Optimization of the valence energy variance of the CuH molecule

We developed the concept of split-'t to deal with the large molecules (in terms of the number of electrons and nuclear charge Z). This naturally leads to partitioning the local energy into components due to each electron shell. The minimization of the variation of the valence shell local energy is used to optimize a simple two parameter CuH wave function. Molecular properties (spectroscopic constants and the dipole moment) are calculated for the optimized and nearly optimized wave functions using the Variational Quantum Monte Carlo method. Our best results are comparable to those from the single and double configuration interaction (SDCI) method.

Optimization of trial wave functions for use in quantum Monte Carlo with application to LiH

Methods for both partial and full optimization of wavefunction parameters are explored, and these are applied to the LiH molecule. A partial optimization can be easily performed with little difficulty. But to perform a full optimization we must avoid a wrong minimum, and deal with linear-dependency, time step-dependency and ensemble-dependency problems. Five basis sets are examined. The optimized wavefunction with a 3-function set gives a variational energy of -7.998 + 0.005 a.u., which is comparable to that (-7.990 + 0.003) 1 of Reynold's unoptimized \fin ( a double-~ set of eight functions). The optimized wavefunction with a double~ plus 3dz2 set gives ari energy of -8.052 + 0.003 a.u., which is comparable with the fixed-node energy (-8.059 + 0.004)1 of the \fin. The optimized double-~ function itself gives an energy of -8.049 + 0.002 a.u. Each number above was obtained on a Bourrghs 7900 mainframe computer with 14 -15 hrs CPU time.

Reduced local energy calculations on X¹Sigmaâ ½gHâ and 1¹S He /|nGerald F. Thomas. -- 260 St. Catharines [Ont.] : Dept. of Chemistry, Brock University,

The one-electron reduced local energy function, t ~ , is introduced and has the property < tL)=(~>. It is suggested that the accuracy of SL reflects the local accuracy of an approximate wavefunction. We establish that <~~>~ <~2,> and present a bound formula, E~ , which is such that where Ew is Weinstein's lower bound formula to the ground state. The nature of the bound is not guaranteed but for sufficiently accurate wavefunctions it will yield a lower bound. ,-+ 1'S I I Applications to X LW Hz. and ne are presented.

Variational Monte Carlo estimation of the dissociation energy of CuH using correlated sampling

A new approach to treating large Z systems by quantum Monte Carlo has been developed. It naturally leads to notion of the 'valence energy'. Possibilities of the new approach has been explored by optimizing the wave function for CuH and Cu and computing dissociation energy and dipole moment of CuH using variational Monte Carlo. The dissociation energy obtained is about 40% smaller than the experimental value; the method is comparable with SCF and simple pseudopotential calculations. The dipole moment differs from the best theoretical estimate by about 50% what is again comparable with other methods (Complete Active Space SCF and pseudopotential methods).