A new form of transcorrelated Hamiltonian inspired by range-separated DFT

TL;DR

This paper introduces a novel transcorrelated Hamiltonian with a new correlation factor inspired by range-separated DFT, which improves convergence and reproduces known results with a tunable parameter.

Contribution

A new correlation factor for transcorrelated Hamiltonians is developed, enabling better convergence and a continuous physical interpretation through a tunable parameter.

Findings

Faster convergence of eigenvalues with the new Hamiltonian.

The correlation factor reproduces results similar to the frozen Gaussian geminal.

The Hamiltonian's physical content varies smoothly with the parameter .

Abstract

The present work introduces a new form of explicitly correlated factor in the context of the transcorrelated methods. The new correlation factor is obtained from the r 12 $\approx$ 0 mathematical analysis of the transcorrelated Hamiltonian, and its analytical form is obtained such that the leading order in 1/r 12 of the scalar part of the effective two-electron potential reproduces the long-range interaction of the range-separated density functional theory. The resulting correlation factor exactly imposes the cusp and is tuned by a unique parameter $\mu$ which controls both the depth of the coulomb hole and its typical range in r 12. The transcorrelated Hamiltonian obtained with such a new correlation factor has a straightforward analytical expression depending on the same parameter $\mu$, and its physical contents continuously change by varying $\mu$ : one can change from a non divergent repulsive Hamiltonian at large $\mu$ to a purely attractive one at small $\mu$. We investigate the convergence of the ground state eigenvalues and right-eigenvectors of such new transcorrelated Hamiltonian as a function of the basis set and as a function of $\mu$ on a series of two-electron systems. We found that the convergence towards the complete basis set is much faster for a quite wide range values of $\mu$. We also propose a specific value of $\mu$ which essentially reproduce the results obtained with the frozen Gaussian geminal introduced by Ten-No [CPL-330,169 (2000)].