ramasesha, Prof. P. Balaram and

Prof. S. Chandrasekharan who have helped to understand different facets of chemistry. Prof. K.

L.Sebastian with whom I did my first research project, encouraged me to learn quantum

chemistry. I am indebted to Prof. Chandrasekhar who taught me the usefulness of computational

chemistry in elucidating different facets of chemical problems. I can never forget his lectures

where he used to quote arguments between famous chemists on well known chemical

conundrums, nourishing within us a culture of debate.

However, nothing will be complete if I don’t mention the name of my friends who made

my stay at IISC so joyful. Sanjeeb (Hati), Debangshu (Pagla), Prabuddha (Podu), Biswaroop

(Bishu), Pinaki (nipaki), Debangshu (Gultu), Suhrit (Surut), Indranil (Bicha), Arpan (Jonaki) and

JK are those people with whom I have shared a camaraderie which is unparalleled. Also I will

like to thank my friends, Subhashish’da, Manas, Rangeet, Borda, Abhijit’da, Kelta,

Aniruddha’da and Kabirul. We were all part of a big family, away from home for the first time,

vii

learning to help and appreciate each other. The music lessons that I received from Nandini’di and

Subarna’di were invaluable.

During my Ph.D program at the University of Georgia, I met Lubos and Chait who were

not only good friends but also helped me by sharing their understanding of quantum mechanics

and chemistry. With Lubos I have frequented the eateries in Athens down town innumerable

times and have discussed and argued at length on different topics. I will always remember him as

my “politically incorrect” friend, who can lighten up anybody’s spirit anytime with his knacky

sense of humor. The numerous debates that I had with Chait had helped me enrich my

understanding of different chemical problems. I appreciate Alexey’s sporting spirit who had

always joined Chait and me for a game of pool when the research hours seemed never ending. I

will also like to thank all the senior and junior graduate students who have made my stay at

Center for Computational Quantum Chemistry so cherishable.

My solitude in this country, away from my homeland had been reduced due to the

presence of certain people. Especially, I will like to thank Dalia who has been a special person in

my life. She has influenced me through her literary inclinations, her political awareness, her love

for poetry and music and the utmost care she has taken of me during the last year of my Ph. D. I

am also very much indebted to college friend, JK who has always kept in touch after coming to

the United States.

Researching at CC(Q)C was an wonderful experience, especially due to the presence of

excellent teachers and mentors. However, CC(Q)C is impaired without the patient and diligent

assistance of Ms. Linda Rowe. She with Amy and Karen has rescued us time and again from

paperwork disaster.

viii

I will like to profess my deepest gratitude to Dr. Yamaguchi who has been a patient

teacher. His approach towards chemical problems, his inexorable thirst for knowledge and most

importantly his humility has taught invaluable lessons, both as a scientist and as a human being.

Also I will like to thank Dr. Allen for his rigorous molecular spectroscopy course which has

nourished my knowledge of quantum chemistry.

It has been an honor to interact with Prof. Schleyer. The more I have interacted with him,

the more I have been at awe about his incessant quest and incisive reasoning. Like a tall tree, he

has given me the support and at the same time has challenged me to grow higher. I am fortunate

to receive his guidance.

However, nothing would have been possible without Prof. Schaefer. I wish to thank him

for providing us the amazing resource centre called CC(Q)C. And on a personal level, the kind of

support that I have received from him is exemplary. As his first Indian student, I have seen his

deep regard for the Indian scientific community, which is very significant for me as the

representative of my otherwise materially impoverished country, which nevertheless has a deep

culture of scientific and literary learning. There have been times, when I have faltered in my

path. But Prof. Schaefer’s encouragement and enthusiasm has always ignited my spirits. Like a

true teacher, he had his faith in me; at the same time he had taught me never to be complacent of

my achievements.

Lastly, I will like to thank my family. They are my source and without them I am no one.

Mamoni, Mary, Mama, Rajadadu, Dadu, Amma, Apu and Didun are the ones who have indulged

me so dearly, at times almost to the point of spoiling me. Saikat has been a loving friend, and

almost a brother. My sister is my friend and confidante. I wish her all the success in life.

ix

My father built the foundation of my knowledge. He was my first teacher. I will never

forget the time when I was seven, and he taught me fractions. As I became an adult he turned

into a trusted friend. I respect him for his integrity and his dynamism. I envy him for his energy.

Well, what to say about my mother. I love her. And as days pass by, I realize how close

we are. But more than being my mother I respect her as an individual who has taught me the

values of kindness and humility. Every time I think about her, I remember Charles Chaplin’s

famous last speech from The Great Dictator……“Our knowledge has made us cynical; our

cleverness, hard and unkind. We think too much and feel too little. More than machinery we

need humanity. More than cleverness we need kindness and gentleness. Without these qualities,

life will be violent and all will be lost.”

x

TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS.............................................................................................................v

LIST OF TABLES........................................................................................................................ xii

LIST OF FIGURES ..................................................................................................................... xiv

CHAPTER

1 INTRODUCTION AND LITERATURE REVIEW .....................................................1

1.1 ORIGIN AND THE HISTORY OF DEVELOPMENT OF DFT.......................3

1.2 BASIC EQUATIONS OF MODERN DFT ........................................................4

1.3 EXCHANGE-CORRELATION FUNCTIONALS.............................................6

1.4 OVERVIEW OF CHAPTERS ............................................................................7

1.5 REFERENCES....................................................................................................9

2 DO LINEAR CHAIN PERFLUOROALKANES BIND AN ELECTRON................11

2.1 ABSTRACT ......................................................................................................12

2.2 INTRODUCTION.............................................................................................12

2.3 COMPUTATIONAL METHODS ....................................................................15

2.4 RESULTS AND DISCUSSION .......................................................................17

2.5 CONCLUDING REMARKS ............................................................................25

2.6 REFERENCES..................................................................................................25

xi

3 THE PECULIAR TREND OF MONOCYCLIC PERFLUOROALKANE

ELECTRON AFFINITIES WITH INCREASING RING SIZE.............................44

3.1 ABSTRACT ......................................................................................................45

3.2 INTRODUCTION.............................................................................................45

3.3 COMPUTATIONAL METHODS ....................................................................49

3.4 RESULTS AND DISCUSSION .......................................................................52

3.5 CONCLUDING REMARKS ............................................................................61

3.6 REFERENCES..................................................................................................62

4 HIGH ELECTRON AFFINITIES OF PERFLUORO-BICYCLO[N, N, 0]

ALKANES ..............................................................................................................88

4.1 ABSTRACT ......................................................................................................89

4.2 INTRODUCTION.............................................................................................89

4.3 COMPUTATIONAL METHODS ....................................................................92

4.4 RESULTS AND DISCUSSION .......................................................................94

4.5 CONCLUDING REMARKS ..........................................................................101

4.6 REFERENCES................................................................................................102

5 CONCLUSION..........................................................................................................114

xii

LIST OF TABLES

Page

Table 2.1: Adiabatic electron affinities of linear chain CnF2n+2 in eV (n = 3 to 8). Zero point

corrected EAs are shown in parentheses........................................................................................29

Table 2.2: Vertical electron affinities of linear chain CnF2n+2 in eV (n = 2 to 8). ..........................30

Table 2.3: Vertical detachment energies of linear chain CnF2n+2 in eV (n = 2 to 8). .....................31

Table 2.4: Comparison of AEA of branched chain PFAs to those of their straight chain

analogues. Zero point corrected EAs are shown in parentheses. ..................................31

Table 2.5: Dihedral angles along the carbon backbone of n-PFAs (n- CnF2n+2 ) for n=4 to 8. (The

carbons are numbered from one end of the chain) ........................................................32

Table 3.1: Planarization energies (in kcal/mol) computed as the difference between the energy of

the c-PFA species in Dnh symmetry and the energy of the same species in its most

favorable conformational minimum..............................................................................69

Table 3.2: Adiabatic electron affinities of cyclic perfluoroalkanes in eV with the DZP++ basis

set. Zero-point corrected AEAs are shown in parentheses............................................69

Table 3.3: Comparison of AEAs for cyclic with straight chain PFAs at B3LYP/DZP++. Zero-

point energy corrected results are in parentheses. .........................................................70

Table 3.4: Adiabatic electron affinities of geometry constrained cyclic perfluoroalkanes in eV.

(Zero-point corrections are not included)......................................................................71

xiii

Table 3.5: Vertical electron affinities of cyclic perfluoroalkanes in eV. (Zero-point corrections

are not included)............................................................................................................71

Table 3.6: Vertical detachment energies of cyclic perfluoroalkanes anions in eV. (Zero-point

corrections are not included) .........................................................................................72

Table 3.7: Adiabatic electron affinities of CF3-monosubstituted PFAs in eV. Zero-point corrected

AEAs are shown in parentheses. ...................................................................................72

Table 4.1: Adiabatic electron affinities of BCPFAs in eV. Zero point corrected EAs are shown in

parentheses...................................................................................................................................105

Table 4.2: Vertical electron affinities of BCPFAs in eV. Zero point corrected EAs are shown in

parentheses. .................................................................................................................106

xiv

LIST OF FIGURES

Page

Figure 2.1: Optimized molecular geometries of: (a) Neutral n-C2F6 (D3d symmetry), (b) Anionic

n-C2F6 (Cs symmetry). All bond lengths reported are in Angstroms...........................33

Figure 2.2: Optimized molecular geometries of: (a) Neutral n-C3F8 (C2v symmetry), (b) Anionic

n-C3F8 (Cs symmetry). All bond lengths reported are in Angstroms...........................34

Figure 2.3: Optimized molecular geometries of: (a) Neutral n-C4F10 (C2 symmetry), (b) Anionic

n-C4F10 (C1 symmetry). All bond lengths reported are in Angstroms. ........................35

Figure 2.4: Optimized molecular geometries of: (a) Neutral n-C5F12 (C2v symmetry), (b) Anionic

n-C5F12 (C1 symmetry). All bond lengths reported are in Angstroms. ........................36

Figure 2.5: Optimized molecular geometries of: (a) Neutral n-C6F14 (C2 symmetry), (b) Anionic

n-C6F14 (C1 symmetry). All bond lengths reported are in Angstroms. ........................37

Figure 2.6: Optimized molecular geometries of: (a) Neutral n-C7F16 (C2v symmetry), (b) Anionic

n-C7F16 (Cs symmetry). All bond lengths reported are in Angstroms..........................38

Figure 2.7: Optimized molecular geometries of: (a) Neutral n-C8F18 (C2 symmetry), (b) Anionic

n-C8F18 (C1 symmetry). All bond lengths reported are in Angstrom...........................39

Figure 2.8: Optimized molecular geometries at the B3LYP/DZP++ level of theory: (a) Neutral

branched C4F10 (C1 symmetry), (b) Anionic branched C4F10 (C1 symmetry). All bond

lengths reported are in Angstroms.................................................................................40

xv

Figure 2.9: Optimized molecular geometries at the B3LYP/DZP++ level of theory: (a) Neutral

branched C5F12 (C1 symmetry), (b) Anionic branched C5F12 (C1 symmetry). All bond

lengths reported are in Angstroms.................................................................................41

Figure 2.10: Spin density plots for molecular anions at B3LYP/DZP++, (a) n-C2F6 (b) n-C3F8,

(c) n-C4F10, (d) n-C5F12, (e) n-C6F14, (f) n-C7F16, (g) n-C8F18, (h) branched- C4F10

(i) branched- C5F12. ......................................................................................................42

Figure 2.11: Comparison between (a) negative hyperconjugation in carbanions and (b) the

interaction of the partly-filled C-F σ* radical anion SOMO with empty anti-periplanar

C-F σ* orbital. ...............................................................................................................43

Figure 3.1: Optimized molecular geometries of: (a) Neutral c-C3F6 (D3h symmetry), (b) Anionic

n-C3F6 (D3h symmetry). All bond lengths reported are in Angstroms..........................................73

Figure 3.2: Optimized molecular geometries of: (a) Neutral c-C4F8 (D2d symmetry), (b) Anionic

c-C4F8 (D4h symmetry). All bond lengths reported are in Angstroms. ........................74

Figure 3.3: Optimized molecular geometries of: (a) Neutral c-C5F10 (C2 symmetry), (b) Anionic

c-C5F10 (Cs symmetry). All bond lengths reported are in Angstroms..........................75

Figure 3.4: Optimized molecular geometries of: (a) Neutral c-C6F12 (D3d symmetry), (b) Anionic

c-C6F12 (Cs symmetry). All bond lengths reported are in Angstroms..........................76

Figure 3.5: Optimized molecular geometries of: (a) Neutral c-C7F14 (C2 symmetry), (b) Anionic

c-C6F12 (C1 symmetry). All bond lengths reported are in Angstroms. ........................77

Figure 3.6: Optimized molecular geometries at the B3LYP/DZP++ and KMLYP/DZP++ level of

theory: (a) Neutral CF3-c-C3F5 (Cs symmetry), (b) Anionic branched CF3-c-C3F5 (Cs

symmetry). All bond lengths reported are in Angstroms. .............................................78

xvi

Figure 3.7: Optimized molecular geometries at the B3LYP/DZP++ and KMLYP/DZP++ level of

theory: (a) Neutral CF3-c-C4F7 (Cs symmetry), (b) Anionic branched CF3-c-C4F7 (Cs

symmetry). All bond lengths reported are in Angstroms. .............................................79

Figure 3.8: Optimized molecular geometries at the B3LYP/DZP++ and KMLYP/DZP++ level of

theory: (a) Neutral CF3-c-C5F9 (Cs symmetry), (b) Anionic branched CF3-c-C5F9 (Cs

symmetry). All bond lengths reported are in Angstroms ..............................................80

Figure 3.9: Optimized molecular geometries at the B3LYP/DZP++ and KMLYP/DZP++ level of

theory: (a) Neutral CF3-c-C6F11 (Cssymmetry), (b) Anionic branched CF3-c-C6F11 (Cs

symmetry). All bond lengths reported are in Angstroms. .............................................81

Figure 3.10: Spin density plots for molecular anions at B3LYP/DZP++, (a) c-C3F6 (b) c-C4F8,

(c) c-C5F10, (d) c-C6F12 and (e) c-C7F14 ....................................................................82

Figure 3.11: SOMO plots for molecular anions at B3LYP/DZP++, (a) c-C3F6 (b) c-C4F8, (c) c-

C5F10, and (d) c-C6F12. ................................................................................................83

Figure 3.12: SOMO plots for molecular anions at B3LYP/DZP++, (a) c-C3F6 (b) c-C4F8, (c) c-

C5F10, and (d) c-C6F12. ................................................................................................84

Figure 3.13: Comparison between (a) negative hyperconjugation in carbanions and (b) the

interaction of the partly-filled C-F σ* radical anion SOMO with empty anti-periplanar

C-F σ* orbital. ...............................................................................................................85

Figure 3.14: Plot of computed zero-point corrected AEAs with respect to the ring size of cyclic

perfluoroalkanes. ...........................................................................................................86

Figure 3.15 Plot of computed zero-point corrected AEAs with respect to increasing ring size of

CF3-c-PFAs. ..................................................................................................................87

xvii

Figure 4.1: Optimized molecular geometries of: (a) Neutral 1,1-BCPFA (C2v symmetry), (b)

Radical Anionic 1,1-BCPFA (D2h symmetry). All bond lengths reported are in

Angstroms and angles are in degrees .........................................................................107

Figure 4.2: Optimized molecular geometries of: (a) Neutral 2,2-BCPFA (C2 symmetry ), (b)

Radical anionic form of 2,2-BCPFA (C2v symmetry). All bond lengths reported are in

Angstroms. ..................................................................................................................108

Figure 4.3: Optimized molecular geometries of: (a) Neutral cis 3,3-BCPFA (C2 symmetry), (b)

Radical Anionic form of cis 3,3-BCPFA (Cs symmetry). All bond lengths reported are

in Angstroms. ..............................................................................................................109

Figure 4.4: Optimized molecular geometries of: (a) Neutral trans 3,3-BCPFA (C2h symmetry),

(b) Radical Anionic form of trans 3,3-BCPFA (Cs symmetry). All bond lengths

reported are in Angstroms. ..........................................................................................110

Figure 4.5: Optimized molecular geometries of: (a) Neutral trans 4,4-BCPFA (C2h symmetry),

(b) Radical Anionic form of trans 4,4-BCPFA (Cs symmetry). All bond lengths

reported are in Angstroms. ..........................................................................................111

Figure 4.6: Spin Density plots of (a) 1,1,-BCPFA(radical anion, (b) 2,2-BCPFA radical anion

(top and bottom view) , (c) cis 3,3-BCPFA radical anion, (d) trans-3,3-BCPFA radical

anion, (e) trans4,4-BCPFA radical anion. ...................................................................112

Figure 4.7 SOMO plots of (a) 1,1,-BCPFA(radical anion, (b) 2,2-BCPFA radical anion (c) cis

3,3-BCPFA radical anion, (d) trans-3,3-BCPFA radical anion, (e) trans4,4-BCPFA

radical anion. ...............................................................................................................113

CHAPTER 1

INTRODUCTION AND LITERATURE REVIEW

Chemistry, made an early entry in my life. When I reminisce about my childhood my thoughts

get flooded with the picture of me tampering with a battery and trying to electrolyze a salt

solution. I also remember spending hours concocting the perfect chemical mixture for making

fireworks more colorful. Chemistry for me is not limited to an academic subject, but is a part of

my childhood idle hours. Though from my words it may seem that I was taking small steps

towards becoming an experimental chemist, however with time I got metamorphosed into a

person of more theoretical pursuits in the field of chemistry. As I got introduced to molecular

orbital theory I realized the beauty and power of it in interpreting varied chemical phenomena

and molecular structural features. Over the years, Dr. Dipak Mandal (Presidency College,

Kolkata) and Dr. Jayaraman Chandrasekhar (Indian Institute of Science) groomed me through

their excellent lectures about how one can interpret molecular structural features and properties

by invoking molecular orbital theory. During my years as a graduate student at the Center for

Computational Chemistry in University of Georgia I was introduced to many powerful

techniques in computational quantum chemistry which not only provide better theoretical

understanding but also accurately quantify various experimentally measurable molecular

properties. Computational quantum chemistry, which pursues chemical knowledge in a

theoretical approach, is a domain which is both fascinating and challenging. It has since become

my path to explore various questions in chemistry.

2

Computational quantum chemistry employs physical laws in mathematical terms to make

predictions on different chemical phenomena and molecular structural facets. . It aids

experimentalists, not only providing theoretical perspective but also by making predictions both

in time and cost-effective manner. While experiments are difficult (and sometimes not feasible),

expensive and time consuming, theoretical investigations through computational chemistry

provide an alternative tool in areas of molecular structure and property determination. The

chemistry with computers has not only validated experimental findings, but on many occasions

has been used to rebut erroneous experimental claims. This theoretical approach also provides

the option to tread into areas where experiments cannot, study molecules which have not been

synthesized yet. This essentially makes computational chemistry, an efficient and accurate

soothsayer in the arena of active research in chemistry. Computational chemistry has been

established as a wonderful option to make reliable predictions about molecular structures and

properties.

