The Hartree-Fock Method for Atoms: A Numerical Approach

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The Hartree—Fock eigenvalue problem governed by the 3D integro-differential operator is the basic model in ab initio electronic structure calculations. Several years ago the idea to solve the Hartree—Fock equation by a fully 3D grid based numerical approach seemed to be a fantasy, and the tensor-structured methods did not exist. In fact, these methods evolved during the work on this challenging problem.

In this paper, our recent results on the topic are outlined and the black-box Hartree—Fock solver by tensor numerical methods is presented. The arising 3D convolution transforms with the Newton kernel are replaced by a combination of 1D convolutions and 1D Hadamard and scalar products. The two-electron integrals are computed via multiple factorizations. The performance of the black-box solver in Matlab implementation is compatible with the benchmark packages based on the analytical pre evaluation of the multidimensional convolution integrals.

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More options …. Computational Methods in Applied Mathematics. Editor-in-Chief: Carstensen, Carsten. See all formats and pricing.

Online ISSN See all formats and pricing Online. Thus accurate computational methods are needed not only for the prediction of atomic properties but in the development of atomic physics theory, particularly for superheavy elements. I am a founding member of the Computational Atomic Structure group -- CompAS -- that supports the development of software for the study of a wide range of atomic properties. Of particular interest are energy levels for spectra, ionization energies, isotope effects, transition probabilities and lifetimes.

The Hartree–Fock Method for Atoms: A Numerical Approach

Recent Review : Advanced multiconfiguration methods for complex atoms: Part I - Energies and wave functions. Godefroid, T. The Hartree-Fock Method for Atoms. New-York: Wiley. A universal basis set for cations and anions generated with the generator coordinate Hartree-Fock method.

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A universal Gaussian basis set for positive and negative ions from H through Xe. Gaussian basis sets for isoelectronic series of the He to Ne.

Adapted Gaussian basis sets for atoms Cs to Lr based on the generator coordinate Hartree-Fock method. J Comp Chem A further study on the discretisation of the Griffin-Hill-Wheeler equation. Z Phys D 3: Int J Quantum Chem Symp The generator coordinate Hartree-Fock method applied to the choice of a contracted Gaussian basis for first-row atoms.

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Generator coordinate Hartree-Fock method applied to the choice of a contracted Gaussian basis for the second-row atoms. Int J Quantum Chem. Self-consistent field theory for open shells of electronic systems. Rev Mod Phys All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License.

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Services on Demand Journal. Roothaan-HF wave functions are convenient for many purposes, as indicated by the large impact of the work of Clementi and Roetti CR How to cite this article.