# Towards Balanced Description of Ground and Excited States with Transcorrelated F12 Methods

## TL;DR

This paper introduces an extended F12 correlator design within a transcorrelated framework that achieves a balanced description of ground and excited states, improving accuracy and efficiency in quantum chemical calculations.

## Contribution

The authors develop a new F12 geminal design that extends to occupied and valence unoccupied states, enabling balanced treatment of ground and excited states in a unitary transcorrelation approach.

## Key findings

- Reduces basis set requirements for accurate energies and properties.
- Achieves balanced description of ground and low-energy excited states.
- Improves accuracy of CCSD and EOM-CCSD calculations.

## Abstract

By correlating only the 1-particle states occupied in the reference determinant the conventional design for the single-reference R12/F12 explicitly-correlated methods biases them towards the ground state description thereby making treatment of response properties of the ground state, and energies and other properties of excited states less robust. While the use of multireference methods and/or extensions of the standard SP projected geminals can achieve a more balanced description of ground and excited states, here we show that the same goals can be achieved by extending the action of F12 correlators to the occupied and valence unoccupied 1-particle states only. This design choice reflects the strong dependence of the optimal correlation lengthscale of the F12 ansatz on the orbital energies/structure, and helps to avoid the unphysical raising of the ground state energy if the F12 geminals are used to correlate pairs of all 1-particle states. The improved F12 geminal design is incorporated into the unitary transcorrelation framework to produce a unitary 2-body Hamiltonian that incorporates the short-range dynamical correlation physics for ground and low-energy excited states in a balanced manner. This explicitly-correlated effective Hamiltonian reduces the basis set requirement on the correlation-consistent basis cardinal number by 1 or more over the uncorrelated counterpart for the description of the ground state coupled-cluster singles and doubles (CCSD) energies, the vertical excitation energies and harmonic vibrational frequencies of equation-of-motion CCSD low-energy excited states.