Over the years density functional theory (DFT) has become an important device in

computational chemistry in making reliable estimates and predictions of molecular structures and

properties. Originally developed as a tool to study condensed matter problems in physics, DFT

has become very popular in theoretical explorations of chemical phenomena. Though Hartree-

Fock theory based highly electron correlated ab-initio methods have proven to be impeccably

accurate in determining molecular structures and properties, their use is limited to small

molecular systems, as these methods are computationally expensive. The cheap scaling and

efficient implementation of analytic derivatives of DFT based techniques have made them a cost-

effective tool in carrying out theoretical investigations in intermediately large molecular systems.

Throughout this dissertation DFT has been used to elucidate structural changes which occur on

3

electron attachment in different families of Perfluoroalkanes (PFAs) and computing electron

affinities.

1.1 ORIGIN AND THE HISTORY OF DEVELOPMENT OF DFT

The origin of density functional predates the inception of Hartree Fock theory [1, 2].

Fermi and Thomas derived an expression for the kinetic energy of electrons based on their

density in an infinite potential [3]. This expression is valid for non-interacting gases. After more

than two decades, Slater proposed the Xα method as a simplification to HF theory [4]. The non-

local Fock operator was approximated using a local operator within the uniform electron gas

model. The main breakthrough in density functional theory came after Hohenberg-Kohn

proposed their groundbreaking theorem [5], which stated that the ground state energy of an

electronic system can be solely determined by the electronic density. Through a reduction ad

absurdum approach they showed that the electronic density is a unique feature, which determines

the ground state energy. The next quantum leap in the advancement of DFT was witnessed when

Kohn and Sham reformulated the partitioning of the energy functional and introduced the

concept of the orbitals in DFT, the Kohn-Sham orbitals [6]. This led to increased use of DFT in

investigating chemical problems. Over the past few years DFT has been successfully used to

predict electron affinities for a wide variety of molecules [7]. The more accurate high level ab

initio methods can only be applied to compute electron affinities of very small molecules, DFT

has been become the popular tool to compute electron affinities of intermediately large

molecules. DFT has even been used to compute electron affinities of DNA nucleic acids and

bases [8]. DFT has been employed throughout this dissertation to compute electron affinities of

different families of perfluoroalkane molecules.

4

1.2 BASIC EQUATIONS OF MODERN DFT

DFT unlike ab initio employs electron density to calculate energy and properties of a

molecular system. The Hohenberg-Kohn theorem states that the ground state energy and any

observables of a system can be determined from the ground state electron density, ρ(r). The

many electron Hamiltonian can be written down as:

∑∑∑∑>=

+−

−∇−=N

ji ij

N

i iA

AM

A

N

iiel rrR

ZH 1||2

11

2 …………………………………….eq (1.1)

The electronic energy functional can be partitioned as

[ ] [ ] [ ] [ ]ρρρρ extee VVTE ++= 0 ………………………………………………………….eq(1.2)

[ ] [ ] [ ]ρρρ extHK VFE += …………………………………………………………………eq(1.3)

where [ ] [ ] [ ]ρρρ extHK VTF += 0 (a system independent functional), Vext arising from the

coulombic attraction term between the nuclei and the electrons and [ ]ρ0T arises from the kinetic

energy term in the electronic Hamiltonian.

The energy of the electronic system has been partitioned into kinetic energy functional of

interacting electrons, electron-electron interaction energy functional arising from the rij-1 term in

the electronic hamiltonian, and external potential energy functional. The Vee functional contains

J[ρ], the coulombic repulsion term between electrons.plus the classical coulombic repulsion plus

a non-classical term The first theorem of Hohenberg-Kohn states that the exact ground state

electronic density ρ(r) uniquely determines E[ρ] and Vext. Unfortunately there is no way to

determine the actual density ρ(r), the ground state electronic density. Also there is no way to

figure out the exact functional FHK[ρ]. The second theorem by Hohenberg-Kohn introduces the

concept of using a trial density and subsequent use of variational theorem to arrive to the energy

of the system. This was followed by an ingenious step of invoking a non-interacting system of

5

[ ] [ ] [ ] [ ] [ ])()( 0 ρρρρρ JVTTE eeSXC −+−=

)()])([(

)|'|/)'(()()(r

rEdrrrrrVrv XC

exteff δρρδ

ρ +−+= ∫)

electrons, which mimic the actual system of interacting electrons and using the density derived

from them as the trial density. This was the first time orbitals, which are essentially one electron

functions were introduced to DFT. A Slater (which is antisymmetrized product of orbitals, one

electron functions, φi) determinant was used as a trial wave function. This led to repartitioning

of the FHK[ρ] functional.

[ ] [ ] [ ] [ ]ρρρρ XCsHK EJTF ++= …………………………… …………………………eq(1.4)

where,

Ts is the kinetic energy of the non-interacting electrons and J[p] is the energy contribution from

coulombic repulsion of the non-interacting electron. The EXC[p] is the exchange-correlation

energy which includes energy corrections for the kinetic energy, energy correction for exchange

and coulombic self-interaction and electron correlation. Reformulating these functionals in terms

of orbitals and applying the variational principal with the constraint of orthonormality of the

orbitals the actual Kohn-Sham equations are obtained. The optimized orbitals are obtained by

self consistently solving the Kohn Sham equations. The Kohn-Sham equations are:

( ) iiieffi rv ϕεϕ =

+∇− 2

21

………………………………………………………………..eq(1.5)

where,

and the energy of the system is given by:

[ ] [ ])()()|'|/)()'((21][ rVrEdrrrrrE extXC

N

ii ρρρρερ ++−−= ∫∑ ………………………..eq(1.6)

where, [ ])()( rVdrVr extext ρρ =∫)

In the energy expression EXC, the exchange-correlation functional is unknown and so different

functionals have been developed to approximate that part.

6

1.3 EXCHANGE-CORRELATION FUNCTIONALS

Different methodologies have been pursued to design a proper exchange-correlation functional

which will provide for the exchange and correlation corrections. The early implementations of

the Kohn-Sham method used functionals, which were developed from electron gas data. The two

popular choices were spin unpolarized (LDF/LDA (Local Density Functional/Approximation)

[9] and spin polarized (LSD {Local Spin Density) where arguments require both α and β electron

densities [10], rather than a total density. Initially the LSDA functional, which treats electron

density locally as a uniform gas in conjunction of a spin polarization parameter, was widely used

to treat chemical problems. This functional employs the 1980 correlation functional of Vosko,

Wilk, and Nusair [11] and the exchange functional of Slater [12]. However, this correlation

functional over-binds the molecules and total energies are in error by up to 10%. Additionally,

correlation energies are overestimated by up to a factor of two. The LSDA functional’s original

form was abandoned, as it was found to over bind molecules. New families of functionals

originated to provide corrections to the LSDA functional. Out of those the most popular ones are:

the Generalized Gradient Approximation (GGA) based functionals and the hybrid functionals.

The GGA functionals employs a non-local component which is a derivative of the density.

Among the most popular GGA functionals is the “B” exchange functional [13] developed by

Becke. They are usually used in conjunction of the correlation functionals “LYP” and “P86” [14,

15]. The hybrid exchange functionals use a mixture of pure exchange with Hartree-Fock

exchange. The most commonly used exchange functionals are “B3” and “BH” [16, 17], both

developed by Becke. The B3 and BH hybrid functionals are widely used in conjunction with the

“LYP” correlation functionals, and usually known in scientific literature as the “B3LYP” and

“BHLYP” functionals. Throughout this thesis we have used both pure and hybrid functionals,

7

B3LYP, BLYP, and BP86. In particular cases we have also hybrid functionals like BHLYP and

KMLYP [18].

1.4 OVERVIEW OF CHAPTERS

Chapter 2 explores electron affinity trends in linear chain perfluoroalkanes (general

formula n-CnF2n+2) with increasing chain length. Linear chain Perfluoroalkanes (PFAs) are

known to bind electrons. Through the application of density functional theory, the unique

structural changes which are witnessed on electron attachment for linear PFA skeletons were

studied. Interestingly it was discovered that the “extra electron” in the PFA radical anions was

primarily localized in an elongated antibonding σ* orbital of the C-F bond attached to the central

carbon of the chain. Spin density plots revealed the extent of localization of the unpaired electron

in the radical anion. All the radical anions studied have a striking common structural feature, the

presence of a remarkably long C-F bond associated with the middle carbon of the chain. The

adiabatic electron affinities of all the linear chain PFAs are predicted to be positive (except for n-

C2F6 at KMLYP/DZP++ and BHLYP/DZP++). The electron affinities range from 0.23 eV to

0.70 eV at the B3LYP/DZP++ level of theory for linear chain PFAs for carbon chain length

ranging from 2 to 8. The AEAs increased from with increasing chain length from n=2 to n=7 and

then a slight decrease was observed for n=7 to n=8. We observe that there is a substantial surge

in AEA as we move from chain length n=2 to n=3 and then the increment in AEA falls with

increasing chain length. The particular trend of AEA is observed with increasing chain length of

the linear chain PFA is with the increase in -CF2 units in the chain the no. of negative inductive

effect exerting groups increase, hence conferring stability to the radical anion and at longer chain

length the inductive effect of distant –CF2 units are weak, so increase in AEA stops beyond a

certain chain length. The branched PFAs with tertiary C-F bonds have much higher AEA than

8

their linear chain counterparts. The i-C4F10 has an AEA of 1.23 eV as compared to the 0.45 eV of

n-C4F10. The i-C4F10 radical anion is stabilized by negative hyperconjugation and inductive

effect.

Chapter 3 is a report on the investigation of electron affinity trends in mono-cyclic PFAs

(general chemical formula, c-CnF2n) with increasing ring size. The adiabatic electron affinities,

the vertical electron affinities and vertical detachement energies have been computed for 2 to 7

membered PFA rings. A DFT study revealed that the structural changes which are observed on

electron attachment to c-PFAs vary over the different ring sizes. The 3- , 4- and 5- membered

PFA rings form a delocalized radical anion whereas the 6- and 7- membered rings form radical

anions which are more localized in nature. The 3- , 4- and 5- membered radical anions have

planar to near planar structures where the “unpaired electron” is delocalized over the molecular

plane through overlap of the C-F σ* orbitals. However, the 6- and 7- membered ring PFA radical

anions prefer puckered structural forms and the “unpaired electron” is localized in an

exceptionally long C-F bond. The AEA trends reveal that the AEAs of the mono-cyclic PFAs

increase with increasing ring size ranging from to 3- to 5- membered rings and beyond that a

dramatic drop in AEA was observed for the 6- and 7- membered rings. Ring strain and

planarization energy of these PFA rings have been implicated to explain the observed AEA

trends. The zero-point corrected AEA ranges from 0.4 eV to 1.0 eV at the B3LYP/DZP++ level

of theory for the c-PFAs. CF3- substitution of these cyclic PFAs leads to substantial increase in

AEAs. Generally it was observed that the presence of tertiary C-F bonds enhances the electron

binding ability of a PFA molecule.

Chapter 4 extends the exploration of electron affinities studies to a family of PFAs

which inherently possess tertiary C-F bonds, perfluoro-bicyclo[n, n, 0]alkanes (n,n,-BCPFAs).

9

The adiabatic and vertical electron affinities of n.n.-BCPFAs (for n=2 to n=4) have been

computed using hybrid density functional methods. The structural in these bicyclic rings vary

significantly with varying ring size. The cis isomer of 1,1 BCPFA is the only PFA molecule

which binds an electron in the bridgehead C-C σ*, as compared to the C-F σ* orbital in other

PFAs. All the BCPFAs studied exhibited substantially high AEAs as compared to those of the

previous mono-cyclic and linear PFAs. The zero point corrected AEAs of the BCPFAs range

from 0.9 eV to 2.3 eV at the B3LYP/DZP++ level of theory.

1.5 REFERENCES

[1] Hartree, D. R. Proc. Camb. Phil. Soc.1928, 24, 426.

[2] Slater, J. C. Phys. Rev. 1930, 35, 210.

[3] (a) Fermi, E. Rend. Accad. Lincei 1927, 6, 602. (b) Thomas, L. H. Proc. Camb. Phil. Soc.

1927, 23, 542.

[4] Slater, J. C. Phys. Rev. 1951, 81, 385.

[5] Hohenberg, P.; Kohn, W. Phys. Rev. 1964, 136, B864.

[6] Kohn, W.; Sham, L. J. Phys. Rev. 1964, 136, B864.

[7] Rienstra-Kiracofe, C. J.; Tschumper, G.S.; Schaefer, H. F. Chem. Rev. 2002, 102, 231.

[8] Richardson, N. A.; Weselowski, S. S.; Schaefer, H. F. J. Am. Chem. Soc. 2002, 124, 10163.

[9] Dirac, P. A. M. Proc. Cambridge Philos. Soc. 1930, 26, 376. [10] Von Weiszäcker, C. F. Z. Phys. 1935, 96, 431. [11] Vosko, S. J.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200. [12] Slater, J. C. Quantum Theory of Molecules and Solids: The Self-Consistent Field for

Molecules and Solids, Vol. IV. McGraw-Hill: New York, 1974.

[13] Becke, A. D. Phys. Rev. A. 1988, 38, 3098. [14] Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B., 1988, 37, 785.

10

[15] Perdew, J. P. Phys. Rev B, 1986, 33, 8822.

[16] Becke, A. D. J. Chem. Phys., 1993, 98, 5648.

[17] Becke, A. D. J. Chem. Phys., 1993, 98, 1372.

[18] Kang, J. K.; Musgrave, C. B. J. Chem. Phys. 2001, 115, 11040.

CHAPTER 2

DO LINEAR CHAIN PERFLUOROALKANES BIND AN ELECTRON?1

1 Ankan Paul, Chaitanya S. Wannere and Henry F. Schaefer Journal of the Physical Chemistry A 2004, 108, 9428. Reprinted by permission of the American Chemical Society, Copyright 2004.

12

2.1 ABSTRACT

The adiabatic electron affinities (AEAs), vertical electron affinities (VEAs) and vertical

detachment energies (VDEs) of linear chain perfluoroalkanes (PFAs), n-CnF2n+2 (n=2 to 8) are

predicted using carefully calibrated computational methods [Chem. Rev. 2002, 102, 231].

Density functional theoretical methods and hybrid Hartree-Fock/density functional methods have

been used with double-ζ quality basis sets with polarization and diffuse functions, DZP++.

Vibrational frequency analyses were performed to compute the zero point energy corrections and

determine the nature of the stationary points. The estimated adiabatic electron affinities of linear

chain PFAs (CnF2n+2), from n = 3 to 8, turn out to be appreciable, ranging from 0.26 eV to 0.64

eV (B3LYP/DZP++ method). The corresponding zero-point corrected values are a bit larger,

ranging from 0.39 eV to 0.71 eV. C2F6 is the only n-PFA exhibiting a negative adiabatic electron

affinity. The trends in AEAs of the n-PFA show that the AEA increases with increasing chain

length until n = 7 and then slightly decreases at n = 8. The VEAs of all the linear chain PFAs are

negative. VEAs increase with the increasing length of the linear hain PFAs. The VDEs indicate

that all the straight chain PFA anions considered are bound with respect to electron loss. It was

also observed that PFA molecules show enhanced AEAs when they are branched. The presence

of tertiary C-F bonds in PFAs results in high AEAs compared to those of their straight chain

counterparts.

2.2 INTRODUCTION

Perfluoroalkanes (PFAs) are used in numerous industrial applications [1, 2]. Due to their

chemical inertness, solvent resistance, extreme hydrophobicity, thermal stability, high lubricity,

and low dielectric constant, PFAs are excellent candidates for inert solvents, lubricants, sealants,

surfactants, oxygen carriers and anesthetics [3-9]. Cyclic PFAs are replacing the previous choice,

13

SF6, as tracers in atmospheric dispersion studies [10]. The unusual solubility characteristics of

PFAs have led to the emergence of a new field in catalytic chemistry known as fluorous bi-phase

chemistry [11]. Given the strength of carbon fluorine bonds in saturated systems and the lack of

functionality, PFAs have generally been perceived to be chemically inert. PFAs have earned the

dubious distinction of being “immortal molecules” [12]. The low reactivity of PFAs is

responsible for their long life time in the atmosphere, earning them membership in the notorious

club of potential Greenhouse gases [13]. Chemical innovations involving PFAs have broken the

myth of “chemical inertness” of this class of molecules. In their seminal work on PFAs, about

four decades ago, Tatlow and coworkers reported that defluorination of perfluoroalkanes can be

achieved by activation of the C-F bonds [14]. Macnicol and Robertson showed that reactivity in

perfluoroalkanes can be induced using arenethiolate nucleophiles under mild conditions [15].

PFAs do, in fact, have an interesting and developing chemistry originating from carbon-fluorine

bond activation [15-21]. All the well established reactions exploit the enhanced activity of the

tertiary C-F bonds, which has been termed as “Achilles Heel” of PFAs, to initiate reductive

defluorination.

The chemistry of perfluoroalkanes is dominated by the transfer of electrons. The different

pathways that have been exploited to initiate chemistry in PFAs are electron attachment in gas

phase (negative ion mass spectrometry) [22-34], electron transfer from metal surfaces (e.g. iron

or other transition metal complexes) or from electron rich organic donors (e.g. thiolates) [15] to

the σ* orbital of a C-F bond in the substrate. Such processes follow a radical anion mechanism,

where loss of fluoride initiates a cascade of reactions leading to unsaturated products. For

example, defluorination of perfluorodecalin is generally considered to occur by the transfer of

electrons to the σ* orbital of the most electron deficient tertiary carbon-fluorine bond to give a

14

radical anion. Loss of fluoride leads to a tertiary free radical which picks up another electron and

forms a carbanion. This is followed by fluoride loss forming a double bond at the fused part of

the two six member rings. Repeated electron transfer and fluoride elimination eventually leads to

formation of octafluoronapthalene [35, 36].

The preference for radical anion mechanisms in the defluorination reactions of PFAs

suggests the presence of appreciable electron affinities in this class of molecules. The possibility

of PFAs possessing appreciable electron affinities has made them important candidates for

electron attachment and scattering studies [22-34, 37-39]. Christophorou and co-workers have

carried out extensive high pressure electron attachment studies on linear chain PFAs [23-32].

They have shown that low energy electrons attach to n-PFAs dissociatively and/or non-

dissociatively depending on the chain length [23, 24, 28]. Parent negative ion formation was

observed only for n-CnF2n+2, for n=3 to 6 [24]. Electron attachment to CF4 and C2F6 was found to

be dissociative in nature [23, 24]. Moreover, it was noted that for branched i-C4F10 (perfluoro-

iso-butane) the parent anion formation was much more abundant compared to that for n-C4F10

[23]. Although comprehensive studies have been carried out on electron attachment rate

coefficients of n-PFAs, there is a scarcity of scientific literature on the electron affinities of these

molecules, both on the experimental and theoretical fronts. On the theoretical side, Leibman used

molecular orbital considerations to explain the higher electron affinities of cyclic

perfluoroalkanes compared to those of the linear chain counterparts [40]. King et. al. have

predicted, based on hybrid HF/DFT methods, that C2F6 has a negative adiabatic electron affinity

[41]. Moreover, their computations of vertical detachment energies for C2F6 reveal that this

anionic species is unbound with respect to electron loss. Falcetta, Choi, and Jordan have carried

out studies on negative ion states of C2F6 using ab initio techniques and they have computed

15

vertical electron affinities for C2F6 [42]. Estimates of the vertical electron affinities (VEAs) of

linear chain PFAs and PFAs have been reported by Ishii et. al. using electron transmission (ETS)

technique [33]. The plethora of experimental evidence that stable radical anion species can be

formed from the larger perfluoroalkanes inspired us to initiate a theoretical investigation on

straight chain perfluoroalkanes. Currently there is no theoretical insight about the adiabatic

electron affinity trends in n-PFAs and the structural features of the corresponding radical anion

species. We have used a set of set of reliable density functional methods (pure and hybrid) to

compute vertical and adiabatic electron affinities and vertical detachment energies for straight

chain CnF2n+2 (n=2-8). Moreover, we have investigated the significant changes in electron

affinity which occur on branching in two of these molecules, namely C4F10 and C5F12.

