Application of graphical methods of spin algebras to limited CI approaches. I. Closed shell case

Abstract

AbstractsThe time independent diagrammatic technique based on the mathematical methods of quantum electrodynamics (second quantization, Wick's theorem, Feynman-like diagrams) is combined with graphical techniques of spin algebras to derive general expressions for the matrix elements of spin independent one-and two-particle operators between spin symmetry adapted ground, mono-and bi-excited configurations of a closed shell system. Two coupling schemes are considered for bi-excited states and their relative merits are discussed. Finally, the results are used to derive compact expressions for the coupling coefficients of the direct configuration interaction from molecular integrals (CIMI) method.La technique de diagrammes indkpendante du temps d'origine quanto-Clectrodynamique (seconde quantification, thCoreme de Wick, diagrammes de type de Feynman) a CtC combinte avec des proctdes graphiques des algebres de spin pour obtenir des expressions gtntrales pour les Cltments des matrices reprksentant des opCrateurs a une et a deux particules, par rapport a des configurations adaptees i la symCtrie de spin, fondamentales, mono-et bi-excittes d'un systeme a couches completes. Deux schCmas de couplage ont CtC considtrts pour les ttats bi-excites et leurs merites relatifs ont Cte discutCs. Les rCsultats ont CtC utilists pour obtenir des expressions compactes pour les coefficients de couplage dans la mCthode CIMI.Das von den mathematischen Methoden der Quantenelektrodynamik (zweite Quantelung, Wick'scher Satz, Feynman-Diagramme).herruhrende zeitunabhangige Diagrammverfahren wird mit graphischen Spinalgebramethoden kombiniert, um allgemeine Ausdrucke der Matrixelemente von Ein-und Zweiteilchenoperatoren zwischen Spinsymmetrieangepassten Grund,-einmal und zweimal angeregten Konfigurationen eines Systems mit abgeschlossenen Schalen zu erhalten. Zwei Kopplungsverfahren werden fur zweimal angeregte Zustande vorgeschlagen und ihre relative Vorzuge werden diskutiert. Schliesslich werden die Ergebnisse angewandt um kompakte Ausdrucke fur die Kopplungskoeffizienten in der cmI-Methode herzuleiten.

Angular Momentum Diagrams

“…[31][32][33][34][35]). A more general exploitation of this type is then based on the permutation or symmetric group representation theory [36] or on the unitary group approach (UGA) (see, e.g., Refs.…”

A Critical Assessment of Coupled Cluster Method in Quantum Chemistry

“…In the CC context, this approach was first employed in [128], and its different versions were discussed in [129]. The essence of the technique is to choose a suitable coupling scheme and to represent the OSA configurations in terms of products of Clebsch-Gordan coefficients [129,214,215]. The latter are then represented by the angular momentum diagrams, and the orbital diagrams of CC theory are converted into the corresponding spin graphs [129,214].…”

Method of Moments of Coupled-Cluster Equations: Externally Corrected Approaches Employing Configuration Interaction Wave Functions

“…The required CCSD calculations were performed with the orthogonally spin-adapted [10,[77][78][79][80] CCSD code described elsewhere [35]. The triply and quadruply excited moments of the CCSD equations, used in the CISDt-based MMCC(2,3) and CISDtq-based MMCC (2,4) (2), respectively, were calculated with the new code obtained by modifying the computer program described in Ref.…”