Electronic structure calculations with interpolating tensor product wavelet basis

TL;DR

This paper presents a novel three-dimensional wavelet basis for electronic structure calculations, enabling efficient and accurate solutions of Schrödinger equations for atoms and molecules using advanced numerical methods.

Contribution

It introduces a new interpolating tensor product wavelet basis for electronic structure calculations and demonstrates its effectiveness on various atomic and molecular systems.

Findings

Accurately computed eigenstates of H and He atoms.

Successfully modeled molecules like H2, H2+, and LiH.

Compared performance favorably with existing methods.

Abstract

We introduce a basis set consisting of three-dimensional Deslauriers--Dubuc wavelets and solve numerically the Schr\"odinger equations of H and He atoms and molecules $\mathrm{H}_2$, $\mathrm{H}_2^+$, and $\mathrm{LiH}$ with HF and DFT methods. We also compute the 2s and 2p excited states of hydrogen. The Coulomb singularity at the nucleus is handled by using a pseudopotential. The eigenvalue problem is solved with Arnoldi and Lanczos methods, Poisson equation with GMRES and CGNR methods, and matrix elements are computed using the biorthogonality relations of the interpolating wavelets. Performance is compared with those of CCCBDB and BigDFT.