2.3 COMPUTATIONAL METHODS

Energies, optimized structures, harmonic vibrational frequencies and spin densities were

obtained using three generalized gradient optimized (GGA) exchange correlation functionals,

B3LYP, BLYP, and BP86. These are combinations of Becke’s exchange correlation functionals,

the 3 parameter HF/DFT hybrid functional (B3) [43] or the pure exchange functional (B) [44],

with the correlation functional of Lee, Young and Parr (LYP) [45] or that of Perdew (P86) [46,

47]. All computations were performed using double-ζ quality basis sets with polarization and

diffuse functions. The DZP++ basis sets were constructed by augmenting the 1970 Huzinaga-

Dunning [48, 49] sets of contracted double- ζ basis functions with one set of five d-type

polarization functions for each C and F. In addition to this, even tempered s and p type basis

functions were added to each C and F. The even tempered functions were designed following

Lee and Schaefer’s prescription [50]:

13

2

2

1diffuse 2

1 ααα

αα

α

+=

16

Where α1, α2, α3 are three smallest Gaussian orbital exponents of s and p type primitive functions

for a given atom (α1 < α2 <α3). The final DZP++ set contains nineteen functions per C and F

atom (10s6p1d/5s3p1d). This basis set with the earlier mentioned DFT and hybrid HF/DFT

methods have been used in systematic calibrative EA studies on a wide range of molecules [51].

The combination of the BLYP and B3LYP functionals with the DZP++ basis sets has been

shown to predict electron affinities with average errors of less than 0.15eV. In the present

investigation restricted and unrestricted DFT methods were used for the neutral species and the

anionic species respectively. All structures were optimized employing analytic gradients with

tight convergence criteria. Harmonic vibrational frequencies were computed without the

application of any scaling factor. Numerical integration was performed using the GAUSSIAN94

default grid of 75 radial shells with 302 angular points per shell [52]. Adiabatic electronic

affinities (AEA) were computed as the difference between the appropriate neutral and anion

species at their respective optimized geometries:

AEA = Energy (optimized neutral) – Energy (optimized anion)

The vertical electron affinities (VEA) were computed as the energy difference between the

neutral and the anion, at the neutral’s optimized geometry:

VEA = Energy (optimized neutral) – Energy (anion at optimized neutral geometry)

The vertical detachment energies (VDE) were computed as the difference between the anion and

the neutral, at the anion’s optimized geometry:

VDE = Energy (neutral at anion optimized geometry) – Energy (optimized anion)

For all anionic species plots of total spin density were computed. This quantity is given, within

the DFT approximations used here, by the difference of density of α and β assigned electrons.

)()()( rrr βα ρρρ −=s

17

The total spin density allows us examine the extent of delocalization of the unpaired electron

within the molecular framework.

2.4 RESULTS AND DISCUSSION

The AEA, VEA, and VDEs are tabulated in Tables 2.1, 2.2, and 2.3 respectively, while,

optimized geometries of n-CnF2n+2, and their corresponding radical anions are shown in Figures

2.1 through 2.7 respectively. The branched C4F10 and C5F12 and their corresponding radical anion

optimized molecular geometries are shown in Figures 2.8 and 2.9. A discussion of the EAs will

ensue after the analysis of the optimized geometrical structures of the neutral and the anions. The

optimized molecular geometries of all the other PFA molecules and their molecular anions

studied are provided in the supporting information.

2.4.1. THE NEUTRAL LINEAR CHAIN PFAS

Jorgensen and coworkers have analyzed different conformations of C4F10, C5F12 and C6F14 [53].

Perusal of the recent literature on perfluroalkanes reveals that a good amount of computational

work has been done on development of force fields and on conformational analysis for the

linear chain PFA molecules [53-63]. Following the literature on PFAs we have arrived to our

conformational choices for these molecules. It is known [53] that linear chain PFAs will prefer

all trans (staggered) conformations as the global minima. However, possible deviations from the

ideal all trans conformation may be expected due to destabilizing steric 1,5-diaxial interactions

[53]. For the odd numbered linear chain PFAs (CnF2n+2; where n is odd) we have imposed C2v

symmetry, while for the even numbered (except for n=2) linear chain PFAs our preferred choice

was C2h symmetry. Geometry optimizations of the linear chain PFAs using all three density

functionals and subsequent harmonic vibrational frequency analysis at the respective stationary

points showed that all the linear chain PFAs except C3F8 prefer a lower symmetry. Imposition of

18

C2v symmetry for C5F12 and C7F16 and C2h symmetry for C4F10, C6F14 and C8F18 leads to small

imaginary vibrational frequencies, which disappear when molecular geometries are allowed to

distort to C2 symmetry. Understandably, due to large conformational flexibility in these linear

chain PFAs the corresponding potential energy surfaces are expected to be flat. In C3F8, where

the number of 1,5 diaxial interactions is a minimum compared to other long chain n-PFAs, a

global minimum of C2v symmetry with the all trans conformation is preferred. C3F8 prefers the

all trans (staggered) conformation since the bond dipole-dipole repulsions are minimized and

dominate over 1-5 diaxial interactions, making the staggered conformation of C3F8 a global

minimum. The gas phase experimental structure of n-C3F8 has been reported as the staggered

conformer [64]. With the growth in carbon chain length, the number of 1,5 diaxial interactions

increases, causing deviations from the staggered conformations. Dixon has shown in his work on

the torsional potential about the central C-C bond in perfluoro-n-butane that the global

conformational minimum is a twist-anti form. The latter structure shows a twist in the carbon

backbone by an angle of 15° about the central C-C bond (away from the 180° for the all trans

structure) at the SCF level with a 6-31G* basis set [57, 58]. The optimized geometry at

B3LYP/DZP++ exhibits a similar twist of 13° in the carbon backbone about the central C-C

bond. All the long chain n-PFAs from n= 4 to 8 show similar deviations. The twist angle in the

C-C backbone of n-C4F10 predicted by the current work is in satisfactory agreement with the

previously reported MP2 and B3LYP optimized geometries [53, 58, 59, 54]. Our optimized

structures for the longer neutral n-PFAs with C2 symmetry show that the n-PFA backbone is

helical in nature, in concordance with previous reports in the literature [53, 54]. Information

about the dihedral angles along the C-C backbones of the n-PFAs is summarized in Table 2.5.

Analysis of the bond lengths shows that the B3LYP method predicts the shortest bond lengths

19

for both C-C and C-F bonds among all the three functionals, whereas BLYP predicts the longest

bonds.

2.4.2. RADICAL ANIONS OF LINEAR CHAIN PFAS

The optimized bond lengths and the corresponding molecular geometries of n-CnF2n+2 (n = 2 to

8) are indicated in Figures 2.1b through 2.7b respectively. The study of the optimized structures

of the molecular anions reveals that drastic changes occur within the molecular framework on

electron attachment. The linear chain PFA anions show a consistent change in geometry

compared to those of their corresponding neutral species. The most conspicuous change occurs

for one of the C-F bonds, namely that located on the central carbon for the odd numbered n-PFA

anion and on one of the central carbons in even numbered n-PFA anions. Molecular geometry

optimization using three different functionals (with subsequent vibrational frequency analysis)

imposing C2v symmetry on CnF2n+2, where n is odd, leads to single large imaginary frequency

which shows distortion towards the asymmetric stretch of the C-F bonds on the central -CF2 unit.

While C3F8 and C7F14 prefer Cs symmetry, C5F12 prefers C1 geometry. Imposing Cs symmetry

on C5F12 followed by geometry optimization and harmonic frequency analysis shows a presence

of very small imaginary frequency at all levels of theory (e.g., 11i cm-1 at B3LYP/DZP++),

which corresponds to torsional twisting of the -CF2 units in the molecular framework. In all the

odd numbered PFA anions significant C-F bond length elongation occurs on one of the two C-F

bonds located in the center of the chain. For example, with B3LYP/DZP++ the C-F bond length

in question in C3F8 is exceptionally long, 2.046 Å (Figure 2.2b), whereas at the same level of

theory C-F bond length in the neutral molecule has a typical value, 1.351 Å. In C5F12 the longest

C-F bond has a length of 2.012 Å and the longest C-F bond in C7F16 measures up to 2.009 Å at

B3LYP/DZP++ level of theory. Moreover, there is C-C bond shortening in the anionic species

20

compared to their neutral analogues for the C-C bonds, which are associated with the central

carbon in the chain. The C-C bond distances associated with the central carbon in C3F8 are

about 1.484 Å at the B3LYP/DZP++ level, whereas in the neutral C3F8 the same C-C bond has

slightly longer distance, 1.567 Å. In addition, C-F bonds that are trans to the longest C-F bonds

also are slightly elongated compared to the quasi-syn ones. Similar bond length patterns are also

observed in the other odd numbered n-PFA anions.

The structural features of even numbered n-PFA anions are similar in nature to those of

the odd numbered chains. The optimized structures of all the even numbered n-PFA anions

exhibit an exceptionally long C-F bond, which is located on one of the central carbons in the

chain. n-C2F6 prefers a Cs structure (Figure 2.1b) and the other even numbered n-PFA anions

prefer C1 structures as minima. Analysis of the optimized geometries of n-C4F10 (Figure 2.3b)

at all the three levels of theory reveals the presence of an exceptionally long C-F bond (2.028 Å

at B3LYP/DZP++) on the second carbon from the end of the chain. In the vicinity of the

exceptionally long C-F bond in C4F10 we observe C-C bond shortening and slight elongation of

C-F bond trans to the longest C-F bond, similar to those observed for the odd numbered PFA

anions. All the other even numbered n-PFA anions show similar structural features. The longest

C-F bond in C6F14¯ is associated with the third carbon from the end of the chain and for C8F18

the fourth carbon from the end of the chain holds the longest C-F bond. In C6F14 the longest C-F

bond has a length of 2.006 Å and the longest C-F bond in C8F18 is 2.030 Å long at

B3LYP/DZP++ level of theory. For C4F10 and C6F14

we were able to detect other low- lying

minima possessing C2h symmetry. The C2h minimum for the C4F10 anion lies above the C1

structure by 17 kcal/mol, whereas the C2h minimum for C6F14 is 13 kcal/mol higher in energy

than the C1 minimum (B3LYP/DZP++).

21

The structural changes that occur on attaching an electron to a PFA may be explained

with the help of spin density plots. All the spin density plots for the molecular anions (Figure

2.10) were obtained at the B3LYP /DZP++ level of theory. For all the n-PFA anions the spin

density is mainly associated with their corresponding longest C-F bonds. The elongation of the

C-F bonds is due to the addition of an extra electron to an antibonding C-F σ* orbital. An

increase in the electron density in the C-F σ* orbital leads to a lengthening of the respective C-F

bond. The shortening of the C-C bonds which are associated with the carbon bearing the

exceptionally long C-F bond, and also the observed lengthening of the C-F bonds trans to the

longest C-F bond, can be explained on the basis of a negative hyperconjugation-like

phenomenon. The half filled C-F σ* orbital corresponding to the longest C-F bond in the anions

mentioned above may have substantial overlap with the empty trans C-F σ* orbital. This in

effect leads to negative hyperconjugation-like phenomenon (see Figure 2.11). In Figure 2.11 we

show how the overlap of a half filled C-F σ* orbital with an empty C-F σ* orbital trans to it can

lead to C-F bond lengthening and C-C bond shortening.

2.4.3. ELECTRON AFFINITIES OF LINEAR CHAIN PFAS

Examination of the AEA data in Table 2.1 reveals that the BLYP method rather

consistently predicts the highest EAs for all the species, while B3LYP estimates for the AEAs

are the lowest. The zero-point corrected AEAs are consistently higher than the corresponding

uncorrected values. This of course reflects the smaller ZPVEs of the anions. The AEA

predictions show a monotonic increase with increasing chain length for n-CnF2n+2, from n=2 to

n=7. C8F18 and C7F16 have similar AEA values. All the linear chain PFAs, with the exception of

C2F6, have positive AEAs. The high pressure electron attachment studies on straight chain n-

PFAs reveal that for n > 2 nondissociative electron attachment occurs [23,24]. C2F6 undergoes

22

only dissociative electron attachment, whereas the other longer chain n-PFAs exhibit both

dissociative and nondissociative electron attachment [24]. Based on electron attachment studies

of C3F8, C4F10, C5F12 and C6F14, Christophorou and co-workers have suggested that these

molecules possess positive electron affinities [23, 24, 26, 29, 30]. Our findings lend an

explanation to their experimental observation. As noted earlier, the extra electron in the n-PFA

anionic species occupies the C-F σ* orbital. The presence of the more negative inductive effect

exerting CF2 groups may lower the energy of the C-F σ* orbital, leading to an increase in AEA.

The extra electron goes to the central carbon C-F bond for odd carbon containing PFA anions.

For even carbon PFA anions, the “last” electron goes to the C-F bond on one of the central

carbons, as those specific carbons have the maximum number of -CF2 groups in their vicinity.

From C2F6 to C7F16 the AEA increases as the number of negative inductive effect exerting –CF2

unit increases. The incremental change in AEA along the series of n-PFA decreases as we move

from n=2 to n=7. This can be rationalized by the understanding that the increase in negative

inductive effect on addition of –CF2 units away from the electron binding center weakens with

the increasing chain length. As one moves from C7F16 to C8F18 we observe that the increase in

the AEA ceases, plausibly pointing to the idea that the further addition of -CF2 groups far away

from the electron binding center has negligible effect.

The VEAs show a similar trend. None of the straight chain PFAs investigated has a

positive VEA. Analysis of the predictions shows that the VEA increases with the chain length of

the PFAs. The VEA results indicate that among the neutral straight chain PFA molecules the

LUMO is high lying. The LUMO energy is lowered with chain length growth due to the increase

in the number of negative-inductive-effect exerting CF2 groups [33]. The observed trend in VEA

is in agreement with the previous experimental reports [24, 33]. Though all three density

23

functionals predict the right trend they consistently overestimate the VEAs compared to the

experimentally reported values [24, 33]. The VEA data reveal that if a linear chain PFA has to

bind an electron adiabatically it has to lower the energy of its LUMO. We observe through

molecular geometry optimization of the molecular anions that drastic changes within the

molecular framework take place upon electron attachment. Bond elongation leads to a lowering

of the energy of the corresponding antibonding σ* orbital, giving rise to a low energy orbital that

can efficiently bind an electron.

The VDEs indicate that all the molecular anionic species considered in this work are

bound with respect to electron loss. Earlier it was demonstrated by King et. al. that C2F6 is

unbound with respect to electron loss [41]. King et. al. based their predictions on a D3d geometry

for the C2F6 anion. In contrast to their results, we have found that a Cs structure is the global

minimum for the C2F6 anion. The Cs minimum is 15 kcal/mol energetically lower than the D3d

minimum at B3LYP/DZP++ level of theory! When the optimized Cs geometry of C2F6 is taken

into consideration for the VDE computations we find that it has a positive VDE, indicating C2F6

may form a bound anion. The high predicted VDEs for the longer chains show that all these

molecular anions can exist.

2.4.4. ELECTRON AFFINITIES OF BRANCHED CHAIN C4F10 AND C5F12

The theoretical AEAs of branched C4F10 (perfluoro-iso-butane, i-C4F10) and C5F12 (perfluoro-iso-

pentane, i-C5F12) are listed in Table 2.4. Branched C4F10 has a much higher AEA than that for the

linear chain n-C4F10 (1.09eV and -0.36eV respectively). This trend persists for the AEAs of the

C5F12 isomers. The optimized anionic i-C4F10 shows a substantial elongation of the tertiary C-F

bond (2.039 Å) (see Fig. 2.9b) as compared to that for the neutral C3 symmetry structure (1.366

Å) (see Fig. 2.9a). The tertiary C-F bond is the longest bond in the molecular anion of branched

24

C4F10. Tertiary C-F bond length elongation is also observed in i-C5F12. This prediction lends

support to the generally accepted mechanism of defluorination of perfluorodecalin by reducing

agents like Na in organic media, where it is believed that a molecular anion is formed, followed

by cleavage of the tertiary C-F bond [35, 36]. Christophorou and co-workers reported the

formation of a stable parent anion species on electron attachment to i-C4F10 [23]. Our predicted

geometry for i-C4F10 is a plausible molecular structure for the parent anion species formed on

electron attachment to i-C4F10. The lengthening of the tertiary C-F bond in the molecular anion

of i-C4F10 also indicates that a defluorination step will involve cleaving of the exceptionally long

tertiary C-F bond in the subsequent step [35, 36]. In branched C5F12 there is one C-F tertiary

bond along with secondary and primary C-F bonds. In the optimized molecular geometry of the

anion at B3LYP/DZP++ again we encounter an exceptionally long tertiary C-F bond. This

indicates that the extra electron prefers to go to the tertiary C-F bond. The spin density plots (see

Fig. 2.10) for the branched anions reveal that the extra electron is accommodated in their tertiary

C-F σ* orbitals. The enhanced AEA of PFA with tertiary C-F bonds may be explained on the

basis of the tertiary C-F bonds having the maximum number of negative hyperconjugative-effect

exerting C-F bonds trans to it. Through the negative hyperconjugative effect the empty C-F σ*

orbitals trans to the longest C-F bond help to delocalize the extra charge through σ*- σ*

interactions between the C-F bonds, as demonstrated earlier. The geometric changes in moving

from the branched neutrals to the branched anions show the same structural effects as expected

from negative hyperconjugation; the shortening of the C-C bond associated with elongated C-F

bond bearing carbon and the lengthening of the C-F bonds which are trans in orientation to the

elongated C-F bonds.

25

2.5 CONCLUDING REMARKS

Through this work we have shown that the straight chains PFAs (with the exception of

C2F6) have substantial adiabatic electron affinities. In addition, the VEA predictions reveal that

none of the straight chain PFAs possesses a positive VEA. Moreover, the VEA increases with

extension of the chain length of a PFA. Analysis of the VDE data shows that all the straight

chain molecular anions considered in this research are bound with respect to electron loss. The

C2F6 anion, which was thought to possess a negative VDE [41], has a more energetically

favorable Cs minimum which possesses a positive VDE. Spin density studies of the anions

convincingly establish that the n-PFAs bind the extra electron in a C-F σ* antibonding orbital. It

was also observed that branched PFAs possessing tertiary C-F bonds have much higher AEAs

compared to those of their straight chain analogues indicating that branched chain molecules can

be better candidates for electron attachment studies.

ACKNOWLEDGEMENTS

Ankan Paul would like to thank Dr. Alexey Timoshkin and Mr. Lubos Horny for their insightful

comments and discussions. This research was supported by National Science Foundation under

Grant CHE-0136184.

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Phys. Rev. A. 1999, 59, 2006.

