Theoretical treatment of anharmonic effect on molecular absorption, fluorescence spectra, and electron transfer

It is well-known that the mirror image between absorption and fluorescence spectra is held for the displaced harmonic-oscillator system, and also this mirror image is independent to the chiral symmetry in which the excited-state potential energy surface is right-handed or left-handed with respect to the ground-state potential energy surface. As the first-order approximation of anharmonic correction is added into the displaced harmonic oscillator, this mirror image is broken down, and then the spectra can be depended on the chiral symmetry mentioned above. Both absorption and fluorescence coefficients are derived analytically within the first-order anharmonic approximation and numerical test is carried out to demonstrate the breaking down of the mirror image. Based on the same analysis, the electron transfer rate is derived analytically within the first-order anharmonic approximation. This rate might take the form of Arrhenius's equation but not form of Marcus's equation. Furthermore, it is found that this rate is also depending on the chiral symmetry.