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

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 $$ to $$.