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Additional info for Advances in Chemical Physics: Intermolecular Forces, Volume 12
In practical calculations, the ijj would be taken as a finite truncated set; the larger the set, the smaller the truncation errors. As Murrell, RandiC, and Williams70 point out, in such a truncated set it is frequently advisable to include ionic terms in the set of since the wave function in the intermediate region is likely to have a substantial ionic character, as will be discussed in Section VII and in the following treatment of charge transfer interactions. The problem now is to approximate the “second-order’’ term, €(’), 48 J.
D. The Second-Order Energy. The second-order energy for resonant interactions of two like atoms has the same form as for nonresonant interactions (since the cross terms vanish because of selection rules). However, the induction energy is given by 42 J. 0. HIRSCHFELDER AND W. J. MEATH and the dispersion energy is given by e. Resonance within One Molecule. Some atoms or molecules have degenerate states which are separated by the perturbation produced by a second different molecule. In such cases, there is a possiblity of resonance.
11). 40108 a. 60 co E'F:) E'(V,. 0 (ref. 7 (ref. 2 (ref. 29b). fully minimized and hence the close agreement between the nonadiabatic and experimental dissociation energies may be fortuitous. These calculations show that the Born-Oppenheimer approximation is excellent and the deviations from it are small even for H, (at least for the ground state, see subsection 2 below). For molecules with nuclei of greater mass, the Born-Oppenheimer approximation should be even more accurate. 24 J. 0. HIRSCHFELDER AND W.