Particle-Breaking Hartree–Fock Theory for Open Molecular Systems

Abstract

In this work we present the particle-breaking Hartree–Fock (PBHF) model which is a mean-field approach to open molecular systems. The interaction of a system with the environment is parametrized through a particle-breaking term in the molecular Hamiltonian. The PBHF wave function is constructed through an exponential unitary transformation of a Slater determinant with a given number of electrons. We consider only the closed-shell formalism. The parametrization results in a linear combination of Slater determinants with different numbers of electrons, i.e., the PBHF wave function is not an eigenfunction of the number operator. As a result, the density matrix may have fractional occupations which are, because of the unitary parametrization, always between 0.0 and 2.0. The occupations are optimized simultaneously with the orbitals, using the trust-region optimization procedure. In the limit of a particle-conserving Hamiltonian, the PBHF optimization will converge to a standard Hartree–Fock wave function. We show that the average number of electrons may be decreased or increased depending on whether the particle-breaking term affects occupied or virtual orbitals.

Performance Tests of the Second-Order Approximate Internally Contracted Multireference Coupled-Cluster Singles and Doubles Method icMRCC2

“…The database of excitations put together by Thiel and co-workers has been used before in numerous benchmark studies of excited-state methods. − For our calculations, we had to skip some of the larger examples in the set (like the nucleobases and naphthalene) as their sizes and the required active spaces lead to too extensive run times with our current implementation. Altogether, still 20 molecules and 114 vertical excitations were computed, the investigated states and their computed energies are listed in the Supporting Information.…”

Particle-Breaking Unrestricted Hartree–Fock Theory for Open Molecular Systems

“…We consider a Hamiltonian consisting of the standard nonrelativistic molecular electronic Hamiltonian, H mol , and a particle-breaking term, H pb (see ref ) H = H normalm normalo normall + H normalp normalb The particle-breaking Hamiltonian describes an interaction with some environment that causes a spread in the number of electrons. Any particle-conserving interactions with the environment may be included in H mol , as is done in, e.g., multiscale, embedding, or multilevel approaches, but will not be considered further here.…”

“…The parameters λ p q̅ σ are chosen to be spin independent, i.e., λ p q̅ α = λ p q̅ β = λ p q̅ . Compared to the PBRHF model, the particle-breaking Hamiltonian in PBUHF is a one-body creation or annihilation operator in the system and can therefore connect N and N ± 1 states.…”

“…In our recent publication, 1 we presented the particle-breaking restricted Hartree–Fock (PBRHF) model for molecular systems which are open to electronic charge fluctuations due to interaction with an environment of electronic nature. The target molecule is allowed to be electronically open, so that the effect of the environment on the molecule is taken into account without explicit inclusion of the environment itself.…”

Early-Career and Emerging Researchers in Physical Chemistry Volume 2

“…Tests on several different types of oscillators, including those with high anharmonicities, indicate excellent performance of the method. Finally, Høyvik and co-workers develop a particle-non-conserving extension of Hartree–Fock theory for treating open systems, of which a molecule coupled to an electron source or drain is a prototypical example. This PBHF model is constructed by augmenting the Hamiltonian with a particle-non-conserving term and reduces to conventional Hartree–Fock in the limit that the particle-non-conserving terms vanish.…”