Electric Dipole Polarizability Calculation for Periodic and Non-Periodic Systems using Atomic-Orbitals-based Linear Response Theory

We present electric dipole polarizability calculations employing atomic-orbitals based linear response theory within the Kohn-Sham Density Functional Theory (KS-DFT) framework, considering both non-periodic and periodic boundary conditions. We adopt the optimization scheme introduced by T. Helgaker et al. in Chemical Physics Letters 327, 397 (2000) for the single-electron atomic-orbitals density matrix. We conduct a comparative analysis between the static polarizability computed using atomic orbitals-based and previously implemented molecular orbitals-based methods. In our calculations involving periodic boundary conditions, we implement polarizability calculation using velocity representation of the electric dipole operator in atomic orbitals-based algorithm, subsequently comparing the results with those computed using the Berry-phase formulation and velocity representation in molecular orbitals-based algorithm. We investigate 10 small and medium-sized molecules in the gas phase, analyze liquid-phase systems with up to 256 water molecules, and the solid-state structures of anatase TiO₂ and bulk WO₃. All polarizability results obtained from the AO-based solver exhibit good agreement with MO-based results. From our example calculations, we find that the AO-based solver exhibits better computational scaling and less memory demand than the MO-based solvers, which makes it better suited for very large systems.