SO(3) quadratures in angular-momentum projection

Shimizu, Noritaka; Tsunoda, Y.

doi:10.1016/j.cpc.2022.108583

Cited by 2 publications

(3 citation statements)

References 33 publications

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“…where the weights w(Ω g ) are determined by the quadrature methods chosen. 42,43 The most efficient scheme is either a Lebedev quadrature for the angles α and β, and a periodic trapezoidal quadrature for the γ angle (denoted as Lebedev trapezoidal), or a periodic trapezoidal quadrature for α and γ, and a Gauss quadrature for cos β (denoted as Gauss trapezoidal). For a detailed recent study on quadrature rules for angular momentum projection, see ref 43.…”

Section: Implementation Of the Projected Ne-hf Methodsmentioning

confidence: 99%

“…We discretize the integrals entering the Hill–Wheeler equations, and since the parity projection is straightforward as opposed to the rotational projection, we disregard the former and write the projected matrix elements as where the weights w (Ω g ) are determined by the quadrature methods chosen. , The most efficient scheme is either a Lebedev quadrature for the angles α and β, and a periodic trapezoidal quadrature for the γ angle (denoted as Lebedev trapezoidal), or a periodic trapezoidal quadrature for α and γ, and a Gauss quadrature for cos β (denoted as Gauss trapezoidal). For a detailed recent study on quadrature rules for angular momentum projection, see ref . The numerical integration can be easily parallelized over the quadrature points since the matrix elements at each quadrature point, g , can be evaluated independently.…”

Section: Implementation Of the Projected Ne-hf Methodsmentioning

confidence: 99%

“… 42 , 43 The most efficient scheme is either a Lebedev quadrature for the angles α and β, and a periodic trapezoidal quadrature for the γ angle (denoted as Lebedev trapezoidal), or a periodic trapezoidal quadrature for α and γ, and a Gauss quadrature for cos β (denoted as Gauss trapezoidal). For a detailed recent study on quadrature rules for angular momentum projection, see ref ( 43 ). The numerical integration can be easily parallelized over the quadrature points since the matrix elements at each quadrature point, g , can be evaluated independently.…”

Section: Implementation Of the Projected Ne-hf Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Symmetry-Projected Nuclear-Electronic Hartree–Fock: Eliminating Rotational Energy Contamination

Feldmann,

Baiardi,

Reiher

2023

J. Phys. Chem. A

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We present a symmetry projection technique for enforcing rotational and parity symmetries in nuclear-electronic Hartree–Fock wave functions, which treat electrons and nuclei on equal footing. The molecular Hamiltonian obeys rotational and parity inversion symmetries, which are, however, broken by expanding in Gaussian basis sets that are fixed in space. We generate a trial wave function with the correct symmetry properties by projecting the wave function onto representations of the three-dimensional rotation group, i.e., the special orthogonal group in three dimensions SO(3). As a consequence, the wave function becomes an eigenfunction of the angular momentum operator which (i) eliminates the contamination of the ground-state wave function by highly excited rotational states arising from the broken rotational symmetry and (ii) enables the targeting of specific rotational states of the molecule. We demonstrate the efficiency of the symmetry projection technique by calculating the energies of the low-lying rotational states of the H2 and H3 + molecules.

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Section: Implementation Of the Projected Ne-hf Methodsmentioning

confidence: 99%

Section: Implementation Of the Projected Ne-hf Methodsmentioning

confidence: 99%

Section: Implementation Of the Projected Ne-hf Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Symmetry-Projected Nuclear-Electronic Hartree–Fock: Eliminating Rotational Energy Contamination

Feldmann,

Baiardi,

Reiher

2023

J. Phys. Chem. A

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Recent Progress of Shell-Model Calculations, Monte Carlo Shell Model, and Quasi-Particle Vacua Shell Model

Shimizu

2022

Physics

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Nuclear shell model is a powerful approach to investigate nuclear structure microscopically. However, the computational cost of shell-model calculations becomes huge in medium-heavy nuclei. I briefly review the theoretical framework and the code developments of the conventional Lanczos diagonalization method for shell-model calculations. In order to go beyond the conventional diagonalization method, the Monte Carlo shell model and the quasiparticle-vacua shell model were introduced. I present some benchmark examples of these models.

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SO(3) quadratures in angular-momentum projection

Cited by 2 publications

References 33 publications

Symmetry-Projected Nuclear-Electronic Hartree–Fock: Eliminating Rotational Energy Contamination

Symmetry-Projected Nuclear-Electronic Hartree–Fock: Eliminating Rotational Energy Contamination

Recent Progress of Shell-Model Calculations, Monte Carlo Shell Model, and Quasi-Particle Vacua Shell Model

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