Ch 14. Electronic Spectroscopy MS310 Quantum Physical Chemistry Absorption of VIS or UV can lead to...

Ch 14. Electronic SpectroscopyCh 14. Electronic Spectroscopy

MS310 Quantum Physical Chemistry

• Absorption of VIS or UV can lead to transitions between the ground state and excited stated electronic states of atoms and molecules.

• The excited state relaxes to the ground state through a combination of fluorescence, internal conversion, intersystem crossing, and phosphorescence.

• UV photoemission can be used to obtain information about the orbital energies of molecules.


14.1 The energy of electronic transitions14.1 The energy of electronic transitions

See the gap of electronic, vibrational, rotational transition. ∆Eelectronic >> ∆Evibrational >> ∆Erotational

Range of rotational and vibrational transition : μ-wave & IR range However, range of electronic transition : UV-Vis range → a specific electronic transition will contain vibrational and rotational fine structure

Transmitted and reflected light complement the absorbed light. Ex) A leaf is green. ( Chlorophyll absorbs in the blue and red ∵ spectrum.)

A human eye is a very sensitive detector of radiation. (One part in 106 - 500 photons/mm2·sec)


Electronic spectroscopy : see electronic state directly → very powerful to see the structure and chemical composition

However electronic excitation perturb the state of molecule much more than rotational and vibrational excitation.

→ Example, (a) bond length in electronically state of O2 is 30% longer than that in ground state.

(b) Formaldehyde in its ground state is a planar molecule, but pyramidal in its lowest two excited states. Its chemical reactivity can be quite different from that of ground state molecule.


14.2 Molecular term symbol14.2 Molecular term symbol

How describe the electronic state of molecule? → introduce ‘molecular term symbol’

Component of L and S(ML and MS) : along the molecular axis S : only good quantum number in diatomic molecule

If molecule has a inversion center : use g and u symbol (otherwise, do not use anything)

F

D

P

S

SMSLMLM SSLL

3

2

1

0

Term AtomicTermMolecular

and |,|define 12


1both,sametheoccupysetwotheif

: sign )( statetriplet : O of state ground

shell)(closed

1,12,2

O Ex)

parity,212,0

H Ex)

–

32

3

2

2

2

g

g

yx

g

ggg

gS

Consider + and – symbol. 1) all MOs are filled : + 2) partially filled MOs are σ symmetry : + 3) partially filled MOs of π symmetry : if Σ arise, - for triplet and + for singlet

14.3 Transition between electronic states of 14.3 Transition between electronic states of

diatomic moleculesdiatomic molecules


Diatomic molecule : most easily interpretable electronic spectra

4 electronic potential energy surface of lowest excited state of oxygen molecule.

Using this notation - X : ground state - A, B, C, … : excited state(multiplicity : 2S+1) - a, b, c, … : describe degenerated state

See dissociation of oxygen molecule - X, a, b, A state : O(3P) + O(3P) - B state : O(3P) + O(1D)




Symbol 3Σg- describes ground-state O2 completely

However, for convenient, use ‘molecular configuration’

X 3Σg-, a 1∆g, b 1Σg

+ : belong to the ground-state configuration, (1σg)2(1σu*)2(2σg)2(2σu*)2(3σg)2(1πu)2(1πu)2(1πg*)1(1πg*)1

but different ML and MS

A 3Σu+, B 3Σu

- : belongs to excited-state configuration, (1σg)2(1σu*)2(2σg)2(2σu*)2(3σg)2(1πu)1(1πu)2(1πg*)1(1πg*)2

→ several molecular terms are generated from same configuration

Selection rule is given by ∆Λ=0, ±1 and ∆S=0 Λ : component of total angular momentum L


∆Λ=0 : Σ ↔ Σ transition, ∆Λ= ±1 : Σ ↔ Π transition

Further selection rule given by +/- and g/u parity

Homonuclear diatomic molecule - u ↔ g transition : allowed - u ↔ u and g ↔ g transition : forbidden - Σ- ↔ Σ- and Σ+↔ Σ+ transition : allowed - Σ+ ↔ Σ- transition : forbidden

Use this rules in case of O2. - X 3Σg

- → a 1∆g and X 3Σg- → b 1Σg

+ transition : forbidden (by g↔g transition is forbidden) - X 3Σg

- → A 3Σu+ transition : forbidden

(by Σ+ ↔ Σ- transition forbidden)

Therefore, lowest allowed transition : X 3Σg- → B 3Σu

- transition. Energy of this transition : band between 175nm to 200nm → reason of air is transparent.


