Electrostatic Hellmann—Feynman Theorem Applied to the Long-Range Interaction of Two Hydrogen Atoms

The electrostatic Hellmann—Feynman theorem is used to calculate exactly the leading term in the 1/R expansion of the force of interaction between two well-separated hydrogen atoms, −6 C6/R7. The exact wavefunction can be expanded in the series ∑ n=0∞ψnR−n.The expectation value of the approximate wavefunction ψ0+ψ3 gives the exact value of C6/R6. However, with the use of the electrostatic Hellmann—Feynman theorem it is necessary to know ψ0, ψ3, ψ4, and that part of ψ7 which has the same angular dependence as the electron coordinate za1 in order to determine −6C6/R7. Only 7% is contributed by ψ3 and ψ4; the other 93% is due to the ψ7. The relevant part of ψ7 is determined as the solution to a mixed second-order perturbation equation (first order with respect to each of two perturbations).