Potential energy surface extracting vibrational

Within the separable harmonic approximation, the < f i(t) > and < i i(t) > overlaps are dependent on the semi-classical force the molecule experiences along this vibrational normal mode coordinate in the excited electronic state, i.e. the slope of the excited electronic state potential energy surface along this vibrational normal mode coordinate. Thus, the resonance Raman and absorption cross-sections depend directly on the excited-state structural dynamics, but in different ways mathematically. It is this complementarity that allows us to extract the structural dynamics from a quantitative measure of the absorption spectrum and resonance Raman cross-sections. 

Most ab initio analyses of vibrational spectra invoke a double-harmonic assumption wherein the potential energy surface in the vicinity of the minimum is fit to a function that involves only quadratic dependence of the energy with respect to the nuclear motions. The intensities of the normal vibrational modes are extracted from the derivatives of the dipole moment, taken as linear with respect to nuclear coordinates. Within this approximation, the intensities of the fundamentals are proportional to the square of the dipole moment derivatives with respect to normal coordinates ". ... 

The nature of vibrationally and rotationally predissociating states of atom-diatom Van der Waals molecules and the fundamental considerations governing their predissociation are discussed. Particular attention is focussed on the influence of the potential energy surface and the information about it which might be extracted from accurate measurements of predissociation lifetimes. Most of the results discussed pertain to the molecular hydrogen-inert gas systems, and details of previously unpublished three-dimensional potential energy surfaces for diatomic hydrogen with krypton and xenon are presented. 

Our task is to find approximate solutions to the time-independent Schrodinger equation (Eq. (2)) subject to the Pauli antisymmetry constraints of many-electron wave functions. Once such an approximate solution has been obtained, we may extract from it information about the electronic system and go on to compute different molecular properties related to experimental observations. Usually, we must explore a range of nuclear configurations in our calculations to determine critical points of the potential energy surface, or to include the effects of vibrational and rotational motions on the calculated properties. For properties related to time-dependent perturbations (e.g., all interactions with radiation), we must determine the time development of the... 

All investigations presented in Sects. 4-6 have employed Bom-Oppenheimer dynamics (BOMD). We apply no scaling factor of any kind to the vibrations extracted from the dynamics. The sampling of vibrational anharmonicities, i.e., potential energy surface, dipole anharmonicities, mode couplings, anharmonic... 

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