# Convex Hartree–Fock theory for modeling ground state conical intersections

## TL;DR

This paper introduces a modified Hartree–Fock method to better model ground state conical intersections in nonadiabatic molecular dynamics.

## Contribution

The novel Convex Hartree–Fock framework optimizes reference states in a tailored subspace to capture ground state conical intersections efficiently.

## Key findings

- Convex Hartree–Fock successfully captures ground state conical intersections where traditional methods fail.
- The method is validated across multiple test cases and compared to time-dependent Hartree–Fock benchmarks.

## Abstract

Accurate modeling of conical intersections is crucial in nonadiabatic molecular dynamics, as these features govern processes such as radiationless transitions and photochemical reactions. Conventional electronic structure methods, including Hartree–Fock, density functional theory, and their time-dependent extensions, struggle in this regime. Due to their single reference nature and separate treatment of ground and excited states, they fail to capture ground state intersections. Multiconfigurational approaches overcome these limitations, but at a prohibitive computational cost. In this work, we propose a modified Hartree–Fock framework, referred to as Convex Hartree–Fock, that optimizes the reference within a tailored subspace by removing projections along selected Hessian eigenvectors. The ground and excited states are then obtained through subsequent Hamiltonian diagonalization. We validate the approach across several test cases and benchmark its performance against time-dependent Hartree–Fock within the Tamm-Dancoff approximation.

Accurate modeling of conical intersections is essential for describing the nonadiabatic molecular dynamics behind photoinduced processes, but conventional single-reference electronic structure methods fail to capture the associated ground state intersections. In this work, the authors propose a modified Hartree–Fock framework, referred to as Convex Hartree–Fock, that optimizes the reference within a tailored subspace by removing projections along selected Hessian eigenvectors, offering an alternative to more expensive multiconfigurational approaches.