Intermonomer

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]... 

The general potential U (8) has not been used before 1999 [52] because its numerical matrix representation requires huge basis sets, incompatible with the common computers. In order to avoid this situation, an approximation has been undertaken in previous studies the adiabatic approximation [54,55], Following an idea of Stepanov [56], Marechal and Witkowski assumed that the fast mode follows adiabatically the slow intermonomer motions, just as the electrons are assumed to follow adiabatically the motions of the nuclei in a molecule. It has been shown [57] that the adiabatic approximation is only suitable for very weak hydrogen bonds, as discussed in the next section. 

The damped effective Hamiltonian l holds for a single excitation of the fast mode and involves, according to some unitary transformations, a driven term that describes the intermonomer motion. Within the sub-base (89b), it may be given by... 

While most CA s of disaccharides have depended only on intrinsic characteristics of the molecule, experimental results depend strongly on the environment. By experiment, Kamide and Saito ( ) have shown that the degree of flexibility of cellulose and its derivatives is strongly dependent on the dielectric constant of the solvent as well as the exact type and degree of substitution. Since a substantial portion of the polymer flexibility depends on the extent of variability of the torsion angles at the intermonomer linkage, the dependence of polymer flexibility on type of solvent and substitution means that the disaccharide flexibility also should depend on those factors. Non-polar solvents allowed the molecules to have greater flexibility than did polar solvents (35). 

Twenty-three years have elapsed since the American Chemical Society published a book devoted to papers from a symposium exclusively about lignin. In the preface to Lignin Structure and Reactions (Advances in Chemistry Series 59, 1966), the symposium chairperson remarked that the current presentation of lignin structure is oversimplified.. . . more ingenious work is needed to establish the sequence of units—the most prominent singular task of future lignin research. Presumably, the author of these words had in mind the sequence of intermonomer linkages rather than the units themselves (which differ only in their aromatic methoxyl substitution pattern), and from this perspective his observation could be as true in 1989 as it was in 1966. 

In the second, some intermonomer spin fluctuation is introduced by combining two n.n. triplets into a singlet the corresponding operator is... 

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 dispersion nonadditivity Eib arises from the coupling of intermonomer pah-correlations in subsystems XY and YZ via the intermolecular interaction operator Vzx. This contribution can be expressed as a generalized Casimir-Polder formula,... 

II. C.3). Implicitly, the intermonomer coupling within a chain is therefore taken to be only a perturbation of the monomer electronic structure. 

The details of SAPT are beyond the scope of the present work. For our purposes it is enough to say that the fundamental components of the interaction energy are ordinarily expanded in terms of two perturbations the intermonomer interaction operator and the intramonomer electron correlation operator. Such a treatment provides us with fundamental components in the form of a double perturbation series, which should be judiciously limited to some low order, which produces a compromise between efficiency and accuracy. The most important corrections for two- and three-body terms in the interaction energy are described in Table 1. The SAPT corrections are directly related to the interaction energy evaluated by the supermolecular approach, Eq.(2), provided that many body perturbation theory (MBPT) is used [19,28]. Assignment of different perturbation and supermolecular energies is shown in Table 1. The power of this approach is its open-ended character. One can thoroughly analyse the role of individual corrections and evaluate them with carefully controlled effort and desired... 

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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