Biorthonormal Orbital Optimization with a Cheap Core-Electron-Free Three-Body Correlation Factor for Quantum Monte Carlo and Transcorrelation

We
introduce a novel three-body correlation factor that
is designed
to vanish in the core region around each nucleus and approach a universal
two-body correlation factor for valence electrons. The transcorrelated
Hamiltonian is used to optimize the orbitals of a single Slater determinant
within a biorthonormal framework. The Slater–Jastrow wave function
is optimized on a set of atomic and molecular systems containing both
second-row elements and 3d transition metal elements. The optimization
of the correlation factor and the orbitals, along with an increase
in the basis set, results in a systematic lowering of the variational
Monte Carlo energy for all systems tested. Importantly, the optimal
parameters of the correlation factor obtained for atomic systems can
be transferred to molecules. Additionally, the present correlation
factor is computationally efficient and uses a mixed analytical–numerical
integration scheme that reduces the costly numerical integration from R6 to R3.