Ordinary field‐theoretic methods for self‐consistent wave functions which describe bond formation and dissociation. II. Commutative coupling case

England, Walter B.

doi:10.1002/qua.560230314

Cited by 14 publications

(3 citation statements)

References 37 publications

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“…For example, we have used the linear and quadratic formulations to describe the fragmentation of diatomic molecules [53]. In these studies, the quadratic formulation furnishes a rigorous description of the simplest possible geminal.…”

Section: Lewis Structures and Feynman Diagramsmentioning

confidence: 99%

Lewis structures and Feynman diagrams: The treatment of geminal correlation in Fock space

England

Sorensen

Silver

1986

Int. J. Quantum Chem.

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Lipkin's method is used to rigorously transpose field-theoretic, self-consistent descriptions of Cooper pairs and Bose condensation to Lewis structures and resonance. The effective one-body equations can be simplified according to models of valence. The resultant self-consistent problem may require not much more work than the Hartree-Fock problem. The effort required for MBPT remains comparable to the Hartree-Fock case.

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Section: Lewis Structures and Feynman Diagramsmentioning

confidence: 99%

Lewis structures and Feynman diagrams: The treatment of geminal correlation in Fock space

England

Sorensen

Silver

1986

Int. J. Quantum Chem.

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“…Hence, for a particle-conserving molecular Hamiltonian, both HFB and PBHF will reduce to an HF state. Despite this, several approaches − for describing strong correlation in particle-conserving molecular systems have been inspired by HFB. A notable example is the constrained pairing-mean-field theory (CPMFT), which is built upon ζ-HFB where the pairing energy term is scaled by a factor ζ .…”

Section: Introductionmentioning

confidence: 99%

Particle-Breaking Hartree–Fock Theory for Open Molecular Systems

2023

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In this work we present the particle-breaking Hartree–Fock (PBHF) model which is a mean-field approach to open molecular systems. The interaction of a system with the environment is parametrized through a particle-breaking term in the molecular Hamiltonian. The PBHF wave function is constructed through an exponential unitary transformation of a Slater determinant with a given number of electrons. We consider only the closed-shell formalism. The parametrization results in a linear combination of Slater determinants with different numbers of electrons, i.e., the PBHF wave function is not an eigenfunction of the number operator. As a result, the density matrix may have fractional occupations which are, because of the unitary parametrization, always between 0.0 and 2.0. The occupations are optimized simultaneously with the orbitals, using the trust-region optimization procedure. In the limit of a particle-conserving Hamiltonian, the PBHF optimization will converge to a standard Hartree–Fock wave function. We show that the average number of electrons may be decreased or increased depending on whether the particle-breaking term affects occupied or virtual orbitals.

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“…A vacuum with BCS structure was adopted 15 in our previous work. Lipkin's side conditions for finite systems 16 were investigated 17–20 and a two parameter model for finite nuclei 21–25 was adopted. The zero‐point or vacuum has the BCS structure and diagonalizes pairing ODLRO.…”

Section: Introductionmentioning

confidence: 99%

Valence states of the cyano radical Feynman's way

Sorensen

England

2002

Int J of Quantum Chemistry

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Scaled Feynman diagrams are proposed as perturbative corrections to the total energy. The proposal is tested by calculating potential energy curves for the valence states of the cyano radical. Unique features of the valence state are part of the starting approximation. The latter is computed with a standard quantum chemical method. For a particular method, the scale is independent of the valence state. At each bond distance, one set of quasiparticles and Feynman diagrams is used for all valence states. Scaling will be useful whenever perturbative corrections can be expressed with Feynman diagrams. In the cyano radical, competition for the odd electron between the σ and π orbitals produces a variety of valence states. Many are quasidegenerate. The 16 states investigated here are doublets and quartets with triple bonds, double bonds, 'resonance' bonds, bonds intermediate to double and triple bonds, and bonds intermediate to single and double bonds. Energy curves and spectroscopic constants are reported for the lowest lying quartets and two or more lowest doublets of ± , , and symmetries, and also 1 2 symmetry. Inner and outer minima in the energy curve for 3 2 are assigned to H and G, respectively. A more accurate assignment of a 4 + is made. Relative to experiment, maximum (average) errors in bond distance, frequency, and the adiabatic excitation energy are 1.6 pm (1 pm), 60 cm −1 (50 cm −1 ), and 19 kJ/mol (5 kJ/mol), respectively. The error in the ground state dissociation energy is 11 kJ/mol. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 90: 516-533, 2002

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Ordinary field‐theoretic methods for self‐consistent wave functions which describe bond formation and dissociation. II. Commutative coupling case

Cited by 14 publications

References 37 publications

Lewis structures and Feynman diagrams: The treatment of geminal correlation in Fock space

Lewis structures and Feynman diagrams: The treatment of geminal correlation in Fock space

Particle-Breaking Hartree–Fock Theory for Open Molecular Systems

Valence states of the cyano radical Feynman's way

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