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Ch 14. Electronic Spectroscopy
• 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.
MS310 Quantum Physical Chemistry
14.1 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)
MS310 Quantum Physical Chemistry
 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.
MS310 Quantum Physical Chemistry
14.2 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
define  | M L |,  L  M L  L and  S  M S  S  2 S 1 




0
1
2
3
Molecular Term








Atomic Term
S
P
D
F
 If molecule has a inversion center : use g and u symbol
(otherwise, do not use anything)
MS310 Quantum Physical Chemistry
 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
Ex) H 2

  0, 2 S  1  2, parity g  2  g
Ex) O 2
2 x , 2 y
  1,   1
(closed shell)  g  g  g  3  g
ground state of O 2 : triplet state  (  ) sign : 3  g
if the two e – s occupy the same  , both   1  
MS310 Quantum Physical Chemistry
14.3 Transition between electronic states of
diatomic 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)
MS310 Quantum Physical Chemistry
MS310 Quantum Physical Chemistry
MS310 Quantum Physical Chemistry
 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
MS310 Quantum Physical Chemistry
 ∆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.
MS310 Quantum Physical Chemistry
 If molecule take energy, photodissociation reaction occurs
O2  h  2O 
→ Maximum wavelength : 242nm
 In stratosphere, oxygen atom react with oxygen molecule
and form ozone.
O   O2  M  O3  M *
Ozone absorb the photon : 220nm to 350nm
→ filtering UV radiation of the sun.
MS310 Quantum Physical Chemistry
14.4 The vibrational fine structure of electronic
transition 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
 (r1 ,..., rn , R1 ,..., R m )   electronic (r1 ,..., rn , R1fixed ,..., R mfixed )
  vibrational ( R 1 ,..., R m )
Discuss in 8.5, transition occurs if transition dipole moment is
not zero.
 fi   *f (r1 ,..., rn , R1 ,..., R m )ˆ i (r1 ,..., rn , R1 ,..., R m )d  0
MS310 Quantum Physical Chemistry
n
Dipole moment operator is given by ̂   e  ri
i 1
Use this equation, transition dipole moment becomes
 fi  S   *f (r1 ,..., rn , R 1fixed ,..., R mfixed )ˆ i (r1 ,..., rn , R 1fixed ,..., R mfixed )d
l
* vibrational
  ( vibrationa
(
R
,...,
R
))
i
( R 1 ,..., R m )d
f
1
m
   *f (r1 ,..., rn , R 1fixed ,..., R mfixed )ˆ i (r1 ,..., rn , R 1fixed ,..., R mfixed )d
See first integral of second equation, it means ‘overlap’
between ground and excited state.
Franck-Condon factor S is given by
l * vibrational
2
S 2 |  ( vibrationa
)

