On the systematic improvement of fixed-node diffusion quantum Monte Carlo energies using pair natural orbital CI guide functions

Abstract

Abstract with nodes specified by Hartree-Fock wavefunctions, fixed-node DQivIC calculations recover typically 93 to 95% of the correlation energy for species like N, N2, and H20. Adding a few more determinants to the wavefunction has been found to give little if any improvement, but it is clear that very large CI functions will give improvement. In this paper the authors report the use of PNOs, pseudo-natural orbitals or pair-natural orbitals,a developed in the 1960s for compact multi-determinant wavefunctions in efficient CI calculations with limited computer speeds. With PNOs, transformations are made to produce pairs of orbitals which are either identical or orthogonal, and the CI expansion is much shorter than for the general CI function. With the more compact trial functions, DQMC calculations are much more efficient, and computation requirements are no longer prohibitive. For each of the species N, N2, and H20 calculations were carried out with trial functions containing from one to hundreds of determinants. Configurations making only small contributions to the calculated energy were deleted. In each case, the recovery of correlation energy is improved to 97 to 98% and this compares well with that of analytic MRCI calculations, but the best nonvariational methods for molecules of this size, such as CCSD(T)-R12, give energies closer to the estimated limits for these species. For large systems, the much more favorable N3 scaling observed for DQMC may be expected to favor DQMC.