Deterministic optimization of Jastrow factors

Highly flexible Jastrow factors have found significant use in stochastic electronic structure methods such as variational Monte Carlo (VMC) and diffusion Monte Carlo, as well as in quantum chemical transcorrelated (TC) approaches, which have recently seen great success in generating highly accurate electronic energies using moderately sized basis sets. In particular, for the latter, the intrinsic noise in the Jastrow factor due to its optimization by VMC can pose a problem, especially when targeting weak (non-covalent) interactions. In this paper, we propose a deterministic alternative to VMC Jastrow optimization, based on minimizing the "variance of the TC reference energy" in a standard basis set. Analytic expressions for the derivatives of the TC Hamiltonian matrix elements are derived and implemented. This approach can be used to optimize the parameters in the Jastrow functions, either from scratch or to refine an initial VMC-based guess, to produce noise-free Jastrows in a reproducible manner. Applied to the first row of atoms and molecules, the results show that the method yields Slater-Jastrow wavefunctions whose variances are almost as low as those obtained from standard VMC variance optimization, but whose energies are lower and comparable to those obtained from energy-minimization VMC. We propose that the method can be used both in the context of the transcorrelated method and in standard VMC as a new way to optimize Jastrow functions.