Tensor Approximation of Slater-Type Orbital Basis Functions

Abstract

This paper deals with a tensor representation of the Slater-type orbital basis functions. Localized basis systems are primarily used in electronic structure calculations. A choice of the system is usually limited to Gaussian-type orbitals due to the impossibility of the analytical evaluation of necessary integrals using other basis types. Unfortunately, it is not possible to use direct discretization techniques due to the dimensionality of the problem so the numerical integration is problematic. Tensor Numerical Methods overcome this problem by using special data representations, which are discussed. Finally, it is demonstrated how to use these methods to construct a tensor approximation of Slater-type orbital basis functions including an error estimate and its numerical verification.

Keywords

• electronic structure
• gaussian-type orbital
• sinc approximation
• slater-type orbital
• tensor numerical methods.