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 TiO $_{2}$ and bulk WO $_{3}$ . 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.