A programmable spin-free method for configuration interaction

Sarma, C. R.; Rettrup, Sten

doi:10.1007/bf00551652

Cited by 22 publications

(23 citation statements)

References 13 publications

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“…Each arc is labeled by three indices (s,iJ), where ( i J ) are the labels of the vertex to which the arc is directed and s is the corresponding case number, as listed in Eq. (9).…”

Section: Shavittmentioning

confidence: 95%

“…Drake and Schlesinger [8] have derived a factorization formula for matrix elements of a product of two generators using the angular momentum recoupling technique and without invoking a sum over intermediate states (see also Sarma and Rettrup [9]). Here we shall follow a different approach, based on Eq.…”

Section: Matrix Element Contributions Of Two-electron Integralsmentioning

confidence: 99%

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Matrix element evaluation in the unitary group approach to the electron correlation problem

Shavitt

2009

Int. J. Quantum Chem.

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Computationally effective formulations are presented for the evaluation of matrix elements of unitary group generators and products of generators between Gelfand states. These matrix elements are the coefficients of the orbital integrals in the expressions for the Hamiltonian matrix elements in the Gelfand basis, and as such are the key elements in any application of the unitary group approach to wave-function calculations. The present formulations, which, like previous analyses, result in a simple factorization of the generator matrix elements, are based on a graphical representation of the Gelfand basis, and do not require orbital permutations or an interpretation of the Gelfand states in terms of Young tableaus. It is shown that the resulting formalism can lead to very efficient procedures for "direct" configuration-interaction calculations, and probably also for perturbation-theory treatments.

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“…Each arc is labeled by three indices (s,iJ), where ( i J ) are the labels of the vertex to which the arc is directed and s is the corresponding case number, as listed in Eq. (9).…”

Section: Shavittmentioning

confidence: 95%

Section: Matrix Element Contributions Of Two-electron Integralsmentioning

confidence: 99%

Matrix element evaluation in the unitary group approach to the electron correlation problem

Shavitt

2009

Int. J. Quantum Chem.

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“…However, since the quantity 7j does not appear in the final formulas we will forego this generalization. Inserting now (25) into (15), we see that only the double coset generated by the unit element gives a nonvanishing contribution. …”

Section: One-electron Matrix Elementsmentioning

confidence: 96%

Configuration interaction matrix elements. I. Algebraic approach to the relationship between unitary group generators and permutations

Wormer

Paldus

1979

Int J of Quantum Chemistry

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AbstractsMatrix elements of unitary group generators between spin-adapted antisymmetric states are shown to be proportional to spin matrix elements of so-called "line-up" permutations. The proportionality factor is given explicitly as a simple function of the orbital occupation numbers. If one bases the theory on ordered orbital products, the line-up permutations are given a priori. The final formulas have a very simple structure; this is a direct consequence of the fact that the spin functions have been taken to be geminally antisymmetric.I1 est dCmontrB que les BlCments de matrice des gtnirateurs du groupe unitaire par rapport a des Btats antisymktriques et adapt& au spin sont proportionnels aux BlBments de matrice du spin de certaines permutations, dites de "line-up." Le facteur de proportionalit6 est donrit explicitement comme une fonction simple des nombres d'occupation orbitalaires. Les permutations "line up" sont donndes a priori, si la thkorie est basBe sur des produits d'orbitales ordonnb. Les formules finales ont une structure trks simple, ce qui dCcoule directement du fait que les fonctions de spin ont CtC choisies de faqon a &tre gdminalement antisymttriques.Es wird gezeigt, dass die Matrixelemente der Generatoren der unitaren Gruppe zwischen spinangepassten antisymmetrischen Zustanden den Spinmatrixelementen gewisser so-genannten "line-up"-Permutationen proportional sind. Der Proportionalitatsfaktor wird explizit als eine einfache Funktion der orbitalen Besetzungszahlen gegeben. Die "line-up"-Permutationen werden a priori gegeben, wenn die Theorie auf geordnete Orbitalprodukte basiert. Die endgiiltigen Formeln haben eine sehr einfache Struktur, was eine direkte Folge der Tat sache ist, dass die Spinfunktionen als geminal-antisymmetrisch gewahlt worden sind.

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“…. , (13) with (9) and (7) form an orthonormal basis (15) Because f commutes with the permutation @, its matrix element with projected (16) functions is known to be (see, e.g., Ref. 19) ,6,,,vA1b,Alb' Therefore the N!…”

Section: Classification Of Energy Levelsmentioning

confidence: 99%

Interaction energy in small N‐particle systems and the permutation group

Holas

Działak

Olszewski

1988

Int J of Quantum Chemistry

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The distribution of energy levels of an N-identical-particle system among the irreducible representations of the permutation group is examined for a "spin-free" problem. There are calculated the sums of powers of the eigenenergies obtained from the original N!-fold degenerate energy level when the interaction between the particles is switched on. The first-order perturbation theory is applied. Some results of the present approach are shown to be equivalent to the results of the Weyl's theory of the permutation group. The distribution of energy levels is found to be symmetric with respect to the average energy level belonging to a self-conjugate representation. For a special case of the Coulomb interaction the wave function of the highest level is fully symmetric, whereas that of the lowest level is fully antisymmetric with respect to the interchange of the coordinates of any two particles. The average energy and the dispersion of the levels belonging to a given representation are calculated for some N .

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A programmable spin-free method for configuration interaction

Cited by 22 publications

References 13 publications

Matrix element evaluation in the unitary group approach to the electron correlation problem

Matrix element evaluation in the unitary group approach to the electron correlation problem

Configuration interaction matrix elements. I. Algebraic approach to the relationship between unitary group generators and permutations

Interaction energy in small N‐particle systems and the permutation group

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