If molecule take energy, photodissociation reaction occurs

Ozone absorb the photon : 220nm to 350nm → filtering UV radiation of the sun.

OhO 22 → Maximum wavelength : 242nm

In stratosphere, oxygen atom react with oxygen molecule and form ozone.

*32 MOMOO

14.4 The vibrational fine structure of electronic 14.4 The vibrational fine structure of electronic

transition in diatomic moleculestransition in diatomic molecules


Selection rule ∆n= ±1 : only for vibrational transition → not valid for electronic transition

Determination of the change of vibrational quanta → see Born-Oppenheimer approximation

Apply this approximation, wavefunction is given by

)R,...,R(

)R,...,R,r,...,r()R,...,R,r,...,r(

1

1111

mlvibrationa

fixedm

fixedn

electronicmn

Discuss in 8.5, transition occurs if transition dipole moment is not zero.

0)R,...,R,r,...,r(ˆ)R,...,R,r,...,r( 1111* dmnimnf

fi


Dipole moment operator is given by

Use this equation, transition dipole moment becomes

n

iie

1

r̂

d

d

dS

fixedm

fixedni

fixedm

fixednf

mlvibrationa

imlvibrationa

f

fixedm

fixedni

fixedm

fixednf

fi

)R,...,R,r,...,r(ˆ)R,...,R,r,...,r(

)R,...,R())R,...,R((

)R,...,R,r,...,r(ˆ)R,...,R,r,...,r(

1111*

1*

1

1111*

2*2 |)(| dS lvibrationai

lvibrationaf

See first integral of second equation, it means ‘overlap’ between ground and excited state.Franck-Condon factor S is given by


Franck-Condon principle : transition occurs to vertical line on energy diagram. (when transition occurs, there are no change of atomic position.)

See this figure Transition occurs from n=0 to several n when electronic transition and depends on the position of ‘ground state’.


How can Franck-Condon principle determine the n value?

When transition occurs, there are no position change. Transition probability depends on the Franck-Condon factor S. → ‘overlap’ between 2 states determine the transition

State of ‘maximum’ probability where equilibrium position of ground state, n=0 : excited state, n=4!


If photon energy is so high(ν > E/h,

E : corresponding energy of highest

bounded state of excited state

→ continuous energy spectrum

Transition to ‘no bounded’ state of

molecule, i.e, case of H2+ bonding

state to excited(nonbonding) state.


14.5 UV-vis light absorption in polyatomic14.5 UV-vis light absorption in polyatomic

moleculesmolecules Case of polyatomic molecule :large moment of inertia → small gap between 2 rotational levels : more than 1000 rotational levels in ~1cm-1

Therefore, UV-vis spectra of large molecule : broad.

Spectra of 1-atom, diatom, and polyatom


The number of allowed state ↓ when temperature↓

Spectra of MeOH at 300K and 9K. - 300K : so many states are allowed and they are overlapped → broad peak

- 9K : only a few states are allowed because average energy of molecule is proportional to temperature → very sharp peak


How can discuss it? ‘chromophores’

In large molecule, charasteristic frequency is determined by neighboring 2 atoms. (For example, -C=C- or –O-H, C=C, C=O, C≡N, C=S, etc)

Each chromophore : characteristic frequency in UV

After, see ground-state and excited-state of formaldehyde (H2CO)


Ground-state configuration in the localized notation : (1sO)2(1sC)2(2sO)2(σCH)2(σ’CH)2(σCO)2(πCO)2(nO)2(πCO*)0

1s and 2s electron of C and O : not used(nonbonding) Also, lone pair of O(nO) is localized into O atom. C-H bond, 1 of C-O bond : σ, another C-O bond : π

σ bond of C-O : formed by sp2 hybridization orbital, the lowest energy

π bond of C-O : formed by 2p orbital : next lowest energy π* orbital : antibonding, next energy lone pair electrons : between π and π* state


Approximate MO diagram

First transition : nO to πCO* : n → π* transition→ Result configuration(1sO)2(1sC)2(2sO)2(σCH)2(σ’CH)2(σCO)2(πCO)2(nO)1

(πCO*)1

Second transition : πCO to πCO* : π → π* transition→ Result configuration(1sO)2(1sC)2(2sO)2(σCH)2(σ’CH)2(σCO)2(πCO)1(nO)2

(πCO*)1


However, spin of unfilled orbital is not specified : cannot describe completely

Energy gap between singlet and triplet : typically lies 2 to 10eV.


