The Treatment of Heitler and London

For very large values of rAB we know that in its normal state the system consists of two normal hydrogen atoms. Its wave functions (the state having two-fold degeneracy) are then Ui,x(l) Ui,s(2) and i,B(l) Wi ,(2) or any two independent linear combinations of these two (the wave function ul /((l) representing a hydrogenlike Is wave function for electron 1 about nucleus A, 

—Coordinates used for the hydrogen molecule, represented diagram- 

It is seen that A is the orthogonality integral introduced in Section 42a, and given by Equation 42-11. With Hi i = Hu and Hi H = Hi11, the equation can be immediately solved to give 

Ei is the function known as the integral logarithm.1 (The integral K was first evaluated by Sugiura, after Heitler and London had developed an approximate expression for it.) J represents the Coulomb interaction of an electron in a Is orbital on nucleus A with an electron in a Is orbital on nucleus B, and K is the corresponding resonance or exchange integral. 

It is seen that even this very simple treatment of the problem leads to results in approximate agreement with experiment. 

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