title: Electron correlation effects in third-order densities.
abstract: The electronic energy of a system of fermions can be obtained from the second-order reduced density matrix through the contracted Schrödinger equation or its anti-Hermitian counterpart. Both energy expressions depend on the third-order reduced density matrix (3-RDM) which is usually approximated from lower-order densities. The accuracy of these methods depends critically on the set of N-representability conditions enforced in the calculation and the quality of the approximate 3-RDM. There are no benchmark studies including most 3-RDM approximations and, thus far, no assessment of the deterioration of the approximations with correlation effects has been performed. In this paper we introduce a series of tests to assess the performance of 3-RDM approximations in a model system with varying electron correlation effects, the three-electron harmonium atom. The results of this work put forward several limitations of the currently most used 3-RDM approximations for systems with important electron correlation effects.
authors.affiliation: Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain. ematito@gmail.com and Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química, University of Girona, 17071 Girona, Catalonia, Spain.
authors.forename: Mauricio
authors.initials: M
authors.lastname: Rodriguez-Mayorga
authors.affiliation: Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain. ematito@gmail.com and Department of Chemistry, University of California Berkeley, 94720, Berkeley, CA, USA.
authors.forename: Eloy
authors.identifier: http://orcid.org/0000-0002-6558-7821
authors.initials: E
authors.lastname: Ramos-Cordoba
authors.affiliation: Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química, University of Girona, 17071 Girona, Catalonia, Spain.
authors.forename: Ferran
authors.initials: F
authors.lastname: Feixas
authors.affiliation: Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain. ematito@gmail.com and IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain.
authors.forename: Eduard
authors.identifier: http://orcid.org/0000-0001-6895-4562
authors.initials: E
authors.lastname: Matito