Variation-perturbation theory within a time-dependent Kohn–Sham formalism: An application to the determination of multipole polarizabilities, spectral sums, and dispersion coefficients

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Abstract
The variation-perturbation method within time-dependent Kohn–Sham theory is used to calculate atomic multipole polarizabilities, spectra sums, and multipole–multipole two-body dispersion coefficients. The first-order corrections to Kohn–Sham amplitudes and phases were obtained from a direct variational approach and from the method of Cauchy moments. The multipole Cauchy moments were used to construct Padé approximants, which gave us upper and lower bounds to the two-body dispersion coefficients. Four approximations to the exchange-correlation energy were investigated in the present work and the gradient expansion for atoms proved to be most satisfactory.