# A Jeziorski-Monkhorst fully uncontracted Multi-Reference perturbative treatment I: principles, second-order versions and tests on ground state potential energy curves

## TL;DR

This paper introduces a second-order multi-reference perturbation method based on a Jeziorski-Monkhorst expansion, enabling accurate, size-extensive calculations of ground state potential energy curves with reduced computational cost.

## Contribution

It presents a novel second-order multi-reference perturbation approach using Slater determinants as perturbers, improving accuracy and efficiency over existing methods.

## Key findings

- Accurately reproduces FCI potential energy curves for molecules with bond breaking.
- Ensures size-extensivity with local orbitals and a new zeroth-order energy definition.
- Provides smooth potential energy curves without numerical instabilities.

## Abstract

The present paper introduces a new multi-reference perturbation approach developed at second order, based on a Jeziorsky-Mokhorst expansion using individual Slater determinants as perturbers. Thanks to this choice of perturbers, an effective Hamiltonian may be built, allowing for the dressing of the Hamiltonian matrix within the reference space, assumed here to be a CAS-CI. Such a formulation accounts then for the coupling between the static and dynamic correlation effects. With our new definition of zeroth-order energies, these two approaches are strictly size-extensive provided that local orbitals are used, as numerically illustrated here and formally demonstrated in the appendix. Also, the present formalism allows for the factorization of all double excitation operators, just as in internally contracted approaches, strongly reducing the computational cost of these two approaches with respect to other determinant-based perturbation theories. The accuracy of these methods has been investigated on ground-state potential curves up to full dissociation limits for a set of six molecules involving single, double and triple bond breaking. The spectroscopic constants obtained with the present methods are found to be in very good agreement with the full configuration interaction (FCI) results. As the present formalism does not use any parameter or numerically unstable operation, the curves obtained with the two methods are smooth all along the dissociation path.