Pag.

Chemical Concepts from Density Functional Theory

Paul Geerlings

General Chemistry, Vrije Universiteit Brussel, Brussels, Belgium

55th Sanibel Symposium

February 15-20, 2015

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Chemistry from the Linear Response Function

Pag.

0. Introduction Interpretive Chemistry : the ongoing need for interpretational concepts and models in quantum chemistry

13/04/2015 2

• Chemistry as an experimental science → accumulation of data of countless number of molecules (CA > 50.000.000 Substances!)

Need for unifying theories, concepts, models to rationalize, interpret, predict …… in order to avoid an encylopaedic “science”.

• Nowadays: Computational Chemistry (WATOC …)

Accumulation of accurate data on countless number of molecules, reactions,…

Aren’t we generating a new encyclopaedia??

STILL need for unifying concepts and models to systematize the theoretical data.

Pag.13/04/2015 3

Looking back

• many concepts are MO/VB based cf. HOMO/LUMO, frontier MO theory rationalization of the Woodward Hoffmann rules, …

• Nowadays DFT is the workhorse par excellence for computational studies on medium and large systems

Isn’t there a need for density based concepts?

Part of DFT founded by RG Parr (1978)

CONCEPTUAL DFT

CHEMICAL DFT or CHEMICAL REACTIVITY DFTor

Pag.13/04/2015 4

Today’s talk

1. - A very brief introduction to Conceptual DFT

1. - Concentrating on the linear response function

• Evaluation

• Representation

• Chemistry from the linear response function

- Concepts: inductive and mesomeric effects, aromaticity,…

- Substrates: carbon chains, organic rings, inorganic rings,…

- An excursion into Alchemical Derivatives: exploring Chemical Space

3. – Conclusions

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1. Conceptual DFT

Fundamentals of DFT : the Electron Density Function as Carrier of Information

Hohenberg Kohn Theorems (P. Hohenberg, W. Kohn, Phys. Rev. B136, 864 (1964))

ρ(r) as basic variable:

13/04/2015 5

( )v r( )rρ

N

opH “everything”

Pag.13/04/2015 6

•

•

• • •

•

•

•

••

•

compatiblewith asingle v(r)

ρ(r) for a givenground state

- nuclei- position/charge

electrons

v(r)

Visualisation of the HK Theorem

Pag.

• Variational Principle

FHK Universal HohenbergKohn functional

Lagrangian Multiplier

• Practical implementation : Kohn Sham equations

Computational breakthrough

HKF

v(r)+ =(r)

δµ

δρ

13/04/2015 7

( ) ( ) ( )HKE r v r dr + F r= ρ ρ ∫

Pag.

Starting point for DFT perturbative approach to chemical reactivity

E = E[N,v]Consider Atomic, molecular system, perturbed in number of electrons and/or external potential

dE =∂E

∂N

v(r)

dN +δE

δv(r)

∫

N

δv(r)dr

identification first order perturbation theory

identification

ρ r( )

Electronic Chemical Potential (R.G. Parr, R.A. Donnelly, M.Levy, W.E. Palke, J. Chem. Phys., 68,

3801 (1978))

= - χ (Iczkowski - Margrave electronegativity)

μ

13/04/2015 8

Pag.13-4-2015 913-4-2015 9

Chemical hardnessFukui function

∂E

∂N

v(r)

= µ

∂2E

∂N2

v(r)

= η∂2E

∂Nδv(r)=

δµ

δv(r)

N

=∂ρ(r)

∂N

v

E[N,v]

= f(r)

Identification of two first derivatives of E with respect to N and v in a DFT context → response functions in reactivity theory

Linear response Function

2

N

E(r, r ')

v(r) v(r ')

δ= χ

δ δ

= −

Electro-negativityElectronic

Chemical Potential

χN

E(r)

v(r)

δ= ρ

δ

• P. Geerlings, F. De Proft, W. Langenaeker, Chem. Rev. , 103, 1793, 2003

• P. Geerlings, F. De Proft, PCCP, 10, 3028 (Third order derivatives)

• P. Geerlings, P.W. Ayers, A. Toro Labbé, P.K. Chattaraj, F. De Proft, Acc. Chem. Res., 55, 2012 (WH rules)

13/04/2015 9

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Hardness and fukui function have been widely explored but what about the remaining second order derivative?

