Linear polarizability calculation for rare-gas atoms in the time-dependent local-density approximation with a scissors operator.

Abstract

We report a modified time-dependent local-density-approximation (TDLDA) calculation of the linear polarizability of rare-gas atoms. The modification we use takes the self-energy into account by introducing a scissors operator; we simply increase the energy differences of the occupied and unoccupied orbitals from the LDA calculation by a constant. The energy shift is (1) estimated with a single oscillator model and (2) determined such that the modified TDLDA with the scissors operator gives the experimental value of the static linear polarizability. The ratio of the energy shift to the lowest LDA energy difference between occupied and unoccupied orbitals for each atom is calculated. These ratios are found to be comparable to the corresponding ratios of the energy shift to the energy gap in the scissors operator in a solid. The modified TDLDA calculation with the scissors operator agrees better with the experimental results, for the frequency dependence of the linear polarizability, than the TDLDA calculation. We apply the Schmidt-Ruedenberg even-tempered Gaussian basis in our calculation and find that the energy-optimized basis set gives a rather poor convergence rate for the linear polarizability. However, a good convergence rate can easily be obtained by adding a few diffuse basis functions to an energy-optimized basis set.