Hydrogen bonding adiabatic representation

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. 

In contrast to the subsystem representation, the adiabatic basis depends on the environmental coordinates. As such, one obtains a physically intuitive description in terms of classical trajectories along Born-Oppenheimer surfaces. A variety of systems have been studied using QCL dynamics in this basis. These include the reaction rate and the kinetic isotope effect of proton transfer in a polar condensed phase solvent and a cluster [29-33], vibrational energy relaxation of a hydrogen bonded complex in a polar liquid [34], photodissociation of F2 [35], dynamical analysis of vibrational frequency shifts in a Xe fluid [36], and the spin-boson model [37,38], which is of particular importance as exact quantum results are available for comparison. 

In contrast, there will be many cases where continuum solvent models are less useful. These include situations where one of the goals of the simulation is to obtain a detailed picture of solvent structure, or where there is evidence that a particular structural feature of the solvent is playing a key role (for example, a specific water-macromolecule hydrogen bond). In these situations, however, explicit representation of some water combined with implicit solvation may suffice. Another example is when molecular dynamics simulations are used to study kinetic, or time-dependent phenomena. The absence of the frictional effects of solvent will lead to overestimation of rates. In addition, more subtle time-dependent effects arising from the solvent will be missing from continuum models. Continuum solvent models are in effect frilly adiabatic, in the sense that for any instantaneous macromolecular conformation, the solvent is taken to be completely relaxed. For electrostatic effects, this implies instantaneous dielectric and ionic double layer relaxation rates, and for the hydrophobic effect, instantaneous structural rearrangement. An exception would be dielectric models that involve a frequency-dependent dielectric. Nevertheless, continuum solvent models should be used with caution in studying the time dependence of macromolecular processes. 

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