: linear response function

Fundamental Importance: Information about propagation in the density throughout the system of an (external potential) perturbation at position r’

( )χ r,r'

( ) ( )( )

( )

2

' '

N N

δρ rδ E= =δv r δv r δv r

13/04/2015 10

Pag.

2. The Linear Response Function

• Work on formal aspects and mathematical aspects (Parr, Senet, Cohen, Ayers)

• Some numerical work (Coulson, Baekelandt, Cioslowski)

• NO direct, practical, generally applicable, nearly exact approach available and/or exploited

2.1. Introduction

13/04/2015 11

Hückel MO Theory: mutual atom-atom polarizability πrs = ∂qr/ ∂αs

C.A. Coulson and H.C. Longuet Higgins, Proc.Roy.Soc.LondonA, 192, 16 (1947)

Pag.

2.2. A simple perturbational approach; an independent particle model

(P.W.Ayers, Faraday Discussions, 135, 161, 2007)

: occupied orbitals : unoccupied orbitals : orbital energies

( )( )

( )( ) ( ) ( ) ( )* *N 2

i a a i

i=1 a=N 2+1 i aN

δρ r φ r φ r φ r' φ r' = χ r,r' =4 δv r' ε -ε

∞

∑ ∑

iφ aφ i aε ,ε

∗∗∗∗

( ) ( )( )KS Nδρ r δv r'∗∗∗∗ Zeroth order approximation to the linear response kernel for

the interacting system

2.2.1. Preliminaries

• Numerical evaluation: time consuming → benchmark

• Can we calculate in a simpler way?

• Closed shell N-electron system in the KS ansatz; frozen orbital approach

• 1st order Perturbation Theory → → taking functional derivative w.r.t

( )χ r,r'

( ) ( )1ρ r ( )v r

13/04/2015 12

P.W Ayers, F. De Proft, A. Borgoo, P. Geerlings, JCP, 126, 224107, 2007.

N. Sablon, F. De Proft, P.W. Ayers, P. Geerlings, JCP, 126, 224108, 2007.

Pag.

2.2.2. Atoms revisited

• Earlier work: A. Savin, F. Colonna, M. Allavena, J. Chem. Phys, 115, 6827, 2001

some light elements

• Light elements (KS ansatz; PBE). Spherical potential perturbation

. plot : radial distribution of the linear response kernel( )2 ' '2r χ r,r r

He Be

• Similar to Savin’s plots

• Positive and negative region, for He, duplicated in Be shell structure

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Along diagonal: increasing depletion of ( )v r ( )rρ

Pag.

One dimensional version for a fixed ( )2 'r χ r,r ( )r'=0 2r' r χ r,0→

He

Be

• Positive perturbation δv(r’) v(r’) becomes less negative electron density depletion in the vicinity of the nucleus

• ( ) ( ) ( )ρ r dr' χ r,r' δv r'∆ = ∫( ) ( )δv r' Aδ r ' 0 A>0= −Pointlike

perturbation

( ) ( )ρ r Aχ r,0∆ =

Alternating positive and negative regions due to conservation of number of electrons

also in 2D plot

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Extending → the noble gases

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χ(r,0) for Ar in the x,y plane

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A direct application → polarizability calculations

( )ij i jα = - dr dr' r χ r,r' r'∫ i,j= x,y,z

• Comparison with high level calculations

• Absolute values deviate, trend is respected

13/04/2015 17

Z. Boisdenghien, C. Van Alsenoy, F. De Proft, P. Geerlings,J. Chem. Theor. Comp. 9, 1007 (2013)

Pag.13/04/2015 18

Extension to open shell atoms/ Spin polarized linear Response

Transition to a spin-polarized version of in the context of spin polarized conceptual DFT

