Fully self-consistent optimization of the Jastrow-Slater-type wave function using a similarity-transformed Hamiltonian

Abstract

For highly accurate electronic structure calculation, the Jastrow correlation factor is known to successfully capture the electron correlation effects. Thus, the efficient optimization of the many-body wave function including the Jastrow correlation factor is of great importance. For this purpose, the transcorrelated + variational Monte Carlo (TC+VMC) method is one of the promising methods, where the one-electron orbitals in the Slater determinant and the Jastrow factor are self-consistently optimized in the TC and VMC methods, respectively. In particular, the TC method is based on similarity-transformation of the Hamitonian by the jastrow factor, which enables efficient optimization of the one-electron orbitals under the effective interactions. In this study, by test calculation of a helium atom, we find that the total energy is systematically improved by using better Jastrow functions, which can be naturally understood by considering a role of the Jastrow factor and the effective potential introduced by the similarity-transformation. We also find that one can partially receive a benefit of the orbital optimization even by one-shot TC+VMC, where the Jastrow parameters are optimized at the Hartree-Fock+VMC level, while a quality of the many-body wave function is inferior to that for self-consistent TC+VMC. A difference between TC and biorthogonal TC is also discussed. Our study provides important knowledge for optimizing many-body wave function including the Jastrow correlation factor, which would be of great help for development of highly accurate electronic structure calculation.

TC++: First-principles calculation code for solids using the transcorrelated method

“…The combination of the TC method with the post-HF methods was also reported for solid-state calculations: calculation of optical absorption spectra by TC-CI singles [29], and TC-MP2 calculation for simple solids [30]. Several QMC methods using the Jastrow factor can also be combined with the TC method [9,31,32,33,34,35]. In particular, similarity-transformed FCIQMC, the combination of the TC and FCIQMC methods, has recently been much attention [14,36,37,38,39,40,41,42].…”