Force constants hydrogen-bond bending

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. 

In addition to k values, force constants (Table 6) for the hydrogen bond bending have been calculated from root-mean square angles from hyperfine interactions, using a triatomic model ... 

All of the discussion so far has applied to isolated dimers. Observations made about O H-O hydrogen bonds in the solid state can, however, be rationalised on the basis of the rules given above for angular geometries and the relative magnitudes of the force constants associated with bending the hydrogen bond in two ways. 

The oscillation amplitudes and of ° of HBr and DBr, the hydrogen bromide oscillation force constants and the hydrogen-bond bending wave numbers Vb for HC H(D) r. 

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). 

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.

---