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

## TL;DR

This paper introduces a new method to better describe both ground and excited states in quantum chemistry calculations.

## Contribution

The novel approach extends F12 correlators to occupied and valence unoccupied orbitals, achieving balanced ground and excited state descriptions.

## Key findings

- The new F12 geminal design avoids unphysical raising of ground-state energy.
- The method reduces basis set requirements for accurate ground and excited state calculations.
- It improves description of CCSD energies, excitation energies, and vibrational frequencies.

## 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 toward the ground-state
description, thereby making the 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 length
scale 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 ground-state coupled-cluster singles and doubles
(CCSD) energies, vertical excitation energies, and harmonic vibrational
frequencies of equation-of-motion CCSD low-energy excited states.