Basis functions for electronic structure calculations on spheres.

Area of Science:

• Computational physics
• Quantum chemistry
• Materials science

Background:

• Electronic structure calculations are fundamental to understanding molecular and material properties.
• Basis functions are essential components of these calculations, influencing efficiency and accuracy.
• Spherical harmonics are commonly used but can be less efficient for localized electron systems.

Purpose of the Study:

• To introduce a novel basis function, the spherical Gaussian, for electronic structure calculations.
• To derive general expressions for one- and two-electron integrals using this new basis.
• To assess the computational efficiency of spherical Gaussians compared to existing methods.

Main Methods:

• Developed general expressions for one- and two-electron integrals for spherical Gaussians in D dimensions.
• Proposed an efficient computational algorithm utilizing the Cauchy-Schwarz bound.
• Performed numerical calculations for the D=2 case to compare performance.

Main Results:

• Established the mathematical framework for spherical Gaussian basis functions.
• Demonstrated an efficient computational algorithm for their implementation.
• Showcased superior efficiency of spherical Gaussians over spherical harmonics for strongly localized electrons in D=2.

Conclusions:

• Spherical Gaussians offer a promising alternative basis set for electronic structure calculations.
• The proposed method shows significant advantages in computational efficiency for specific electron localization scenarios.
• This work paves the way for more efficient quantum mechanical simulations.