The Approximations Involved in Calculations of Atomic Interaction and Activation Energies

The assumptions underlying the computation of interaction energy among several atoms, and especially of activation energies, have been analyzed and discussed for the case of small overlapping of the one-electron wave functions involved. Some formal justification has been found for several types of approximation which have hitherto been used without adequate examination. Computations of the energy of several three-electron systems are presented as material illustrating the applicability of some of the assumpIions to typical cases. It is concluded that in general any modification of the complete Heitler-London treatment of the system may lead to errors comparable in magnitude to the quantity to be computed. The so-called "semi-empirical method," which involves many such modifications, owes its success to a happy cancellation of errors, and, until some theoretical explanation of this cancellation is found, it must assume the status and responsibilities of a purely empirical method.