Numerically Integrable Confined Basis Functions for Band Structure Calculations

Abstract

Numerical atomic and Slater-type radial functions are matched with polynomials which vanish at a predetermined radius. Outside this radius the functions are identically equal to zero. Such functions with a different number of derivatives continuous at the cutoff and matching radii were used for band structure calculations of copper. The utilization of Gauss quadratures, constructed without accounting for discontinuity of the basis functions, was shown to ensure the required accuracy of numerical integration for matrix element calculations with the basis functions that have three lowest derivatives discontinuous at the cutoff and matching radii. In the case of matching radius variations over a wide range, the quality of the basis set is virtually independent of this value. Increasing the cutoff radius improves the basis quality. Moreover, a basis limit is reached even at the cutoff radius smaller than a two-fold distance between the nearest neighbors. The resulting basis set is not inferior in quality to conventional bases of atomic or Slater-type functions and, in contrast to conventional functions, requires no special techniques of numerical integration. The proposed basis set enables a reduction of computational time by a factor of 2 approximately.