Quantum Monte Carlo with reoptimised perturbatively selected configuration-interaction wave functions

ABSTRACT

We explore the use in quantum Monte Carlo (QMC) of trial wave functions consisting of a Jastrow factor multiplied by a truncated configuration-interaction (CI) expansion in Slater determinants obtained from a CI perturbatively selected iteratively (CIPSI) calculation. In the CIPSI algorithm, the CI expansion is iteratively enlarged by selecting the best determinants using the perturbation theory, which provides an optimal and automatic way of constructing truncated CI expansions approaching the full CI limit. We perform a systematic study of variational Monte Carlo (VMC) and fixed-node diffusion Monte Carlo (DMC) total energies of first-row atoms from B to Ne with different levels of optimisation of the parameters (Jastrow parameters, coefficients of the determinants, and orbital parameters) in these trial wave functions. The results show that the reoptimisation of the coefficients of the determinants in VMC (together with the Jastrow factor) leads to an important lowering of both VMC and DMC total energies, and to their monotonic convergence with the number of determinants. In addition, we show that the reoptimisation of the orbitals is also important in both VMC and DMC for the Be atom when using a large basis set. These reoptimised Jastrow-CIPSI wave functions appear as promising, systematically improvable trial wave functions for QMC calculations.

GRAPHICAL ABSTRACT

Keywords:

• Configuration interaction
• fixed node diffusion Monte Carlo
• perturbation theory
• quantum Monte Carlo

Acknowledgments

It is a great pleasure to dedicate this paper to Andreas Savin who is among the early contributors to the development of quantum Monte Carlo for quantum chemistry [67–70] and who has always encouraged this line of research. We thank Michel Caffarel, Anthony Scemama, and Cyrus Umrigar for discussions.

Disclosure statement

No potential conflict of interest was reported by the authors.