Force constants hydrogen-bond stretching

Figure 5.4 Comparison of intermolecular stretching force constants hydrogen bond versus halogen bond.

Stretching, bond bending, torsions, electrostatic interactions, van der Waals forces, and hydrogen bonding. Force fields differ in the number of terms in the energy expression, the complexity of those terms, and the way in which the constants were obtained. Since electrons are not explicitly included, electronic processes cannot be modeled. 

Table 8. Vibrational frequencies and force constants for hydrogen bond stretching and bending. The Lennard-Jones 6/12 potential well depth parameter, E, is also given.

Here, Do represents the equilibrium dissociation energy and or is a parameter related to the vibrational force constant. Figure 3 provides a comparison of the two potential functions used to describe the carbon-hydrogen bond stretch based on the Dauber-Osguthorpe et al. (1988) forcefield parameters. Although both represent the equilibrium... 

Representative force constants (f) for stretching of chemical bonds sure listed in this table. Except where noted, all force constants are derived from values of the harmonic vibrational frequencies (0. Values derived from the observed vibration2il fundamentals v, which are noted by a, are lower than the harmonic force constants, typically by 2 to 3% in the case of heavy atoms (often by 5 to 10% if one of the atoms is hydrogen). Values are given in the SI unit newton per centimeter (N/cm), which is identical to the commonly used cgs unit mdyn/A. 

The inequality of the C—H bonds in the radical cation implies that all C—H bonds do not have the same force constants. In a simplistic approximation, the zero-point vibrational energy (ZPVE) of a C—H stretching vibration will be proportional to (k/mn), where k is the force constant of the C—H bond and j// is the mass of the hydrogen nucleus. The effect on the ZPVE of replacing one proton by a deuteron will hence depend on the deuteration site, such that the ZPVE will be lowered more if the deuteron occupies a site with a larger fcrce constant, i.e. a shorter bond. This, in general, means a site with low unpaired spin density. 

It has been known for a long time that amines which have a hydrogen on a carbon attached to the nitrogen so that the C—H bond is antiperiplanar to the lone pair, show abnormally low stretching frequencies for those C—H bonds. In order to reproduce this (Bohlmann) effect MM3 corrects the natural bond lengths and force constants of such C—H bonds by31 ... 

When the acidity or the basicity of the solute molecule is high enough to stretch the OH or OD bond to the point of rupture, then the molecule dissociates into ions in solution. Therefore the dissociation constants also serve as a measure of acidity or basicity of solute molecules, especially those which are subject to significant ionization. Since the coulombic forces causing repulsion of ions at membrane-solution interfaces extend to distances farther than those involved in the polar hydrogen bonding repulsions of nonionized solutes at such interfaces, one would expect that a dissociated molecule to be repelled and, in... 

To obtain the anharmonic terms in the potential, on the other hand, the choice of coordinates is important 130,131). The reason is that the anharmonic terms can only be obtained from a perturbation expansion on the harmonic results, and the convergence of this expansion differs considerably from one set of coordinates to another. In addition it is usually necessary to assume that some of the anharmonic interaction terms are zero and this is true only for certain classes of internal coordinates. For example, one can define an angle bend in HjO either by a rectilinear displacement of the hydrogen atoms or by a curvilinear displacement. At the harmonic level there is no difference between the two, but one can see that a rectilinear displacement introduces some stretching of the OH bonds whereas the curvilinear displacement does not. The curvilinear coordinate follows more closely the bottom of the potential well (Fig. 12) than the linear displacement and this manifests itself in rather small cubic stretch-bend interaction constants whereas these constants are larger for rectilinear coordinates. A final and important point about the choice of curvilinear coordinates is that they are geometrically defined (i.e. independent of nuclear masses) so that the resulting force constants do not depend on isotopic species. At the anharmonic level this is not true for rectilinear coordinates as it has been shown that the imposition of the Eckart conditions, that the internal coordinates shall introduce no overall translation or rotation of the body, forces them to have a small isotopic dependence 132). 

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