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Feixas GeronÃ¨s, Ferran
RodrÃguez Mayorga, Mauricio Matito i Gras, Eduard SolÃ i Puig, Miquel 

2015 February 1  
Several approximations to the thirdorder reduced density matrices (3RDM) are applied to compute approximate threecenter electron sharing indices (3cESI) and average number of three particles (3AN) for correlated and uncorrelated wave functions with different atomic partition schemes. Exact and approximated 3cESI are calculated for a set of molecules with threecenter twoelectron (3c2e) and threecenter fourelectron (3c4e) bonding. Results show that 3c2e bonding is associated with positive values of 3cESI irrespective of the method of calculation, atomic partition employed, and approximation to the thirdorder density matrix used. Singledeterminant calculations yield negative 3cESI values for 3c4e bonds, whereas the exact CASSCF 3cESIs are positive or close to zero. Some approximations to the 3RDM preserve the negative sign of the 3ESI for 3c4e bonds, however they perform poorly on the calculation of 3AN. The adequacy of the 3RDM approximation to calculate 3AN is also analyzed, revealing that Valdemoroâ€™s approximation to the 3RDM is the best approximation while Mazziottiâ€™s and naturalorbital based approximations yield the lowest maximum errors The following organizations are thanked for financial support: the Spanish Ministry (MICINN, Project numbers CTQ201123156/BQU and CTQ201125086/BQU and MINECO, Europa Excelencia project CTQ201341236ERC), the Generalitat de Catalunya (Projects number 2009SGR637, 2014SGR931, 2009SGR528, and Xarxa de Referencia en Quimica Tearica i Computacional), the Marie Curie Career Integration grant PCI09GA2011294240 (E.M.), and the FEDER fund (European Fund for Regional Development) for the Grant UNGI084E003. Support for the research of M. Sola was received through the ICREA Academia 2009 prize for excellence in research funded by the DIUE of the Generalitat de Catalunya. F.F. and M.RM, acknowledges financial support from the Beatriu de Finds program (AGAUR) for the postdoctoral grant BP_A_00339 (F.F.) and doctoral fellowship FIDGR201400003 (M.R.M.) Excellent service by the Centre de Serveis Cientifics i Academics de Catalunya (CESCA) is gratefully acknowledged 

application/pdf  
2210271X  
http://hdl.handle.net/10256/11357  
eng  
Elsevier  
MICINN/PN 20122014/CTQ201123156 MICINN/PN 20122014/CTQ201125086 MINECO/PE 20132015/CTQ201341236ERC AGAUR/20092014/2009 SGR637 AGAUR/20142016/2014 SGR931 AGAUR/20092014/2009 SGR528 AGAUR/BP_A_00339 AGAUR/2014/FIDGR201400003 ReproducciÃ³ digital del document publicat a: http://dx.doi.org/10.1016/j.comptc.2014.09.030 Articles publicats (DQ) info:eurepo/grantAgreement/EC/FP7/294240 

Â© Computational and Theoretical Chemistry, 2015, vol. 1053, p. 173179  
Tots els drets reservats  
Matriu densitat, Teoria de la
Density matrices 

Threecenter bonding analyzed from correlated and uncorrelated thirdorder reduced density matrices  
info:eurepo/semantics/article  
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