Core electrons, quantum Monte Carlo

An overview of quantum Monte Carlo electronic structure studies in the context of recent effective potential implementations is given. New results for three electron systems are presented. As long as care is taken in the selection of trial wavefunctions, and appropriate frozen core corrections are included, agreement with experiment is excellent (errors less than 0.1 eV). This approach offers promise as a means of avoiding the excessive configuration expansions that have plagued more conventional transition metal studies. 

PPs are a basic tool in Quantum Monte Carlo (QMC) calculations [146-150], The computational effort of QMC for an -electron system scales as 0 r ). It is estimated that for the additional Z- scaling with nuclear charge Z the exponent is reduced from jc 5.5 — 6.5 to jc 3.4 when the cores are replaced by PPs [151]. So-called soft PPs which avoid the 1/r and 1/r singularities in the effective one-electron potential have been derived at the nonrelativistic level for Be to Ne and A1 to Ar for use in QMC calculations by the group of Lester [152,153]. 

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. 

C. W. Greeff, W. A. Lester, and B. L. Hammond,/. Chem. Phys., 104,1973 (1996). Electronic States of A1 and AI2 Using Quantum Monte Carlo with an Effective Core Potential. 

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