dftatom: A robust and general Schr\"odinger and Dirac solver for atomic structure calculations

TL;DR

The paper introduces dftatom, a versatile and accurate solver for atomic structure calculations that handles various potentials and meshes, achieving high precision for heavy atoms and verified against benchmarks.

Contribution

It presents a robust, general Fortran implementation of a solver for Schrödinger, Dirac, and Kohn-Sham equations with systematic convergence control and high accuracy, including open-source code and detailed validation.

Findings

Achieves absolute energies with $10^{-8}$ Hartree accuracy for uranium.

Provides detailed convergence studies and computational parameters.

Verifies results against analytic and benchmark density-functional data for Z=1--92.

Abstract

A robust and general solver for the radial Schr\"odinger, Dirac, and Kohn--Sham equations is presented. The formulation admits general potentials and meshes: uniform, exponential, or other defined by nodal distribution and derivative functions. For a given mesh type, convergence can be controlled systematically by increasing the number of grid points. Radial integrations are carried out using a combination of asymptotic forms, Runge-Kutta, and implicit Adams methods. Eigenfunctions are determined by a combination of bisection and perturbation methods for robustness and speed. An outward Poisson integration is employed to increase accuracy in the core region, allowing absolute accuracies of $10^{-8}$ Hartree to be attained for total energies of heavy atoms such as uranium. Detailed convergence studies are presented and computational parameters are provided to achieve accuracies commonly required in practice. Comparisons to analytic and current-benchmark density-functional results for atomic number $Z$ = 1--92 are presented, verifying and providing a refinement to current benchmarks. An efficient, modular Fortran 95 implementation, \ttt{dftatom}, is provided as open source, including examples, tests, and wrappers for interface to other languages; wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines.