Orbital-dependent backflow wave functions for real-space quantum Monte Carlo

Abstract

We present and motivate an efficient way to include orbital dependent many-body correlations in trial wave function of real-space Quantum Monte Carlo methods for use in electronic structure calculations. We apply our new orbital-dependent backflow wave function to calculate ground state energies of the first row atoms using variational and diffusion Monte Carlo methods. The systematic overall gain of correlation energy with respect to single determinant Jastrow-Slater wave functions is competitive with the best single determinant trial wave functions currently available. The computational cost per Monte Carlo step is comparable to that of simple backflow calculations.

Variational and diffusion quantum Monte Carlo calculations with the CASINO code

“…Note that since the backflow displacement is a vector function, the electron-electron-nucleus term requires two separate functions Φ T and Θ T to span the plane defined by the two electrons and the nucleus. There exist alternative forms of backflow in the literature, including analytical, 52 recursive, 54 and orbital-dependent 55 formulations. A deepneural-network-based wave function has been proposed recently consisting of a short multideterminant expansion populated with flexible orbitals and backflow-like features.…”

Electronic band gaps from quantum Monte Carlo methods

“…The difference might be due to a different functional form or optimization procedure. A systematic study on the bias of the fixed-node approximation such as done with more general backflow correlations [49,50] or multi-determinant trial wave functions [51], possible for small supercells, could be done in the future. So far, in our analysis of C and Si, we have imposed the experimentally known dielectric constant in the leading order Madelung correction.…”

A new scheme for fixed node diffusion quantum Monte Carlo with pseudopotentials: Improving reproducibility and reducing the trial-wave-function bias

“…However, it is worth mentioning that if the system under consideration is not too large (say, generally not more than a few atoms) better functions can be used, such as multi-determinant expansions of Slater determinants [34][35][36][37][38][39] , valence-bond wave functions 40 , the antisymmetrized geminal product 41,42 , the Pfaffian 43 , and others (see for instance the review by Austin et al 44 ). Moreover, the backflow transformation [45][46][47] can be employed to further improve any of the aforementioned ansätze, at the price of a significantly larger computational cost. The Jastrow factor describes the dynamical correlation between the electrons, by including explicit functions of the electron-electron distances.…”