A Investigation of Exact Quantum Monte Carlo Methods for Small Molecules.

Michel Caffarel, Carlo, UK +2 more

Fei Lin, Jurij Šmakov, Erik Schwartz Sørensen +2 more

We generalize the imaginary-chemical-potential quantum Monte Carlo (QMC) method proposed by Dagotto [Phys. Rev. B 41, R811 (1990)] to systems without particle-hole symmetry. The generalized method is tested by comparing the results of the QMC simulations and exact diagonalization on small Hubbard molecules, such as tetrahedron and truncated tetrahedron. Results of the application of the method to the C60 Hubbard molecule are discussed.

Michel Caffarel, Florent Xavier Gadéa, David M. Ceperley

A method for accelerating the rate of convergence of the long-time (or small-temperatur) limit of quantum Monte Carlo approaches is presented. To do that, a variation of the Lanczós algorithm suitable for QMC data is introduced. This algorithm allows one to extract more information from correlation functions at small times, thus avoiding large statistical fluctuations associated with large times. It is first applied to an exactly soluble system and then to the LiH molecule. Calculations using both the fixed-node and nodal-release approaches are discussed.

Tanaka Shigenori

Deidre M. Cleland, Manolo C. Per

This work investigates the accuracy of real-space quantum Monte Carlo (QMC) methods for calculating molecular geometries. We present the equilibrium bond lengths of a test set of 30 diatomic molecules calculated using variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) methods. The effect of different trial wavefunctions is investigated using single determinants constructed from Hartree-Fock (HF) and Density Functional Theory (DFT) orbitals with LDA, PBE, and B3LYP functionals, as well as small multi-configurational self-consistent field (MCSCF) multi-determinant expansions. When compared to experimental geometries, all DMC methods exhibit smaller mean-absolute deviations (MADs) than those given by HF, DFT, and MCSCF. The most accurate MAD of 3 ± 2 × 10(-3) Å is achieved using DMC with a small multi-determinant expansion. However, the more computationally efficient multi-determinant VMC method has a similar MAD of only 4.0 ± 0.9 × 10(-3) Å, suggesting that QMC forces calculated from the relatively simple VMC algorithm may often be sufficient for accurate molecular geometries.

Dmitry Yu. Zubarev, Brian M. Austin, William A. Lester