Vibrations, normal modes valence

This type of representation of the potential energy in terms of the internal (valence) degrees of freedom is called a Valence Force Field. Valence force fields have long been used in vibrational spectroscopy in order to carry out normal mode analysis[j ]. Basically what the terms in equation (2) express are the energies required to deform each internal coordinate from some unperturbed... 

Force Constants of Acetylene. From the vibrational frequencies of the normal modes, one can calculate the force constants for the different bond stretches and angle bends in the C2H2 molecule. In the most complete valence-bond, harmonic-oscillator approximation, the potential energy for C2H2 can be written as ... 

Figure 3-18. Dynamical data for the perfect chain of HCI and DCI based on a valence force field, (a) Dispersion eurves (b) k = 0 normal modes (c) densities of vibrational states.

In collaboration with experimental groups, we have recently studied some chlorinated-benzene crystals, 1,2,4,5-tetrachlorobenzene (TCB) [59] and 1,4-dichlorobenzene (DCB) [60], as well as solid tetracyanoethene (TCNE) [58]. In these studies we have used empirical atom-atom potentials, of exp-6 type [see Eq. (6)], which we have supplemented with the Coulomb interactions between fractional atomic charges. Lattice dynamics calculations have been performed by the harmonic method, with inclusion of intramolecular vibrations [70], see Eqs. (17) to (24). The normal modes of the free molecules have been calculated from empirical Valence Force Fields, using the standard CF-matrix method [101, 102]. The results of these calculations are used here to illustrate some phenomena occurring in more complex molecular crystals. These phenomena are well known the numerical results show their quantitative importance, in some specific systems. 

Vibrational data are available from normal mode analysis of vibrational spectra, in particular from the symmetric stretching modes that employ valence force fields. For naphthalene, we obtain= 3.81 X10 kJ mol" Using the same averaging manner, we can estimate the average bond length... 

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