# Convex Hartree-Fock theory: A simple framework for ground state conical intersections

## TL;DR

Convex Hartree-Fock introduces a modified approach that efficiently models ground state conical intersections, overcoming limitations of traditional methods by optimizing within a tailored subspace and enabling accurate excited state calculations.

## Contribution

This work presents Convex Hartree-Fock, a novel framework that improves modeling of conical intersections by optimizing the reference state within a specific subspace, reducing computational costs.

## Key findings

- Successfully models ground state conical intersections.
- Outperforms traditional Hartree-Fock and TDHF in benchmarks.
- Validates approach across multiple test cases.

## 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.