BSHF: A program to solve the Hartree–Fock equations for arbitrary central potentials using a B-spline basis

Waide, D. T.; Green, D. G.; Gribakin, G. F.

doi:10.1016/j.cpc.2019.107112

Cited by 6 publications

(10 citation statements)

References 18 publications

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“…The relevant HF equations and the numerical implementation used here are described fully in Ref. [10]. In the Hartree-Fock approximation [1][2][3], the total wavefunction of an N -electron system of energy E is approximated by a Slater determinant (or sum of Slater determinants, in general) that is an antisymmetrised product of N singleelectron spin orbitals φ α j (x j ), viz.…”

Section: Hartree-fock Methods and Its Present B-spline Basis Numerical Implementationmentioning

confidence: 99%

“…Here the first term in the bracket is the kinetic energy operator, and the second term is a local central potential V (r). For an atom with atomic number Z, V (r) = −Z/r, but in the BSHF program [10] it can also be chosen to be an arbitrary central potential, e.g., a harmonic confining potential, for a system of electrons to approximate the electron gas in the background of a uniform positive-charge distribution [17]. The Hartree-Fock potentialV HF = N i=1 Ĵ i −K i is a sum of the direct and (non-local) exchange terms J i φ j (x) = dx i φ * i (x )ρ −1 φ i (x )φ j (x) andK i φ j (x) = dx i φ * i (x )ρ −1 φ j (x )φ i (x), where ρ = |r − r|.…”

Section: Hartree-fock Methods and Its Present B-spline Basis Numerical Implementationmentioning

confidence: 99%

“…The Hartree-Fock calculations were performed using the BSHF code [10] with n = 40 Bsplines of order k = 6. The ground-state orbital and total energies are shown in Tables 2 and 3, in which successive columns show the energies for a system with an extra fully occupied orbital added, starting from the 1s 2 configuration in the left-most column.…”

Section: Hartree-fock Calculations For Harmonically Confined Electron Gasmentioning

confidence: 99%

“…The number of electrons represented by each solution was then calculated by integrating over n(r). Figure (10) shows N e plotted against the parameter n 0 for system with ! = 1.0.…”

Section: Fitting Modelmentioning

confidence: 99%

“…Special measures need to be taken to ensure that iterations for a large class of systems converge and that they converge quickly. Here, we use a numerical implementation of the self-consistent Hartree-Fock equations based on a Bspline approach and a new algorithm for achieving self-consistency (BSHF) [10] that allows the use of arbitrary central potentials. Specifically, convergence is aided by gradually increasing the magnitude of the electron-electron Coulomb interaction to its true value.…”

Section: Introductionmentioning

confidence: 99%

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B-spline basis implementation of the Hartree-Fock method for arbitrary central potentials

Waide

Green

Gribakin

2020

J. Phys.: Conf. Ser.

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An implementation of the Hartree-Fock (HF) method capable of robust convergence for well-behaved arbitrary central potentials is presented. The Hartree-Fock equations are converted to a generalized eigenvalue problem by employing a B-spline basis in a finite-size box. Convergence of the self-consistency iterations for the occupied electron orbitals is achieved by increasing the magnitude of the electronelectron Coulomb interaction gradually to its true value. For the Coulomb central potential, convergence patterns and energies are presented for a selection of atoms and negative ions, and are benchmarked against existing calculations. The present approach is also tested by calculating the ground states for an electron gas confined by a harmonic potential and also by that of uniformly charged sphere (the jellium model of alkali-metal clusters). For the harmonically confined electron-gas problem, comparisons are made with the Thomas-Fermi method and its accurate asymptotic analytical solution, with close agreement found for the electron energy and density for large electron numbers. We test the accuracy and effective completeness of the excited state manifolds by calculating the static dipole polarizabilities at the HF level and using the Random-Phase Approximation. Using the latter is crucial for the electron-gas and cluster models, where the effect of electron screening is very important. Comparisons are made for with experimental data for sodium clusters of up to ∼100 atoms.

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Section: Hartree-fock Methods and Its Present B-spline Basis Numerical Implementationmentioning

confidence: 99%

Section: Hartree-fock Methods and Its Present B-spline Basis Numerical Implementationmentioning

confidence: 99%

Section: Hartree-fock Calculations For Harmonically Confined Electron Gasmentioning

confidence: 99%

“…The number of electrons represented by each solution was then calculated by integrating over n(r). Figure (10) shows N e plotted against the parameter n 0 for system with ! = 1.0.…”

Section: Fitting Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

B-spline basis implementation of the Hartree-Fock method for arbitrary central potentials

Waide

Green

Gribakin

2020

J. Phys.: Conf. Ser.

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Anisotropic photoelectron emission delay in two-dimensional atomic arrangements

2021

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Many-body theory calculations of positron scattering and annihilation in noble-gas atoms via the solution of Bethe–Salpeter equations using the Gaussian-basis code EXCITON+

Hofierka,

Rawlins,

Cunningham

et al. 2023

Front. Phys.

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Scattering phase shifts and annihilation rates for low-energy positrons interacting with noble gas atoms are calculated ab initio using many-body theory implemented in the Gaussian-orbital code EXCITON+. Specifically, we construct the positron–atom correlation potential (self-energy) as the sum of three classes of infinite series describing the screened polarization, virtual positronium formation, and positron-hole repulsion found via the solution of Bethe–Salpeter equations for the two-particle propagators. The normalization of the continuum states is determined using the shifted pseudostates method [A. R. Swann and G. F. Gribakin, Phys. Rev. A 101, 022702 (2020)]. Comparison with the previous sophisticated B-spline many-body approach, which is restricted to atoms [J. Ludlow, D. G. Green, and G. F. Gribakin, Phys. Rev. A 90, 032712 (2014)], validates the EXCITON+ code, which can be used for multicentered targets including molecules, clusters, and condensed matter. Moreover, the relative effects of higher-order diagrams are quantified. It is found that the screening of the electron–positron Coulomb interaction represented by the infinite ring-diagram series (random-phase approximation) is compensated effectively by the additional electron-hole attraction corrections to it (the Bethe–Salpeter equation approximation) and that the use of the screened Coulomb interaction (screened at BSE level) in place of the bare Coulomb interaction in the virtual positronium and positron-hole ladder diagrams has negligible effect on both the phase shifts and Zeff. Our scattering length for Ne and Kr is in improved agreement with the convergent close-coupling result, and for Ar, the scattering length is in better agreement with the experiment compared with the previous B-spline many-body approach.

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BSHF: A program to solve the Hartree–Fock equations for arbitrary central potentials using a B-spline basis

Cited by 6 publications

References 18 publications

B-spline basis implementation of the Hartree-Fock method for arbitrary central potentials

B-spline basis implementation of the Hartree-Fock method for arbitrary central potentials

Anisotropic photoelectron emission delay in two-dimensional atomic arrangements

Many-body theory calculations of positron scattering and annihilation in noble-gas atoms via the solution of Bethe–Salpeter equations using the Gaussian-basis code EXCITON+

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