Molecule Types Vibrational Structure | <Prev Next> |

PGOPHER will simulate the vibrational
structure associated with an electronic state or transition,
including anharmonic and Renner-Teller effects and vibronic
mixing. Ionization can also be simulated, providing spin effects
can be ignored. Currently C_{1}, C_{i}, C_{2},
C_{s}, D_{2}, C_{2v}, C_{2h}, D_{2h},
C_{∞v} and D_{∞h} symmetry are
explicitly supported. See the worked examples listed below for a
quick start.

Note that when using this mode, rotational structure associated with the transition is not simulated. For compatibility with the rotational modes, J will often be displayed but is fixed at zero. (The J range is used to select the maximum vibrational angular momentum to include when simulating spectra.)

A harmonic oscillator basis set is used of the form:

|v_{1}l_{1}>
|v_{2}l_{2}>…|…ΛΣ…>

where v_{i} are the standard vibrational quantum numbers
and l_{i} the corresponding
vibrational angular momenta (only required for degenerate modes).
Λ and Σ are the electronic quantum numbers, normally
only required for linear molecules. Anharmonic, Renner-Teller and
other vibronic interactions are accounted for by off-diagonal
matrix elements (expressed as perturbations in the
language of PGOPHER)
and a matrix diagonalisation if required.

To calculate the intensities of the
vibrational transitions associated with an electronic transition
multidimensional Franck-Condon factors are calculated. As the
vibrational basis used for each state is different (the basis is
determined by the normal modes) the normal modes in the two states
(Q, Q') must be related by:

Q' = JQ + K

where K represents the change in equilibrium geometry
and J accounts for mixing
between modes (The Dushinsky effect).
J and K can be input directly, or
calculated from the l
matrices from the two states. See P. Chen, "Photoelectron
Spectroscopy of Reactive Intermediates" (Chapter 8 of Unimolecular
and Bimolecular Ion_Molecule Reaction Dynamics, ed C Y Ng, T Baer
and I Powis, Wiley, 1994) for a brief review of the theory.

- Making a basic data file for simulating vibrational structure
- Worked Example - The Photoelectron
Spectrum of H
_{2}O - Worked Example - Predicting the
Photoelectron Spectrum of H
_{2}O using ab initio Calculations - Importing l matrices
- Manual entry of the l matrix
- The l Matrix Window
- The Dushinsky Transformation Window
- Molecule Settings
- Electronic State Settings
- Vibrational Modes
- Nuclear Co-ordinates
- Perturbations
- Multidimensional Franck Condon factors
- Vibrational Mode Changes
- Sample Data Files