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New approximation to the third-order density: application to the calculation of correlated multicenter indices

In this work we present the formulas for the calculation of exact three-center electron sharing indices (3c-ESI) and introduce two new approximate expressions for correlated wave functions. The 3c-ESI uses the third-order density, the diagonal of the third-order reduced density matrix, but the approximations suggested in this work only involve natural orbitals and occupancies. In addition, the first calculations of 3c-ESI using Valdemoro’s, Nakatsuji’s and Mazziotti’s approximation for the third-order reduced density matrix are also presented for comparison. Our results on a test set of molecules, including 32 3c-ESI values, prove that the new approximation based on the cubic root of natural occupancies performs the best, yielding absolute errors below 0.07 and an average absolute error of 0.015. Furthemore, this approximation seems to be rather insensitive to the amount of electron correlation present in the system. This newly developed methodology provides a computational inexpensive method to calculate 3c-ESI from correlated wave functions and opens new avenues to approximate high-order reduced density matrices in other contexts, such as the contracted Schrödinger equation and the anti-Hermitian contracted Schrödinger equation

The authors are indebted to Mauricio Rodriguez-Mayorga for his assistance with some calculations. F.F. and E.M. acknowledge financial support of the Beatriu de Pinos program from AGAUR for the postdoctoral grants BP_A_00339 (F.F.) and BP_B_00236 (E.M.). This research has been also funded by the EU under the Marie Curie Career Integration grant PCI09-GA-2011-294240 (E.M.), the Spanish MINECO Europa Excelencia project CTQ2013-41236-ERC (E.M.), the Spanish MICINN Project No. CTQ2011-23156/BQU, the Catalan DIUE through projects No. 2009SGR637 and 2009SGR528, Xarxa de Referencia en Quimica Teorica i Computacional and by the FEDER grant UNGI08-4E-003 (European Fund for Regional Development). Support for the research of M.S. was received through the ICREA Academia 2009 prize for excellence in research funded by the DIUE of the Generalitat de Catalunya. Technical and human support provided by IZO-SGI, SGIker (UPV/EHU, MICINN, GV/EJ, ERDF, and ESF) is gratefully acknowledged. We also thank the Centre de Supercomputacio de Catalunya (CESCA) for partial funding of computer time

© Journal of Chemical Theory and Computation, 2014, vol. 10, p. 3055-3065

American Chemical Society (ACS)

Author: Feixas Geronès, Ferran
Solà i Puig, Miquel
Barroso, Juan Manuel
Ugalde, Jesus M.
Matito i Gras, Eduard
Date: 2014
Abstract: In this work we present the formulas for the calculation of exact three-center electron sharing indices (3c-ESI) and introduce two new approximate expressions for correlated wave functions. The 3c-ESI uses the third-order density, the diagonal of the third-order reduced density matrix, but the approximations suggested in this work only involve natural orbitals and occupancies. In addition, the first calculations of 3c-ESI using Valdemoro’s, Nakatsuji’s and Mazziotti’s approximation for the third-order reduced density matrix are also presented for comparison. Our results on a test set of molecules, including 32 3c-ESI values, prove that the new approximation based on the cubic root of natural occupancies performs the best, yielding absolute errors below 0.07 and an average absolute error of 0.015. Furthemore, this approximation seems to be rather insensitive to the amount of electron correlation present in the system. This newly developed methodology provides a computational inexpensive method to calculate 3c-ESI from correlated wave functions and opens new avenues to approximate high-order reduced density matrices in other contexts, such as the contracted Schrödinger equation and the anti-Hermitian contracted Schrödinger equation
The authors are indebted to Mauricio Rodriguez-Mayorga for his assistance with some calculations. F.F. and E.M. acknowledge financial support of the Beatriu de Pinos program from AGAUR for the postdoctoral grants BP_A_00339 (F.F.) and BP_B_00236 (E.M.). This research has been also funded by the EU under the Marie Curie Career Integration grant PCI09-GA-2011-294240 (E.M.), the Spanish MINECO Europa Excelencia project CTQ2013-41236-ERC (E.M.), the Spanish MICINN Project No. CTQ2011-23156/BQU, the Catalan DIUE through projects No. 2009SGR637 and 2009SGR528, Xarxa de Referencia en Quimica Teorica i Computacional and by the FEDER grant UNGI08-4E-003 (European Fund for Regional Development). Support for the research of M.S. was received through the ICREA Academia 2009 prize for excellence in research funded by the DIUE of the Generalitat de Catalunya. Technical and human support provided by IZO-SGI, SGIker (UPV/EHU, MICINN, GV/EJ, ERDF, and ESF) is gratefully acknowledged. We also thank the Centre de Supercomputacio de Catalunya (CESCA) for partial funding of computer time
Format: application/pdf
ISSN: 1549-9618 (versió paper)
1549-9626 (versió electrònica)
Document access: http://hdl.handle.net/10256/10336
Language: eng
Publisher: American Chemical Society (ACS)
Collection: MINECO/PE 2013-2015/CTQ2013-41236-ERC
MICINN/PN 2012-2014/CTQ2011-23156
AGAUR/2009-2014/2009 SGR-637
AGAUR/2009-2014/2009 SGR-528
Reproducció digital del document publicat a: http://dx.doi.org/10.1021/ct5002736
Articles publicats (D-Q)
info:eu-repo/grantAgreement/EC/FP7/294240
Is part of: © Journal of Chemical Theory and Computation, 2014, vol. 10, p. 3055-3065
Rights: Tots els drets reservats
Subject: Schrödinger, Equació de
Schrödinger equation
Funcions d’ona
Wave functions
Química quàntica
Quantum chemistry
Title: New approximation to the third-order density: application to the calculation of correlated multicenter indices
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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