Order of transition energy : n → π*, π → π*, σ → σ* transition

n → π* : require both nonbonding pairs and multiple bonds. occurs in molecule containing carbonyls, thiocarbonyls, nitro, azo, and imine groups and in unsaturated halocarbons

π → π* : require multiple bonds. occurs in alkenes, alkynes, and aromatic compounds

σ → σ* : if none of the other transitions is possible, it occurs.


Generalization of the transition to arbitrary molecules → ground state : singlet / excited states : either a singlet or triplet

In transition, singlet →singlet. → Triplet state is generated by ‘internal conversion’, not direct.

Radioactive transition : photon emission and absorption (solid vertical lines)

Nonradiactive transition : energy transfer between different degree of freedoms and forbidden by dipole selection rule (singlet → triplet, dashed line)

Pathway of excited states to ground state : depends on rate of number of competing processes.

14.6 Transition among the ground and excited 14.6 Transition among the ground and excited

statesstates



Atomic spectroscopy : selection rule ∆S=0 strictly obeyed. Molecular spectroscopy : forbidden transition occurs but transitions corresponding to ∆S=0 are much stronger than forbidden transition by selection rule

Beer’s law(also called Beer-Lambert’s law) : If I0 is incident light intensity and It is transmitted light intensity, dependence of It/I0 on the concentration c and the path length l

Molar extinction coefficient ε : measure of the strength of the transition, measured at maximum spectral line Integral absorption coefficient A=∫ε(ν)dν : integration over the spectral line includes associated vibrational and rotational transitions : probability of absorption

14.7 Singlet-triplet transitions : absorption and 14.7 Singlet-triplet transitions : absorption and

fluorescencefluorescence

lcI

I t )log(0



εmax of spin-allowed and singlet-triplet transition. - spin-allowed transition(∆S=0) : 10~5x104 dm3 mol-1 cm-1

- spin-forbidden transition(∆S=1) : 1x10-4~1 dm3 mol-1 cm-1

Spin-orbit coupling is not negligible, ∆S=1 transition is not forbidden but intensity of this transition is weak. (ten thousand to ten million times weak)

→ However, this transition is very important when discuss the phosphorescence.

Nonradioactive transition by collision : internal conversion

Nonradioactive transition to excited vibrational state : intersystem crossing

In experiment, wavelength of absorption and fluorescenceis small different. Why? : ‘difference’ of vibrational and rotational state


Pattern of absorption and fluorescence


Intersystem between singlet and triplet : forbidden in the Born-Oppenheimer approximation.

However, it occurs in many molecules.This probability depends on 2 factors : very similar molecular geometry, strong spin-orbit coupling

14.8 Intersystem crossing and phosphorescence14.8 Intersystem crossing and phosphorescence


S0 → S1 transition : dipole-allowed transition → high probability. → By Franck-Condon principle, electron : same position of excited state (n=4 state)

Energy of ground state of S1 : approximately same as vibrational excited state of T1

- If spin-orbit coupling is strong enough to initiate a spin flip : S1

→ T1 transition occurs - S1 → T1 transition : molecule cross over from S1 to T1 state and it rapidly relax to the lowest vibrational excited state of T1

However, T1 state decays radiatively to the ground state, S0 in the dipole transition forbidden process, called as ‘phosphorescence’.

- Time of fluorescence : less than 10-7 s- Time of phosphorescence : more than 10-3 s

①. Allowed : Singlet-singlet absorption (S0 +hv S1) ②. Allowed : Singlet-singlet emisstion, fluorescence (S1 S0 + hv) ③. Allowed : Transition btw state of the same spin, internal conversion (S1 S0 + heat)④. Forbidden : Triplet-singlet absorption (S0 + hv T1) ⑤. Forbidden : Triplet-singlet emission, phosphorescence (T1 S0 +hv) ⑥. Forbidden : Transition btw triplet state & ground state, ISC (T1 S0 + hv) ⑦. Forbidden : Transition btw excited state of different spin, ISC (S1T1 +heat)

① ② ③ ④ ⑤ ⑥

⑦

⑨

⑧

⑩ΨΨ*

ΨΨ*

ΨΨ*

S0

S1

T1

ε( S0 S1 )

kF kIC

kST

ε( S0 T1 )

kP kTS

Ground state orbital configuration

Singlet orbital orbital configuration

Triplet orbital orbital configuration

State energy diagrams : electronic and spin isomers

25% 100%

Need to Mix singlet and triplet states

; make both singlet and triplet decay allowed

Heavy metals(Pt, Ir, etc…)

Ligand molecular orbitals

Use metal-Organic complex with heavy transition metals.

