biostudies-literaturePaul Nee Matveeva RNorges Forskningsr?d1533-1542https://www.ebi.ac.uk/biostudies/studies/S-EPMC10910564biostudies-literatureUnknown128(8)We recently introduced the particle-breaking restricted Hartree-Fock (PBRHF) model, a mean-field approach to address the fractional charging of molecules when they interact with an electronic environment. In this paper, we present an extension of the model referred to as particle-breaking unrestricted Hartree-Fock (PBUHF). The unrestricted formulation contains odd-electron states necessary for a realistic description of fractional charging. Within the PBUHF parametrization, we use two-body operators as they yield convenient operator transformations. However, two-body operators can change only the particle number by two. Therefore, we include noninteracting zero-energy bath orbitals to generate a linear combination of even and odd electron states. Depending on whether the occupied or virtual orbitals of a molecule interact with the environment, the average number of electrons is either decreased or increased. Without interaction, PBUHF reduces to the unrestricted Hartree-Fock wave function.The journal of physical chemistry. AParticle-Breaking Unrestricted Hartree-Fock Theory for Open Molecular Systems.PMC10910564275506325574Paul Nee Matveeva RHoyvik IMFolkestad SDSannes BSfalseParticle-Breaking Unrestricted Hartree-Fock Theory for Open Molecular Systems.We recently introduced the particle-breaking restricted Hartree-Fock (PBRHF) model, a mean-field approach to address the fractional charging of molecules when they interact with an electronic environment. In this paper, we present an extension of the model referred to as particle-breaking unrestricted Hartree-Fock (PBUHF). The unrestricted formulation contains odd-electron states necessary for a realistic description of fractional charging. Within the PBUHF parametrization, we use two-body operators as they yield convenient operator transformations. However, two-body operators can change only the particle number by two. Therefore, we include noninteracting zero-energy bath orbitals to generate a linear combination of even and odd electron states. Depending on whether the occupied or virtual orbitals of a molecule interact with the environment, the average number of electrons is either decreased or increased. Without interaction, PBUHF reduces to the unrestricted Hartree-Fock wave function.2024-01-01T00:00:00Z2024 Feb2026-06-16T04:52:56.177Z2025-04-05T11:38:14.844ZS-EPMC109105643835169910.1021/acs.jpca.3c07231