Chirp-wave Expansion of the Electron Wavefunctions in Atoms

TL;DR

This paper introduces a generalized expansion method for electron wavefunctions in atoms using fractional Fourier series with chirp basis sets, improving convergence and efficiency in describing electron densities.

Contribution

It presents a novel chirp-wave basis set approach that optimizes wavefunction expansion and enhances convergence compared to traditional plane-wave methods.

Findings

Chirp basis sets improve convergence of electron density descriptions.

The method efficiently captures oscillations of electron core states.

Chirp characteristics can be optimized variationally for better results.

Abstract

The description of the electron wavefunctions in atoms is generalized to the fractional Fourier series. This method introduces a continuous and infinite number of chirp basis sets with linear variation of the frequency to expand the wavefunctions, in which plane-waves are a special case. The chirp characteristics of each basis set can be adjusted through a single parameter. Thus, the basis set cutoff can be optimized variationally. The approach is tested with the expansion of the electron wavefunctions in atoms, and it is shown that chirp basis sets substantially improve the convergence in the description of the electron density. We have found that the natural oscillations of the electron core states are efficiently described in chirp-waves.