The kinetic energy change on covalent bond formation

Stimulated by an analysis of the classical molecular orbital and valence bond descriptions of the two-electron normal covalent bond (both faulty), the argument is made that there exist good representations of the kinetic energy change DeltaT, on nonpolar covalent bond formation in a diatomic molecule, of the form DeltaT(R) = integralF(R - r')S(r')dr'. Here F is a nonlinear response function which itself involves the overlap S. The kinetic change is known to satisfy the sum rule integral(0) (infinity)DeltaT(R)dR = Z(alpha)Z(beta) exactly; it is shown how this can be built into the treatment by the use of Fourier transform methods. Also considered is integral(0) (infinity)DeltaT(R)R(2)dR, which is an important additional property of the kinetic energy change. Representation of DeltaT(R) as a Morse function, already known to be highly accurate, is shown to exactly conform to the proposed form.