Potential energy surface anharmonic

Hobza, P., Bludsky, O. Suhai, S., 1999, Reliable Theoretical Treatment of Molecular Clusters Counterpoise-Corrected Potential Energy Surface and Anharmonic Vibrational Frequencies of the Water Dimer , Phys. Chem. Chem. Phys., 1, 3073. 

Even when the harmonic approximation is not quantitatively justified it provides a convenient starting point for exact treatments. Thus, even if the potential energy surface is anharmonic in the bottleneck, it is often smooth enough for there to be a principal saddle point that can be found by minimizing IVU 2. 

Such a method has recently been developed by Miller. et. al. (28). It uses short lengths of classical trajectory, calculated on an upside-down potential energy surface, to obtain a nonlocal correction to the classical (canonical) equilibrium probability density Peq(p, ) at each point then uses this corrected density to evaluate the rate constant via eq. 4. The method appears to handle the anharmonic tunneling in the reactions H+HH and D+HH fairly well (28), and can... 

The harmonic approximation is unrealistic in a dynamical description of the dissociation dynamics, because anharmonic potential energy terms will play an important role in the large amplitude motion associated with dissociation. An accurate potential energy surface must be used in order to obtain a realistic dynamical description of the dissociation process and, as in the quasi-classical approach for bimolecular collisions, a numerical solution of the classical equations of motion is required [2]. 

In our discussion the usual Born-Oppenheimer (BO) approximation will be employed. This means that we assume a standard partition of the effective Hamiltonian into an electronic and a nuclear part, as well as the factorization of the solute wavefunction into an electronic and a nuclear component. As will be clear soon, the corresponding electronic problem is the main source of specificities of QM continuum models, due to the nonlinearity of the effective electronic Hamiltonian of the solute. The QM nuclear problem, whose solution gives information on solvent effects on the nuclear structure (geometry) and properties, has less specific aspects, with respect the case of the isolated molecules. In fact, once the proper potential energy surfaces are obtained from the solution of the electronic problem, such a problem can be solved using the standard methods and approximations (mechanical harmonicity, and anharmonicity of various order) used for isolated molecules. The QM nuclear problem is mainly connected with the vibrational properties of the nuclei and the corresponding spectroscopic observables, and it will be considered in more detail in the contributions in the book dedicated to the vibrational spectroscopies (IR/Raman). This contribution will be focused on the QM electronic problem. 

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