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

Abstract

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 6 to 3 .

Partial Separability of the Schrödinger Equation Combined with a Jastrow Factor

“…With the choice of this simple effective two-parameter wave function, the energy value is 0.007 E h above the estimated exact value. More elaborated Jastrow factors for atoms, molecules, and solids are proposed in the literature, for example. , The aim of the present work is to show the interest of the partial separability of the Schrödinger equation using simple ansatz, and the possibility to consider sophisticated Jastrow factor with more parameters when higher accuracy is required.…”

“…These factors lead to complex forms of the I 1 integral that require calculations involving numerical integrations of a larger number of dimensions than those needed when using the two-body correlation factor. Recently, in the context of the transcorrelated approach, a new three-body, electron–electron–nucleus, correlation factor with the electron–electron and electron–nucleus terms factorized has been proposed with orbital optimization in the presence of correlations. A similar idea is used here including the electron–electron terms in the Ω factor and the electron–nucleus terms in Φ, with all the functions optimized simultaneously as we show below.…”

“…A similar idea is used here including the electron–electron terms in the Ω factor and the electron–nucleus terms in Φ, with all the functions optimized simultaneously as we show below. As a difference, the electron–nucleus–electron term of this work is intended to account for the screening of the nuclear field acting on one electron due to the presence of the other electron, while in ref , the three-body correlation factor is designed to vanish around each nucleus to include in the Jastrow factor electron–electron correlations in the valence region. Within the scheme of this work, both kinds of three-body correlations can be included with no extra computational demand.…”

Orbital optimisation in xTC transcorrelated methods

“…The non-Hermitian nature of the transcorrelated Hamiltonian prevents the standard methods to optimise the orbitals, and the biorthogonal orbital optimisation has to be employed. 79,[102][103][104] In this work, we present a combination of the bi-orthogonal orbital optimisation framework with the xTC version of the transcorrelation, and demonstrate the accuracy of the non-iterative perturbation based methods on top of the transcorrelated Hamiltonian, and the effect of the orbital optimisation on the results of other truncated methods.…”