Validity of the Assumption of Two-Body Interactions in Molecular Physics. I

The energy of interaction between a group of two spherical atoms ($\mathrm{AB}$), which are close together, and an identical atom $C$, which is farther away, is evaluated by applying second-order perturbation theory. The calculations are carried out for three hydrogen atoms with parallel spins and for three helium atoms. Permutations of electrons between atoms $A$ and $B$ are taken into account by using an antisymmetric zero-order wave function for the group ($\mathrm{AB}$). It is found that, in general, second-order interactions between ($\mathrm{AB}$) and $C$ are not equal to a sum over isolated pairs ($\mathrm{AC}$) and ($\mathrm{BC}$); in practically all cases the second-order interactions are weaker than when calculated on an additive basis. Numerical results are given for three special cases: a linear array, a right triangle, and an integrated effect, as functions of the distances between the three atoms. A comparison is made with the triple-dipole energy as calculated by Axilrod. It is shown that the nonadditive effect calculated in this paper is usually considerably larger than the triple-dipole energy for the same triangular configuration and that it may contribute significantly to the stability of the face-centered cubic lattice of the heavy rare gases.