The Diffusion Quantum Monte Carlo Method

QMC calculations are especially well suited to be run on parallel computers. The Quantum Monte Carlo at Home project using the home computers of tens of thousands of volunteers to run FN-DQMC calculations (qmcathome.org) has calculated accurate interaction energies for the DNA base pairs adenine-thymine and guanine-cytosine. This project will be changing its focus to run quantum-mechanical calculations at home in such areas as protein-ligand interactions and development of new materials for batteries. 

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Joslin and Goldman [105] in 1992 studied this problem by using the Diffusive Quantum Monte Carlo Methods. By resorting to the hard spherical box model, they performed calculations, not only on the ground state of helium atom, but also for H- and Li+. In this method the Schrodinger equation is... 

The FN-DQMC calculation in the table uses the diffusion quantum Monte Carlo method. quantum Monte Carlo (QMC) method uses a random process to solve the Schrftdinger equation. Many QMC methods exist, but the diffusion QMC (DQMC) method is most commonly used for molecular calculations. Defining the imaginary time variable t s itjh. 

OOSok Sokolova, S., Ltlchow, A. An ab initio study ofTiC with the diffusion quantum Monte Carlo method, Chem. Phys. Lett. 320 (2000) 421 24. 

Today, the most important QMC method for molecules is the diffusion quantum Monte Carlo method (DMC). It has been presented in the review articles mentioned above and in detail in the monograph by Hammond et al Here only an overview is given without mathematical rigor. A mathematical analysis of the DMC method, and in particular of its fixed-node approximation, has recently been published by Cances et al. ... 

Carlo method (VQMC), the diffusion quantum Monte Carlo method (DQMC), the Green s function quantum Monte Carlo method (GFQMC), and the path integral quantum Monte Carlo method (PIQMC). These methods are by their nature strongly related and each has its own peculiar advantages and disadvantages relative to the others. 

The diffusion quantum Monte Carlo method (DQMC) approaches the solution of the Schrodinger equation in a way completely different from that of variational methods. The basic ideas were given above in the succinct description quoted from the original report by Metropolis and Ulam. Here we give a more complete description. 

The standard quantum mechanical problem of the harmonic oscillator may be used to demonstrate the diffusion quantum Monte Carlo method. The system is illustrated in Figure 2. The potential energy is given by the function V = Vikx. The potential energy may be shifted by an arbitrary constant energy to make V negative in the central region near x = 0 and positive away from the center. 

The Diffusion Quantum Monte Carlo (DQMC) algorithm and related methods such as the Vibrational Quantum Monte Carlo approach have the important property of scahng well with system size (number of degrees of freedom). At the same time the method can be pursued in principle to yield a numerically exact energy. DQMC was introduced... 

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. 

The fourth method used for quantum chemical calculations is the quantum Monte Carlo (QMC) method, in which the Schrodinger equation is solved numerically. There are three general variants of QMC variational MC (VMC), diffusion QMC (DQMC), and Green s function QMC (GFQMC), all of which... 

Finally, we stress that the quantum chemical method presented here has the advantage over DFT-based techniques that it also furnishes wavefunctions that can be used to perform computations of spectra, and therefore have a better contact with the experiment. Another advantage of this approach is that, unlike the diffusion Monte-Carlo method, it can coherently be applied to studies of fermion and mixed boson/fermion doped clusters. An example can be found in our recent work on the Raman spectra of (He)w-Br2(X) clusters [27,28]. 

This review is a brief update of the recent progress in the attempt to calculate properties of atoms and molecules by stochastic methods which go under the general name of quantum Monte Carlo (QMC). Below we distinguish between basic variants of QMC variational Monte Carlo (VMC), diffusion Monte Carlo (DMC), Green s function Monte Carlo (GFMC), and path-integral Monte Carlo (PIMC). 

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