Perturbation theory. A comparison with results obtained in the Heitler-London approximation

5 Perturbation theory. A comparison with results obtained in the Heitler London approximation 

If the modulus of the matrix elements (/)2 (s)(k), / g is small compared with the quantities SM(/) — i M(s), tken eclns (3-115) can be solved by taking an expansion in terms of a small matrix T)(1) (2)(k). For simplicity, we consider here the case when the matrices and /X2)(kj are real and equal. In this 

Substituting the quantities (3.124) into eqns (3.123) for f g and comparing expressions of the same order in the expansion parameter we obtain 

Now we substitute the expressions (3.124) and (3.125) into eqns (3.123) putting f = h and thus obtain the energy correction as 

We now compare this expression for the energy (k) with the corresponding expression obtained in the Heitler-London approximation. We have in mind the result by Craig (12) (13)  

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