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Two new constraints for the cumulant matrix

We suggest new strict constraints that the two-particle cumulant matrix should fulfill. The constraints are obtained from the decomposition of〈Ŝ²〉, previously developed in our laboratory, and the vanishing number of electrons shared by two non-interacting fragments. The conditions impose stringent constraints into the cumulant structure without any need to perform an orbital optimization procedure thus carrying very small or no computational effort. These constraints are tested on the series of Piris natural orbital functionals (PNOF), which are among the most accurate ones available in the literature. Interestingly, even though all PNOF cumulants ensure correct overall 〈Ŝ²〉 values, none of them is consistent with the local spin structure of systems that dissociate more than one pair of electrons. A careful analysis of the local spin components reveals the most important missing contributions in the cumulant expression thus suggesting a means to improve PNOF5. The constraints provide an inexpensive tool for the construction and testing of cumulant structures that complement previously known conditions such as the N-representability or the square of the total spin angular momentum, 〈Ŝ²〉

This research has been funded by the European Union (EU) under the Marie Curie Career Integration Grant No. PCI09-GA-2011-294240 (E.M.), the Spanish MINECO Europa Excelencia project CTQ2013-41236-ERC (E.M.), the Spanish MICINN Project Nos. CTQ2011-23441/BQU and CTQ2011-23156/BQU, the Eusko Jaurlaritza (SAIOTEK Program S-PC13UN005), and by the FEDER Grant No. UNGI08-4E-003 (European Fund for Regional Development). We are grateful for the computational resources granted at the MareNostrum computer of the Barcelona Supercomputing Center

© Journal of Chemical Physics, 2014, vol. 141, p. 234101

American Institute of Physics (AIP)

Manager: Ministerio de Economía y Competitividad (Espanya)
Ministerio de Ciencia e Innovación (Espanya)
Author: Ramos Cordoba, Eloy
Salvador Sedano, Pedro
Piris, Mario
Matito i Gras, Eduard
Abstract: We suggest new strict constraints that the two-particle cumulant matrix should fulfill. The constraints are obtained from the decomposition of〈Ŝ²〉, previously developed in our laboratory, and the vanishing number of electrons shared by two non-interacting fragments. The conditions impose stringent constraints into the cumulant structure without any need to perform an orbital optimization procedure thus carrying very small or no computational effort. These constraints are tested on the series of Piris natural orbital functionals (PNOF), which are among the most accurate ones available in the literature. Interestingly, even though all PNOF cumulants ensure correct overall 〈Ŝ²〉 values, none of them is consistent with the local spin structure of systems that dissociate more than one pair of electrons. A careful analysis of the local spin components reveals the most important missing contributions in the cumulant expression thus suggesting a means to improve PNOF5. The constraints provide an inexpensive tool for the construction and testing of cumulant structures that complement previously known conditions such as the N-representability or the square of the total spin angular momentum, 〈Ŝ²〉
This research has been funded by the European Union (EU) under the Marie Curie Career Integration Grant No. PCI09-GA-2011-294240 (E.M.), the Spanish MINECO Europa Excelencia project CTQ2013-41236-ERC (E.M.), the Spanish MICINN Project Nos. CTQ2011-23441/BQU and CTQ2011-23156/BQU, the Eusko Jaurlaritza (SAIOTEK Program S-PC13UN005), and by the FEDER Grant No. UNGI08-4E-003 (European Fund for Regional Development). We are grateful for the computational resources granted at the MareNostrum computer of the Barcelona Supercomputing Center
Format: application/pdf
ISSN: 0021-9606 (versió paper)
1089-7690 (versió electrònica)
Document access: http://hdl.handle.net/10256/10337
Language: eng
Publisher: American Institute of Physics (AIP)
Collection: MINECO/PE 2013-2015/CTQ2013-41236-ERC
MICINN/PN 2012-2014/CTQ2011-23441
MICINN/PN 2012-2014/CTQ2011-23156
Reproducció digital del document publicat a: http://dx.doi.org/10.1063/1.4903449
Articles publicats (D-Q)
info:eu-repo/grantAgreement/EC/FP7/294240
Is part of: © Journal of Chemical Physics, 2014, vol. 141, p. 234101
Rights: Tots els drets reservats
Subject: Electrons
Electrons
Spin (Física nuclear)
Nuclear spin
Moment angular (Física nuclear)
Angular momentum (Nuclear physics)
Title: Two new constraints for the cumulant matrix
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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