(F. De Proft, E. Chamorro, P. Perez, M. Duque, F. De Vleeschouwer, P.Geerlings,

Chem. Modell. 6, 63-111 (2009))

( )r, r 'χ

N, Ns representation [ ]s sE E N, N , v, v=

s

1v (v v )

2α β= −

1v (v v )

2α β= +

sN N Nα β= −

( )r, r 'χ ( )( ) ( )

( )( )

s s

2

NN

N,N N,N

rEr, r '

v r v r ' v r '

δρδχ = =

δ δ δ

usual DFT potential

related to B s B zv B (r)= µ

Pag.13/04/2015 19

Introduction of

( )( ) ( ) ( )

s s

2

sNS

s N,N N,N

Er, r '

v r v r ' v r '

δ δρχ = =

δ δ δ s α βρ = ρ − ρ

( )( )

( )( )

( )NS

rrr, r '

v r ' v r '

βαδρδρ

χ = −δ δ

: two terms can be expanded (IPM)

Pag.13/04/2015 20

Li

α − β α β

• Symmetry r, r’

• Middle region negative: sensitivity of to larger than that of

Aρ v∆

βρ

(cf. )N Nα β>

~ ( ) of Be α + β

cf. ground state configuration

~ ( ) of He but contracted

α + β

(higher Z)

Pag.13/04/2015 21

Li B O

Decreasing difference in sensitivity

NSχ

Difference in n Difference in l No (n,l) difference

Z. Boisdeghien, S. Fias, F. De Proft, P. Geerlings, PCCP, 16, 14614 (2014)S. Fias, Z. Boisdenghien, F. De Proft, P. Geerlings, J.Chem. Phys, 141, 184107, 2014

Pag.

How to extend its use for molecules to look for chemical information

condensation at stake in a first approach

13/04/2015 22

M. Torrent-Sucarat, P. Salvador, M. Solà, P. Geerlings, J. Comp. Chem., 29, 1064, 2008

2.2.3. From atoms to molecules

Pag.

An example: : atom condensed values

Numerical methodPresent method

Correlation coefficient between the matrix elements of the two methods:

H C O H2

H -1.22

C 0.68 -4.35

O 0.34 2.99 -3.67

H 0.19 0.68 0.34 -1.22

H2CO

Y = 0.99x - 0.01 R2= 0.96 Slope ∼ 1

H C O H2

H -1.21

C 1.19 -4.82

O 0.42 2.45 -3.28

H -0.40 1.19 0.42 -1.21

N. Sablon, P.W.Ayers, F. De Proft, P. Geerlings, J.Chem.Theor. Comp., 6, 3671, 2010

For other simple molecules (H2O, NH3, CO, HCN, NNO) always a high correlation coefficient is obtained with a very small intercept; the slope varies between 1 and 2.

13/04/2015 23

Pag.

Transmission of a perturbation through a carbon chain

NXχOXχ

Saturated systems

• density response of C atoms on heteroatom perturbation decreases monotonously with distance

• exponential fit: r2= 0.982 ( vide infra) Characterizing and quantifying the inductive effect.

(X= C0, C1, C2 …)

Inductive and mesomeric effects

13/04/2015 24

Pag.

Unsaturated systems

• alternating values• C1, C3, C5 of the chain: minimaC0, C2, C4, C6 : maxima

R= OH, NH2: resonance structures

C1, C3, C5 : mesomeric passive atoms→ follow same trend as alkane structures (inductive effect)

C0, C2, C4, C6 : mesomeric active atoms → effect remains consistently large even after 6 bonds (small decrease due to

superposition of inductive and mesomeric effect)

135

6 4 2

N. Sablon, F. De Proft, P. Geerlings, JPCLett., 1, 1228, 2010

13/04/2015 25

Pag.

