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## Photoelectron Spectroscopy

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**Photoelectron Spectroscopy**• Lecture 3: vibrational/rotational structure • Vibrational selection rules • Franck-Condon Effect • Information on bonding • Ionization reorganization energy**H2+**18 17 16 15 Ionization Energy (eV) H2 0 1 0 2 r (Å) 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.**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: 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**H2+**18 17 16 vertical adiabatic 15 Ionization Energy (eV) H2 0 1 0 2 r (Å) Vertical Ionization is the most probable Lowest energy transition: Adiabatic transition (ν0 ➔ ν0) 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)**20**19 18 17 16 15 Ionization Energy (eV) Bond Character of Orbitals 2u :N≡N: 1g 2p 2p 2g (N-N) cm-1 Ground state 2330 1st ion state 2100 2nd ion state 1810 3rd ion state 2340 1u 2s 2s 1u 1g Ground state = 1g+ First ion state = 2g+ Second ion state = 2u Third ion state = 2u**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 = 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.**<2**<1 NO 1+ <3 <0 <4 <5 <6 11.5 11.0 10.5 10.0 9.5 Ionization Energy (eV) Example: Nitric Oxide h for neutral NO is 1,890 cm-1 vibrational spacing here is 2,260 cm-1 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 These can be related by an S of 1.8.**A**t2 t1 B 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**+ ●**8 •+ 8 0 Distortion Coordinate Reorganization Energy + ● + ● + +**•+**= 8 69.7 meV Reorganization Energy h = 173.3 meV (1,400 cm-1) S = 0.358 h = 42.3 meV (340 cm-1) S = 0.182 = (hk)•(Sk) 7.9 7.7 7.5 7.3 Ionization Energy (eV)**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.