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[48] Dunning, T. H. J. Chem. Phys. 1970, 53, 2823.

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[52] Gaussian 94, Revision E.2, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.;

Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J.

A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.;

Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P.

Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.;

Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-Gordon, M.;

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29

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Table 2.1. Adiabatic electron affinities of linear chain CnF2n+2 in eV (n = 3 to 8). Zero point corrected EAs are shown in parentheses.

Molecules

B3LYP

BLYP

BP86

C2F6

-0.52

(-0.37)

-0.33

(-0.19)

-0.43

(-0.29)

C3F8

0.26

(0.39)

0.43

(0.56)

0.35

(0.48)

C4F10

0.40

(0.53)

0.57

(0.70)

0.50

(0.63)

C5F12

0.50

(0.65)

0.68

(0.83)

0.60

(0.74)

C6F14

0.56

(0.69)

0.73

(0.87)

0.67

(0.81)

C7F16

0.58

(0.71)

0.75

(0.89)

0.69

(0.83)

C8F18

0.52

(0.66)

0.71

(0.85)

0.64

(0.78)

30

Table 2.2. Vertical electron affinities of linear chain CnF2n+2 in eV (n = 2 to 8).

a. Hunter, S. R.; Christophorou, L. G.; J. Chem. Phys. 1984, 80, 6150. b. Ishii, I.; McLaren, R.; Hitchcock, A. P.; Jordan, K. D.; Choi, Y.; Robin, M. B. Can. J. Chem. 1988, 66, 2104.

Molecules

B3LYP

BLYP

BP86

Expt.1

A

Expt.2

B

C2F6

-1.17

-1.16

-1.05

-4.6

C3F8

-1.03

-0.96

-0.96

-2.55

-3.34

C4F10

-0.92

-0.77

-0.78

-1.95

-2.37

C5F12

-0.85

-0.60

-0.61

-1.55

-1.64

C6F14

-0.63

-0.36

-0.36

-1.20

-1.20

C7F16

-0.53

-0.19

-0.20

-

-

C8F18

-0.36

-0.07

-0.06

-

-

31

. Table 2.3. Vertical detachment energies of linear chain CnF2n+2 in eV (n = 2 to 8).

Table 2.4. Comparison of AEA of branched chain PFAs to those of their straight chain analogues. Zero point corrected EAs are shown in parentheses.

Method

Branched-C4F10

n-C4F10

Branched-C5F12

n-C5F12

B3LYP/DZP++

1.11 eV

(1.23 eV)

0.40 eV (0.53 eV)

1.21 eV

(1.33 eV)

0.50 eV (0.65)

Molecules

B3LYP

BLYP

BP86

C2F6

3.08

2.81

2.68

C3F8

3.41

3.31

3.16

C4F10

3.43

3.24

3.16

C5F12

3.50

3.31

3.23

C6F14

3.51

3.31

3.21

C7F16

3.55

3.33

3.23

C8F18

3.65

3.42

3.32

32

Table 2.5. Dihedral angles along the carbon backbone of n-PFAs for n=4 to 8. (The carbons are numbered from one end of the chain)

Molecule

B3LYP BLYP BP86

C4F10 C1-C2-C3-C4

166.9

169.5

165.6

C5F12

C1-C2-C3-C4 C2-C3-C4-C5

163.4 163.4

164.4 164.4

163.2

163.2

C6F14 C1-C2-C3-C4 C2-C3-C4-C5 C3-C4-C5-C6

163.3 162.1 163.3

163.91 162.59 163.91

162.92 161.88 162.92

C7F16

C1-C2-C3-C4 C2-C3-C4-C5 C3-C4-C5-C6 C4-C5-C6-C7

163.1 162.2 162.2 163.1

163.8 162.7 162.7 163.8

162.8 162.0 162.0 162.8

C8F18

C1-C2-C3-C4 C2-C3-C4-C5 C3-C4-C5-C6 C4-C5-C6-C7 C5-C6-C7-C8

163.6 162.0 162.1 162.0 163.6

164.3 162.4 162.5 162.4 164.3

163.2 161.8 162.0 161.8 163.2

33

B3LYP 1.339BLYP 1.358BP86 1.351

1.5641.5801.575

B3LYP 2.076BLYP 2.090BP86 2.024

1.3631.3821.373

1.5091.5111.503

1.3521.3721.366

1.3951.4431.442

1a

1b Figure 2.1. Optimized molecular geometries of: (a) Neutral n-C2F6 (D3d symmetry), (b) Anionic n-C2F6 (Cs symmetry). All bond lengths reported are in Angstroms.

34

B3LYP 1.484BLYP 1.490BP 86 1.487

2.0462.0732.031

1.3651.3821.374

1.3521.3721.366

1.4011.4361.426

1.3481.3681.361

1.351 1.369

1.363

B3LYP 1.567BLYP 1.584BP86 1.577

1.339 1.358

1.352

1.339 1.358

1.351

2a

2b Figure 2.2. Optimized molecular geometries of: (a) Neutral n-C3F8 (C2v symmetry), (b) Anionic n-C3F8 (Cs symmetry). All bond lengths reported are in Angstroms

35

B3LYP 1.341 BLYP 1.364BP86 1.355

1.4891.4991.494 1.483

1.4941.491

2.0282.0401.998

1.3631.3811.373

1.3501.3691.363

1.3481.3671.361

1.4001.4281.419

1.4111.4661.448

1.3331.3531.347

1.5711.5831.577

1.3621.3781.374

1.3661.3851.380

3a

3b

Figure 2.3. Optimized molecular geometries of: (a) Neutral n-C4F10 (C2 symmetry), (b) Anionic n-C4F10 (C1 symmetry). All bond lengths reported are in Angstroms.

1.352 1.369 1.362

1.570 1.586

1.588

1.570 1.588

1.581

1.337 1.359 1.352

1.337 1.359

1.352

B3LYP 1.339BLYP 1.359BP86 1.352

36

1.340 1.359 1.353

B3LYP 1.339BLYP 1.358BP86 1.352

1.573 1.591 1.583

1.337 1.356

1.349 1.352 1.371

1.364

1.349 1.368

1.361

1.352 1.371 1.364

1.571 1.589

1.582

1.340 1.361 1.353

B3LYP 1.366BLYP 1.387BP86 1.381

1.572 1.587 1.580

1.404 1.442 1.430

1.362 1.380 1.373

1.419 1.461 1.448

1.362 1.382 1.377

1.567 1.581 1.574

1.481 1.487 1.482

1.332 1.352 1.346

1.487 1.494 1.491 1.364

1.3811.374

2.012 2.022 1.976

1.350 1.370

1.363

1.332 1.352 1.342

1.358 1.378

1.371

4a

4b

Figure 2.4. Optimized molecular geometries of: (a) Neutral n-C5F12 (C2v symmetry), (b) Anionic n-C5F12 (C1 symmetry). All bond lengths reported are in Angstroms.

37

1.349 1.368

1.361

1.576 1.594

1.586

1.351 1.370

1.363

1.340 1.359 1.353

B3LYP 1.571BLYP 1.589BP86 1.582

1.352 1.371

1.364

1.351 1.371 1.363 1.337

1.356 1.349

1.339 1.358

1.352

1.574 1.592

1.584

5a

5b Figure 2.5. Optimized molecular geometries of: (a) Neutral n-C6F14 (C2 symmetry), (b) Anionic n-C6F14 (C1 symmetry). All bond lengths reported are in Angstroms.

B3LYP 1.350BLYP 1.367BP86 1.363

1.3321.3521.346

1.3571.3781.370

1.5671.5821.574

1.4831.4901.486

1.4841.4901.486

1.5781.5941.586

1.4181.4571.444

1.4131.4531.442

2.0062.0111.964

1.3631.3801.373

1.3481.3691.362

1.3511.3611.374

1.5741.5921.584

1.3531.3751.368

1.3451.3641.357

1.3421.3611.354

1.3601.3781.371

1.3611.3811.376

38

1.363 1.378

1.372 2.009 2.008 1.963

1.348 1.369

1.363

1.583 1.597

1.590

1.357 1.375

1.368

1.484 1.491

1.487

1.417 1.459

1.4471.574 1.592

1.585

1.345 1.363 1.357

1.3421.361

1.358

1.353 1.375

1.368

B3LYP 1.351BLYP 1.371BP86 1.363

6a

6b Figure 2.6. Optimized molecular geometries of: (a) Neutral n-C7F16 (C2v symmetry), (b) Anionic n-C7F16 (Cs symmetry). All bond lengths reported are in Angstroms.

1.349 1.368 1.361

1.577 1.595 1.587

1.351 1.370

1.363B3LYP 1.352BLYP 1.371BP86 1.364

1.574 1.592

1.584

1.339 1.358 1.352

1.340 1.359

1.353 1.571 1.589

1.582 1.351 1.370

1.363

1.351 1.370 1.363

1.337 1.356

1.349

39

2.030 2.032 1.983

1.367 1.382 1.375

1.482 1.489

1.485

1.341 1.361

1.355

1.367 1.387

1.378

1.340 1.359

1.353

1.571 1.589

1.582

1.355 1.373

1.366

1.350 1.370

1.363

1.341 1.370

1.363

1.352 1.372

1.378

1.579 1.594

1.586

1.413 1.452

1.4411.355 1.373

1.366 1.4821.489

1.485

1.418 1.459

1.446

1.343 1.361

1.354

1.577 1.591

1.583

1.364 1.384

1.377 1.342 1.363 1.356

B3LYP 1.353BLYP 1.374BP86 1.367

1.339 1.359 1.352

1.571 1.589

1.582

7a

7b Figure 2.7. Optimized molecular geometries of: (a) Neutral n-C8F18 (C2 symmetry), (b) Anionic n-C8F18 (C1 symmetry). All bond lengths reported are in Angstrom

1.351 1.370 1.363

1.352 1.371 1.364

1.574 1.592

1.584 1.577

1.596 1.588

1.351 1.370 1.363

1.577 1.595

1.584

1.339 1.357 1.364

1.352 1.371

1.364

1.351 1.374

1.363

1.349 1.368 1.361

B3LYP 1.337BLYP 1.356BP86 1.349

1.340 1.359 1.353

40

1.572

1.341

1.340

1.366

1.337

8a

8b

Figure 2.8. Optimized molecular geometries at the B3LYP/DZP++ level of theory: (a) Neutral branched C4F10 (C1 symmetry), (b) Anionic branched C4F10 (C1 symmetry). All bond lengths reported are in Angstroms.

2.039

1.349

1.495

1.354

1.390

41

1.3661.352

1.5791.582

1.573

1.338

1.341

1.338

1.3401.339

1.339

1.353

1.5731.338

1.338

1.339

9a

9b Figure 2.9. Optimized molecular geometries at the B3LYP/DZP++ level of theory: (a) Neutral branched C5F12 (C1 symmetry), (b) Anionic branched C5F12 (C1 symmetry). All bond lengths reported are in Angstroms.

2.034

1.352

1.349

1.387

1.5041.496

1.497

1.352

1.387

1.351

1.364

1.408

1.570

1.332

1.357

1.348

42

(a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 2.10. Spin density plots for molecular anions at B3LYP/DZP++, (a) n-C2F6

(b) n-C3F8, (c) n-C4F10, (d) n-C5F12, (e) n-C6F14, (f) n-C7F16, (g) n-C8F18, (h) branched- C4F10 (i) branched- C5F12.

43

F

Electron density moved into C-F σ∗ orbital increases the C-F bond length

Overlap shortens the C-C bond

Filled orbital on carbanion center

Partly filled C-F σ∗ orbital corresponding tothe longest C-F bond in the PFA radical anion

Electron density moved into the C-F σ∗ orbital increases the anti-periplanar C-F bond length

Overlap shortens the C-C bond

(a) Negative hyperconjugation in the carbanion

(b) Interaction of the partly filled C-F σ∗ orbital of PFA radical anion with anti-periplanar C-F σ∗ orbital

Figure 2.11. Comparison between (a) negative hyperconjugation in carbanions and (b) the interaction of the partly-filled C-F σ* radical anion SOMO with empty anti-periplanar C-F σ* orbital.

CHAPTER 3

THE PECULIAR TREND OF MONOCYCLIC PERFLUOROALKANE ELECTRON

AFFINITIES WITH INCREASING RING SIZE1

1 Ankan Paul, Chaitanya S. Wannere, Paul V. R. Schleyer and Henry F. Schaefer submitted to Journal of the American Chemical Society, 12/09/2005.

45

3.1 ABSTRACT

The adiabatic electron affinities (AEAs), vertical electron affinities (VEAs) and vertical

detachment energies (VDEs) of cyclic perfluoroalkanes, c-CnF2n (n = 3 to 7), and their

monotrifluoromethyl derivatives were computed using various pure and hybrid density

functionals with DZP++ (polarization and diffuse function augmented double-ζ) basis sets. The

theoretical AEA of c-C4F8 at KMLYP/DZP++, 0.70 eV, agrees with the 0.63 ± 0.05 eV

experimental value. c-C3F6(-), c-C4F8(-), and c-C5F10(-) are unusual in preferring planar ring

structures with Dnh symmetries. The ZPE corrected AEAs of c-CnF2n increase from n=3 (0.24

eV) to n=5 (0.77 eV) but then dramatically fall off to 0.40 eV for both n=6 and n=7. All the other

functionals predict the same trend. This is due to a change in the structural preference: Cs c-

C6F12(-) and C1 c-C7F14(-) are predicted to favor non-planar rings, each with an exceptionally

long C-F bond. (There also is a second, higher energy D3d minimum for C6F12(-).) The SOMOs

as well as the spin density plots of the c-PFA radical anions reveal that he “extra” electron is

largely localized on the unique Fs in the larger n=6 and n=7 rings, but is delocalized in the

multiatom SOMO’s of the 3 to 5 membered ring radical anions. The computed AEAs are much

larger than the corresponding VEAs; the latter are not consistent with different functionals. The

AEAs are substantially larger when a c-CnF2n fluorine is replaced by a –CF3 group. This behavior

is general: PFAs with tertiary C-F bonds have large AEAs. The VDEs for all the anions are

substantial, ranging from 1.89 eV to 3.64 eV at the KMLYP/DZP++ level.

3.2 INTRODUCTION

The exceptional properties of perfluoroalkanes (PFAs) not only elicit scientific interest, but also

have led to multifarious industrial applications [1, 2]. The attributes of chemical inertness,

extreme hydrophobicity, thermal stability, low viscosity, and low dielectric constant make PFAs

excellent candidates for lubricants, sealants, surfactants, oxygen carriers, anesthetics, and inert

46

solvents [3-9]. The unusual solubility trend of PFAs has led to the emergence of a new field

called “fluorous biphase chemistry” [10]. The concern of the present theoretical paper, the strong

electron attaching properties of the PFAs, has also been exploited in tracer studies in atmospheric

dispersion investigations [11]. The remarkable chemical inertness of PFAs arises from the

unusually strong C-F bonds. Their chemical passivity has earned them the reputation of

“immortal molecules” [12]. The notion of immortality is further corroborated by their unusually

long lifetimes in the atmosphere. Given the fact that these molecules possess the notorious

attributes of global warming potential, their long lifetimes could be of great concern [13].

Recently Morris et. al. have shown that electron attachment can reduce the lifetime of

perfluorocyclobutane in the atmosphere from 3200 years to 1400 years [14].

Chemical reactivity can be induced in PFAs through free electrons and reducing media.

Seminal research by Tatlow and co-workers, as well as by Macnicol and Robertson has shown

that PFAs can be defluorinated by using reducing agents [15, 16]. Macnicol and Robertson used

an organic reductant, sodium benzenethiolate to reduce trans-perfluorodecalin to C10(SPh)10 [16].

Reductive defluorination of PFA proceeds through electron transfer from the electron-rich

reagent to the PFA. Particularly, now it is known that PFAs with tertiary C-F bonds are more

prone to undergo reduction [17]. Tertiary C-F bonds in PFAs have been implicated as the

“Achilles heel”, a potentially fatal feature towards chemical transformation in these unusually

inert molecules [17, 18]. Richmond and co-workers has shown defluorination of

perfluoromonomethylcyclohexane and perfluorodecalin can be achieved using organometallic

nucleophiles at room temperature [17b, 17c]. Crabtree’s group has made also significant

contributions in developing reagents and photosensitization techniques to defluorinate PFAs

using various transition metal containing organometallic reagents [17d-17f]. Reductive

47

defluorination of saturated perfluoroalkanes has led to the emergence of the challenging frontier

of “C-F” bond activation in chemistry [19]. Though there are numerous reports on defluorination

of PFAs possessing tertiary C-F bonds, reactions involving defluorination of PFAs devoid of

tertiary C-F bonds are rare, indicating lower propensity of PFAs without tertiary C-F bonds

towards electron attachment. Richmond and co-workers has developed a Zr based reagent which

defluorinates perfluorocyclohexane, one of the very rare examples of reduction through electron

transfer to a PFA san the tertiary C-F bond [20].

PFAs attach electrons excellently. Extensive experimental electron attachment studies

have demonstrated that both cyclic and acyclic PFAs [21-47] bind low energy electrons and can

have positive electron affinities [22-25, 35-37]. Cyclic PFAs are known to be better electron

scavengers than their acyclic analogues [48]. The electron affinities of PFAs are crucial in

determining their reactivity. Electron attachment to the PFAs in reducing environments forms

radical anions; defluorination through fluoride ion loss follows [15-19].

c-C4F8 (perfluorocyclobutane) has been the most thoroughly investigated cyclic PFA,

both experimentally and theoretically. Electron attachment yields C4F8¯ over a wide range of

electron energies below 200meV [32, 45]. Bound radical anion of c-C4F8 has been generated

with γ-radiation at 130 K in a neopentane matrix and characterized by ESR spectroscopy [49].

Electron spin resonance studies confirm that the radical anion has a cyclic structure [50]. The

experimentally estimated adiabatic electron affinity of c-C4F8 has been controversial. Miller and

co-workers’ 1994 rate constant measurements of electron attachment to c-C4F8 and subsequent

equilibrium constant determination, estimated the adiabatic electron affinity (AEA) to be 0.63 eV

[41]. Later, Hiraoka et. al. deduced a higher value, 1.05 ± 0.05 eV.46 Recently, Miller and co-

workers challenged Hiraoka et. al.’s findings and confirmed that the AEA of c-C4F8 is 0.63 ±

48

0.05 eV [47]. Their G3(MP2) computations gave 0.59 eV. A similar value of 0.64 eV was

suggested by Gallup based on ab initio MP2/6-311G(dps) computations [51].

Our comprehensive recent study of the electron affinities of straight chain n-PFAs

included an assessment of the AEA trend with increasing chain length [52]. The

perfluorocycloalkanes (c-PFAs), c-CnF2n s are known to possess better electron scavenging

properties than that of the straight chain PFAs [48]. Liebman, based on qualitative molecular

orbital arguments, suggested over three decades ago that electron affinities of c-PFAs would be

higher than their straight chain counterparts [48]. The bonding of c-PFAs depends on ring size.

The angle strain is very large in the smaller rings and only diminishes in the larger rings. Hence,

the nature of the C-C and C-F bonds in the small c-PFAs can be different from that of straight

chain PFAs. These considerations encouraged the present computational exploration of the

consequences of electron binding to c-PFAs: the patterns and trends in AEAs with increasing

ring size and the unusual changes in geometries produced by electron attachment. Furthermore,

electron attachment has been implicated as a primary process of removal of

perfluorocyclobutane, a global warming gas from the atmosphere. Electron affinity trends can

provide insight about the vulnerability of PFAs, the potential global warming agents, to electron

attachment and. hence, are likely to indicate, which of these molecules will have smaller

atmospheric lifetime.