Substituted benzenes vs cyclohexanes

• cyclohexane:

1 iC Cχ (i= 2,3,...6)=

• decreases exponentially (inductive effect)• influence of OH small

χ

• benzene: • maxima at C2, C4, C6: mesomerically active atoms (mesomeric effect)• minima at C3, C5 : mesomerically inactive atoms

Reminiscent of (1,4) Para Delocalisation Index. Sola et al,

Chem. Eur. J. 9, 400 (2003) as a criterion of aromaticity

N. Sablon, F. De Proft, P. Geerlings, Chem.Phys.Lett., 498, 192, 2010

13/04/2015 26

Pag.

Aromaticity

Relation with the para delocalization index (PDI) derived from AIM

Exchange correlation density; integration over atomic basins

• quantitative idea of the number of electrons delocalized or shared between A and B

(X. Fradera, M.A. Austen, R.F.W Bader, JPCA, 103, 304, 1999.)

• investigated as a potential index of aromaticity

(J. Poater, X. Fradera, M. Duran, M. Sola, Chem.Eur. J. , 9, 400, 2003)

• six membered rings of planar PAH’s• successful correlation of the (1,4) (para) delocalization index with NICS, HOMA, …

AB 14δ = δ

1

2

3

4

para

• Does Linear response function contain similar information?1,4χ

( ) ( )1 2 1 2

A B XC

δ A,B = -2 r ,r dr drΓ∫ ∫

13/04/2015 27

Pag.

16 non equivalent sixrings studied by Sola et al.

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Pag.

• typical benzene-type pattern encountered before

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Pag.

→ Linear response function as an “electronic” descriptor of aromaticity

13/04/2015 30

Pag.

Benzene

• Decreasing σ contribution (cfr. Cyclohexane)

• Zig/zag for π and total

• Anti-aromatic molecules:Cyclobutadiene, COT

“inverted zig zag”

S. Fias, P. Geerlings, P. Ayers, F. De Proft, PCCP, 15, 2882 (2013)

13/04/2015 31

Digging further in aromaticity →→→→ σσσσ,ππππ aromaticity (applying σσσσ,ππππ separation)

Pag.

Inorganic rings

13/04/2015 32

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Valence Bond Structures

X= NH, O, PH

Resonance Energy (kJ mol-1) and weights W of the four Valence Bond Structures.

Molecule Eres W(I) W(II) W(III) W(IV)

B3N3H6 61.6 0.05 0.05 0.90 0.00

B3O3H3 27.6 0.02 0.02 0.96 0.00

B3P3H6 132.6 0.21 0.21 0.58 0.00

C6H6 161.4 0.47 0.47 0.03 0.03

J. Engelberts, R. Havenith, J. Van Lenthe, L. Jenneskens, P. Fowler, Inorg. Chem., 44, 5266, 2005

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Pag.

Borazine

• Typical resonance pattern observed in aromatic systems is recovered if one of the N-

atoms is chosen as the reference atom.

• Purely inductive behaviour (exponential decay of electron delocalization with

internuclear distance)

is recovered if one of the B-atoms is chosen as the reference atom.

Dual picture of aromatic character of borazine (cfr. ongoing debate in the literature)

N. Sablon, F. De Proft, M. Sola, P. Geerlings, PCCP, 14, 3960 (2012)

13/04/2015 34

Pag.13/04/2015 35

2.3. Beyond the independent Particle Model

• Using a CPKS approach

( ) ( ) ( ) ( ) ( ) ( )ia , jb

1 * *

i a b j

i,a, j,b,

r, r ' 2 M r r r ' r 'σ τ

−σ σ τ τ

σ τ

χ = − ϕ ϕ ϕ ϕ∑∑

• Independent particle:

• Random Phase:

• General CPKS:

( )ia , jb b j ij abM σ τ στ= ε − ε δ δ δ

( ) ( )ia , jb b j ij abM 2 ia | jbσ τ στ= ε − ε δ δ δ + σ τ

( ) ( ) ( )( )ia , jb b j ij ab xcM 2 ia | jb 2 ia | f r, r ' | jbσ τ στ= ε − ε δ δ δ + σ τ + σ τ

( )( ) ( )

2

xcxc

Ef r, r '

r r '

δ=

δρ δρ

W. Yang, A.J.Cohen, F. De Proft, P. Geerlings, J.Chem.Phys. 136, 144110 (2012)

Pag.

