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Additional resources for Advances in Chemical Physics: Intermolecular Forces, Volume 12
VI. THE HELLMANN-FEYNMAN THEOREM Hellrnannlz3 and FeynmanlZ4have shown that (except for the small forces which arise from the deviations from the Born-Oppenheimer separation and magnetic or relativistic effects) the quantum mechanical forces on the nuclei of a molecule are just exactly the classical electrostatic coulombic forces which result from the charges on the nuclei interacting with the charge density of the electron cloud. Berlin"' dramatized this result by making a diagram showing the regions in which an increment of the electron cloud helps to draw the nuclei of a diatomic molecule together, in contrast to other regions where it would tend to pull the nuclei apart.
J. MEATH coupling schemes. Recently, a more extensive study of the problem has been made by Chang7“ who considered the intermediate coupling scheme and the effect of higher multipole interactions. As an example, consider the effect of fine-structure splitting on the quadrupole-quadrupole energy between two ground-state boron atoms. A probable correlation diagram’“ for the transition from (A,S) to (J,,,Ja) coupling is given in Figure 3. For very large separations, where DEGENERATE (A31 (J, , Jb 1’ Fig.
At large separation this state dissociates into a 1s hydrogen atom and a 2s hydrogen atom. Around R = I O U , , there is an almost crossing of potential curves with the second excited 'Z: state (which also has a double minimum). 4a0, the state ) ~ of H - . An open behaves like the interaction of H + with the ( 1 ~ state shell wave function including nine ionic terms and nine atomic terms was used for the calculation at the outer minimum. On the other hand, at smaller separations the state corresponds to a (lsa)(2sa)configuration.
Advances in Chemical Physics: Intermolecular Forces, Volume 12