On the Calculation of Polarizabilities and Van der Waals Forces for Atoms inSStates

The perturbation scheme of Møller and Plesset, which has as its basis a complete set of solutions of the Fock single-electron differential-integral equation, is extended to the calculation of atomic polarizabilities and van der Waals force constants. The present treatment differs in three respects from the previous treatments of Kirkwood and Buckingham. First, the Hartree-Fock model is used consistently throughout the calculation. Additional functions are introduced to complete the set of single-electron functions. Sum rules are developed for these functions with the aid of their common Hamiltonian. These replace the Kuhn-Reiche sum rules, which do not apply in their usual form. Second, atomic polarizabilities are expressed as a sum of sums in the perturbation scheme. An ordered set of lower bounds is derived for the first of these sums and also for similar expressions for van der Waals force constants. Third, the contribution of each electron is considered separately. The lower bounds are evaluated exactly with the help of the sum rules developed. In this way are obtained for the approximate values of the atomic polarizability of beryllium and argon 4.14×${10}^{-24\mathrm{}}$ ${\mathrm{cm}}^3$ and 1.28×${10}^{-24\mathrm{}}$ ${\mathrm{cm}}^3$, respectively. Likewise the constant $\mu$ in the van der Waals energy, $\frac{-\mu }{R^6}$, is found to be about 222×${10}^{-60\mathrm{}}$ erg ${\mathrm{cm}}^6$ for two beryllium atoms and 63.7×${10}^{-60\mathrm{}}$ erg ${\mathrm{cm}}^6$ for two argon atoms. The observed atomic polarizability of argon is 1.63×${10}^{-24\mathrm{}}$ ${\mathrm{cm}}^3$.