Anharmonicity constants, hydrogen bonds

Figure 2. Extraction of anharmonicity constants ojexe from the comparison of fundamental OH stretching spectra (center) with overtone spectra (top) and OD spectra (bottom) for the case of jet cooled trifluoroethanol (M) and its most stable dimer conformation, which features a hydrogen bond donor stretching band (Dd) and an acceptor stretching band (Da). The deuteration analysis yields slightly different constants than the overtone approach and underestimates the hydrogen bond effect on donor stretching modes [89].

TABLE 2.6. Anharmonicity and Coupling Constants of Hydrogen-bonded X-H Groups... 

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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