Long-range interaction of two ls-hydrogen atoms expressed in terms of natural spin-orbitals

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Abstract
The interaction between two hydrogen atoms in their ground state at large separation is treated by means of a variational form of the perturbation theory, which essentially involves the calculation of the reciprocal of the unperturbed matrix by means of successive inversion. A basic set which avoids the continuum is used. The energy of the system of two hydrogen atoms at large separations is found to be where the separation R is measured in units of c 0. The coefficient of R -6 agrees with the calculations of Pauling and Beach but the coefficient of R -8 is quite different from theirs. The wave function is greatly simplified by introducing natural orbitals. If the wave function is approximated by using only one or two sets of natural orbitals, very little error results in the calculated dispersion energy. Also, it is shown that such an approximation leads to very little error in the mean square deviation of the approximate wave function from the exact function. This illustrates the theorem that an approximate wave function composed of n natural orbitals has a smaller mean square deviation from the true function than an approximate wave function made up from n other sorts of orbitals. An application of long-range intermolecular force calculations to collision theory is also given.