Anharmonic systems, direct evaluation

Amides, alkaline hydrolysis, 215 Anharmonic systems, direct evaluation of quantum time-correlation functions, 93 Apollo DSP—160, CHARMM performance, 129/ simulations, solvent effects, 83... 

The approach to the evaluation of vibrational spectra described above is based on classical simulations for which quantum corrections are possible. The incorporation of quantum effects directly in simulations of large molecular systems is one of the most challenging areas in theoretical chemistry today. The development of quantum simulation methods is particularly important in the area of molecular spectroscopy for which quantum effects can be important and where the goal is to use simulations to help understand the structural and dynamical origins of changes in spectral lineshapes with environmental variables such as the temperature. The direct evaluation of quantum time- correlation functions for anharmonic systems is extremely difficult. Our initial approach to the evaluation of finite temperature anharmonic effects on vibrational lineshapes is derived from the fact that the moments of the vibrational lineshape spectrum can be expressed as functions of expectation values of positional and momentum operators. These expectation values can be evaluated using extremely efficient quantum Monte-Carlo techniques. The main points are summarized below. 

It is possible to obtain the results (5.13,14) by directly evaluating the thermodynamical averages of a and the force constant f (Problem 5.6.1). By starting with the equation of motion (5.4) and its solution (5.7), we have, in addition, gained some insight into the dynamics of the system. The dynamics of a polyatomic anharmonic molecule with several fundamental frequencies. .. (A). .. . is more complicated. Its vibrational motion will not only con-... 

Note added in proof In view of the failure of the harmonic oscillator model to account for the observed rate of activation in unimolecular dissociation reactions (the dissociation lag problem) these calculations have been repeated for a Morse anharmonic oscillator with transition between nearest and next-nearest neighbor levels [S. K. Kim, /. Chem. Phys. (to be published)]. The numerical evaluation of the analytical results obtained by Kim has not yet been carried out. From the results obtained by us and our co-workers [Barley, Montroll, Rubin, and Shuler, /. Chem. Phys. in press)] on the relaxation of vibrational nonequilibrium distributions of a system of Morse anharmonic oscillators it seems clear, however, that the anharmonic oscillator model with weak interactions (i.e., adiabatic perturbation type matrix elements) does not constitute much of an improvement on the harmonic oscillator model in giving the observed rates of activation. The answer to tliis problem would seem to lie in a recalculation of the collisional matrix elements for translational-vibrational energy exchange which takes account of the strong interactions in highly energetic collisions which can lead to direct dissociation. 

The interaction energy reflects a hypothetical dimerization process at 0 K and is not measurable. In order to be related to experimental dissociation energies Do and enthalpies of formation, the deformation energy of monomers and the zero-point vibration energy must be included. The zero-point energies and enthalpy and entropy contributions at nonzero temperature are usually calculated in the harmonic approximation. Since base-pair complexes are weak, anharmonicity can play an important role, especially for stacked systems and particularly at higher temperatures. Nevertheless, except for direct comparison with gas phase experiment, interaction energy evaluation is the sufficient outcome of QM analysis. 

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