The extensive work on electron attachment of perfluorocarbons has revealed that

perfluoro-monomethyl-cycloalkanes, CF3-c-PFA, with the general molecular formula CF3-c-

CnF2n-1), exhibit excellent electron binding properties [53-63]. Like perfluoro-

monomethylcyclohexane, which has been investigated thoroughly [53-57], CF3-c-PFAs possess

tertiary C-F bonds. Since acyclic PFAs with a tertiary C-F can have high adiabatic electron

49

affinities [52], we investigated the effects of -CF3 substitution on the electron binding properties

of c-PFAs here.

3.3 COMPUTATIONAL METHODS

We computed energies, optimized structures, and harmonic vibrational frequencies using

the GAUSSIAN 94 program [64] and the five generalized gradient approximation (GGA)

exchange correlation functionals, BHLYP B3LYP, BLYP, BP86, and KMLYP, described briefly

below:

B3LYP (as implemented in GAUSSIAN 94) is a hybrid of exact, “Hartree-Fock”

exchange with local and gradient-corrected exchange and correlation terms, as proposed by

Becke [65], but with certain modifications to the correlation part. Instead of using the LSDA [66]

and PW91 [67] functional for local correlation, the B3LYP implementation [68] in GAUSSIAN

94 uses a mixture of LYP [69] and the VWN [70] correlation functional.

BHLYP is another hybrid functional, which combines Becke’s “half-and-half” exchange

functional [71], which is a 50-50 hybrid of exact exchange and local spin density approximation,

and the correlation part is described by the LYP functional.

BLYP uses Becke’s pure exchange functional 72 in conjunction to the LYP functional [68].

BP86 combines Becke’s pure exchange functional [72] with Perdew’s P86 [73, 74]

correlation correction.

KMLYP is a recently formulated hybrid functional [75], which combines the HF

exchange functional (ExH) and the Slater exchange functional (Ex

S). The description of

correlation is provided by a combination of the LYP functional (EcLYP) and the correlation

functional of Vosko, Wilk and Nusair (EcVWN). The KMLYP energy functional may be expressed

as: E = Ek + Eze + Eee + ExS + a(Ex

H - ExS) + b(Ec

LYP - EcVWN) + Ec

VWN

50

Where Ek is Kohn-Sham kinetic energy functional, Eze is the nuclear–electron Coulomb energy

functional, and Eee is the classical electron-electron coulomb repulsion energy functional. The

KMLYP parameters were a = 0.557 and b = 0.448 [75].

All computations employed double-ζ basis sets with polarization and diffuse functions. These

DZP++ basis sets augmented the 1970 Huzinaga-Dunning [76, 77] contracted double-ζ basis

sets for C and F with one set of five d-type polarization functions as well as with even

tempered s and p type basis functions [78]. The latter were designed following Lee and

Schaefer’s prescription [78]:

13

2

2

1diffuse 2

1 ααα

αα

α

+=

Where α1, α2, α3 are the three smallest Gaussian orbital exponents of s and p type primitive

functions for a given atom (α1 < α2 <α3). The final DZP++ set contains nineteen functions per C

and F atom (10s6p1d/5s3p1d). This basis set had been employed earlier with pure and hybrid

DFT methods in systematic calibration EA studies on a wide range of molecules [79]. The

combination of the BLYP and B3LYP functionals with the DZP++ basis set reproduced

experimental electron affinities with average errors of less than 0.15 eV. However, the BLYP,

BP86 and B3LYP with the DZP++ basis set combination occasionally overestimate adiabatic

electron affinities, especially when closed shell neutral saturated molecules give open shell

anions on electron attachment [80]. However, Brinkmann and Schaefer have shown that the

KMLYP/DZP++ level reproduces satisfactorily the adiabatic electron affinity of SF6, a difficult

example of this type [80]. In contrast, the B3LYP, BLYP, BP86 and BHLYP functionals, with

51

the same DZP++ basis set, perform poorly in this respect. This suggests that the KMLYP/DZP++

level also may give the best results in the present study.

Restricted and unrestricted DFT methods were used for the neutral and the anionic

species, respectively. All structures were optimized using analytic gradients with tight

convergence criteria. The computed harmonic vibrational frequencies and zero point energies

were not scaled. Numerical integration was performed using the GAUSSIAN94 default grid of

75 radial shells with 302 angular points per shell. Adiabatic (AEA) and verical electronic

affinities (VEA), as well as the vertical detachment energies (VDE) (see Tables 3.1, 3.2 and 3.3,

respectively) were computed as follows:

AEA = Energy (optimized neutral) – Energy (optimized radical anion)

VEA = Energy (optimized neutral) – Energy (radical anion at the neutral geometry)

VDE = Energy (neutral at radical anion optimized geometry) – Energy (optimized anion)

Total spin densities, computed as the density difference between the α and β electrons,

reveal the extent of the unpaired electron delocalization in the radical anions.

)()()( rrr βα ρρρ −=s

The neutral and anion molecular geometries of the c-PFAs, CnF2n (n=3-7, Figures 3.1 –

3.9) were optimized with five pure and hybrid density functional methods. The planarization

energies of the c-PFA rings, the corresponding AEAs, the VEAs and the VDEs are reported in

tables through 3.1 to 3.4. The B3LYP AEAs of the c-PFAs are compared with the AEAs of their

linear chain counterparts in Table 3.4. AEAs computed by constraining the geometries of the c-

PFA and their anions to Dnh symmetry are summarized in Table 3.5. The spin density plots of all

the radical anions studied are shown in Figure 3.10 and 3.11. The singly occupied molecular

52

orbitals (SOMOs) for the anions of c-C3F6, c-C4F8, c-C5F10, c-C6F12 are shown in Figure 3.12.

The adiabatic electron affinities of CF3-c-CnF2n-1( n=3 to 6) are listed in Table 3.6.

3.4 RESULTS AND DISCUSSION

3.4.1 NEUTRAL CYCLIC PFAS

The structures of the neutral c-PFAs parallel those of their hydrocarbon counterparts. All

the functionals gave similar geometries. The planarization energies of the c-PFAs ranged from 0

to 64 kcal/mol at the KMLYP/DZP++ level of theory (see Table 3.1). c-C3F6 favors D3h

symmetry, but D4h c-C4F8 is the transition structure for interconversion of the degenerate D2d

minima [47]. Two conformations of the c-C5F10 five-membered perfluoroalkane ring, the Cs

envelope and the C2 half-chair form have almost identical energies (within 0.01 kcal/mol at

B3LYP/DZP++). While C2 c-C5F10 was the minimum at all levels, the Cs geometry had only a

very small imaginary frequency (8i cm-1 at B3LYP/DZP++). Planar D5h c-C5F10 had a degenerate

set of imaginary frequencies (22i cm-1) and was 4.5 kcal/mol higher in energy at the same level.

Perfluorocyclohexane, c-C6F12 prefers the chair cyclohexane conformation (D3d symmetry). The

most stable conformation of the seven-membered perfluorocycloheptane ring has C2 symmetry

(Figure 3.5a).

The pure functionals, BLYP and BP86, which generally predict longer C-C and C-F

bonds than the B3LYP, KMLYP and BHLYP hybrid functionals, performed less well in

reproducing the only experimentally known geometry (for c-C4F8). The electron diffraction C-C

(1.566 ± 0.008 Å) and C–F (1.333 ± 0.002 Å) bond lengths [81] are reproduced best at BHLYP

(see Figure 2). The KMLYP and B3LYP CC bond lengths also are satisfactory, while those

given at BLYP and BP86 are too long. The experimental ring puckering angle in c-C4F8, 17.5°,

53

is not reproduced well, even by the hybrid functionals (10.6° at KMLYP, 9.5° at B3LYP, and

7.5° at BHLYP); the pure functional puckering angles are even smaller (Figure 3.2).

3.4.2 MONOCYCLIC PFA RADICAL ANIONS

Remarkable changes in all the c-PFA geometries result after electron attachment. In

general, the CC bonds shorten and the CF bonds lengthen. These changes are quite uniform in

the three, four, and five membered ring c-PFA radical anions where the extra electron occupies a

high symmetry SOMO with C-C bonding but C-F anti-bonding character. Consequently, the C-C

bond length in the c-C3F6¯ D3h minimum, 1.436 Å at BHLYP/DZP++ (Figure 3.1b), is much

shorter than that (1.516 Å) in the corresponding neutral. The C-F bond lengths are opposite:

much longer (1.409 Å) in c-C3F6¯ vs. 1.320 Å in neutral c-C3F6 (also at BHLYP/DZP++).

The neutral c-C4F8 and the c-C4F8¯ anion exhibit the same C-C and C-F bond length

relationships (Figure 3.2). But there is a further significant difference. While c-C4F8 favors a

puckered D2d geometry, the c-C4F8¯ anion prefers D4h symmetry with all the functionals as well

as at MP2 [47, 51]. The higher, planar symmetry facilitates more effective delocalization of the

odd electron to all the fluorines simultaneously. Other cyclic PFA radical anions tend toward

planar or more nearly planar geometries (see Table 3.1).

KMLYP predicts a planar D5h structure for the c-C5F10¯ radical anion. This illustrates a

trend in the performance of DFT, as all the other functionals favor Cs symmetry to a small extent

energetically. The deviation of the radical anion geometry from D5h symmetry increases with the

decreasing percentage of exact exchange in the functional employed. Thus, the pure BP86 and

BLYP functionals predict the largest degree of ring puckering. However, all the c-C5F10¯ radical

anion structures exhibit C-C bond shortening and C-F bond lengthening relative to the neutral

molecule (Table 3.2).

54

The c-C6F12¯ radical anion is unique in this cyclic set in having two low lying minima,

which differ significantly in their geometries and electronic structures. Both isomers, one with

D3d and the other with Cs symmetry, are predicted by all hybrid functionals (except BP86, which

only gives the D3d form). The D3d radical anion isomer has the same point group as its neutral

precursor, c-C6F12, but there are significant differences in the geometrical parameters. The c-

C6F12¯ axial C–F bonds are lengthened more than the equatorial C–F’s (by 0.020 Å at

BHLYP/DZP++), the C–C bonds are shortened, and the ring is flattened.

The D3d c-C6F12¯ structure marks the transition from the smaller planar Dnh or nearly

planar rings facilitating optimum delocalization of the odd electron in the c-PFA radical anions

to the larger highly non-planar rings, where angle strain reduction is more important

energetically than evenly distributed electron delocalization.

The relative energies of the two c-C6F12¯ minima depend on the theoretical method. The

second, Cs isomer is 9.8, 6.8, 3.5 and 0.13 kcal/mol lower in energy that the D3d form at the

KMLYP/DZP++, BHLYP/DZP++, B3LYP/DZP++ and BLYP/DZP++ levels, respectively. D3d

c-C6F12¯ is the only minimum with pure BP86 functional.

The second c-C6F12¯ (Cs) radical anion isomer as well as the only c-C7F14¯ minimum

(with C1 symmetry) have a pronounced structural feature not present in the smaller radical anion

rings: a single, exceptionally long C-F bond. In Cs c-C6F12¯, this is one of the C–F axial bonds (r

= 1.972 Å at BHLYP/DZP++). The distorted Cs c-C6F12¯ structure may be considered to be

either as an intermediate leading to the separated perfluorocyclohexyl radical and the fluoride

anion, C6F11. + F¯, or as a complex between the two. This complexation energy is 42 kcal/mol at

B3LYP/DZP++. The alternative dissociation energy of c-C6F12¯ into C6F11¯ and F. is 50

kcal/mol. The straight chain perfluoroalkane radical anions, n-CnF2n+2¯, also have one

55

extraordinarily long C-F bond on a carbon in the middle of the chain [52]. In general, the C-C

bonds associated with the carbon bearing the long C-F bond are shorter (rCC =1.470 Å for c-

C6F12¯ (Cs) at BHLYP/DZP++) than the other C-C bonds. Only the C–F bonds anti-periplanar

to the exceptionally long C–F bond in c-C6F12¯ (Cs) are lengthened relative to the other C–F

bonds. This is described in Figure 13, in which this situation is compared with negative

hyperconjugation. That the odd electron occupies a rather localized SOMO, also is shown clearly

by the spin density plots in Figure 3.10 (compare Figure 3.10d with Figures 3.10a,b,c for the

smaller rings).

Like Cs c-C6F12¯, the sole c-C7F14¯ radical anion minimum (C1, Figure 3.5b) has a

remarkably long C-F bond, r = 1.982 Å at BHLYP/DZP++. The other structural features of the

Cs c-C6F12– and c-C7F14

– radical anions are quite similar (see Figure 3.10), also to those of

straight chain n-PFA– radical anions.52 This implies that the larger (but not the smaller) PFA

rings actually behave like the straight chain PFAs after electron attachment.

This curious dichotomy between the structures of the smaller and the larger c-PFA

radical anions is due to competition between two effects. (a) The enhanced stabilization due to

delocalization of the “extra electron” over the entire molecule. This delocalization is possible

only in planar, nearly planar, or highly symmetrical geometries but not in highly puckered rings

or in acyclic n-PFAs. (b) The strain energy, which must be overcome in planarizing the c-PFA

radical anion rings in order to benefit from the optimum electron delocalization. This strain

energy is too great for the larger rings due to high angle strain in the planar conformations (see

Table 3.1 and the discussion in the Electron Affinities section, below).

The bond length differences between the neutral and PFAs and their radical anions

correspond nicely to the SOMO and spin density plots of c-C3F6¯, c-C4F8¯, c-C5F10¯and c-

56

C6F12¯ (Figures 3.10 and 3.12, at B3LYP/DZP++). The SOMOs of the smaller ring radical

anions all have higher symmetry: a2” in c-C3F6¯, a2u in c-C4F8¯, and a” in c-C5F10¯. Notably, the

C-C bonding and C–F antibonding character of all these SOMOs corresponds to the computed C-

C bond shortening and C-F bond lengthening predicted for the 3–, 4–, and 5–membered radical

anions. The D3d (but not the Cs) c-C6F12¯ minimum is similar. It’s a’ symmetry SOMO

corresponds mainly to a C-F σ* antibonding orbital for the long C-F bond; the delocalization

throughout the C-C framework is very modest. Likewise, the Cs c-C6F12¯ spin density plot shows

the unpaired electron to be localized mainly in the C-F σ* orbital.

3.4.3 ELECTRON AFFINTIES OF CYCLIC PFAS

The magnitude of the computed adiabatic electron affinities (AEAs) for the c-PFAs in

Table 3.2 vary inversely with the percentage of exact exchange in the functionals employed. The

pure functionals, BP86 and BLYP (which do not include exact exchange), give the largest AEAs.

The values from the B3LYP hydrid functional are smaller, and those predicted by KMLYP and

BHLYP, with have the highest percentage of exact exchange, are the smallest. Brinkmann et.

al’s computational AEAs of the related closed-shell molecule, SF6, were similar [80]. The zero-

point corrections increase the AEAs, since the frequencies of the radical anions are consistently

smaller than those of the corresponding neutral PFAs. Note that the computed AEAs of the c-

PFAs are higher than those of their linear chain counterparts (the n-PFAs) with the same number

of fluorinated carbons (Table 3.5). Our findings thus verify Liebman’s prediction that cyclic

PFAs should have higher electron affinities than their linear chain analogs [48].

The latest evaluations of the adiabatic electron affinity of c-C4F8 are 0.63 ± 05 eV

experimentally and 0.59 eV and 0.64 eV at the G3(MP2) and MP2/6311G(dps) levels

respectively [47, 51]. Our computations range from 0.47 eV to 1.30 eV depending on the

57

functional used (see the discussion above and Table 3.2). The zero-point corrected

KMLYP/DZP++ AEA, 0.70 eV, agrees best. Thus, KMLYP may be the most suitable for

predicting AEAs of related closed-shell neutral molecules. As noted above, KMLYP also

reproduces the AEA of SF6 best [80].

All the functionals predict an intriguing variation: the AEAs of the c-PFAs increase with

ring size from 3 to 5 and then decrease abruptly for the six- and seven–membered rings (see

Figure 3.14). c-C5F10 has the highest AEA (0.77 eV at KMLYP/DZP++ + ZPE). The AEAs of

the six-membered c-PFA are lower than those for the four-membered ring, but on average

slightly greater than the c-C7F14 AEAs.

This variation of AEAs in the c-PFAs is quite unlike that of the straight chain n-PFA (n-

CnF2n+2) series, where the AEAs increase with chain length [52]. This increase, which is due to

anion stabilization by the larger number of electronegative CF2 groups, falls off and ceases

beyond n=7. 52 Since the number of CF2 groups increases with ring size, one would expect the

AEAs to increase as well, and to level off beyond a certain ring size. The incongruity between

this expected monotonic ASE trend and that actually observed for the c-PFAs (Figure 3.14) is

due to changes in the binding mode of the “extra electron” with increasing c-PFA ring size.

The c-C3F6¯, c-C4F8¯, and c-C5F10¯ radical anions favor planar or essentially planar

geometries, since all the fluorines are equivalent and help delocalize the unpaired electron in the

symmetrical SOMO (Figure 3.12). This also is evident in the spin density plots for c-C3F6¯, c-

C4F8¯, and c-C5F10¯ (Figure 3.10), which show that the extra electron is delocalized effectively

to all the fluorines of each molecule. In contrast, for Cs n=6 and n=7 the extra electron is rather

localized in a single C-F σ* orbital (Figure 10). Consequently, there is an abrupt decrease in the

AEA from the five– to the six-membered ring. As discussed above for the geometries, the

58

computed AEA trends with increasing ring size (Figure 3.14) also arise from two competing

factors: the stabilization due to the better delocalization of the extra electron in planar structures

vs the strain energy associated with planarization of the rings.

The behavior of the planar forms of even the larger PFA rings in Dnh symmetries can

readily be investigated computationally. The planarization energies are quite substantial for the

six- and seven-membered neutral c-PFAs (31.1 and 64.1 kcal/mol, respectively, at the KMLYP

level, Table 3.1). The angle strain in the planar D6h six-membered ring, which is essentially

eliminated in its non-planar minimum, becomes greater and greater in the Dnh planar forms of the

larger rings. In contrast, the angle strain of four- and five-membered neutral PFA rings is

increased in non-planar geometries; torsional strain is responsible for their relatively small non-

planar preferences.

Electron attachment reduces the planarization energies considerably, by about 14

kcal/mol, of the radical anions of the six– and seven–membered rings (to 16.4 kcal/mol for c-

C6F12¯ and 50.6 kcal/mol for c-C7F14¯ at KMLYP/DZP++, Table 3.1). Unlike their neutral four–

and five–membered ring counterparts, c-C4F8¯ and c-C5F10¯ are planar at KMLYP/DZP++. The

planar radical anions are stabilized by the effective delocalization of the “extra electron” to all

the fluorines, in contrast to the much greater localization of the “extra electron” in the non-planar

forms. However, the ca. 14 kcal/mol stabilization of c-C6F12¯ and c-C7F14¯ radical anions in the

Dnh molecular geometries reduces, but is not large enough to overcome the high planarization

energies. Hence, these radical anions prefer “localized” structures resembling the n-PFA

molecular anions. Not surprisingly, the AEAs of c-C6F12 and c-C7F14 also are like those of their

linear counterparts [52]. For example, the AEA difference between c-C7F14 and n-C7F16 is only

0.06 eV at B3LYP/DZP++ (Table 3.3). In contrast, the smaller c-PFAs have much higher AEAs

59

than their straight chain counterparts [52]. For instance, the AEA of n-C4F10 is 0.32 eV, whereas

the AEA of c-C4F8 is 0.84 eV at B3LYP/DZP++.