Planar Metallic Systems: Unintegrated plots

Aromaticity order2- - + 2+

4 3 2 2 3 4Al > Al Ge ³ Al Ge AlGe < Ge≥ ≤

Expected order (Feixas et al)

Mainly σ aromatic (∼ 65%)

Insertion of C: decreasing aromaticity, sequence unaltered; but increasing σ component

13/04/2015 36

• The use of unintegrated plots

Benzene 2-

4Al

σ

• in plane• perturbation

at top nucleus

π

• 0.5 au above plane• perturbation in that

plane at top nucleus

σ π

Delocalized Nature of the linear Response more pronounced in the σ electron density

σ Aromatic character

S. Fias, Z. Boisdenghien, T. Stuyver, M. Audiffred, G. Merino, P. Geerlings, F. De Proft, J. Phys. Chem. A, 117, 3556 (2013)

( )13 241χ + χ

2→

Pag.13/04/2015 37

2.4 An extension to Alchemical Derivatives:exploring Chemical Space

• Alchemical derivatives: O.A. Von Lilienfeld, R.D. Lins, U. Röthlisberger, Phys.Rev.Lett., 95, 153002, (2005)O.A. Von Lilienfeld, IJQC, 13, 1676 (2013)

MN,Z ,

E

Zβ

α

∂

∂ ℝ

: change in molecular energy upon changing atomic nuclear charge

alchemical potential cf

M MZ ,R v

E E

N N

∂ ∂ = = µ

∂ ∂ electronic chemical potential

2

2

N,Z ,R

E

Z Zγ

α β

∂ ∂ ∂

cf

2

2

v

E

N

∂= η

∂ electronic chemical hardness

alchemical hardness

Pag.13/04/2015 38

Chemical Significance: navigation through the huge Chemical Compound Space for tracing interesting compounds by “Transmutation Reactions”

N=cte

∆Z= ± 1

Chemical Compound Space: set of all possible combinations of chemical elements prone to form stable compounds

P. Kirkpatrick, C. Ellis, Nature, 432, 823 (2004)

Pag.13/04/2015 39

Instead of calculating the energy of each of the “transmutants”, concentrate on the central compound and its alchemical derivatives

M M M M MdE E N, d , E N, , = + − ℤ ℤ ℝ ℤ ℝ

( )M

1 2 MZ , Z ...Z=ℤ nuclear charge vector

( )M

1 2 MR , R ...R=ℝ nuclear position vector

2

N,Z , N,Z ,

E EdZ dZ dZ ...

Z Z Zβ γ

α α βα α βα α β

∂ ∂= + + ∂ ∂ ∂ ∑ ∑∑

ℝ ℝ

alchemical potential alchemical hardness ( diagonal and off-diagonal)

electronic part electronic part

( )rdr

r Rα

ρ−

−∫( )

N,...

rZ

d rr R

β

α

∂ρ ∂

−∫

Pag.13/04/2015 40

Connection with linear response function

( ) ( )( ) ( )2 2

'

N N

v r v r 'E E dr dr '

Z Z Z Zv r v rα α ββ

∂ ∂∂ δ= ∂ ∂ ∂ ∂δ δ ∫ ∫

( )1 1

r, r ' dr dr'r R r Rα β

= χ− −

∫

Pag.13/04/2015 41

Evaluation of the alchemical potential and hardness

Coupled Perturbed Kohn Sham Theory (cf linear response function)

M.Lesiuk, R. Balawender, J. Zachara, J.Chem.Phys., 136, 034104(2012)

Prediction of energies of molecules with charge of the central nuclei changed by ± 1

( ) ( ) ( )iN

i

ii 1

1 EE Z 1 E Z 1

i! Z=

∂± = + ±

∂ ∑

‖

0E

Cf CH4

(HF)

