Photoelectron Spectroscopy
• Lecture 3: vibrational/rotational structure
– Vibrational selection rules
– Franck-Condon Effect
– Information on bonding
– Ionization reorganization energy
Potential Energy Surface Description of the
Ionization of Dihydrogen
Ionization Energy (eV)
18
H2+
17
16
15
H2
0
0
1
r (Å)
2
Much more on this next time!!
Note: this is not vibronic coupling!
• In electronic absorption spectroscopy, vibronic coupling
refers to vibrational lowering of symmetry, which makes
forbidden electronic transitions allowed.
• Direct ionization transitions are already always allowed.
Vibrational Overlap Integral
The specific intensities of the different vibrational components
are governed by the Franck-Condon Principle and are
expressed by the vibrational overlap integral:
I   S' vib *S vib dR
Svib is the vibrational wavefunction in the ground state
S’vib is the vibrational wavefunction in the excited state.
The square of the vibrational overlap integral in called the
Franck-Condon factor.
Vibrational Selection Rules
• Most molecules exist in the totally symmetric zero-point vibrational
level of the ground state
• Totally symmetric modes of the ionic state are therefore observed.
• If the vibrational levels have quantum numbers n, then the selection
rule is
Δn = 0, ±1, ±2, etc.
• In other words, transitions between any vibrational levels of the
ground electronic state and excited electronic state(s) for any totally
symmetric vibration will be allowed.
• For large molecules, structure for several symmetric modes may be
interdigitated
Vertical Ionization is the most probable
Ionization Energy (eV)
18
H2 +
17
vertical
adiabatic
16
15
Lowest energy transition: Adiabatic
transition (ν0 ➔ ν0)
Most probable (tallest) transition: Vertical
transition
H2
0
0
1
r (Å)
2
Ground state vibrational population follows a
Boltzmann distribution:
e-E/kT
kT at room temperature is 0.035 eV (300 cm-1)
Bond Character of Orbitals
2u
:N≡N:
1g
2p
2p
2g
(N-N) cm-1
Ground state 2330
1st ion state
2100
2nd ion state 1810
3rd ion state
2340
1u
2s
1u
2s
1g
Ground state = 1g+
First ion state = 2g+
Second ion state = 2u
Third ion state = 2
20
19
18
17
16
Ionization Energy (eV)
15
Will vibrational structure be
observed on core ionizations?
Bancroft, Inorg. Chem. 1999, 38, 4688.
Svensson, J. Chem. Phys. 1997, 106, 1661.
Core equivalent model
“Atomic cores that have the same charge may be considered
to be chemically equivalent”
W.L. Jolly, Acc. Chem. Res. 1970.
• Removing a core electron is equivalent to adding a proton to the nucleus
– Core-ionized atom Z is equivalent to atom Z+1
• Eg., core-ionized CH4 is equivalent to NH4+
– In CH4 C-H = 1.09 Å, in NH4+ N-H = 1.01 Å
– Therefore potential well is shifted for core ionization, and vibrational
transitions other than 0 to 0 will be observed
• Core-ionized W(CO)6 is equivalent to Re(CO)6+
– W(CO)6 W-C = 2.07 Å, Re(CO)6+ Re-C = 2.01 Å
Quantitative Measure of Geometry
Changes
In a harmonic oscillator model, the intensities of the individual
vibrational components (Franck-Condon factors) will follow a
Poisson distribution:
S n S
In  e
n!
S = distortion parameter (Huang-Rhys factor)
Width of ionization envelope indicates amount of geometry change
between ground state and ion state.
Modeling of band shape to analyze S and the vibrational frequencies
allows us to quantitate geometry change, reorganization energy, etc.
Example: Nitric Oxide
NO
<2
1+
<1
<3
<0
h for neutral NO is 1,890 cm-1
vibrational spacing here is 2,260 cm-1
<4
<6 <5
11.5
11.0
10.5
10.0
9.5
Ionization Energy (eV)
Quanta
Rel. FC
0
51
1
100
2
93
3
52
4
21
5
6
6
2
S n S
In 
e
n!
These can
be related by
an S of 1.8.
S
1
2
k (Q) 2
h
Solving for Q allows us to
estimate that the NO distance has
changed by 0.085 Å in the ion
state. Must be a shortening of NO
distance to account for increase in
vibrational frequency
Reorganization Energy
A
t2
t1
B
Factors Controlling Electron-Transfer Reactions Rates
• G°, the free energy change
• Hab (or t), electronic coupling
• , the reorganization energy
 = i + o, inner-sphere and outer-sphere contributions
i: vibrational reorganization energy, hole-phonon coupling
Reorganization Energy
+●
+●
+
+
+●
8•+
80
Distortion Coordinate
Reorganization Energy
S n S
In  e
n!
h = 173.3 meV (1,400 cm-1)
S = 0.358
h = 42.3 meV (340 cm-1)
S = 0.182
 = (hk)•(Sk)
7.9
7.7
7.5
Ionization Energy (eV)
•+
=69.7 meV
8
7.3
Unresolved Vibrational Structure
Photoelectron spectra of larger molecules usually look more like this:
How should we analyze data like these?
Spectral fitting with consideration for chemical implications.
Summary
• Ionization from electronic levels includes transitions to
discrete vibrational/rotational levels.
• Bonding character of individual electrons gives rise to
ionization band structure.
• This band structure can be analyzed to give quantitative
information on geometry changes, reorganization
energies – bonding.
• If vibrational structure is not resolved, ionization bands
will still have a shape related to bonding differences.