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

Description

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

Sujets

• Consejo Superior de Investigaciones Científicas
• Universidad de Buenos Aires

Informations

• Publié par: pefav
• Nombre de lectures: 16
• Langue: English

Extrait

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

C. Valdemoro 1 , L. M. Tel 2 , E. Pe´  rez-Romero 2 , D. R. Alcoba 3

1 titutodeInssaci´FyetaMta ´ menaml,tacasindFu ConsejoSuperiordeInvestigacionesCient´ca,sSerrano123,28006Madrid,Spain 2 tnemQedom´uFaciepDtaar´sica, Universidad de Salamanca, 37008 Salamanca, Spain 3 rapeDdotnemat,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

evfssoltsureheTsnoitacilppalareofr VXX

A 2-RDM puricationprocedure has lately been inserted after each CSE iteration.

singlet states, which will be shown here, reach a precision of 10   5 au.

The main spin conditions for Correlation matrices corresponding to tsleubdo and to triplets will 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:

2 D i 2 1 <|a i † a j † a m a l |> 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

weherhtmetair nby:  drodrTreisnanoitD  x 2 is , esthonec (x-2tair.) XX RTMDuced Re- dityMDens 24/5.p–6

X M  2 D , =M 2

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