title: Considerations on describing non-singlet spin states in variational second order density matrix methods.
abstract: Despite the importance of non-singlet molecules in chemistry, most variational second order density matrix calculations have focused on singlet states. Ensuring that a second order density matrix is derivable from a proper N-electron spin state is a difficult problem because the second order density matrix only describes one- and two-particle interactions. In pursuit of a consistent description of spin in second order density matrix theory, we propose and evaluate two main approaches: we consider constraints derived from a pure spin state and from an ensemble of spin states. This paper makes a comparative assessment of the different approaches by applying them to potential energy surfaces for different spin states of the oxygen and carbon dimer. We observe two major shortcomings of the applied spin constraints: they are not size consistent and they do not reproduce the degeneracy of the different states in a spin multiplet. First of all, the spin constraints are less strong when applied to a dissociated molecule than when they are applied to the dissociation products separately. Although they impose correct spin expectation values on the dissociated molecule, the dissociation products do not have correct spin expectation values. Secondly, both under "pure spin state conditions" and under "ensemble spin state" conditions is the energy a convex function of the spin projection. Potential energy surfaces for different spin projections of the same spin state may give a completely different picture of the molecule's bonding. The maximal spin projection always gives the most strongly constrained energy, but is also significantly more expensive to compute than a spin-averaged ensemble. In the dissociation limit, both the problem of nondegeneracy of equivalent spin projections, size-inconsistency and unphysical dissociation can be corrected by means of subspace energy constraints.
authors.affiliation: Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 S3, 9000 Ghent, Belgium. helen.vanaggelen@ugent.be
authors.forename: Helen
authors.initials: H
authors.lastname: van Aggelen
authors.forename: Brecht
authors.initials: B
authors.lastname: Verstichel
authors.forename: Patrick
authors.initials: P
authors.lastname: Bultinck
authors.forename: Dimitri
authors.initials: D
authors.lastname: Van Neck
authors.forename: Paul W
authors.initials: PW
authors.lastname: Ayers