Journal ArticleDOI
Discrete Variational Method for the Energy-Band Problem with General Crystal Potentials
TLDR
In this paper, a variational method for efficiently calculating energy bands and charge densities in solids is presented; the method can be viewed as a weighted local energy procedure or alternately as a numerical integration scheme.Abstract:
A general variational method for efficiently calculating energy bands and charge densities in solids is presented; the method can be viewed as a weighted local-energy procedure or alternately as a numerical integration scheme. This rapidly convergent procedure circumvents many of the difficulties associated with the evaluation of matrix elements of the Hamiltonian in an arbitrary basis and treats the general nonspherical potential with no more complication than the usual "muffin-tin" approximation. Thus the band structure of ionic and covalent materials can be calculated with realistic crystal potentials. As an example, the method is applied to the one-electron model Hamiltonian with a nonspherical local potential, using a linear combination of atomic orbitals basis. Matrix elements of the Hamiltonian are evaluated directly without decomposition into atomic basis integrals; no "tight-binding" approximations are made. Detailed calculations are presented for the band structure and charge density of bcc lithium which demonstrate the feasibility of our method, and reveal the sensitivity of the energy bands to nonspherical and exchange components of the crystal potential. Various prescriptions for the construction of crystal potentials are considered, and convenient least-squares expansions are described. The extension of these methods to nonlocal potentials such as are encountered in the Hartree-Fock self-consistent-field procedure is discussed.read more
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Journal ArticleDOI
An all‐electron numerical method for solving the local density functional for polyatomic molecules
TL;DR: In this paper, a method for accurate and efficient local density functional calculations (LDF) on molecules is described and presented with results using fast convergent threedimensional numerical integrations to calculate the matrix elements occurring in the Ritz variation method.
Journal ArticleDOI
Numerical integration for polyatomic systems
G. te Velde,Evert Jan Baerends +1 more
TL;DR: In this paper, a numerical integration package is presented for three-dimensional integrals occurring in electronic structure calculations, applicable to all polyatomic systems with periodicity in 0 (molecules), 1 (chains), 2 (slabs), or 3 dimensions (crystals).
Journal ArticleDOI
The determination of molecular structures by density functional theory. The evaluation of analytical energy gradients by numerical integration
Louis Versluis,Tom Ziegler +1 more
TL;DR: In this paper, an algorithm based on numerical integration was proposed for the evaluation of analytical energy gradients within the Hartree-Fock-Slater (HFS) method.
Journal ArticleDOI
Discrete Variational Xα Cluster Calculations. I. Application to Metal Clusters
TL;DR: In this article, the SCC-DV-Xα molecular orbital method was applied to metal clusters and the numerical basis functions were utilized in the present calculations, and it was proved that the self-consistent charge (SCC) approximation to the SCF method gives accurate orbital energies.
Journal ArticleDOI
Three-dimensional numerical integration for electronic structure calculations
TL;DR: In this article, two three-dimensional numerical schemes are presented for molecular integrands such as matrix alements of one-electron operators occuring in the Fock operator and expectation values of one electron operators describing molecular properties.