Photoelectron Spectroscopy

• Lecture 3: vibrational/rotational structure– Vibrational selection rules– Franck-Condon Effect– Information on bonding– Ionization reorganization energy

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0

Ioni

zatio

n E

nerg

y (e

V)

H2+

r (Å)0 1 2

H2

Potential Energy Surface Description of the Ionization of Dihydrogen

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.

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 S dRvib v ib ' *

Svib is the vibrational wavefunction in the ground stateS’vib is the vibrational wavefunction in the excited state.

The square of the vibrational overlap integral in called the Franck-Condon factor.

Vibrational Overlap Integral

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

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verticaladiabatic

Lowest energy transition: Adiabatic transition (ν0 ν➔ 0)

Most probable (tallest) transition: Vertical transition

Ground state vibrational population follows a Boltzmann distribution:

e-E/kT

kT at room temperature is 0.035 eV (300 cm-1)

Vertical Ionization is the most probable

Ground state = 1g+

Ionization Energy (eV)151617181920

First ion state = 2g+

Second ion state = 2u

Third ion state = 2u

(N-N) cm-1

Ground state 23301st ion state 21002nd ion state 18103rd ion state 2340

:N≡N:2p

2s

2p

2s

1g

2g

1u

2u

1u

1g

Bond Character of Orbitals

Will vibrational structure be observed on core ionizations?

Svensson, J. Chem. Phys. 1997, 106, 1661.

Bancroft, Inorg. Chem. 1999, 38, 4688.

Core equivalent model

• 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

“Atomic cores that have the same charge may be considered to be chemically equivalent”W.L. Jolly, Acc. Chem. Res. 1970.

Quantitative Measure of Geometry Changes

IS

nen

nS

!

In a harmonic oscillator model, the intensities of the individual vibrational components (Franck-Condon factors) will follow a Poisson distribution:

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

Quanta Rel. FC

0 51

1 100

2 93

3 52

4 21

5 6

6 2

11.5 11.0 10.5 10.0 9.5

Ionization Energy (eV)

0

NO 1+12

3

4

56

IS

nen

nS

!

These can be related by an S of 1.8.

h for neutral NO is 1,890 cm-1

vibrational spacing here is 2,260 cm-1

hQk

S2

21 )(

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

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

t1

t2A

B

Reorganization Energy

++ ● + ●

+

Distortion Coordinate

+ ●

•+

0

Reorganization Energy

•+ = 69.7 meV

7.9 7.7 7.5 7.3

h = 173.3 meV (1,400 cm-1)S = 0.358

h = 42.3 meV (340 cm-1)S = 0.182

= (hk)•(Sk)

Ionization Energy (eV)

IS

nen

nS

!

Unresolved Vibrational StructurePhotoelectron 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.