Brock University - Department of Chemistry

Accurate Treatment of Systems Containing Heavy Atoms.

From the perspective of quantum Monte Carlo (QMC), the difficulty of systems containing heavy atoms is due to electrons in various shells experiencing forces which vary over several orders of magnitude. There is an extremely slow rate of convergence for the inner-most electrons, necessitating use a very small simulation time-step, inappropriate for the valence electrons. This ruins the efficiency of the simulation, making the algorithm no longer feasible beyond Z » 10. (See Rothstein (1997).)

Others have dealt with this problem by resorting to pseudopotential methods, where the core electrons are absent from the simulation, greatly reducing the complexity and computational demands of the problem. Unfortunately, this tack suffers from the lack of rigor; pseudopotential methods do not rest on a firm theoretical foundation, which we think is a necessary condition to
improve these methods.

Using "core-valence partitioned" wavefunctions (a product of the wavefunction for the core electrons only multiplied by wavefunction for the valence ones), Staroverov et al (1998) performed all-electron variational Monte Carlo (VMC) simulations on first row atoms to address this issue. The success of these calculations coupled with the difficulties of QMC sampling imply the following line of research for highly accurate calculations on heavy-atom containing molecules: Avoid QMC sampling problems by using VMC-no time-step parameters are required, and use all-electron partitioned wavefunctions to avoid the approximations inherent in the valence hamiltonian and energy (Rothstein (1997)).

We are presently implementing this approach for second row atoms and beyond. The Ar calculations will be particularly important, as the partitioned wavefunction will then form the core for calcuations on the transition metal elements. As well as providing insight on how well partitioned wavefunctions perform, this will enable us to perfect our programs (Snajdr et al (1998)) for optimizing wavefunctions of this type with a large number of basis functions. Extension to transition metal containing molecules will then follow.

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