Thus, the abrupt downturn in the AEA trend for the c-PFAs (Chart 3.1) is due to the

change in the binding mode of the “extra electron.” When both the neutral and the radical anion

geometries of the c-PFAs were constrained to Dnh symmetry (planar rings), the AEAs increase

with increasing ring size and then fall off slightly (Table 3.4; note that the data are not ZPE

corrected). The planar constraint forces the c-PFAs to bind the extra electron in a similar fashion

and hence leads to an AEA trend similar to that observed for the n-PFAs. AEAs increase when

more fluorines are present, but a limit is reached.

The VEAs (Table 3.5) are generally negative and vary rather eratically from one

theoretical level to another. There are no consistent trends, in contrast to the AEAs, but KMLYP

predicts that the VEAs decrease with increasing ring size, plausible in view of the increasing

number of inductively stabilizing –CF2 units.

With the exception of the BP86 data (Table 3.6), the VDEs of the 3–, 4–, and 5–

membered ring radical anions are nearly the same at each DFT level and are consistently much

smaller than the 6– and 7–membered ring radical anion VDEs. The small ring neutral and radical

anion geometries are nearly the same, but the larger ring radical anions have elongated C..F

bonds, a very unfavorable structural feature for the neutrals.

3.4.4 PERFLUOROMETHYLCYCLOALKANES STRUCTURES AND ELECTRON

AFFINITIES

Our earlier finding that the presence of a tertiary C-F bond in branched PFAs enhanced

electron binding [52] confirmed electron attachment results on PFAs with a tertiary C-F bond,

e.g., i-C4F10 and perfluoro-monomethylcyclohexane [43]. These species form stable radical

60

anions when bombarded with low energy electrons. Moreover, defluorination in perlfuoro-

monomethyl-cyclohexane can be achieved by employing solvated electrons [82], which involves

the loss of the “vulnerable” fluorine on the tertiary C-F bond of the molecule, initiated through

radical anion formation and subsequent fluoride ion loss. Do the intriguing variations in behavior

of the c-PFA rings towards electron attachment extend to the perfluoro-monomethyl-

cycloalkanes (CF3-c-PFAs), CF3-c-CnF2n-1 (for n=3 to 6)?

Not so, as the optimized geometries of the neutral CF3-c-PFAs and their radical anions

show (Figures 6b to 9b). In sharp contrast to the c-PFA radical anions, all the CF3-c-PFA radical

anions have similar geometric features, characterized by an exceptionally long tertiary C-F bond,

and resemble Cs c-C6F12¯ and c-C7F14¯ (Figures 3.4b and 3.5b). The tertiary C-F bond length is

1.337 Å in neutral CF3-c-C6F12, but 1.935 Å in CF3-c-C6F12¯ (at KMLYP/DZP++). This

structure, like c-C6F12¯ (see above and Figure 3.4), also is that of an F– anion bound to an open-

shell perfluorocarbon radical. All the C-C bonds to the substituted carbon in CF3-c-C6F12¯ are ca.

0.06 Å shorter than those in the neutral analog. Moreover, the C-F bonds anti-periplanar to the

elongated tertiary C-F bond are lengthened. The extra electron in CF3-c-C6F12¯ is accommodated

in a σ* orbital dominated by the tertiary C-F bond but with the properly aligned three anti-

periplanar C-F bonds helping to delocalize the negative charge through negative

hyperconjugation (see Figure 3.13). These geometric features of CF3-c-C6F12¯ are very similar to

those of i-C4F10¯ [52]. Although there are many experimental reports concerning the perfluoro-

monomethyl-cyclohexane radical anion in the literature, 53-63 theoretical geometries and electron

affinities have not been predicted before. Our zero point corrected AEA of perfluoro-

monomethyl-cyclohexane, 1.25 eV at KMLYP/DZP++, confirms the experimental value, 1.06 ±

0.15 eV.57 The unusually long tertiary C-F bond in CF3-c-C6F12¯ suggests that defluorination

61

could take place readily by electron attachment followed by F¯ cleavage. PFAs with tertiary C-F

bonds should generally be vulnerable to reducing agents.

The spin density plots of the CF3-c-PFA radical anions confirm that the extra electron

occupies the tertiary C-F σ* orbital–dominated SOMO. The AEAs of the mono-CF3 substituted

perfluorocycloalkanes (Table 3.7) are substantially higher than those of the analogous c-PFAs at

the same theoretical level. The CF3-c-CnF2n-1 AEAs increase from n=3 to n=5 but then decrease

slightly at n=6 (see Figure 3.15.). However, this small fall-off in AEA contrasts with the sharp

decrease from n=5 to n=6 exhibited by the c-PFAs (Figure 3.14). The trend of CF3-c-CnF2n-1

AEAs vs ring size (Figure 3.15) is strikingly similar to the AEA trends for n-PFAs.52 The

binding mode of the extra electron is similar in all the CF3-c-CnF2n-1– radical anions: the AEAs

are dominated by the presence of the tertiary C-F bond and the stabilizing –CF3 substituent,

which provides additional negative hyperconjugative and inductive stabilization. The ring CF2

groups provide additional inductive stabilization.

3.5 CONCLUDING REMARKS

The ability of most perfluoroalkanes to attract electrons is remarkable. The electron count

of the resulting radical anions violates the octet rule, at least formally. However, the “extra”

electron in most PFA radical anions is accommodated in the σ* orbital of an elongated C–F

bond. As in the acyclic PFA radical anions, this feature was found here in the larger cyclic c-

PFAs as well as in all the mono-CF3 substituted c-PFA rings 84. The AEAs of these CF3-c-CnF2n-1

radical anions are the largest computed here (e.g., 1.32 eV for CF3-c-C5F9 at KMLYP + ZPE).

The extra electron in the tertiary C–F bond is stabilized inductively by the greater number of

electronegative fluorines in the vicinity as well as by negative hyperconjugation.

62

The adiabatic electron affinities of smaller cyclic perfluoroalkanes with 3– to 5–

membered rings are exceptional. Their AEAs not only are greater than those of comparable

acyclic PFAs, but also those of the larger rings. The trend with increasing ring size is unusual.

The AEAs of c-PFAs increase, but only from c-C3F6 to c-C5F10, which has the largest AEA

among all the c-PFAs. Of the various density functionals investigated, the KMLYP/DZP++ ASE

estimate (0.70 eV) of c-C4F8 reproduces experiment (0.63 ± 0.05 eV) 47 best. The radical anions

of these smaller rings are planar or nearly so and the negative charge is delocalized to all the

fluorines: the SOMOs have high symmetry and exhibit cyclic electron delocalization.

The significant decrease in the AEA of c-C6F12 (which has a Cs and a less stable D3d

isomer) stems from the inability of the c-C6F12– radical anion to adopt a planar ring conformation

– the strain energy is too great. c-PFAs radical anions with more than five carbons have non-

planar rings. Both the Cs c-C6F12¯ and the C1 c-C7F14¯ radical anion minima have an

exceptionally long C-F bond akin to the same structural feature in acyclic n-PFA radical

anions.52 The same is true of all radical anions of the perfluoro-monomethylcycloalkanes CF3-c-

CnF2n-1. Although –CF3 substitution increases the adiabatic electron affinities substantially, these

rings do not show the anomalous AEA delocalization behavior of the smaller

perfluorocycloalkanes.

ACKNOWLEDGEMENT. A. P. This research was supported by National Science Foundation

Grants CHE-0136184 and, in part, CHE-0209857.

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68

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[83] This conclusion was tested and confirmed by computations on the 1,3,5-tris-equatorial-

perfluorocyclohexane radical anion. The C3v symmetry of its neutral precursor was not

retained, even though this might have permitted delocalization of the extra electron

simultaneously to three axial C–F bonds. Instead, a lower symmetry minimum with only a

single, elongated C–F bond was favored. Moreover, the AEA of perfluoro-1,1-dimethyl-

cyclobutane, which does not have a tertiary C-F bond ( 0.92 eV B3LYP/DZP++ +ZPE ) was

substantially lower than the AEA of CF3-c-C5F11.

69

Table 3.1.Planarization energies (in kcal/mol) computed as the difference between the energy of the c-PFA species in Dnh symmetry and the energy of the same species in its most favorable conformational minimum.

Species Planarization energies

at B3LYP/DZP++ (kcal/mol)

Planarization energies at KMLYP/DZP++

(kcal/mol) c-C3F6 0.0 (planar minimum) 0.0 (planar minimum) c-C4F8 0.10 0.21 c-C5F10 4.54 5.16 c-C6F12 28.47 31.12 c-C7F14 58.23 64.06 c-C3F6

− 0.0 (planar minimum) 0.0 (planar minimum) c-C4F8

− 0.0 (planar minimum) 0.0 (planar minimum) c-C5F10

− 0.15 0.0 (planar minimum) c-C6F12

− 17.06 16.35 c-C7F14

− 48.25 50.60 Table 3.2.Adiabatic electron affinities of cyclic perfluoroalkanes in eV with the DZP++ basis set. Zero-point corrected AEAs are shown in parentheses.

Molecule

KMLYP

B3LYP

BLYP

BP86

BHLYP

c-C3F6 Neutral – D3h Anion- D3h

0.07 (0.24)

0.47 (0.64)

0.69 (0.85)

0.73 (0.89)

-0.12 (0.06)

c-C4F8 Neutral- D2d Anion-D4h

0.52 (0.70)

0.85 (1.04)

1.05 (1.23)

1.13 (1.30)

0.28 (0.47)

c-C5F10 Neutral- Cs Anion-Cs

0.59 (0.77)

0.94 (1.12)

1.17 (1.35)

1.25 (1.42)

0.33 (0.51)

c-C6F12 Neutral- D3d Anion- Cs

0.27 (0.40)

0.68 (0.82)

0.89 (1.04)

0.94 (1.16)

0.19 (0.33)

c-C7F14 Neutral- C2 Anion- C1

0.27 (0.40)

0.64 (0.77)

0.83 (0.98)

0.80 (0.96)

0.18 (0.32)

70

Table 3.3. Comparison of AEAs for cyclic with straight chain PFAs at B3LYP/DZP++. Zero-point energy corrected results are in parentheses.

No. of carbons in the ring

or chain

AEA of c-CnF2n

AEA of n-CnF2n+2

[a]

n=3

0.47

(0.64)

0.26

(0.39)

n=4

0.85

(1.04)

0.40

(0.53)

n=5

0.94

(1.12)

0.50

(0.65)

n=6

0.68

(0.82)

0.56

(0.69)

n=7

0.64

(0.77)

0.58

(0.71) [a] Reference 53.

71

Table 3.4. Adiabatic electron affinities of geometry constrained cyclic perfluoroalkanes in eV. (Zero-point corrections are not included)

Neutral and anion constrained to Dnh

symmetry

B3LYP/DZP++

KMLYP/DZP++

c-C3F6

0.47

0.07

c-C4F8

0.86

0.53

c-C5F10

1.13

0.82

c-C6F12

1.18

0.91

c-C7F14

1.08

0.86

Table 3.5.Vertical electron affinities of cyclic perfluoroalkanes in eV. (Zero-point corrections are not included)

Molecule

KMLYP

B3LYP

BLYP

BP86

BHLYP

c-C3F6 -1.11 -0.71

-1.17

-0.72

-1.33

c-C4F8 -0.80

-0.40 -0.18 -0.25 -0.99

c-C5F10

-0.77 -0.22 0.04 0.08 -1.0

c-C6F12

-0.66 -0.33 -0.01 -0.01 -0.87

c-C7F14

-0.61

-0.30

0.05 0.06

-0.81

72

Table 3.6.Vertical detachment energies of cyclic perfluoroalkanes anions in eV. (Zero-point corrections are not included)

Table 3.7. Adiabatic electron affinities of CF3-monosubstituted PFAs in eV. Zero-point corrected AEAs are shown in parentheses.

Molecule

B3LYP/DZP++

KMLYP/DZP++

CF3-c-C3F5

0.96

(1.09)

0.57

(0.70)

CF3-c-C4F7

1.27

(1.39)

0.90

(1.03)

CF3-c-C5F9

1.51

(1.62)

1.20

(1.32)

CF3-c-C6F11a

1.45

(1.56)

1.13

(1.25)

a) Experimental value 1.06±0.15 eV. [58]

Molecule

KMLYP

B3LYP

BLYP

BP86

BHLYP

c-C3F6 1.89 2.18

2.31

2.35

1.69

c-C4F8

1.88

2.17 2.33 2.39 1.64

c-C5F10

1.82 2.11 2.31 2.38 1.55

c-C6F12

3.64 3.45 3.11 1.94 3.52

c-C7F14 3.58

3.39

3.01 2.07

3.44

73

FF

CC

FF

C

F

F

KMLYP 1.504 B3LYP 1.536BHLYP 1.516BLYP 1.556BP86 1.551

1.3061.3371.3201.3561.331

FF

CC

FF

C

F

F

KMLYP 1.427B3LYP 1.450BHLYP 1.436BLYP 1 .464BP86 1.463

1.3911.4361.4091.4921.448

1a

1b

Figure 3.1. Optimized molecular geometries of: (a) Neutral c-C3F6 (D3h symmetry), (b) Anionic n-C3F6 (D3h symmetry). All bond lengths reported are in Angstroms.

74

F

F

C

F

C

F

F

C

F

C

F

FKMLYP 1.307B3LYP 1.339BHLYP 1.321BLYP 1.357BP86 1.350

1.3121.3441.3261.3621.356

1.548 1.582 1.563 1.601 1.594

1. 566±0.008 Expt.1.333±0.002

2a

2b Figure 3.2. Optimized molecular geometries of: (a) Neutral c-C4F8 (D2d symmetry), (b) Anionic c-C4F8 (D4h symmetry). All bond lengths reported are in Angstroms.

F F

F F

C C

C C

F F

F F

KMLYP 1.370B3LYP 1.411BHLYP 1.388BLYP 1.434BP86 1.425

1.4861.5101.4971.5241.520

75

F

F

F

C

F

C

F

C

F

C

F

C

F

F

F

KMLYP 1.359B3LYP 1.403BHLYP 1.377BLYP 1.428

1.499 1.398 1.375 1.419

1.3591.4061.3781.412

1.499 1.5211.5101.533

1.4991.5201.5101.530

1.3591.4071.3781.437

1.3591.3911.3731.409

1.3591.3931.3741.435

1.4991.5221.5101.535

3a

3b

Figure 3.3. Optimized molecular geometries of: (a) Neutral c-C5F10 (C2 symmetry), (b) Anionic c-C5F10 (Cs symmetry). All bond lengths reported are in Angstroms.

F

F

C

F

F

C C

FF

F

C

C

F

F

F

KMLYP 1.319B3LYP 1.348BHLYP 1.330BLYP 1.367BP86 1.360

1.3201.3521.3341.3731.365

1.5301.5591.5421.5761.5671.526

1.5671.5491.5841.577

1.3121.3431.3251.3611.354

1.3141.3441.3261.3631.356

1.5541.5861.5681.6041.597

76

4a

4b

Figure 3.4. Optimized molecular geometries of: (a) Neutral c-C6F12 (D3d symmetry), (b) Anionic c-C6F12 (Cs symmetry). All bond lengths reported are in Angstroms.

F

F

FC F

C

F

C

F

F

C

F

C

FC

F

F

F

K M LY P 1.918B 3L YP 1.951B H LY P 1.972B L YP 1 .899

1.3251.3571.3411.374

1.3291.3651.3421.387

1.3661.4171.3831.454

1.5251.5571.5461.567

1.457 1.476 1.470 1.480

1.5301.5581.5461.567

1.3201.3621.3411.380

1.3251.3581.340

1.3141.3501.3281.376

1.3321.3661.3461.364

F

F

F

C

C

F

F

C

F

F

C

F

F

C

C

F

F

F

KM LYP 1.315 B3LYP 1.347BHLYP 1.333BLYP 1.371BP86 1.363

1.3181.3511.3291.3661.359

1.5331.5661.5491.5841.576

77

F

F

F

C

F

C

F

C

F

F

FC

CF

F

C

F

C

F

FF

KMLYP 1.913BHLYP 1.973B3LYP 1.926BLYP 1.925BP86 1.840

1.3251.3401.3601.3781.3731.345

1.3621.4031.4471.432

1.4751.4881.5011.5151.513

1.3241.3391.3601.3811.374

1.3311.3461.3721.4011.393

1.4701.4841.4821.4881.488

1.5361.5471.5741.5881.577

1.5371.5531.5641.5731.563

1.3211.3441.3651.3891.384

1.3201.3351.3521.3721.367

1.3191.3341.3521.3741.368

1.3301.3451.3651.3861.379

1.3211.3351.3541.3771.372

5a

5b Figure 3.5. Optimized molecular geometries of: (a) Neutral c-C7F14 (C2 symmetry), (b) Anionic c-C6F12 (C1 symmetry). All bond lengths reported are in Angstroms.

F

F

F

F

CCC

FF

F

F

CC

F

F

F

C

C

F

FF

KMLYP 1.316BHLYP 1.331B3LYP 1.349BLYP 1.367BP86 1.361

1.3161.3311.3491.3681.361

1.3161.3311.3481.3681.361

1.5501.5671.5861.6051.596

1.5361.5531.5711.5881.580

1.5361.5531.5701.5871.579

1.3161.3301.3481.3671.360

1.3191.3331.3521.3711.364

1.3151.3291.3501.3671.360

78

F

F

F

C

F

CC

F

F

C

F

F

B3LYP 1.353KMLYP 1.321

1.5311.504

1.3451.311

1.3401.301

1.5441.510

1.3371.305

1.3361.304

1.5131.484

6a

F

FF

C

F

CCF

F

C

F

F

B3LYP 1.921KMLYP 1.855

1.3821.342

1.3551.320

1.4521.434

1.4781.459

1.3891.346

1.3721.334

1.4921.470

6b Figure 3.6. Optimized molecular geometries at the B3LYP/DZP++ and KMLYP/DZP++ level of theory: (a) Neutral CF3-c-C3F5 (Cs symmetry), (b) Anionic branched CF3-c-C3F5 (Cs symmetry). All bond lengths reported are in Angstroms.

79

F

F

C

F F

F

C

F

C

C

F

C

F

F

F

B3LYP 1.356KMLYP 1.323

1.3451.311

1.5461.516

1.3431.310

1.3411.308

1.3421.310

1.5841.548

1.5781.545

1.3391.307

1.3431.311

F

F

F

F

CC

C

F

FC

F

F

C

F

F

B3LYP 1.955KMLYP 1.884

1.4861.465

1.3831.342

1.3531.319

1.4911.469

1.5621.535

1.3941.352

1.3571.321

1.3631.327

1.3641.328

7a

7b

Figure 3.7. Optimized molecular geometries at the B3LYP/DZP++ and KMLYP/DZP++ level of theory: (a) Neutral CF3-c-C4F7 (Cs symmetry), (b) Anionic branched CF3-c-C4F7 (Cs symmetry). All bond lengths reported are in Angstroms.

