Theory and software for large Quantum Monte Carlo super-computer simulations over exponential type orbitals

摘要

Slater-type orbitals (STO) are rarely used as atomic basis sets for molecular structure and property calculations, since integrals are expensive to evaluate, reliable basis sets are scarce and exact properties such as Kato's cusp condition and the correct exponential decay of the electron density are not significantly better described numerically than with commonly used Gaussian basis sets. We adopt the systematic parallelized development of integration routines for multi-centre integrals, and high-quality basis sets over STOs, useful for modern electron correlation calculations via compact low-variance trial wave-functions for QMC (Quantum Monte Carlo). Molecular QMC applications are also rare, because the method is comparatively complicated to use, however it is extremely precise and can be made to include nearly all the correlation energy. It also scales well for large numbers of processors (1000s at nearly 100 percent efficiency). Applications need to be carried out on a large scale, to determine electronic structure and properties of large (about 100 atoms) molecules of chemical interest, including intermolecular interactions, best described using Slater trial wave-functions for QMC. Such functions combined as hydrogen-like atomic orbitals possess the correct nodal structure for the high precision FN-MC (Fixed Node Monte Carlo) methods, which include more than 95 percent of the electron correlation energy. High quality quantum Monte-Carlo calculations require good trial wave-functions. This is particularly true of the most accurate fixed node Monte Carlo approach. This need is satisfied by Sturmian functions which possess suitable nodal behavior. These functions are exponential type orbitals (ETOs) with the required long-range analytical behavior for molecular wave-functions. Hydrogen-like atomic orbitals are a (familiar but restricted) special case of Sturmians. Quantum Monte Carlo simulations require correlated wave-functions which are usually obtained by optimizing the trial wave-function with an explicitly correlated Jastrow factor with the interparticle distance as variable. Sturmians are also good starting points for the construction of geminal trial functions that explicitly include inter-particle (electron-electron) distances. These Sturmian geminals are functions of the electron-electron vector. This paper discusses the use of Sturmians (as a function of the usual electron position vector) and in particular the evaluation of molecular integrals in a Sturmian basis. Their analytical computation can be pursued by techniques that include symbolic computation methods. These ideas have been used to construct an improved Slater-Type Orbital Package (STOP) for the evaluation of three- and four-center molecular integrals that are needed to perform meaningful molecular calculations. Presented at the Theoretical and Computational Chemistry Conference (TACC 2008), Shanghai, China, 21-26 September 2008.