Monte Carlo simulations potential energy surfaces

Since his arrival at McMaster in 1988, Randall Dumont has focused on statistical theories and their origin in quantum and classical mechanics. His interests include the development of Monte Carlo implementations of statistical theory wherein dynamical processes are simulated by random walks on potential energy surfaces. The breakdown of statistical theory and the appearance of nonexponential population decay are also topics of his ongoing investigations. Other questions of interest are the incorporation of quantum effects into statistical theory and the effects of collisions on reaction processes. He has a special interest in argon cluster evaporation in vacuum197 and in the description of simple isomerization reactions.198 His other interests include the semiclassical description of classically unallowed processes such as tunneling.199... 

In practice, the value of the reaction coordinate r is determined from the gas-phase potential energy surface of the complex. Then we use the pair-distribution function for the system (for example, determined by a Monte Carlo simulation) and the intramolecular potential energy Vjatra to calculate the relation between the two rate constants. Alternatively, one may determine the potential of mean force directly in a Monte Carlo simulation. With the example in Fig. 10.2.6 and a reaction coordinate at rj, we see that the potential of mean force is negative, which implies that the rate constant in solution is larger than in the gas phase. Physically, this means that the transition state is more stabilized (has a lower energy) than in the gas phase. If the reaction coordinate is at r, then the potential of mean force is positive and the rate constant in solution is smaller than in the gas phase. 

To express the collective solvent reaction coordinate as in equation (6), it is necessary to define the specific diabatic potential surface for the reactant and product state. This, however, is not a simple task, and there is no unique way of defining such diabatic states. What is needed is a method that allows the preservation of the formal charges of the fragments of reactant and product resonance states. At the same time, solvent effects can be incorporated into electronic structure calculations in molecular dynamics and Monte Carlo simulations. Recently, we developed a block-localized wave function (BLW) method for studying resonance stabilization, hyperconjugation effects, and interaction energy decomposition of organic molecules.20-23 The BLW method can be formulated to specify the effective VB states.14... 

Two methods are in common use for simulating molecular liquids the Monte Carlo method (MC) and molecular dynamics calculations (MD). Both depend on the availability of reasonably accurate potential energy surfaces and both are based on statistical classical mechanics, taking no account of quantum effects. In the past 10-15 years quantum Monte Carlo methods (QMC) have been developed that allow intramolecular degrees of freedom to be studied, but because of the computational complexity of this approach results have only been reported for water clusters. 

Monte Carlo simulations use multiple dimensional integrals of statistical mechanics to investigate in this instance, the potential energy of sorbate molecules in the presence of a molecular surface (25,26). 

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