Studies on the Transcorrelated Method

TL;DR

This paper explores the transcorrelated method for accurately describing electron correlation by developing a self-consistent approach to construct an effective Hamiltonian, demonstrating high accuracy in atomic energy calculations.

Contribution

It introduces a new self-consistent framework for the transcorrelated method using the bi-variational principle and SOM minimization, improving energy accuracy for atomic systems.

Findings

Achieved highly accurate energies for closed-shell atoms and ions.

Analyzed the impact of correlator terms on electron cusps.

Compared transcorrelated wavefunctions with Hylleraas functions.

Abstract

We investigate the possibility of using a transcorrelated Hamiltonian to describe electron correlation. Amethod to obtain transcorrelatedwavefunctionswas developed based on the mathematical framework of the bi-variational principle. This involves the construction of an effective transcorrelated Hamiltonian matrix which can be solved in a self-consistent manner. This was optimised using a method we call Second Order Moment (SOM) minimisation to give highly accurate energies for some closed-shell atoms and helium-like ions. The effect of certain correlator terms on the description of electron-electron and electron-nuclear cusps were also examined graphically and some transcorrelated wavefunctions were compared against near-exact Hylleraas wavefunctions.