Basis Set Effect on Linear Response Density Functional Theory Calculations on Periodic Systems

In this work, we present an investigation of the role of basis set size on linear response (LR) calculations of electronic properties of extended systems using density functional theory with periodic boundary conditions (DFT-PBC) and Gaussian-type atomic orbital (GTO) bases. We report the results of electric dipole-electric dipole polarizability, optical rotation, and electronic excitation energies (computed as poles of the LR function) on a series of one-dimensional (1D) and three-dimensional (3D) periodic systems. The basis sets employed are based on the Dunning series: cc-pVXZ, with X ranging from double-ζ to quintuple-ζ, and include the bases augmented with diffuse functions: aug-cc-pVXZ. The calculations are possible thanks to an extension of the coupled-perturbed Kohn-Sham code in the GAUSSIAN software to work with a different number of orbitals at each <i>k</i> point in reciprocal space, as orbitals with small overlap eigenvalues are projected out during the orthonormalization procedure of the basis set before the self-consistent field procedure used to evaluate the energy. The results on the test systems indicate that large basis sets, including diffuse functions, are necessary to reach quantitative agreement with experimental data and the complete basis set limit for LR properties even at DFT-PBC level.