Variationally determined multipole Cauchy moments

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Abstract
The hydrodynamic variational method for obtaining dynamic multipole polarizabilities is extended to determine multipole Cauchy moments. The hydrodynamic functional is replaced by an equivalent series of functionals, obtained by expanding the first-order functions in power series of the applied frequency. As an application of the method, multipole Cauchy moments for the ground states of atomic hydrogen and helium are determined by solving variationally the set of functionals. The resulting moments are then used to construct Padé approximants, from which long-range dispersion coefficients are determined.