A line-shape function in terms of changes in both molecular structure and force constants: a Gaussian approximation

We propose a new expression of a line-shape function (LSF) including the effects of changes in both force constants and the molecular structure within the harmonic-oscillator approximation. This expression enables us to calculate the LSF using only the data on molecular structures, force constants, and electronic energies in the initial and final electronic states without solving the eigenvalue equation for the normal vibration of a molecule. To derive the LSF expression, we consider one-photon emission from a polyatomic molecule thermalized in an electronic excited state, and derive the intensity distribution function for one-photon emission using not Lax and Kubo and Toyozawa's J. Chem. Phys. 20, 1752 (1952); Prog. Theor. Phys. 13, 160 (1955)] generating function method but rather the density-matrix method. As a simple application, a Gaussian approximate LSF is applied to SO(2). As a result, it is found that the effect of change in force constants between the initial and final electronic states cannot be ignored, nor can the effect of change in the molecular structure between these two states. The LSF expression obtained is applicable to studies of not only radiative transition but also of electron-transfer and energy-transfer processes where both changes in molecular structure and force constants between the initial and final electronic states cannot be disregarded.