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Extra info for ADVANCES IN CHEMICAL PHYSICS VOLUME 6
The same can probably be said for rotational motion, but the difference would be more difficult to compute. 111. INTERACTION OF SPECIES It is appropriate to introduce separations of motion into Eq. (3) if the solution of the equation is simplified thereby, or if more physically meaningful interpretations thus arise. 18 Also, as a result of the relative slowness or difficulty in the change of the electronic states of the molecules in “chemical’, collision, one may be able to separate the nuclear and electronic motions.
V= p c (82) It may then be shown using Eq. (81) that the upper limits for the ground and excited energies are given as the roots of the secular determinant : 1 HI1 Hzl - A1,E - AzlE ... Hlz - d1zE Hzz - AZZE ... * * * * * . H1m -AlmE Hzm - AemE ... I =o (83) A. Critical Exposition of the Semiempirical Method In developing a modified London formula for later use in the semiempirical method it is traditi0na127-~~ to follow a derivation, worked out by slate^-,^' of an approximate expression for the total energy, which looks in form exactly like the complementary formula for the interaction energy.
It has been notede2J2that a wave function of any desired accuracy with regard to electron correlation may be obtained by taking a sum of a large number of Slater determinants as a trial function in the variation scheme in accord with Eqs. (82), (83), and (84). Each Slater determinant is itself composed of independent one-electron wave functions, and explicit electron interaction is still avoided. Unfortunately, the convergence is slow, and a very large number of determinants may be required for experimental agreement.