The calculation of dynamic polarizabilities and of the dipole-dipole and dipole-quadrupole contributions to the dispersion energy

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Abstract
By using a single Slater-type 2p orbital with a frequency-dependent exponent in the basis set for the variation solution of the first-order time-dependent perturbation equation, good results are obtained for the dipole dynamic polarizability of the hydrogen atom. The accuracy attained has been reproduced only by variation calculations with larger basis sets. The same happens with the quadrupole dynamic polarizability: a single 3d Slater-type orbital with a similarly optimized exponent in the basis of states for the variation calculation is enough to yield results which are very close to the exact values for all frequencies. Using the frequency-dependent dipole and quadrupole polarizabilities thus obtained we have calculated the dipole and quadrupole contributions to the dispersion energy of two hydrogen atoms and found results which are within 1 per cent of the exact values. Considering the simplicity of our wavefunction as compared with the four-term wavefunction used by Chan and Dalgarno [5] to construct the basis for their variation calculation and the excellent agreement we obtain, it is important to emphasize the value of using optimized frequency-dependent exponents in the basis of states used for the variation calculation.