title: Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function.
abstract: We perform a direct variational determination of the second-order (two-particle) density matrix corresponding to a many-electron system, under a restricted set of the two-index N-representability P-, Q-, and G-conditions. In addition, we impose a set of necessary constraints that the two-particle density matrix must be derivable from a doubly occupied many-electron wave function, i.e., a singlet wave function for which the Slater determinant decomposition only contains determinants in which spatial orbitals are doubly occupied. We rederive the two-index N-representability conditions first found by Weinhold and Wilson and apply them to various benchmark systems (linear hydrogen chains, He, N2, and CN(-)). This work is motivated by the fact that a doubly occupied many-electron wave function captures in many cases the bulk of the static correlation. Compared to the general case, the structure of doubly occupied two-particle density matrices causes the associate semidefinite program to have a very favorable scaling as L(3), where L is the number of spatial orbitals. Since the doubly occupied Hilbert space depends on the choice of the orbitals, variational calculation steps of the two-particle density matrix are interspersed with orbital-optimization steps (based on Jacobi rotations in the space of the spatial orbitals). We also point to the importance of symmetry breaking of the orbitals when performing calculations in a doubly occupied framework.
authors.affiliation: Center for Molecular Modeling, Ghent University , Technologiepark 903, 9052 Zwijnaarde, Belgium.
authors.forename: Ward
authors.initials: W
authors.lastname: Poelmans
authors.affiliation: Department of Inorganic and Physical Chemistry, Ghent University , Krijgslaan 281 (S3), 9000 Gent, Belgium.
authors.forename: Mario
authors.initials: M
authors.lastname: Van Raemdonck
authors.affiliation: Center for Molecular Modeling, Ghent University , Technologiepark 903, 9052 Zwijnaarde, Belgium.
authors.forename: Brecht
authors.initials: B
authors.lastname: Verstichel
authors.affiliation: Center for Molecular Modeling, Ghent University , Technologiepark 903, 9052 Zwijnaarde, Belgium.|Department of Inorganic and Physical Chemistry, Ghent University , Krijgslaan 281 (S3), 9000 Gent, Belgium.
authors.forename: Stijn
authors.initials: S
authors.lastname: De Baerdemacker
authors.affiliation: Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco , Apdo. 644, E-48080 Bilbao, Spain.
authors.forename: Alicia
authors.initials: A
authors.lastname: Torre
authors.affiliation: Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco , Apdo. 644, E-48080 Bilbao, Spain.
authors.forename: Luis
authors.initials: L
authors.lastname: Lain
authors.affiliation: Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria , 1428 Buenos Aires, Argentina.
authors.forename: Gustavo E
authors.initials: GE
authors.lastname: Massaccesi
authors.affiliation: Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria , 1428 Buenos Aires, Argentina.
authors.forename: Diego R
authors.initials: DR
authors.lastname: Alcoba
authors.affiliation: Department of Inorganic and Physical Chemistry, Ghent University , Krijgslaan 281 (S3), 9000 Gent, Belgium.
authors.forename: Patrick
authors.initials: P
authors.lastname: Bultinck
authors.affiliation: Center for Molecular Modeling, Ghent University , Technologiepark 903, 9052 Zwijnaarde, Belgium.
authors.forename: Dimitri
authors.initials: D
authors.lastname: Van Neck