# Similarity transformation of the electronic Schr\"odinger equation via Jastrow factorisation

## TL;DR

This paper introduces a method that uses Jastrow factorization to transform the electronic Schrödinger equation, enabling highly accurate calculations of atomic energies with modest computational resources.

## Contribution

It develops a similarity transformation approach with a non-Hermitian Hamiltonian incorporating three-body interactions, solved via a stochastic configuration-interaction method.

## Key findings

- Achieves near-basis-set-limit accuracy for first-row atoms.
- Uses flexible Jastrow functions for improved correlation modeling.
- Requires modest basis sets and computational effort.

## Abstract

By expressing the electronic wavefunction in an explicitly-correlated (Jastrow-factorised) form, a similarity-transformed effective Hamiltonian can be derived. The effective Hamiltonian is non-Hermitian and contains three-body interactions. The resulting ground-state eigenvalue problem can be solved projectively using a stochastic configuration-interaction formalism. Our approach permits use of highly flexible Jastrow functions, which we show to be effective in achieving extremely high accuracy, even with small basis sets. Results are presented for the total energies and ionisation potentials of the first-row atoms, achieving accuracy within a mH of the basis-set limit, using modest basis sets and computational effort.