The Contracted Schrödinger Equation: Imposing Spin representability Constraints upon the Correlation

The Contracted Schrödinger Equation: Imposing Spin representability Constraints upon the Correlation

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The Contracted Schrödinger Equation: Imposing Spin-representability Constraints upon the Correlation matrix C. Valdemoro1, L. M. Tel2, E. Perez-Romero2, D. R. Alcoba3 1Instituto de Matematicas y Fısica Fundamental, Consejo Superior de Investigaciones Cientıficas, Serrano 123, 28006 Madrid, Spain 2Departamento de Quımica Fısica, Universidad de Salamanca, 37008 Salamanca, Spain 3Departamento de Fısica, Universidad de Buenos Aires, Buenos Aires, Argentina XXVI Niza October 2006 – p.1/42

  • imposing spin

  • fısica fundamental

  • spin conditions

  • consejo superior de investigaciones cientıficas

  • departamento de fısica

  • universidad de buenos aires


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Publié par
Ajouté le 19 juin 2012
Nombre de lectures 16
Langue English
Signaler un abus
The Contracted Schrödinger Equation: Imposing Spin-representability Constraints upon the Correlation matrix
C. Valdemoro1, L. M. Tel2, E. Pe´ rez-Romero2, D. R. Alcoba3
1titutodeInssaci´FyetaMta´menaml,tacasindFu ConsejoSuperiordeInvestigacionesCient´ca,sSerrano123,28006Madrid,Spain 2tnemQedom´uFaciepDtaar´sica, Universidad de Salamanca, 37008 Salamanca, Spain 3rapeDdotnemat,seduBdidaiAernesosicaeF´vers,Uni Buenos Aires, Argentina
XXIVNizaOctober0260–p.1/42
IntroducingoCmments
The iterative solution of the Contracted Schrödinger Equation (CSE) is a recently developed method for the study of the electronic structure of atoms and molecules. In this approach,
the second-order Reduced Density Matrix
(2-RDM) is determined directly without a previous knowledge of the N-electron wave-function.
Here, a general survey of the method will be sketched.
XXIVNizaOctober0206–p.2/42
evfssoltsureheTsnoitacilppalareofrVXX
A 2-RDM puricationprocedure has lately been inserted after each CSE iteration.
singletstates, which will be shown here, reach a precision of 10 5au.
The main spin conditions for Correlation matrices corresponding totsleubdoand totripletswill be presented.
Attention will be centered here on the spin properties of the second-order Correlation Matrices (2-CM) which play a central role in this puricationprocedure.
p–3.4/2ober2006INizaOct
oSemedn®tioisn
A second-order Reduced Density Matrix (2-RDM) is denedin second Quantization as:
2Di21<|aiajamal|> j;lm=
In rstquantization this is equivalent to the integration of the square of the N-electrons wave function over the variables of N-2 electrons.
XXVIiNzacOtober0260–.p4/42
weherhtmetairnby: drodrTreisnanoitDx2is, esthonec(x-2tair.)XXRTMDucedRe-dityMDens24/5.p–6
XM 2D, =M 2
,
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