Quantum Monte Carlo technique applications

Quantum Monte Carlo techniques have considerable potential for application to problems involving open d or f shells where the treatment of electron correlation has proven particularly difficult. However if is to be a viable alternative one must be able to limit the simulations to small numbers of electrons and in addition relativeity must be included. Relativistic effective potentials offer one avenue (at the present time the only avenue) for achieving these conditions. However, as we have indicated, REPs do introduce carpi icat ions. 

Another branch of computational quantum mechanics, quantum Monte Carlo, is described in Chapter 3 by Professor James B. Anderson. Quantum Monte Carlo techniques, such as variational, diffusion, and Green s function, are explained, along with applications to atoms, molecules, clusters, liquids, and solids. Quantum Monte Carlo is not as widely used as other approaches to solving the Schrodinger equation for the electronic structure of a system, and the programs for running these calculations are not as user friendly as those based on the Hartree-Fock approach. This chapter sheds much needed light on the topic. 

The second difference between molecular and solid-state fields is the lack, in the latter, of a reference theoretical method. Post-HF techniques in molecular quantum chemistry can yield results with a controlled degree of accuracy. In the absence of experimental data, the results obtained with different DFT functionals could be compared against those calculated with the reference computational technique. Recent developments in wavefunction methods [9], GW techniques [38], and quantum Monte Carlo (QMC) [39] for solid-state systems aim at filling this gap, and are promising for future work, but at present they still suffer from a limited applicability. 

The credit load for die computational chemistry laboratory course requires that the average student should be able to complete almost all of the work required for the course within die time constraint of one four-hour laboratory period per week. This constraint limits the material covered in the course. Four principal computational methods have been identified as being of primary importance in the practice of chemistry and thus in the education of chemistry students (1) Monte Carlo Methods, (2) Molecular Mechanics Methods, (3) Molecular Dynamics Simulations, and (4) Quantum Chemical Calculations. Clearly, other important topics could be added when time permits. These four methods are developed as separate units, in each case beginning with die fundamental principles including simple programming and visualization, and building to the sophisticated application of the technique to a chemical problem. 

Whereas selective diffusion can be better investigated using classical dynamic or Monte Carlo simulations, or experimental techniques, quantum chemical calculations are required to analyze molecular reactivity. Quantum chemical dynamic simulations provide with information with a too limited time scale range (of the order of several himdreds of ps) to be of use in diffusion studies which require time scale of the order of ns to s. However, they constitute good tools to study the behavior of reactants and products adsorbed in the proximity of the active site, prior to the reaction. Concerning reaction pathways analysis, static quantum chemistry calculations with molecular cluster models, allowing estimates of transition states geometries and properties, have been used for years. The application to solids is more recent. 

The next section gives a brief overview of the main computational techniques currently applied to catalytic problems. These techniques include ab initio electronic structure calculations, (ab initio) molecular dynamics, and Monte Carlo methods. The next three sections are devoted to particular applications of these techniques to catalytic and electrocatalytic issues. We focus on the interaction of CO and hydrogen with metal and alloy surfaces, both from quantum-chemical and statistical-mechanical points of view, as these processes play an important role in fuel-cell catalysis. We also demonstrate the role of the solvent in electrocatalytic bondbreaking reactions, using molecular dynamics simulations as well as extensive electronic structure and ab initio molecular dynamics calculations. Monte Carlo simulations illustrate the importance of lateral interactions, mixing, and surface diffusion in obtaining a correct kinetic description of catalytic processes. Finally, we summarize the main conclusions and give an outlook of the role of computational chemistry in catalysis and electrocatalysis. 

As mentioned, the Chapter will deal uniquely with applications of ab initio quantum chemistry to electrochemistry. There are, of course, many other theoretical and computational methods available to the study of electrochemical problems, such as classical molecular dynamics, Monte Carlo methods, and the more traditional coarsegrained or continuum-type theoretical or computational approaches. Several recent reviews cover these techniques and the advances made in their application in the field of interfacial electrochemistry. " ... 

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