Transitions between singlet and triplet states are called intersystem crossing (ICS); ISC is spin-forbidden spin orbital coupling ISC generate (S1T1) Phosphorescence (T1S0)

S0

S1

T1

Spin orbital coupling

(T1S0)

(S1T1)

Heavy metals core based triplet emitters


Spin-orbital coupling-Intersystem crossing(S1T1) - phosphorescence (T1S0)

Solution process

Introduce of Nano structure


Toward 100% internal quantum efficiency


Laser-induced fluorescence spectroscopy 1. section of DNA is cut into small lengths of 1000~2000 bp using mechanical shearing.

2. it replicates in the solution with A,T,G,C.

- We also add small fraction of ‘modified’ base and this modified base terminate the replication.

- In real case, this modified base is derivative of 2,3- dideoxyribonucleotide.

- DNA polymerase III put the new basis on the 3’-OH of DNA and cannot catalyze the polymerization when this position changes to H. → many ‘pieces’ of original DNA.

- Dye(fluorescence at known wavelength) into the modified base

14.9 Fluorescence spectroscopy and analytical 14.9 Fluorescence spectroscopy and analytical

chemistrychemistry


- In real technique, we prepare 4 solutions and each solution has one type of modified base. → one solution has modified A, another solution has modified T, etc. Trivially, these solutions have normal A,T,G,C)

3. This DNA pieces are sorting with molecular weight by electrophoresis. Add LASER, fluorescence occurs and see the ‘order’ of DNA sequence.

Sensitivity of this method : 130±30 molecules in the volume illuminated by LASER!(It is also 2x10-13 mol/L)



UV spectroscopy : closest to see orbital energy directly Photoionization : molecule ionize with light(photon) Kinetic energy of emitted electron is given by

14.10 UV photoelectron spectroscopy14.10 UV photoelectron spectroscopy

])2

1([ vibrationffkinetic hnEhE

- In UV spectroscopy, must used delocalized model because of

initial of final state is ‘radical’.

- If these assumptions are satisfied, we can calculate Ef by

orbital energy.

1) Nuclear positions are unchanged in the transition(B-O app)

2) Orbitals for atom and ion are same

(frozen orbital approximation)

3) Total electron correlation energy in the molecule and ion

are same.


Case of O2 UV spectroscopy


In neutral molecule, this assumption is valid and known as ‘Koopmans’ theorem’

In real case, difference of numerical calculation and real value is 1 to 3 eV and reason is second and third assumption is not valid any more.

Water molecule. - Experiment with 21.4eV, there are 3 groups of peaks. - By HF calculation, we obtain 4 MOs. With localized MO model, there are 2 O-H bond and 2 lone pairs → 2 groups

Discrepancy of experiment and model : understood by coupling with bonding MOs and lone pairs. It leads to symmetric combinations and antisymmetric combinations.

S : symmetric, A : antisymmetric, σ : bonding, n : nonbonding



13eV peak : attributed to εnA

Corresponding MO : 1b1

Associated with antisymmetric combination

14~16eV peak : attributed to εnS Corresponding MO : 2a1

Associated with symmetric combination


17~20eV peak : attributed to εσA

Corresponding MO : 1b2


Peak attributed to εσS : not observed (higher than experimental energy)Corresponding MO : 1a1



This analysis solve this question. ‘Why do equivalent bonds or lone pairs give rise to several different orbital energies?’

Equivalent O-H bond and lone pairs are ‘interacting’ each others. MO of each bond or lone pairs are mutually orthogonal, but electron distribution in one bond(or lone pair) is not independent to another bond or lone pair by ‘Coulombic interaction’

Case of water, 2 equivalent O-H bonds give 2 distinct MO energy. However, only 2 levels in case of ammonia(3 equivalent bond) and 2 levels in case of methane(4 equivalent bond).