0E 40.214 au= −E

14.752 auZ

∂= −

∂

2

2

E 3.023 au

Z

∂= −

∂

3

3

E 0.135 au

Z

∂= −

∂

( ) ( )0 0 4E Z 1 E NH - 56.500++ = =

( ) ( )0 0 4E Z 1 E BH - 26.950−− = =

cf “exact” 56.565−

26.987−

Pag.13/04/2015 42

For the complete series of six N2 transmutation reactions (B3LYP/cc-pVTZ) an error between “vertical” and alchemical transmutation energies of 0.03 a.u. was obtained

N2 → CO case: 0.004 au ~ 2.5 kcal mol-1

Not “chemical accuracy” yet but the ordering of the energy of the compounds comes out correctly

Straightforward procedure for looking at neighbouring structures when exploring chemical space

Recent quantum chemical interest in Molecular Design

(cf M.Wang, X.Hu, D.N. Beratan, W.Yang, JACS, 128, 3228 (2006))

Pag.13/04/2015 43

A more involved application: transmutation of benzene

( ) nn C H N azines− → →

( ) ( )n n

C C B N azoborines− → − →

iso-electronic transmutations

Azoborines • n-sequence correctly reproduced

• sequence of isomers n=1 (3)n=2 (11) n=3 (3)

correctly reproduced

Transmutation energies and alchemical derivates effective tools for stabilityprediction and exploring CCS

Present work: CC → BN substitution in fullerenes, graphene, …

R. Balawender, M.A. Welearegay, M. Lesiuk, F. De Proft, P. Geerlings, J. Chem.Theor.Comp.,9,5327 (2013)

Pag.

3. Conclusions

• Conceptual DFT offers a broad spectrum of reactivity descriptors in line with the need for

unifying concepts.

• The “missing” second order derivative, the “linear response function”, comes within reach with various techniques of increasing complexity. It is a tool to see how ∆v perturbations are propagated through an atom or molecule. Its physical relevance becomes apparent, thanks to various representations of the kernel for atoms revealing atomic shell structure, and extensions in the context of spin polarized Conceptual DFT

• The computational results on molecules reveal that important chemical information can be retrieved from the linear response function: from inductive and mesomeric effects to the aromatic character of organic and inorganic rings. In the context of alchemical derivatives it opens the gate for exploring chemical compound space in an efficient way.

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Pag.13/04/2015 45

Ongoing

• The role of the linear response function in conduction of molecular electronic devices.

First results: � atom – atom polarizabilities( Hückel-π-type approach)

T.Stuyver, S.Fias, F.De Proft, P.W.Fowler, P.Geerlings, J.Chem.Phys, 147, xxx, 2015

• The role of DFT based reactivity descriptors in molecular design

Inverse design of stable radicals with highly electrophilic or nucleophilic charachter: roleof the electrophilicity ( ² / 2 )ω µ η=

F.De Vleeschouwer, A.Chankisjijev, W. Yang, P.Geerlings, F. De Proft, J. Org. Chem., 73, 9109 (2013)F.De Vleeschouwer, A.Chankisjijev, P.Geerlings, F.De Proft, Eur.J.Org.Chem,506 (2015)

χ

Pag.

Acknowledgements

Acknowledgements

Prof. Frank De Proft, Dr. Stijn Fias, Drs. Zino Boisdenghien, Dr. Freija De Vleeschouwer

Dr. Nick Sablon

Prof. Paul W. Ayers (Mc Master University, Hamilton, Canada)

Prof. Weitao Yang (Duke University, USA) and Dr. A. J. Cohen (Cambridge, UK)

Dr. R. Balawender and Drs. M. Welearegay (Warsaw, Poland)

Dr. M. Torrent – Sucarrat (Brussels, Girona)

Prof. C. Van Alsenoy (Antwerp, Belgium)

Prof. M. Sola (Girona), Prof. Gabriel Merino (Mexico)

Fund for Scientific Research-Flanders (Belgium) (FWO)

and the VUB (Strategic Research Program)

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Inverse Molecular Design

Introduction

• Previous part: application of concepts and indices to understand electronic structure and its relation to reactivity for atoms and indices

• Alchemical Derivatives : a first step towards exploring chemical space

• Exploring the properties of molecules encountered upon navigating through molecular space : molecule � property

• Now: design of new compounds with optimized reactivity indices : property� molecule� Inverse Molecular Design

• Case study: design of stable organic radicals

Pag.

