Molecule Types Vibrational Structure Vibrational Energy Levels and Franck-Condon Factors

# Manual entry of the l matrix

If you want to set up an l matrix, the most convenient starting point is importing the required geometry and l matrix directly from the output of selected ab initio programs (see Importing l matrices) or from a simple force field analysis. If this is not possible, say if you want to import an l matrix from a source that PGOPHER can't read directly, the following steps listed below are the minimum needed:
1. The main menu item File, New, Vibrational Structure will generate a basic settings for two electronic states.
2. Set the basic molecular information by clicking on "VibratingMolecule" and set:
• nModes - the number of vibrational modes
• PointGroup - the symmetry of the molecule
• nNuclei - the number of nuclei
3. Set the symmetry of the ground electronic state is set by clicking on "X" and altering "Symmetry" as required. (The default is totally symmetric.)
4. Set the names of the nuclei by right clicking on the "Nucleus1", "Nucleus1", entries under X and selecting "Rename". If you use the standard element names, possibly with a number (e.g. H1, H2, Br) then the mass can be set by right clicking on the nucleus and selecting "Set Exact Mass". Alternatively, if an approximate mass is entered (at "Mass") "Set Exact Mass" will find the corresponding exact mass. The names and masses need only be set once, though they appear under a state, rather than at the molecule level.
5. The geometry and l matrix are most conveniently entered by right clicking on the state, "X" and selecting "l matrix...". This brings up the l Matrix Window, which will plot the molecular geometry, with the plot updating as you enter it. Enter the equilibrium co-ordinates under "Equilibrium".
6. The l matrix can be entered in the same form; if "Mass Weighted" is selected then the elements are l/sqrt(mass) with units of 1/sqrt(amu). The l matrix should be orthogonal - the "Operate" button contains tools to test and correct this, and the centre of mass.
7. Enter the ground state frequencies and symmetries by clicking on "v1", "v2" ... in turn under "X". As for nuclear masses, the symmetry of a mode only needs to be set in one state.
8. Repeat steps 3 and 5-7 above for the excited state.
9. To make use of the l matrices for Franck-Condon factors, "Calculate" must be set to true under <A|FCF|X>.
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