# Static polarizability and hyperpolarizability in atoms and molecules through a Cartesian-grid DFT

## TL;DR

This paper presents a real-space Cartesian grid DFT approach to calculate static electric response properties of atoms and molecules, demonstrating high accuracy and feasibility across various properties and functionals.

## Contribution

It introduces a systematic Cartesian-grid DFT method for static polarizability and hyperpolarizability, validated against literature and experimental data.

## Key findings

- Excellent agreement with atom-centered-grid results
- Effective use of non-uniform grid-optimization technique
- Viable alternative for response property calculations

## Abstract

Static electric response properties of atoms and molecules are reported within the real-space Cartesian grid implementation of pseudopotential Kohn-Sham (KS) density functional theory (DFT). A detailed systematic investigation is made for a representative set of atoms and molecules, through a number of properties like total ground-state electronic energies, permanent dipole moment ($\bm{\mu}$), static average dipole polarizability ($\overline{\alpha}$). This is further extended to first-hyperpolarizability ($\bm{\beta}$) in molecules. It employs a recently developed non-uniform grid-optimization technique, with a suitably chosen fixed initial applied field. A simple variant of the finite-field method, using a rational function fit to the dipole moment with respect to electric field, is adopted. We make use of Labello-Ferreira-Kurtz (LFK) basis set, which has performed quite well in these scenarios. To assess the efficacy and feasibility, four XC functionals such as LDA, BLYP, PBE and LBVWN are chosen. Present results are compared with available literature (both theoretical and experimental) values, whenever possible. In all instances, they show excellent agreement with the respective atom-centered-grid results, very widely used in many quantum chemistry programs. This demonstrates a viable alternative towards accurate prediction of response properties of many-electron systems in Cartesian coordinate grid.