80

FF

FF

CC

F

C C

F

F

F

F

CC

F

F

F

B3LYP 1.374KMLYP 1.339

1.3371.304

1.3421.309

1.3411.310

1.3521.319

1.3451.313

1.3431.311

1.5561.523

1.5621.529

1.5791.545

1.5851.553

F

F

F

F

CC

F

F

CCF

F

C

F

C

F

F

F

B3LYP 2.016KMLYP 1.955

1.3591.324

1.4811.463

1.4041.358

1.3831.341

1.3511.318

1.5691.542

1.5721.544

1.3641.331

1.3491.314

1.4881.464

8a

8b Figure 3.8. Optimized molecular geometries at the B3LYP/DZP++ and KMLYP/DZP++ level of theory: (a) Neutral CF3-c-C5F9 (Cs symmetry), (b) Anionic branched CF3-c-C5F9 (Cs symmetry). All bond lengths reported are in Angstroms

81

FF

F

F

C

F

C

C

F

C

F

F

F

C

F

F

CC

F

F

F

B3LYP 1.371KMLYP 1.337

1.3501.317

1.3481.315

1.3471.3141.3521.318

1.3531.320

1.3411.315

1.3381.305

1.3401.307

1.5751.540 1.572

1.537

1.5701.535

1.5701.535

FF

FF

FCC

CC

F

F

F

F

C

F

C

FCF

F

F

B3LYP 2.034KMLYP 1.935

1.5161.480

1.5011.471

1.4381.360

1.3811.327

1.4091.344

1.3681.316

1.5811.534

1.5691.522

1.3681.313

1.3851.331

1.3811.325

1.3771.324

9a

9b Figure 3.9. Optimized molecular geometries at the B3LYP/DZP++ and KMLYP/DZP++ level of theory: (a) Neutral CF3-c-C6F11 (Cssymmetry), (b) Anionic branched CF3-c-C6F11 (Cs symmetry). All bond lengths reported are in Angstroms.

82

(a) (b) (c) (d)

(e) Figure 3.10. Spin density plots for molecular anions at B3LYP/DZP++, (a) c-C3F6

(b) c-C4F8, (c) c-C5F10, (d) c-C6F12 and (e) c-C7F14 .

83

(a) (b)

(c) (d) Figure 3.12. SOMO plots for molecular anions at B3LYP/DZP++, (a) c-C3F6

(b) c-C4F8, (c) c-C5F10, and (d) c-C6F12.

84

(a) (b)

(c) (d)

Figure 3.12. SOMO plots for molecular anions at B3LYP/DZP++, (a) c-C3F6 (b) c-C4F8, (c) c-

C5F10, and (d) c-C6F12.

85

F

Electron density moved into C-F σ∗ orbital increases the C-F bond length

Overlap shortens the C-C bond

Filled orbital on carbanion center

Partly filled C-F σ∗ orbital corresponding tothe longest C-F bond in the PFA radical anion

Electron density moved into the C-F σ∗ orbital increases the anti-periplanar C-F bond length

Overlap shortens the C-C bond

(a) Negative hyperconjugation in the carbanion

(b) Interaction of the partly filled C-F σ∗ orbital of PFA radical anion with anti-periplanar C-F σ∗ orbital

Figure 3.13. Comparison between (a) negative hyperconjugation in carbanions and (b) the interaction of the partly-filled C-F σ* radical anion SOMO with empty anti-periplanar C-F σ* orbital.

86

Figure 3.14. Plot of computed zero-point corrected AEAs with respect to the ring size of cyclic perfluoroalkanes.

Zero Point Corrected AEAs of Cyclic PFAs

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 2 4 6 8

Number of Carbons in the Ring

AEA

s in

eV B3LYP

KMLYPBHLYPBLYPBP86

87

Figure 3.15. Plot of computed zero-point corrected AEAs with respect to increasing ring size of CF3-c-PFAs.

Zero-Point Corrected AEA Trends with Increasing Ring Size of Perfluoro-monomethyl-cycloalkanes

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 1 2 3 4 5 6 7

Number of Carbons in the Ring

Zero

-poi

nt c

orre

cted

AEA

in e

V

B3LYPKMLYP

CHAPTER 4

HIGH ELECTRON AFFINITIES OF PERFLUOROBICYCLO [N, N, 0] ALKANES1

1 Ankan Paul, Paul V. R. Schleyer and Henry F. Schaefer To be submitted to Journal of Physical Chemistry A

89

4.1 ABSTRACT

The adiabatic electron affinities (AEAs), vertical electron affinities (VEAs) of bicyclo [n, n, 0]

(where n= 1, 2, 3, 4) perfluoroalkanes (n,n-BCPFA) were computed using hybrid density

functionals with DZP++ (polarization and diffuse function augmented double-ζ) basis sets. The

perfluoro bicyclo [1, 1, 0] butane (1,1-BCPFA) exhibits exceptionally high electron affinity at all

the levels of theory (2.07 eV at the KMLYP/DZP++ level of theory). The perfluoro [2, 2, 0]

octane has the lowest electron adiabatic electron affinity among all the molecules studied. The

zero-point corrected AEAs of the n.n-BCPFAs examined range from 0.92 eV to 2.07 eV at the

KMLYP/DZP++ level of theory. The structural changes which occur over the different ring sizes

are varied and are dictated by the mode of binding the electron by the n.n-BCPFA. Spin density

and SOMO plots reveal 1,1-BCPFA binds the electron in a C-C σ* orbital, whereas the 2,2,-

BCPFA binds the electron in an orbital which is delocalized over the entire molecule. The 4,4-

and 5,5-BCPFA bind the electron in a C-F σ* orbital which is localized on an exceptionally long

tertiary C-F bond. The 1,1-BCPFA radical anion exhibits an exceptionally long bridgehead C-C

bond. Whereas, the 2,2-BCPFA radical anion shows slightly elongated C-F bonds and slightly

shortened C-C bond. The 3,3-BCPFA, both the cis and trans forms and the trans form of 4,4-

BCPFA radical anions show the presence of an exceptionally long tertiary C-F bond.

4.2 INTRODUCTION

Perfluoroalkanes (PFAs) are known for their exceptional stability, owing to the presence

of highly strong C-F bonds. This class of molecules has numerous industrial applications due to

their chemical inertness, low viscosity, and low dielectric constant [1]. The PFAs are also

profusely used as gaseous dielectrics [2]. Negative plasmas of PFAs are used in semi-conductor

industry for SiO2 surface etching [3]. Electron attachment is the most important facet in PFA

90

chemistry. PFAs show very low reactivity. However, they become vulnerable only in presence of

electrons. The seminal work on reduction of PFA by Tatlow and co-workers opened up a new

frontier in PFA chemistry [4]. McNicol and Robertson showed PFA molecules can be reduced

using organic thio-enolate anions in less harsher conditions [5]. PFAs with tertiary C-F bonds are

more likely to undergo reduction than those without one [6]. A tertiary C-F bond in a PFA is the

“Achilles’ Heel”, and reducing environment leads to loss of the Fluorine from the tertiary C-F

bond.

The chemistry of PFAs is dominated by reactions initiated by electron attachment [6].

The propensity of PFAs to form molecular radical anions has thoroughly been studied in electron

attachment experiments on acyclic and cyclic and perfluoro-monomethyl substituted and bicyclic

PFAs [7, 8]. Electron Affinities of some PFAs have been experimentally determined to be

positive [7a-7d]. The isolation of c-C4F8¯ radical anion in neopentane matrix and subsequent

ESR study has shown the radical anions of PFAs are bound species [8]. c-C4F8 is known to have

a positive AEA and electron attachment has been implicated as a major pathway for the removal

of the octafluorocyclobutane from atmosphere [9]. Considering the fact, that PFAs are known for

their exceptionally high global warming potential and very long lifetimes in atmosphere [10],

their vulnerability towards electron attachment can plausibly provide a channel which can reduce

their atmospheric life expectancy. PFAs with high electron affinities are more likely to attach

electrons and this will plausibly provide a channel for removal of these species from the

atmosphere. Electron affinities for these molecules are a significant indicator for their propensity

to react. Through our previous investigations we have shown that linear straight-chain PFAs

have lower electron affinities than the cyclic-PFAs [11, 12]. The striking facet of our previous

investigations is the discovery that some cyclic PFAs can form radical anions where the extra

91

electron is delocalized over the entire molecule [12]. Moreover, it was shown that presence of

tertiary bonds can increase the adiabatic electron affinity of PFAs.

Trans perfluorodecalin (perfluoro-[4, 4, 0] bicycloalkane), composed of two fused

perfluorocyclohexane rings is known to undergo reduction under milder conditions than the

perfluorocyclohexane [13]. Tertiary C-F bonds in trans-perfluorodecalin are vulnerable to

electron attachment facilitating facile reduction. The radical anion formation of trans

perfluorodecalin is a key step in the reduction reactions of perfluorodecalin, which have been

developed over several years [6]. Perusal of chemical literature on perfluoroalkanes reveals the

scarcity of information regarding the structural features of the PFA radical anions which are the

key intermediates involved in the major reaction pathways of PFA reduction chemistry.

Moreover, electron attachment studies on perfluorodecalin are rare [8o]. Though, the reeduction

chemistry of perfluorodecalin employing different chemical reagents is well known, but there

have been no theoretical study related to its key step of reduction involving the radical anion

formation. In the current work we extend our investigation of electron affinities of PFAs to the

family of perfluorobicyclo[n, n, 0]alkanes. n,n-BCPFAs actually provide unique examples of

cyclic PFA frameworks which inherently possess a pair of tertiary C-F bonds. Our previous

investigations on tertiary C-F bond possessing PFAs have shown presence of tertiary C-F bonds

lead to high AEAs [11, 12]. Additionally for smaller bicyclic rings angle strain plausibly can

contribute to intriguing features in electron attachment properties. The perfluoro-bicyclo[n,n,0]

alkanes possess unique molecular frameworks which can provide the opportunity to study the

effect of angle strain and the simultaneous presence of tertiary C-F bonds in dictating electron

attachment properties to PFAs. In this cureent body of work we have elucidated the structural

92

facets of neutral and radical anion forms and the adiabatic and vertical electron affinities of 5

n.n-BCPFAs (n ranging from 1 to 4) have been computed.

4.3 COMPUTATIONAL METHODS

The GAUSSIAN 94 program [14] was used to compute total energies, optimized

structures and harmonic vibrational frequencies for all the molecules with three hybrid

functionals, B3LYP, BHLYP and KMLYP, These three functionals are described below briefly:

B3LYP (as implemented in GAUSSIAN 94) is a hybrid of exact, “Hartree-Fock”

exchange with local and gradient-corrected exchange and correlation terms, as proposed by

Becke [15], but with certain modifications to the correlation part. Instead of using the LSDA [16]

and PW91 [17] functional for local correlation, the B3LYP implementation [18] in GAUSSIAN

94 uses a mixture of LYP [19] and the VWN [20] correlation functional.

BHLYP is a hybrid functional originally proposed by Becke, which in its original form

combines Becke’s “half-and-half” exchange functional (BH), a 50-50 hybrid of exact exchange

and local spin density approximation [20], and the correlation part is described by the LYP

functional [19]. The GAUSSIAN 94 implementation of this functional is a bit different. The

GAUSSIAN 94 version of this functional is shown below:

0.5*Ex(HF) + 0.5*Ex(LSDA) + 0.5*Delta-Ex(Becke88) + Ec(LYP)

KMLYP is a recently developed hybrid functional 76, which combines the HF exchange

functional (ExH) and the Slater exchange functional (Ex

S). The correlation part of the functional is

provided by a combination of the LYP functional (EcLYP) and the correlation functional of Vosko,

Wilk and Nusair (EcVWN). The KMLYP energy functional may be expressed as:

E = Ek + Eze + Eee + ExS + a(Ex

H - ExS) + b(Ec

LYP - EcVWN) + Ec

VWN

93

Where Ek is Kohn-Sham kinetic energy functional, Eze is the nuclear–electron Coulomb energy

functional, and Eee is the classical electron-electron coulomb repulsion energy functional. The

KMLYP parameters were a = 0.557 and b = 0.448 [21].

All computations employed double-ζ basis sets with polarization and diffuse functions

(DZP++). These DZP++ basis sets augmented the 1970 Huzinaga-Dunning [22, 23] contracted

double-ζ basis sets for C and F with one set of five d-type polarization functions as well as with

even tempered s and p type basis functions. [24] The latter were designed following Lee and

Schaefer’s prescribed formula [25]:

13

2

2

1diffuse 2

1 ααα

αα

α

+=

Where α1, α2, α3 are the three smallest Gaussian orbital exponents of s and p type primitive

functions for a given atom (α1 < α2 <α3). The final DZP++ set contains nineteen functions per C

and F atom (10s6p1d/5s3p1d). This basis set had been employed earlier with pure and hybrid

DFT methods in systematic calibration EA studies on a wide range of molecules [26]. Pure

functionals with the DZP++ basis sets are known to overestimate electron affinities of saturated

closed shell molecules which yield open shell species on electron attachment [27]. Our previous

experience with electron affinities of PFAs have shown that pure functionals with the DZP++

basis sets significantly overestimate electron affinities of saturated closed shell PFA molecules

which yield open shell species on electron attachment [13,14]. The performance of the

combination of the hybrid density functionals with DZP++ basis sets were far superior compared

to those of the pure functionals. Particularly KMLYP and BHLYP, which have higher

percentage of exact exchange with the DZP++ basis yielded results in excellent agreement with

experimental finding for adiabatic electron affinity of c-C4F8 [12].

94

Restricted and unrestricted DFT methods were used for the neutral and the anionic

species, respectively. Analytic gradients with tight convergence criteria were employed to obtain

optimized molecular structures. The computed harmonic vibrational frequencies and zero point

energies were not scaled. Numerical integration was performed using the GAUSSIAN94 default

grid of 75 radial shells with 302 angular points per shell. Adiabatic (AEA) and verical electronic

affinities (VEA) (see Tables 4.1, and 4.2, respectively) were computed as follows:

AEA = Energy (optimized neutral) – Energy (optimized radical anion)

VEA = Energy (optimized neutral) – Energy (radical anion at the neutral geometry)

Total spin densities, computed as the density difference between the α and β electrons,

reveal the extent of the unpaired electron delocalization in the radical anions.

)()()( rrr βα ρρρ −=s

The neutral and radical anion molecular geometries of the n,n-BCPFAs, ( for n=1-4,

Figures 4.1 – 4.6) were optimized with three hybrid density functional methods. Both the cis and

trans isomers were considered for AEAs of 3,3-BCPFA. The spin density plots of all the radical

anions studied are shown in Figures 4.7 and 4.8.

4.4 RESULTS AND DISCUSSION

4.4.1. NEUTRAL N,N-BCPFAs The cis forms of the 1,1-BCPFA and 2,2-BCPFA were considered (Figure 4.1a and

Figure 4.2a,b). C2v symmetry was constraints was imposed on their molecular structures and

were subsequently optimized using the three different hybrid functionals with DZP++ basis set.

The cis form with C2v symmetry turned out to be a minimum for the 2,2-BCPFA at both the

B3LYP/DZP++, KMLYP/DZP++ and BHLYP/DZP++ level of theory. Though the 1,1-BCPFA

molecule has not been synthesized yet but perluoro-dimethylated form of the cis-1,1-BCPFA is

known, which shows such strained can actually exist [28]. The C-C bonds in the neutral 1,1-

95

BCPFA range from 1.465 Å to 1.602 Å at the BHLYP/DZP++ level of theory, significantly

shorter than the normal C-C single bond length of 1.54 Å. The C-C bonds are a bit shorter at

KMLYP with the same basis set, ranging from 1.456 Å to 1.571 Å. At all the levels of the theory

the bridgehead C-C bond is the longest, measuring 1.602 Å at the BHLYP/DZP++ of theory. The

2,2-BCPFA prefers a C2v minimum at B3LYP/DZP++. However, at the BHLYP/DZP++ and the

KMLYP/DZP++ levels of theory the optimized C2 structure exhibits a small imaginary

frequency of 15 cm-1 and 20 cm-1. Increasing the grid size does not lead to nullification of the

imaginary frequencies at BHLYP/DZP++ and KMLYP/DZP++. This imaginary frequency

vanishes when the symmetry of the structure is lowered to C2. The C2 symmetry structure of 2,2-

BCPFA is only 0.2 kcal/mol-1 lower in energy than the corresponding C2v structure. Both the cis

and trans isomers of the 3,3-BCPFA were considered. The cis 3.3-BCPFA prefers a C2

symmetric molecular structure at all the levels of theory. Imposing C2v symmetry to cis 3,3-

BCPFA leads to a stationary point, which has a single imaginary frequency on vibrational

frequency analyses. The imaginary frequency mode in the C2v structure leads to a C2 minimum in

the cis 3,3-BCPFA. The trans 3,3-BCPFA prefers a C2h minimum at all the levels of theory. Like

trans-decalin, 4,4-BCPFA exhibits a preference for a C2h symmetric structure as a minimum.

4.4.2. RADICAL ANIONS OF N,N-BCPFA

In general electron attachment leads to radical changes in the molecular geometries of the

BCPFAs. The nature of alterations in molecular geometries of the radical anions with respect to

that of the corresponding neutral species varies widely. All the functionals consistently predict

similar molecular features for a particular radical anion species.

Molecular geometry optimization with C2v symmetry of the 1,1-BCPFA radical anion

leads to a saddle point with two large imaginary frequencies. At B3LYP/DZP++ the C2v

96

optimized structure exhibits two imaginary frequency modes of i555 cm-1 and i365 cm1. The 1,1-

BCPFA radical anion prefers a C2h symmetric structure as a minimum. The 1,1-BCPFA radical

anion has an exceptionally long bridgehead C-C bond (1.962 Å at BHLYP/DZP++) at all the

levels of computation. The C-C bridgehead bond is 0.36 Å longer than the one in the neutral at

BHLYP/DZP++. Electron attachment to 1,1-BCPFA leads nearly to the cleavage of the strained

C-C bridgehead bond. The C-F bonds in the 1,1-BCPFA radical anion show a slight lengthening

as compared to those in the neutral, but the major changes in bond lengths are localized on the

bridgehead carbon-carbon distance.

Unlike, the 1,1-BCPFA radical anion the optimized molecular geometries of 2,2-BCPFA

radical anion with different functionals do not exhibit any overtly long bridgehead C-C bond. On

the other hand in general, C-C bond shortening throughout the carbon framework of the 2,2-

BCPFA radical anion and C-F bond lengthening is observed, with respect to its corresponding

neutral molecular geometry. The 2,2-BCPFA radical anion’s optimized molecular structure

displays signatures of a delocalized anion with similar bond length alteration spread ubiquitously

throughout the ring. In essence, the molecular structure of the 2,2-BCPFA radical anion

resembles those of the 3- 4- and 5- membered mono-cyclic perlfuoroalkane radical anions which

also prefer molecular structures where the “extra electron” is delocalized over the entire

molecule[12]. The inherent structural difference in the molecular geometries of the 1,1- and 2,2-

BCFA radical anions plausibly points out to the difference in angle strain in their parent neutral

molecular forms. In 1,1-BCPFA angle strain can be reduced on electron attachment by

lengthening of its bridgehead C-C bond, whereas in the 2,2-BCPFA radical anion which is

composed of two fused four membered rings angle strain is smaller and the angle strain cannot

be reduced by bridgehead bond lengthening.

