The significance of the strong orthogonality condition for geminal functions in variational calculations

Lin, C. S.; Birss, F. W.

doi:10.1007/bf00526143

Cited by 3 publications

(2 citation statements)

References 6 publications

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“…Lin & Birss (186) give a somewhat similar but less extensive discussion than Kapuy's first paper. Unfortunately, without the strong orthogonality condition, the geminal equations are diffi cult to manage (185,186).…”

Section: Solid State Many Body and Formal Methodsmentioning

confidence: 99%

Quantum Theory of Atoms and Molecules

Golebiewski¹,

Taylor²

1967

Annu. Rev. Phys. Chem.

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Section: Solid State Many Body and Formal Methodsmentioning

confidence: 99%

Quantum Theory of Atoms and Molecules

Golebiewski¹,

Taylor²

1967

Annu. Rev. Phys. Chem.

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“…23 In MP2 methods SO is imposed between the first-order pair functions and the set of occupied pairs. ͑4͒ is satisfied, then Eq.…”

Section: Weak Orthogonality Functionalsmentioning

confidence: 99%

The weak orthogonality functional in explicitly correlated pair theories

Tew

Klopper

Manby

2007

The Journal of Chemical Physics

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Recent advances have seen the convergence of the R12 and Gaussian geminal explicitly correlated methods, such that the principal remaining distinction is the way in which the many-electron integrals are handled. Here we examine the weak orthogonality functional and the resolution of the identity and find that the first, although exact in the limit of infinite basis, introduces a conflict between the physical description of the electronic cusp and the satisfaction of the strong orthogonality constraint. This leads us to propose an improved weak orthogonality functional where the explicitly correlated pair functions are almost orthogonal to the occupied orbitals by construction. For applications where 95%-98% accuracy in the total correlation energy is sufficient, we recommend use of the strong orthogonality functional in combination with the resolution of the identity for three- and four-electron integral evaluations.

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Quadratically convergent iteration procedure for geminal determinations

Loter

Christoffersen

1969

Int J of Quantum Chemistry

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AbstractsA general formalism is presented for the determination of the optimum natural orbitals within the various strongly orthogonal geminals of a wavefunction describing a 2N-electron closed-shell molecule or atom. The relationship to Hartree-Fock-Roothaan theory is established; the algorithm that is developed is quadratically convergent to the desired result, and does not ignore off-diagonal Lagrangian multipliers, or require an infinite series of 2 x 2 orthogonal transformations of the original basis.On prtsente un formalisme gentral pour determiner les orbitales naturelles optimales des geminales orthogonales au sens "fort" d'une fonction d'onde decrivant une molecule on un atome i couches complttes. On Ctablit la relation entre ce formalisme-ci et la thtorie de Hartree-Fock-Roothaan. On dtcrit un algorithme, qui converge quadratiquement au rtsultat dtsirt, qui tient compte des multiplicateurs de Lagrange non-diagonaux et qui n'exige pas une strie infinie de transformations orthogonales 2 x 2 de la base originale.Es wird ein allgemeiner Formalismus fur die Bestimmung der optimalen naturlichen Spinorbitale der "stark" orthogonalen Geminale einer Wellenfunktion fur ein Molekul oder ein Atom mit abgeschlossenen Schalen beschrieben. Die Beziehung zu der HartreeFock-Roothaanschen Theorie wird festgestellt. Ein Iterationsverfahren wird beschrieben, das quadratisch konvergent ist, das die nicht-diagonalen Lagrangeschen Multiplikatoren in Betracht zieht und das eine unendliche Reihe von 2 x 2 orthogonalen Transformationen der ursprunglichen Basis nicht erfordert.

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The significance of the strong orthogonality condition for geminal functions in variational calculations

Cited by 3 publications

References 6 publications

Quantum Theory of Atoms and Molecules

Quantum Theory of Atoms and Molecules

The weak orthogonality functional in explicitly correlated pair theories

Quadratically convergent iteration procedure for geminal determinations

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