d

|
f
i
MS310 Quantum Physical Chemistry
 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’.
MS310 Quantum Physical Chemistry
 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!
MS310 Quantum Physical Chemistry
 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.
MS310 Quantum Physical Chemistry
14.5 UV-vis light absorption in polyatomic
molecules
 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
MS310 Quantum Physical Chemistry
 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
MS310 Quantum Physical Chemistry
 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)
MS310 Quantum Physical Chemistry
 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
MS310 Quantum Physical Chemistry
 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(n
1
1
O) (πCO*)
 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(n
2
1
O) (πCO*)
MS310 Quantum Physical Chemistry
 However, spin of unfilled orbital is not specified
: cannot describe completely
 Energy gap between singlet and triplet : typically lies 2 to 10eV.
MS310 Quantum Physical Chemistry
 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.
MS310 Quantum Physical Chemistry
14.6 Transition among the ground and excited
states
 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.
MS310 Quantum Physical Chemistry
MS310 Quantum Physical Chemistry
14.7 Singlet-triplet transitions : absorption and
fluorescence
 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
log(
It
)  lc
I0
 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
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MS310 Quantum Physical Chemistry
 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 fluorescence
is small different. Why?
: ‘difference’ of vibrational and rotational state
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Pattern of absorption and fluorescence
MS310 Quantum Physical Chemistry
14.8 Intersystem crossing and phosphorescence
 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
MS310 Quantum Physical Chemistry
 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
MS310 Quantum Physical Chemistry
State energy diagrams : electronic and spin isomers
Singlet orbital
orbital configuration
⑨
Ψ*
Ψ
Triplet orbital
orbital configuration
⑦
S1
kF
ε( S0  S1 )
Ψ*
Ψ
S0
⑧
Ground state
orbital configuration
①.
②.
③.
④.
⑤.
⑥.
⑦.
① ② ③
25%
⑩
kST
T1
kIC
kP
Ψ*
Ψ
kTS
ε( S0  T1 )
④ ⑤ ⑥
100%
Allowed : Singlet-singlet absorption (S0 +hv  S1)
Allowed : Singlet-singlet emisstion, fluorescence (S1  S0 + hv)
Allowed : Transition btw state of the same spin, internal conversion (S1  S0 + heat)
Forbidden : Triplet-singlet absorption (S0 + hv  T1)
Forbidden : Triplet-singlet emission, phosphorescence (T1  S0 +hv)
Forbidden : Transition btw triplet state & ground state, ISC (T1  S0 + hv)
Forbidden : Transition btw excited state of different spin, ISC (S1T1 +heat)
Heavy metals core based triplet emitters
Need to Mix singlet and triplet states
; make both singlet and triplet decay allowed
Use metal-Organic complex with heavy transition metals.
S1
Heavy metals
(Pt, Ir, etc…)
T1
Spin orbital coupling
(T1S0)
Ligand molecular orbitals
S0
Transitions between singlet and triplet states are called intersystem crossing (ICS) (S1T1)
; ISC is spin-forbidden  spin orbital coupling  ISC generate (S1T1)  Phosphorescence (T1S0)
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Toward 100% internal quantum efficiency
Spin-orbital coupling
-Intersystem crossing(S1T1)
- phosphorescence (T1S0)
Solution process
Introduce of Nano structure
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14.9 Fluorescence spectroscopy and analytical
chemistry
 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 2,3dideoxyribonucleotide.
- 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
MS310 Quantum Physical Chemistry
- 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)
MS310 Quantum Physical Chemistry
MS310 Quantum Physical Chemistry
14.10 UV photoelectron spectroscopy
 UV spectroscopy : closest to see orbital energy directly
 Photoionization : molecule ionize with light(photon)
 Kinetic energy of emitted electron is given by
1
Ekinetic  h  [ E f  ( n f  )h vibration]
2
- 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.
MS310 Quantum Physical Chemistry
Case of O2 UV spectroscopy
MS310 Quantum Physical Chemistry
 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
MS310 Quantum Physical Chemistry
MS310 Quantum Physical Chemistry
 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
MS310 Quantum Physical Chemistry
 17~20eV peak : attributed to εσA
Corresponding MO : 1b2
Associated with antisymmetric
combination
 Peak attributed to εσS : not
observed
(higher than experimental
energy)
Corresponding MO : 1a1
Associated with antisymmetric
combination
MS310 Quantum Physical Chemistry
 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).
MS310 Quantum Physical Chemistry
14.11 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.
MS310 Quantum Physical Chemistry
MS310 Quantum Physical Chemistry
14.12 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
MS310 Quantum Physical Chemistry
 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
1
E
1  ( R / R0 ) 6
1.0
0.8
E
0.6
0.4
Ro 50 Å
0.2
0.0
0
25
50
R (Å)
MS310 Quantum Physical Chemistry
75
100
1
E
1  ( R / R0 ) 6
Ro = 0.21( JqD n k
-4
2
)
1
6
Fluorescnece Intensity
Then, how to increase R0
J(λ)
Donor
fluorescnece
Acceptor
absorption
Wavelength
• 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
• k2 is a geometric factor related to the relative orientation of the
transition dipoles of the donor and acceptor and their relative
orientation in space.
D
A
R0
D
D
A
A
Donor
Acceptor
(R0, nm)
Naphthalene
LY
Dansyl
LY
FITC
BPE
Dansyl
TNP-ATP
ODR
EM
EM
CY5
2.2
3.5
4.3
5.3
6.0
7.2
Conclusion
 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
14.13 Linear and circular dichroism
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MS310 Quantum Physical Chemistry
14.14 Assigning + and – to Σ terms of diatomic
molecules
 + 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
MS310 Quantum Physical Chemistry
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

Lˆ z   i
, ( )  Ae  i

MS310 Quantum Physical Chemistry
In π2 configuration, 6 combinations are possible.
 1   1 1 ( (1) ( 2)   (1) ( 2))
 2   1 1 ( (1) ( 2)   (1) ( 2))
 3  ( 1 1   1 1 )( (1) ( 2)   (1) ( 2))
 4  ( 1 1   1 1 ) (1) ( 2)
 5  ( 1 1   1 1 )( (1) ( 2)   (1) ( 2))
 6  ( 1 1   1 1 ) (1) ( 2)
Can check easily ψ1~ψ3 are triplet and ψ4~ψ6 are singlet.
Also, ψ1, ψ2 are ∆ term and ψ3~ ψ6 are Σ term.
MS310 Quantum Physical Chemistry
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-
MS310 Quantum Physical Chemistry
Summary
- Electronic spectroscopy : see the ‘level’ of
molecule
- Study term symbol and application
- Beer-Lambert’s Law : connection between
theoretical allowed and forbidden transition to
experimental spectroscopy
- Real application : genome project
MS310 Quantum Physical Chemistry