Atoms, quantum Monte Carlo

James B. Anderson, Quantum Monte Carlo Atoms, Molecules, Clusters, Liquids, and Solids. 

A. Aspuru-Guzik et al., in Quantum Monte Carlo Theory and Applications to Atomic, Molecular and Nano Systems, ed. by M. Rieth, W. Schommers. Handbook of Theoretical and Computational Nanotechnology, vol. 3 (American Scientific Publishers, Stevenson Ranch, CA, 2005), pp. 644-702... 

In this way Filippi, Umrigar and Gonze [27] have recently calculated the exchange potentials corresponding to the exact (not the x-only) densities of some atoms where the exact densities were determined in a quantum Monte-Carlo calculation. Likewise, for any given approximate functional Ec[ g>i ], the corresponding correlation potential... 

Most of the present discussion has been concerned with applications of REPs within the framework of otherwise essentially orbital-based calculations. On the other hand, a recent application 110) involved a quantum Monte Carlo (QMC) procedure. [A useful overview of Monte Carlo electronic structure work has been given by Ceperly and Alder 111). ] Currently, QMC offers little, if any, competition for conventional calculations in that the computer time required to reduce statistical errors to acceptable limits increases rapidly as a function of atomic number and is excessive for all but the smallest systems. Recent fluorine calculations required nearly 100 hours of supercomputer time 112). Although, on the surface, it would appear totally impractical, the appeal of this approach in the context of heavy-element work is its avoidance of extensive basis sets and enormous configuration expansions that plague present studies. 

Two coupling modes are considered for the Pdj CO cluster the first mode (denoted as h) represents vibration of the rigid CO molecule with respect to the transition metal surface. The second mode is either the Pd-Pd vibration wi in the plane of Pd surface atoms (r) or out-of-plane stretch of the surface/sub-surface Pd-Pd bond (z). The total energy surfaces (h,r) and (h,z) are calculated for discrete points and then fitted to a fourth order polynomial. Variational and Quantum Monte Carlo (QMC) methods were subsequently applied to calculate the ground and first excited vibrational states of each two-dimensional potential surfaces. The results of the vibrational frequences (o using both the variational and QMC approach are displayed in Table II. 

K. Delaney, C. Pierleoni and D.M. Ceperley (2006) Quantum Monte Carlo Simulation of the High-Pressure Molecular-Atomic Transition in Fluid Hydrogen. cond-mat/0603750, submitted to Phys. Rev. Letts.,... 

Figure 3.1 Size dependence of cohesive energies per atom (CE/n) of mercury clusters Hgn from calculations using a large-core EC-PP and CPP for Hg. Valence correlation is accounted for either within die hybrid model approach (HM) by a pair-potential adjusted for Hg2 or by pure-diffusion quantum Monte Carlo (PDMC) calculations (Wang etal 2000).

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... 

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). 

In this short review we have pointed out only very few of the basic issues involving the simulation of chemical systems with Quantum Monte Carlo. What has been achieved in the last few years is remarkable very precise calculations of small molecules, the most accurate calculations of the electron gas, silicon and carbon clusters, solids, and simulations of hydrogen at temperatures when bonds are forming. New methods have been developed as well high-accuracy trial wavefunctions for atoms, molecules, and solids, treatment of atomic cores, and the generalization of path-integral Monte Carlo to treat many-electron systems at positive temperatures. 

Aspuru-Guzik A, Kollias AC, Salomon-Ferrer R, Lester WA Jr (2005) Quantum Monte Carlo theory and application to atomic, molecular and nano systems. In Rieth M, Schommers W... 

Anderson JB (1999) Quantum Monte Carlo atoms, molecules, clusters, liquids and solids. In lipkowitz KB, Boyd DB (eds) Reviews in computational chemistry. Wiley, New York... 

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