2419
GEOMETRIC PROGRAMMING IN STATISTICAL MECHANICS
+
equivalent to adding (n(n- 1) - Z(1 1))/2r2 to the Hamiltonian in eq A2. A more drastic approximation can be made by replacing the .zN/rlN in eq A2 by 2a2r2 - 1(1 1)/2r2. The resulting Gaussian functions e-a'BY2nconstitute an inferior basis set and are only used because the multicenter, two-electron integrals become easier to evaluate. I n any case, the point of this discussion is that if a perturbation which is a sum of one-electron operators is included, in eq A l , we can proceed in the same way as before and no new approximations need to be introduced. I n the presence of a perturbation, eq A1 becomes
+
i
iic
field of all the nuclei plus the perturbation. I n the vicinity of the nucleus N the Hamiltonian is approximately "(A)
=
-'/zV'(I)
i
