Numerical calculations of electric response properties using the bubbles and cube framework

We have developed a fully numerical method for calculating the response of the Hartree-Fock orbitals to an external electric field. The Hartree-Fock orbitals are optimized by iterative numerical integration of the Helmholtz kernel. The orbital response is obtained analogously by iterative numerical integration of the Helmholtz kernel of the Sternheimer equation. The orbitals are expanded in atom-centered functions (bubbles) consisting of numerical radial functions multiplied by spherical harmonics. The remainder, i.e., the difference between the bubbles expansion and the exact orbitals, is expanded in numerical tensorial local basis functions on a three-dimensional grid (cube). The methods have been tested by calculating polarizabilities for He, H2 , and NH3 that are compared to literature values.