Long-Range Interaction of Helium Atoms. A. Calculations

The interaction of two nonoverlapping helium atoms is evaluated using the many‐electron theory of atoms and molecules with a Hirschfelder—Linnett‐type of pair function, a Hylleraas intra‐atomic correlation function, and a two‐term atomic Hartree—Fock orbital. Previous work (previous paper) showed that the ``nonoverlapping'' region is separations over 3.7 Å. In atomic units we find $$\mathrm{V=}\frac{\text{−1.353}}{R^6}-\frac{\text{13.25}}{R^8}-\frac{\text{52.45}}{R^{10}}-\frac{\text{94.45}}{R^{10}}$$ for the dipole—dipole (using three variable parameters), dipole—quadrupole (two parameters), quadrupole—quadrupole (one parameter), and dipole—octupole (one parameter) interactions. The accepted correct value of the first coefficient is about 1.47. About 21% of the R⁻⁶ coefficient is due to three‐electron effects which arise as matrix elements between the two‐electron terms in the wavefunction. Neglecting intra‐atomic correlation effects we obtain a coefficient of −1.644 for the first term. An error of 25% results if only a one‐term atomic orbital is used. The relation of these results to many approximate methods of calculation is also discussed.