Intermonomer Correlation Effect

The idea of correlating momentary multipoles stands behind the customary modeling of dispersion interaction in the form of a multipole expansion, including dipole-dipole (D-D), dipole-quadrupole (D-Q), quadrupole-quadrupole (Q-Q), and so on, terms. We owe the earliest variational treatments of this problem not only to Slater and Kirkwood [34], but also to Pauling and Beach [35], However, when the distance R decreases and reaches the Van der Waals minimum separation, the assumption that electrons of A and B never cross their trajectories in space becomes too crude. The calculation of the intermonomer electron 

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Note that Eq. (1-210) represents the only second-order non-additive polarization term. The remaining non-additive polarization terms are all of third-order at least, i.e., in Eq. (1-203) i + j + k>3. The three-body induction energy, E, is defined as that part of E that can be obtained by complete neglect of the intermonomer correlation effects. The difference represents all intermonomer corre-... 

The cornerstone of the strong anharmonic coupling theory relies on the assumption of a modulation of the fast mode frequency by the intermonomer distance. This behavior is correlated by many experimental observations, and it is undoubtly one of the main mechanisms that take place in a hydrogen bond. Because the intermonomer distance is, in the quantum model, represented by the dimensionless position coordinate Q of the slow mode, the effective angular frequency of the fast mode may be written [52,53]... 

Planck s constant as given in the appendix of Ch. 1, a value of 0.06 A is found for 8Qq. This value is not at all small and emphasizes the important geometrical consequence of the anharmonic modulation of the freqnency of by intermonomer modes (4). It gives a value of 0.017 A for 8Qq -8Qq (eq. (7.1)), a value close to 0.02 A, measured by electron diffraction. It shows that the theoretical description of the anharmonic coupling of and intermonomer modes of H-bonds, presented above, not only quite precisely reproduces spectra, but also reproduces such small geometrical effects, which are measured by completely independent methods. The experimentally verified correlation this theoretical description establishes between IR bandshapes and isotopic length variations 8Qq - 8Q° of H-bonds constitutes a strong snpport of its validity. Values of 8 - 5 can be in principle also measured by X-ray... 

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