Variational Cellular Method Research Articles

A new version of the variational cellular method for polyatomic systems

The authors present a new version of the variational cellular method of Ferreira and Leite (1979) for the calculation of the electronic structure of polyatomic systems. This version seems to be simple to use, eliminates the muffin-tin potentials and charge densities, and is as fast as the multiple-scattering method. The authors develop programmable procedures for the definition of the cells and choice of points for the surface integrations of polyatomic structures. When applied to methane, the method gave very good results for the energy, interatomic distance, a1 mode frequency and ionisation energies at a very low computational cost.

Determination of the energy bands of metallic lithium by the variational cellular method

The recently proposed variational cellular method (VCM) is extended to periodic structures with one atom per unit cell. The method as outlined in this paper is applied to the calculation of the band structure of metallic lithium. The results show that the VCM leads to accurate energy levels for Li requiring a small computational effort. It is concluded that the results are sufficiently encouraging to suggest the application of the method to more complex crystals.

Application of the variational cellular method to periodic structures. Energy band of sodium

The first application of the recently proposed variational cellular method (VCM) to periodic structures is reported. The method is applied to the determination of the electronic structure of metallic sodium. The results of these calculations, when compared with previous results obtained through other methods, lead to the conclusion that VCM is an accurate and fast method. Empty-lattice energy eigenvalues for the $\ensuremath{\Delta}$ symmetry line in a body-centered-cubic lattice are found to be correct to 0.001 Ry, when spherical harmonic components up to ${l}_{max}=4$ are used in the cellular expansions.

Theoretical study of the F2molecule using the variational cellular method

Variational cellular method (VCM) calculations for F2 have been carried out at several internuclear distances. The ground and excited state potential curves are presented. The overall agreement between the VCM results and ab initio calculations is fairly good.

A study of the ground states and ionization energies of H2, C2, N2, F2, and CO molecules by the variational cellular method

Self-consistent calculations for the ground state potential curves and ionization energies are reported for the molecules H2, C2, N2, F2, and CO, using the recent proposed variational cellular method. For all these molecules the results are quite good. The calculated binding energies, equilibrium interatomic distances, and energy ionization spectra are in excellent agreement with the available experimental findings.

Self-consistent calculation of the electronic structure ofN2and CO by the variational cellular method

In this paper the variational cellular method is extended to the self-consistent calculation of diatomic molecules. This extension is based on a new variational expression for the total molecular energy the extremum of which defines the one-electron potential of the Schr\"odinger equation. The method was tested in the calculation of ${\mathrm{N}}_{2}$ and CO and the results are very good: the binding energy and the equilibrium interatomic distances were calculated to be within less than 10% of the known experimental results.

General formulation of the variational cellular method for molecules and crystals

A variational form of the cellular method is proposed as a new model to solve the one-electron Schr\"odinger equation for molecules and crystals. The model keeps such good features of the traditional cellular method as the arbitrary partition of space, and eliminates its main drawback, the slow convergence of the cellular expansion series. With the aid of a criterion of precision on the trial wave functions, we discuss the possibilities offered by the method for more accurate calculations of the electronic structures of molecules and solids. As an example of the accuracy and fast convergence of the model, computation of the energy spectrum of the molecular hydrogen ion ${\mathrm{H}}_{2}^{+}$ is presented.

Calculations on the Band Structure of Silicon

The electronic band structure of silicon has been calculated along two axes of momentum space. The results agree qualitatively with experiment, but quantitative values are distorted by uncertainties in the potential used. The variational cellular method used is not too laborious in application, but appears to suffer from unexpected disadvantages at low-symmetry points in momentum space