How do I relate the frequency anharmonic shift to each mode of vibration to intramolecular energy flow pathway.
I have calculated the anharmonic shift of each mode of vibration but don't quite understand what the shift means physically. The anharmonic shift is calculated by perturbation method and the hamiltonian, schrodinger equation is solved by Greens function method. What does that anharmonic shift physically mean?
Hi Hari Pandey,
Anharamoicity arise from the higher order terms(cubic, quadratic,....) of the Taylor expansion of potential energy. To understand the anharmonicity, one has to construct the potential energy surface(PES) for a particular mode and need use approriate function to fit the PES and find the exact anharmoicity shifts.
Consider for example formaldehyde... if i want to get accurate anharmonicy contribution due C-H stretching mode, then i will calculate the energy with respect to distance to get the grid points for PES. Then, this PES will be fitted with appropriate function to find the anharmoicity. This is a diagonal approach, where you focused on C-H mode. But in reality vibrational modes in a molecule are couple to each other. In our example, C-H stretching mode while oscillating may couple with C=O stretch or HC=O bending mode or HCH mode. To account for it we made need to go for 2D PES, which would be tough, but the vibrational energy transfer happens upon coupling of modes and anharmonicity do play a role.
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