14.11 Single molecule spectroscopy14.11 Single molecule spectroscopy

The conformation of a biomolecule refers to the arrangement of its constituent atoms in space and can be discussed in terms of primary, secondary, and tertiary structure.

The primary structure is determined by the backbone of the molecule. The term secondary structure refers to the local conformation of a part of the polypeptide.

Tertiary structure refers to the overall shape of the molecule.



14.12 Fluorescent resonance energy transfer14.12 Fluorescent resonance energy transfer

We refer to the molecule that loses energy as the donor, and the molecule that accepts the energy as the acceptor.

Resonance energy transfer - the photon energy for fluorescence in the donor is equal to the photon energy for absorption in the acceptor


FRET rate

Rab is the distance between donor a and acceptor b

τa is the fluorescence lifetime of donor a

R0 is the Föster radius at which kT equaals 1/τa

FRET Efficiency

60 )/(1

1

RRE

R (Å)0 25 50 75 100

0.0

0.2

0.4

0.6

0.8

1.0

E

Ro 50 Å

• J is the normalized spectral overlap of the donor emission and acceptor absorption• qD is the quantum efficiency for donor emission in the

absence of acceptor (qD = number of photons emitted divided

by number of photons absorbed). • n is the index of refraction• is a geometric factor related to the relative orientation of the transition dipoles of the donor and acceptor and their relative orientation in space.

60 )/(1

1

RRE

Then, how to increase R0

Donorfluorescnece

Flu

ores

cnec

e In

ten

sity

Wavelength

Acceptorabsorption

J(λ)

Donor Acceptor (R0, nm)

Naphthalene Dansyl 2.2LY TNP-ATP 3.5

Dansyl ODR 4.3LY EM 5.3

FITC EM 6.0BPE CY5 7.2

AD

R0AD

D A

FRET provides an efficient way to measure the distance between a donor and an acceptor chromophore

by measuring the FRET efficiency, one can easily get the precise distance between the donor and the acceptor

If choosing the donor and acceptor properly, this experiment can also be carried out in vivo

Conclusion


14.13 Linear and circular dichroism14.13 Linear and circular dichroism



+ and - : change in sign of the molecular wavefunction on reflection in a plane contains the molecular axis. Sign preserve : +, opposite sign : - Case of σ MO : sign preserve → + O2 : (1σg)2(1σu*)2(2σg)2(2σu*)2(3σg)2(1πu)2(1πu)2(1πg*)1(1πg*)1

14.14 Assigning + and – to 14.14 Assigning + and – to ΣΣ terms of diatomic terms of diatomic

moleculesmolecules


Next, see 1πg* and 1πg’* wavefunction.There are 6 combinations of ml = ±1 and s = ±1/2.

However, these π(2px) and π(2py) wavefunctions are not eigenfunctions of Lz operator.

Eigenfunction of Lz operator

iz AeiL )(,ˆ


In π2 configuration, 6 combinations are possible.

Can check easily ψ1~ψ3 are triplet and ψ4~ψ6 are singlet.Also, ψ1, ψ2 are ∆ term and ψ3~ ψ6 are Σ term.

)2()1()(

))2()1()2()1()((

)2()1()(

))2()1()2()1()((

))2()1()2()1((

))2()1()2()1((

11116

11115

11114

11113

112

111


Eigenfunction of Lz : reflection is same as change of sign of Λ : π+1 → π-1 and π-1 → π-1

Therefore, ψ1~ψ3 : does not change the sign because of (-1)x(-1)=1 → these 3 wavefunctions are 1Σg

+

However, ψ4~ψ6 : change the sign because (-1)x(+1)=-1 → these 3 wavefunctions are 3Σg

-


- Electronic spectroscopy : see the ‘level’ of Electronic spectroscopy : see the ‘level’ of moleculemolecule

- Study term symbol and applicationStudy term symbol and application

- Beer-Lambert’s Law : connection between Beer-Lambert’s Law : connection between theoretical allowed and forbidden transition to theoretical allowed and forbidden transition to experimental spectroscopyexperimental spectroscopy

- Real application : genome projectReal application : genome project

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Ch 14. Electronic Spectroscopy MS310 Quantum Physical Chemistry Absorption of VIS or UV can lead to...

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