Diffusion Monte Carlo calculations

Jakowski J, Chalasinski G, Gallegos J, Severson MW, Szczesniak MM (2003) Characterization of AmO clusters from ab initio and diffusion Monte Carlo calculations. J Chem Phys 118 2748-2759... 

Relevant calculations using both versions of MM have been reported for (0H )H20 [21, 26] and H5O2+ [27, 28] and some very recent results will be presented below. Diffusion Monte Carlo calculations, done by and in collaboration with Anne McCoy have also been done on these systems, however, these are not reviewed in detail here. 

Ceperley and Bernu [64] introduced a method that addresses these problems. It is a generalization of the standard variational method applied to the basis set exp(-f ) where is a basis of trial functions 1 s a < m. One performs a single-diffusion Monte Carlo calculation with a guiding function that allows the diffusion to access all desired states, generating a trajectory R(t), where t is imaginary time. With this trajectory one determines matrix elements between basis functions = ( a( i) I /3(fi + t)) and their time derivatives. Using... 

Diffusion Monte-Carlo Calculations of Quasi-Bound States of Rare Gas-Halogen Clusters a Diabatic Approach... 

Diffusion Monte-Carlo calculations of quasi-bound states of rare gas-halogen clusters a diabatic approach... 

There are five important sources of error in these first diffusion Monte Carlo calculations (1) statistical or sampling error associated with the limited number of independent sample energies used in determining the energy from an average of variable potential energies, (2) the use of a finite time step At rather than an infinitesimal time step as required for the exact simulation of a differential equation, (3) numerical error associated with trimcation and/or round-off... 

Zero-Point Energy from Diffusion Monte Carlo Calculations. 

Ra]agopal G, Needs R J, James A, Kenney S D and Foulkes W M C 1995 Variational and diffusion quantum Monte Carlo calculations at nonzero wave vectors theory and application to diamond-structure germanium Phys. Rev. B 51 10 591-600... 

Molecular dynamics calculations are more time-consuming than Monte Carlo calculations. This is because energy derivatives must be computed and used to solve the equations of motion. Molecular dynamics simulations are capable of yielding all the same properties as are obtained from Monte Carlo calculations. The advantage of molecular dynamics is that it is capable of modeling time-dependent properties, which can not be computed with Monte Carlo simulations. This is how diffusion coefficients must be computed. It is also possible to use shearing boundaries in order to obtain a viscosity. Molec-... 

Various methods, such as influence sampling, can be used to reduce the number of calculations needed. See also Lapeyre, B., Introduction to Monte-Carlo Methods for Transport and Diffusion Equations, Oxford University Press (2003), and Liu, J. S., Monte Carlo Strategies in Scientific Computing, Springer (2001). Some computer programs are available that perform simple Monte Carlo calculations using Microsoft Excel. 

We review Monte Carlo calculations of phase transitions and ordering behavior in lattice gas models of adsorbed layers on surfaces. The technical aspects of Monte Carlo methods are briefly summarized and results for a wide variety of models are described. Included are calculations of internal energies and order parameters for these models as a function of temperature and coverage along with adsorption isotherms and dynamic quantities such as self-diffusion constants. We also show results which are applicable to the interpretation of experimental data on physical systems such as H on Pd(lOO) and H on Fe(110). Other studies which are presented address fundamental theoretical questions about the nature of phase transitions in a two-dimensional geometry such as the existence of Kosterlitz-Thouless transitions or the nature of dynamic critical exponents. Lastly, we briefly mention multilayer adsorption and wetting phenomena and touch on the kinetics of domain growth at surfaces. 

Analytic or semi-analytic many-body methods provide an independent estimate of ec( .>0- Before the Diffusion Monte Carlo work, the best calculation was probably that of Singwi, Sjblander, Tosi and Land (SSTL) [38] which was parametrized by Hedin and Lundqvist (HL) [39] and chosen as the = 0 limit of Moruzzi, Janak and Williams (MJW) [40]. Table I shows that HL agrees within 4 millihartrees with PW92. A more recent calculation along the same lines, but with a more sophisticated exchange-correlation kernel [42], agrees with PW92 to better than 1 millihartree. 

In order to reproduce the temporal behavior of water decomposition products, two theoretical approaches based on spur diffusion model and Monte Carlo calculations have been developed. 

Collision Model. Figure 3 shows an instructive, efficient, and convenient method for treating the case of mixed surface and particle-diffusion control. It is instructive because it is easy to visualize. It is efficient because although it is a molecular approach, it does not require Monte Carlo calculations, which are expensive and should be avoided whenever possible. It is convenient because it leads to a set of differential equations... 

The quality of a variational quantum Monte Carlo calculation is determined by the choice of the many-body wavefunction. The many-body wavefunction we use is of the parameterized Slater-Jastrow type which has been shown to yield accurate results both for the homogeneous electron gas and for solid silicon (14) (In the case of silicon, for example, 85% of the fixed-node diffusion Monte Carlo correlation energy is recovered). At a given coupling A, 4>A is written as... 

Ornstein-Uhlenbeck diffusion quantum Monte Carlo calculations on BH and HF with the floating spherical Gaussian orbitals and spherical Gaussian geminals. 

Principally exact solution of the vibrational Schrodinger equation can be found by applying the Diffusion Monte Carlo (DMC) method [40], where the a<-,cnracy for ground state calculations is limited only by the statistical noise, which can be reduced to a desired level bj a sufficient investment of computer time. 

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