An error analysis for Hartree-Fock crystal orbital calculations

Suhai, S.; Bagus, Paul S.; Ladik, J.

doi:10.1016/0301-0104(82)87055-9

Cited by 43 publications

(33 citation statements)

References 11 publications

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“…Gaussian basis functions with diffuse exponents are known to cause numerical instabilities in the SCF procedure for solids [75,[128][129][130][131]. One type of instability is associated with the overcompleteness of a chosen basis, i.e.…”

Section: A Nonrelativistic Theorymentioning

confidence: 99%

All-electron fully relativistic Kohn-Sham theory for solids based on the Dirac-Coulomb Hamiltonian and Gaussian-type functions

2019

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We present the first full-potential method that solves the fully relativistic four-component Dirac-Kohn-Sham equation for materials in the solid state within the framework of atom-centered Gaussian-type orbitals (GTOs). Our GTO-based method treats one-, two-, and three-dimensional periodic systems on an equal footing, and allows for a seamless transition to the methodology commonly used in studies of molecules with heavy elements. The scalar relativistic effects as well as the spin-orbit interaction are handled variationally. The full description of the electron-nuclear potential in the core region of heavy nuclei is straightforward due to the local nature of the GTOs and does not pose any computational difficulties. We show how the time-reversal symmetry and a quaternion algebra-based formalism can be exploited to significantly reduce the increased methodological complexity and computational cost associated with multiple wave-function components coupled by the spin-orbit interaction. We provide a detailed description of how to employ the matrix form of the multipole expansion and an iterative renormalization procedure to evaluate the conditionally convergent infinite lattice sums arising in studies of periodic systems. Next, we investigate the problem of inverse variational collapse that arises if the Dirac operator containing a repulsive periodic potential is expressed in a basis that includes diffuse functions, and suggest a possible solution. Finally, we demonstrate the validity of the method on three-dimensional silver halide (AgX) crystals with large relativistic effects, and two-dimensional honeycomb structures (silicene and germanene) exhibiting the spin-orbit-driven quantum spin Hall effect. Our results are well-converged with respect to the basis set limit using standard bases developed for molecular calculations, and indicate that the common rule of removing basis functions with small exponents should not be applied when transferring the molecular basis to solids.

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Section: A Nonrelativistic Theorymentioning

confidence: 99%

All-electron fully relativistic Kohn-Sham theory for solids based on the Dirac-Coulomb Hamiltonian and Gaussian-type functions

2019

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“…4, by following this method, we have used the proposed methodology with a STO-3G minimal basis set and an extended 4-31G one to compute the polarizabilities per unit cell of infinite polyethylene and polysilane chains to prove they are the asymptotic limit of the values obtained for oligomers of increasing size. In the case of extended basis sets, we encounter the problem of the errors caused by improper lattice sum truncations generally present as extended basis sets are employed [18]. It is shown that the removal of the eigenvectors belonging to small eigenvalues of the k-dependent overlap matrices gives rise to inaccurate results and that we need to keep all the eigenvectors in a way to obtain the polarizability per unit cell, which is the asymptotic limit of the polarizabilities per monomeric unit of the size increasing oligomers.…”

Section: Introductionmentioning

confidence: 99%

Determination of ab initio polarizabilities of polymers: Application to polyethylene and polysilane

Champagne

André

1992

Int J of Quantum Chemistry

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An ab initio method for calculating the longitudinal linear polarizability of polymeric chains is described. This method is equivalent to an uncoupled Hartree-Fock scheme. It is applied to polyethylene and polysilane in minimal STO-3G and extended 4-31G basis sets. The study describes important techniques for solving the difficulties met in actual calculations: band reordering of the band structures, calculation of analytical derivatives of the energy bands &"&) and LCAO coefficients cW(k), and errors caused by the improper lattice sum truncations of the Hartree-Fock matrix.

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“…17,18 Of Ž course, this problem is essentially eliminated at . least numerically as the cluster approaches infinity.…”

Section: Modelmentioning

confidence: 99%

Approaching bulk limit for three-dimensional solids via the cyclic cluster approximation: Semiempirical INDO study

et al. 1999

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An error analysis for Hartree-Fock crystal orbital calculations

Cited by 43 publications

References 11 publications

All-electron fully relativistic Kohn-Sham theory for solids based on the Dirac-Coulomb Hamiltonian and Gaussian-type functions

All-electron fully relativistic Kohn-Sham theory for solids based on the Dirac-Coulomb Hamiltonian and Gaussian-type functions

Determination of ab initio polarizabilities of polymers: Application to polyethylene and polysilane

Approaching bulk limit for three-dimensional solids via the cyclic cluster approximation: Semiempirical INDO study

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