• Homolytic bond cleavage of the molecule A-B into the radicals A and B

A − B → A• + B•

• Characterized by the bond dissociation enthalpy (BDE)

• Use BDE to quantify radical stability through a model

stab: intrinsic stability of the radical

Intrinsic Radical Stability Scale

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Pag.

enhanced electrophilicities

(ω=μ²/2η; ωref=2: borderline betweenelectrophilic and nucleophilic radicals

Intrinsic stabilities

Computed BDE (B3P86/6-311+G**)

enhanced electronegativities

χref=3 (~medium value betweenhighest and lowest Pauling.Electronegativity in database)

Performance of the model:

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Pag.

F.De Vleeschouwer, V.Van Speybroeck, M.Waroquier, P.Geerlings, F.De Proft, J. Org. Chem. 2008, 739109

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Pag.

• Use of this model (against H in A-B) to design stable organic radicals� Start from BDE (A-H)

• Inverse molecular design: find an optimal external potential of the system, generating a molecular system with the associated target properties (cfr W.Yang, X.Hu, D.N.Beratan, W.Yang, J.Am.Chem.Soc., 128, 3228 (2006)

• Challenge ! large number of possible structures accessible through the systematic variation of the composition of the molecular system

e.g. for a given framework : 5 sites and 21 substituents yield 215 combinations ~4x106

Inverse design approach

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Pag.

Approach:

1. Choice of a molecular framework of interest

• determine number of sites that can be modified

• determine number of substituents per site

2. Define property of interest to be optimized (here: stab values)

3. Choice of property optimizing method

M.L.Wang, X.Hu, D.N. Beratan, W. Yang, J. Am. Chem. Soc., 128, 3228 (2006)F.De Vleeschouwer, W. Yang, D.N. Beratan, P. Geerlings, F. De Proft, Phys. Chem. Chem. Phys. 14, 16002

(2012)

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Molecular framework: thiadiazenyl structure

J.Zienkiewicz, P.Kaszynski, J. Org. Chem., 69, 7525 (2004)

Stable radical: stab = 70 kJ mol−1

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5 sites and 21 substituents per site:

size of chemical space = 215 ≅ 4 x 106 molecules

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Pag.

• Choice of property optimizing method: Best-First-Search Methodology

• Algorithm:

• optimizes the property of a molecule by making chemical changes and evaluating the influence of those changes on the property of interest

• chemical changes brought in through the independent site approximation, so the various sites are optimized individually

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(C)-NHCH3

(C)-SOCH3

(C)-OCH3

(C)-SCH3

(C)-SO3H

(C)-COOH

(C)-CF3

(C)-CH3

(C)-CHO

(C)-CFO

(C)-OOH

(C)-SOH

(C)-NH2

(C)-OH

(C)-SH

(C)-CN

(C)-H

(C)-F

(C)-Cl

(C)-Br

(N)

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Results: most stable radicals

stab = 13 kJ mol−1

stab = 19 kJ mol−1

stab = 32 kJ mol−1

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Comparison with other stable organic radicals

20 kJ mol−1 82 kJ mol−1 86 kJ mol−1

33 kJ mol−1 34 kJ mol−1

F.De Vleeschouwer, A.Chankisjijev, W. Yang, P.Geerlings, F. De Proft, J. Org. Chem., 73, 9109 (2013)F.De Vleeschouwer, A.Chankisjijev, P.Geerlings, F.De Proft, Eur.J.Org.Chem, 506 (2015)

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Triphenylmethyl Phenalenyl N,N-diphenyl-N’ - picrylhydrazyl

1,5 - diphenylverdazyl 1,3,5 - triphenylverdazyl