Analysis of the projected Coupled Cluster Method in Electronic Structure Calculation

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dc.contributor.authorSchneider, Reinhold
dc.date.accessioned2021-12-17T10:08:32Z
dc.date.available2021-12-17T10:08:32Z
dc.date.issued2009-02-24
dc.description.abstractThe electronic Schrödinger equation plays a fundamental role in molcular physics. It describes the stationary nonrelativistic behaviour of an quantum mechanical N electron system in the electric field generated by the nuclei. The (Projected) Coupled Cluster Method has been developed for the numerical computation of the ground state energy and wave function. It provides a powerful tool for high accuracy electronic structure calculations. The present paper aims to provide a rigorous analytical treatment and convergence analysis of this method. If the discrete Hartree Fock solution is sufficiently good, the quasi-optimal convergence of the projected coupled cluster solution to the full CI solution is shown. Under reasonable assumptions also the convergence to the exact wave function can be shown in the Sobolev H^1-norm. The error of the ground state energy computation is estimated by an Aubin Nitsche type approach. Although the Projected Coupled Cluster method is nonvariational it shares advantages with the Galerkin or CI method. In addition it provides size consistency, which is considered as a fundamental property in many particle quantum mechanics.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15669
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14442
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otherelectronic Schrödinger equationen
dc.subject.otherquantum chemistryen
dc.subject.othercoupled cluster methoden
dc.subject.otherGalerkin methoden
dc.subject.othererror analysisen
dc.titleAnalysis of the projected Coupled Cluster Method in Electronic Structure Calculationen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2009, 10en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200065N25 Eigenvalue problemsen
tub.subject.msc200065N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methodsen
tub.subject.msc200065Z05 Applications to physicsen
tub.subject.msc200081V55 Molecular physicsen
tub.subject.msc200081V70 Many-body theory; quantum Hall effecten
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