Framework for constructing generic Jastrow correlation factors

We have developed a flexible framework for constructing Jastrow factors which allows for the introduction of terms involving arbitrary numbers of particles. The use of various three- and four-body Jastrow terms in quantum Monte Carlo calculations is investigated, including a four-body van der Waals-like term, and anisotropic terms. We have tested these Jastrow factors on one- and two-dimensional homogeneous electron gases, the Be, B, and O atoms, and the BeH, H${}_2$O, N${}_2$, and H${}_2$ molecules. Our optimized Jastrow factors retrieve more than 90$\%$ of the fixed-node diffusion Monte Carlo correlation energy in variational Monte Carlo for each system studied.

Figure 1

VMC energies $E_{\mathrm{VMC}}$ against the VMC variance for the 2D HEG at $r_s=35$ a.u. using different Jastrow factors, along with the DMC energies for reference. The error bars are smaller than the size of the symbols, and “(BF)” indicates the use of backflow.

Figure 2

Plots of the $A_{1,1}^z$ term (left) and $N_{1,2}$ term (right) of different Jastrow factors for N${}_2$ as a function of the position of an electron in a plane containing the nuclei (black circles).

Figure 3

Difference between the VMC and exact energy against the number of wave function parameters for the H${}_2$ triplet ground state using different Jastrow factors. Only the “multiterm” Jastrow factor enforces the cusp conditions. The error bars are smaller than the size of the symbol where not shown. All of the energies in this plot are lower than $-1$ a.u., and therefore the wave functions predict binding.

Figure 4

Fraction of the DMC correlation energy retrieved by different Jastrow factor terms, added in the specific order depicted in the graph (starting from the bottom), for the molecules studied in this paper.