97

The cis and trans 3,3- and trans 4,4-BCPFA radical anions display strikingly different

structural features as compared to the 1,1- and 2,2-BCPFA radical anions. The cis and trans 3,3-

and 4,4- BCPFA radical anions show the presence of an exceptionally large C-F bond associated

with a bridgehead carbon. Vibrational analyses, of C2v symmetric optimized molecular geometry

of the cis- 3,3-BCPFA leads to a large imaginary frequency mode with all the functionals.

Lowering the symmetry leads to a Cs symmetric minimum with the lowest frequency of 55 cm-1

at B3LYP/DZP++. The most significant structural feature of the cis 3,3-BCPFA radical anion is

an exceptionally long C-F bond measuring 1.910 Å at BHLYP/DZP++ level of theory on one of

the bridgehead carbons. The C-C bonds associated with the carbon bearing the remarkably long

C-F bond are significantly shorter than the other C-C bonds in the molecular framework. The C-

C bond lengths associated with the carbon bearing the remarkably long C-F bond

The parent C2h symmetry of the neutral trans- 3,3-BCPFA is not favored in the radical

anion form. The optimized C2h symmetric molecular structure of trans 3,3-BCPFA radical anion

is a transition state at all levels of theory (imaginary frequency 355 cm-1 at B3LYP/DZP++ level

of theory). The trans 3,3-BCPFA radical anion prefers a Cs symmetric minimum. The Cs

symmetric minimum has an exceptionally long C-F bond. The C-C bonds throughout the ring

exhibit shortening compared to those in the neutrals. Additionally, the C-F bonds throughout the

ring display lengthening with respect to those in the neutral counterpart. The C-C bond

shortening and C-F bond lengthening are more pronounced in the vicinity of the exceptionally

long C-F bond. Note, the striking resemblance in structural features with CF3- substituted

perfluorocylcoalkane (CF3-n-CnF2n-1) radical anion molecular structures [12].

The significant structural features of the trans 4,4-BCPFA (trans- perfluorodecalin)

radical anion resembles those of the trans 3,3-BPCFA anion. The 4,4-BCPFA radical anion is

98

predicted to have a Cs minimum by all the functionals. The remarkably long C-F bond on the

bridgehead carbon is 1.997 Å long at BHLYP/DZP++ levels of theory. The C-C bonds

associated with the carbon with the exceptionally long are shortened by 0.05-0.06 Å with respect

to those in the neutral. The C-F bonds anti-periplanar to the exceptionally long C-F bond in the

radical are longer compared to the other C-F bonds. Not surprisingly, the trans 4,4-BCPFA

radical anion molecular structure shows signature features of negative hyperconjugation. In

perfluorobicyclo[n, n, 0]alkanes for n>4 we expect the change in structural features from neutral

to radical anion will be similar to those of 3,3- and 4,4-BCPFAs, as it is more unlikely for the

larger rings to have planarized forms as planarization energy costs are higher for larger n [].

A nice correlation exists between the SOMO and spin density plots and the bond

alterations which are witnessed in the radical anions with respect to their neutral species. The a’

SOMO of the 1,1-BCPFA radical anion is mainly localized on the bridgehead C-C bond. The

spin density and SOMO plot of 1,1-BCPFA anion indicates that the “extra electron” in the 1,1-

BCPFA radical anion resides in an orbital which is strongly anitbonding with respect to the

bridgehead C-C bond. Hence, the bridgehead C-C 1,1-BCPFA radical anion is exceptionally

long. The a1 symmetric SOMO of the 2,2-BCPFA radical anion is reminiscent of the delocalized

SOMO‘s observed in planar small ring perfluorocycloalkane radical anions. The SOMO and spin

density plots of 2,2-BCPFA radical anion reveal that “extra electron” is located in an orbital

which is bonding with respect to C-C bonds and antibonding with respect to the C-F bonds,

hence resulting into observed C-C and C-F bond alteration in the 2,2-BCPFA radical as

compared to the neutral form. However, the spin density plot and the SOMO plots of cis 3,3-

BCPFA radical anion display localization of the unpaired electron on the remarkably long C-F

bond and its vicinity. The presence of substantial spin density on the fluorine atoms which are

99

anti-periplanar and syn-periplanar to the elongated C-F bond indicates the presence of negative

hyperconjugation. Negative hyperconjugation plays a major role in the stabilization of these

radical anions. The spin density plots of trans 3,3-BCPFA and trans 4,4-BCPFA radical anions

bear striking resemblance to the spin density plots of perfluoro-monomethyl-cycloalkane radical

anions [12]. The spin density is mainly localized in the C-F σ* of the elongated C-F bond and it

spreads out through negative hyperconjugation over the atoms on the three anti-periplanar C-F

bonds to the elongated C-F bond, satisfactorily explaining the C-C bond shortening and anti-

periplanar C-F bond lengthening in the vicinity of the exceptionally long C-F bond.

4.4.3 ELECTRON AFFINITIES OF n,n-BCPFA

B3LYP, the hybrid functional employing the smallest percentage of “exact exchange”

among all the functionals used in the current study predicts the highest adiabatic electron

affinities. The AEAs predicted by KMLYP and BHLYP, which have higher percentage of “exact

exchange” as compared to that in B3LYP, are lower. For instance, the AEA of 2,2-BCPFA is

2.23 eV at the B3LYP/DZP++ level of theory, whereas the AEAs employing KMLYP and

BHLYP with the same basis set are lower, 2.03 eV and 1.92 eV respectively. Previously

reported AEAs of cyclic Perfluoroalkanes have shown similar patterns [].The frequencies of the

radical anions are consistently smaller than those of the corresponding neutral PFAs and so zero-

point corrections increase the AEAs for all the species investigated. The electron affinities of all

the bicyclic PFA species are substantial. The zero-point corrected AEAs of BCPFAs range from

2.32 eV to 1.4 eV at the B3LYP/DZP++ level of theory.

1,1-BCPFA has the highest electron affinity among its counterparts. 1-BCPFA is unusual

compared to the other BCPFAs as it has exceptionally high angle strain. Angle strain is so high

in this molecule that unlike other BCPFAs and other PFAs it binds an electron in bridgehead C-C

100

σ* as compared to other PFAs where the electron is attached through an orbital which has

contributions from the C-F σ* orbitals. Elongation of the bridgehead C-C bond on electron

attachment leads to opening of the C-C-C bond angle throughout the ring and hence a substantial

decrease in angle strain follows. The release of severe angle strain in the radical anion plausibly

is the primary reason for high electron affinity of 1,1-BCPFA. Also the presence of tertiary C-F

on the bridgehead carbon enhances the electron affinity.

The 2,2-BCPFA surprisingly has surprisingly low adiabatic electron affinity as compared

to 1,1-BCPFA. The significant decrease in angle strain from the 1.1-BCPFA to 2,2-BCPFA

markedly changes their electron attachment properties. The 2,2-BCPFA has the lowest AEA

among all the molecules studied. Interestingly the presence of tertiary C-F bonds in 2,2-BCPFA

do not lead to very high electron affinity. Interestingly, the presence of tertiary C-F bonds does

not lead to a radical anion with an exceptionally elongated C-F bond.

The cis isomer of 3,3-BCPFA slightly lower AEA than the trans isomer. The AEA of cis

3,3-BCPFA is 0.36 eV, whereas the AEA of the trans isomer is 0.45 eV at the B3LYP/DZP++

level of theory. Trans perfluorodecalin (trans 4,4-BCPFA) has the highest AEA, 1.67 eV at the

B3LYP/DZP++ level of theory. The perfluorodecalin radical anion is an intermediate species

which is formed during the reduction reaction. The exceptionally high AEA of trans

perfluorodecalin facilitates facile reduction of this molecule. Comparatively the

perfluorocyclohexane has a much smaller AEA, 0.64 eV and hence reduction is much more

difficult.

The VEAs of BCPFAs ranges from eV to eV at the B3LYP/DZP++ level of theory.

Previous investigations of VEAs on linear and mono-cylic PFAs have revealed that the VEAs

computed with hybrid DFT methods were always positive. Some of the n,n,-BCPFAs have

101

positive VEAs, even at KMLYP/DZP++. The AEA trends differ from the VEA trends. 1,1-

BCPFA has the highest AEA but it has the lowest VEA among all the molecules studied.

Obviously, the primary reason of high AEA of 1,1-BCPFA is certainly related to the release of

strain in the relaxed radical anion geometry, whereas the radical anion possessing the parent

neutral molecular geometry is subjected to angle strain and hence yields a low VEA. The 2,2-

BCPFA has a positive VEA at the B3LYP/DZP++ level of theory, but at the other levels it is

slightly negative. This cis isomer of 3,3-BCPFA has a slightly higher VEA than the

corresponding trans isomer. The trans 3,3-BCPFA and trans 4,4-BCPFA has almost similar

VEAs. Trans-perfluorodecalin (4,4-BCPFA) has a positive VEA as compared to

perfluorocyclohexane at KMLYP/DZP++.

4.5 CONCLUDING REMARKS

All the perfluoro[n, n, 0]bicycloalkanes investigated in this work have appreciable

adiabatic electron affinities, ranging from 0.9 eV to 2.2 eV at the KMLYP/DZP++ level of

theory. The 1,1-BCPFA molecule has an exceptionally high AEA, which is attributed to the

release of angle strain in the radical anion form. The 1,1-BCPFA molecule is also exceptional as

it is the only PFA molecule which binds the “unpaired electron“ in its radical anion in the

bridgehead C-C σ* bond. All the other PFA radical anions studied bind the “extra electron” in

orbitals which have major contributions from C-F σ* orbitals. SOMO plots show strong evidence

of negative hyperconjugation in some of the radical anions. The structural perturbations in the

radical anion forms with respect to those of the neutrals are significant and widely vary

depending on the size of the ring.

102

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Table 4.1. Adiabatic electron affinities of BCPFAs. Zero point corrected EAs are shown in

parentheses.

Molecules

B3LYP

BHLYP

KMLYP

1,1-BCPFA

2.19

(2.29)

1.96

(2.07)

2.08

(2.19)

2,2-BCPFA

1.10

(1.29)

0.49

(0.68)

0.74

(0.93)

cis-3,3-BCPFA

1.60

(1.72)

1.15

(1.27)

1.28

(1.40)

trans-3,3-BCPFA

1.89

(2.00)

1.52

(1.62)

.1.70 (1.81)

trans-4,4-BCPFA

1.77

(1.89)

1.36

(1.47)

1.48

(1.59)

106

Table 4.2. Vertical electron affinities of BCPFAs. Zero point corrected EAs are shown in

parentheses.

Molecules

B3LYP

BHLYP

KMLYP

1,1-BCPFA

-0.15

-0.53

-0.27

2,2-BCPFA

0.31

-0.32

-0.07

cis-3,3-BCPFA

0.62

-0.07

0.15

trans-3,3-BCPFA

0.49

-0.24

0.04

trans-4,4-BCPFA

0.46

-0.28

0.01

107

F

F

C F

C

C

F C

F

F

B3LYP 1.422 BHLYP 1.396KMLYP 1.378

1.3731.3551.338

1.9811.9621.944

1.4691.4581.450

95.295.595.7

84.884.584.3

FF

F

C

CC

FF

CF

B3LYP 1.320 BHLYP 1.308KMLYP 1.295

1.6891.6021.571

1.4771.4651.456

1.3561.3341.319 1.360

1.3361.320

1a

1b Figure 4.1. Optimized molecular geometries of: (a) Neutral 1,1-BCPFA (C2v symmetry), (b) Radical Anionic 1,1-BCPFA (D2h symmetry). All bond lengths reported are in Angstroms and angles are in degrees.

108

F

F

F

CF

C

F

C

F

C FC

C

F

F

F

BHLYP 1.327KMLYP

1.3231.309

1.3281.314

1.3301.316

1.5611.546

1.5781.565

1.5611.547

1.5421.526 1.322

1.308

F

F

F

C

C

F

C

F

F

CF

F

C

CF

F

1.5351.5041.512

1.4431.4201.396

1.3931.3681.352

1.3721.3531.338

1.5241.5041.495

1.5561.5421.528

2a

2b

Figure 4.2: Optimized molecular geometries of: (a) Neutral 2,2-BCPFA (C2 symmetry ), (b) Radical anionic form of 2,2-BCPFA (C2v symmetry). All bond lengths reported are in Angstroms.

109

F

F

F

F

C

C

F

F

F

C

C

C

C

F

F

FF

C

C

F

F

F

1.5711.5581.541

B3LYP 1.363BHLYP 1.345 KMLYP 1.329 1.564

1.5481.533

1.5771.5621.546

1.5801.5601.545

1.5661.5481.532

1.3431.3251.311

1.3411.3231.309

1.3491.3311.316

1.3491.3311.317

1.3531.3351.320

1.3421.3241.310

F

F

C

FF

F

CC

C

F

F

F

C

C

F

C

F

C

F

F

F

F

B3LYP 1.893BHLYP 1.910KMLYP 1.839

1.4131.3811.365

1.4981.4861.475

1.3901.3671.350

1.3591.3401.325

1.3541.3341.3201.497

1.4891.476

1.5621.5481.533

1.5591.5441.5291.558

1.5451.530

1.3601.3401.326

3a

3b

Figure 4.3: Optimized molecular geometries of: (a) Neutral cis 3,3-BCPFA (C2 symmetry), (b) Radical Anionic form of cis 3,3-BCPFA (Cs symmetry). All bond lengths reported are in Angstroms

110

F F

F F

C C

F F

F

C

C C

C

F

F F

C C

F F

F F

B3LYP 1.380 BHLYP 1.361KMLYP 1.344

1.3431.3251.314

1.6011.5821.566

1.3431.3261.311

1.5471.5321.517

1.5511.5361.521

1.3431.3281.311

F

F

F

F

C

C

F

C

C

F

F

F C

F

C

C

F

C

FF

FF

B3LYP 1.347BHLYP 1.327KMLYP 1.313

1.4301.3921.368

2.0312.0402.021

1.4701.4701.466

1.4751.4701.463

1.5611.5551.544

1.5901.5731.556

1.5831.5671.551

1.3571.3361.3211.394

1.3691.350

1.3471.3271.3121.363

1.3451.332

1.3641.3471.332

4a

4b

Figure 4.4: Optimized molecular geometries of: (a) Neutral trans 3,3-BCPFA (C2h symmetry), (b) Radical Anionic form of trans 3,3-BCPFA (Cs symmetry). All bond lengths reported are in Angstroms.

111

F

F

F

F

F

CCC

F

F

CC

F

F

F

F

CC

F

F

CCC

F

F

F

F

F

B3LYP 1.374 BHLYP 1.355KMLYP 1.339 1.350

1.3311.317

1.3481.3291.315 1.574

1.5581.540

1.5731.5561.538

1.5681.5501.534

1.3511.3321.318

1.3481.3301.316 1.560

1.5431.528

F

F

F

F

F

C

C

F

F

C

C

F

FC

C

F

F

CC

F

F

C

C

F

F

F

F

F

B3LYP 1.990BHLYP 1.976KMLYP 1.924

1.4921.4871.473

1.5031.4931.479

1.4311.403

1.3971.3721.355

1.5691.554 1.551

1.5361.521

1.3591.3401.326

1.3461.3271.313

1.3651.3451.330

1.5651.5491.533

1.5581.5421.526

1.3601.3401.325 1.355

1.3371.322

1.3481.329

5a

5b

Figure 4.5: Optimized molecular geometries of: (a) Neutral trans 4,4-BCPFA (C2h symmetry), (b) Radical Anionic form of trans 4,4-BCPFA (Cs symmetry). All bond lengths reported are in Angstroms.

112

1

(a)

(b)

(c) (d) (e) Figure 4.6 Spin Density plots of (a) 1,1,-BCPFA(radical anion, (b) 2,2-BCPFA radical anion (top and bottom view) , (c) cis 3,3-BCPFA radical anion, (d) trans-3,3-BCPFA radical anion, (e) trans4,4-BCPFA radical anion.

113

(a)

(b) (c) (d) (e) Figure 4.7 SOMO plots of (a) 1,1,-BCPFA(radical anion, (b) 2,2-BCPFA radical anion (c) cis 3,3-BCPFA radical anion, (d) trans-3,3-BCPFA radical anion, (e) trans4,4-BCPFA radical anion.

CHAPTER 5

CONCLUSION Our systematic density functional study predicts perfluoroalkanes have appreciable

adiabatic electron affinities. Though the experimental reports on adiabatic electron affinities of

PFAs are scarce, comparison of our theoretically predicted AEAs with few known experimental

ones reveal that the KMLYP/DZP++ level of theory can be an accurate and reliable method to

predict electron affinities in these class of molecules . The most reliable experimentally

determined AEA of c-C4F8 is 0.58+ 0.6 eV. The AEA of 0.7 eV of c-C4F8 predicted by

KMLYP/DZP++ is in excellent agreement with the experimentally estimated value. Out

thorough investigation has revealed that the pure functional used in conjunction with DZP++

basis sets tend to overestimate the AEAs. Through this research endeavor we have predicted the

molecular structures for various PFA radical anions. It was shown that the AEAs of PFAs are

very much dictated by the structural features.In several cases we have shown that the structural

features of the PFAs and in their radical anions determine the corresponding AEA trends. Linear

PFAs have the lowest AEAs and their radical anions are characterized by an exceptionally C-F

bond present on the middle carbon of the chain. 3-4- and 5- membered ring mono-cyclic PFAs

on the other hand tend to form delocalized radical anions and have substantially higher AEAs

than their linear chain counterparts. The 6- and 7- membered ring mono-cyclic PFA radical

anions show same structural features as the linear chain PFA anions, the presence of a

remarkably long C-F bond. The AEA trends with increasing ring size, arise from the ability of

the mono cyclic PFAs to form a planar anion, where the unpaired electron is delocalized over the

molecular plane through all the C-F σ* bonds In the n,n-BCPFA radical anions structural

115

features change significantly with changing ring size, hence affecting the AEA trends

substantially. Moreover, we have shown beyond doubt, that the presence of tertiary C-F bond

leads to high AEA in a PFA molecule, the primary reason being stabilization of the radical anion

by negative hyperconjugation by C-F σ* orbitals properly oriented to the tertiary C-F bond and

the added inductive effect of the –CF2 groups in the vicinity of the tertiary C-F bond. High AEA

of the tertiary C-F bond containing PFA is plausibly the primary reason for its vulnerability

towards reduction compared to those PFAs which are devoid of tertiary C-F bonds.

Throughout this dissertation we have shown that density functional methods can be an

effective tool for determining electron affinities of moderately large molecules. The main

problem in using DFT as a predictive tool is the lack of knowledge about the functionals which

can provide accurate answers. The way we have addressed this problem is to use several

functionals, both pure and hybrid and then to compare that data with any reliable experimental

data. The functional which performs the best with regard to reproducing experimental data can

be used as a predictive tool in other similar cases for which experimental results are non existent.

So addressing any chemical problem within the density functional theoretical regime must

involve the use of several functionals to arrive at quantitative accurate answers.