Variational reduced density matrix method in the doubly occupied configuration interaction space using three-particle N-representability conditions

Diego R Alcoba; Pablo Capuzzi; Alvaro Rubio-García; Jorge Dukelsky; Gustavo E Massaccesi; Ofelia B Oña; Alicia Torre; Luis Lain

doi:10.1063/1.5056247

Variational reduced density matrix method in the doubly occupied configuration interaction space using three-particle N-representability conditions

J Chem Phys. 2018 Nov 21;149(19):194105. doi: 10.1063/1.5056247.

Authors

Diego R Alcoba¹, Pablo Capuzzi¹, Alvaro Rubio-García², Jorge Dukelsky², Gustavo E Massaccesi³, Ofelia B Oña⁴, Alicia Torre⁵, Luis Lain⁵

Affiliations

¹ Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina.
² Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain.
³ Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina.
⁴ Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de La Plata, CCT La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Diag. 113 y 64 (S/N), Sucursal 4, CC 16, 1900 La Plata, Argentina.
⁵ Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain.

PMID: 30466273
DOI: 10.1063/1.5056247

Abstract

Ground-state energies and two-particle reduced density matrices (2-RDMs) corresponding to N-particle systems are computed variationally within the doubly occupied configuration interaction (DOCI) space by constraining the 2-RDM to satisfy a complete set of three-particle N-representability conditions known as three-positivity conditions. These conditions are derived and implemented in the variational calculation of the 2-RDM with standard semidefinite programming algorithms. Ground state energies and 2-RDMs are computed for N₂, CO, CN^-, and NO⁺ molecules at both equilibrium and nonequilibrium geometries as well as for pairing models at different repulsive interaction strengths. The results from the full three-positivity conditions are compared with those from the exact DOCI method and with approximated 2-RDM variational ones obtained within two-positivity and two-positivity plus a subset of three-positivity conditions, as recently reported [D. R. Alcoba et al., J. Chem. Phys. 148, 024105 (2018) and A. Rubio-García et al., J. Chem. Theory Comput. 14, 4183 (2018)]. The accuracy of these numerical determinations and their low computational cost demonstrate the usefulness of the three-particle variational constraints within the DOCI framework.