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 using Green’s function methods by iterative numerical integration of the convolution with the Helmholtz kernel. The orbital response is obtained analogously by iterative numerical integration of the convolution with 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 bubble 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, which are compared to the literature values.