Generalized valence force field

Force constants of have been calculated from the data in Table 2 using the general valence force field (GVFF) [148, 149] as well as the Urey-Bradley force field [80] (UBFF) although there is insufficient data to evaluate all the interaction constants since no isotopomers of Se have been measured by vibrational spectroscopy. The stretching and bond interaction force constants were reported as/r = 2.24 andf = 0.53 N cm, respectively [149]. However, because of the uncertainty regarding the Am mode of Se the published force constants [80, 148, 149] maybe unreliable. 

The potential energy expressions used for force field calculations are all descendants of three basic types originating from vibrational spectroscopy (5) the generalized valence force field (GVFF), the central force field, and the Urey-Bradley force field. General formulations for the relative potential energy V in these three force fields are the following ... 

Let us consider the description of a simple three-atom molecule by the three most frequently used spectroscopic parameterization schemes, the general central force field (GCF), the general valence force field (GVF) and the Urey-Bradley force field (UBF Fig. 2.14). 

In the general valence force field (GVFF), all // constants are taken into account. To n normal vibrations of the same symmetry correspond n stretching or deformation constants and ( -l)/2 interaction constants. The GVFF is the most appropriate potential function from a chemical point of view. However, for a few small molecules all force constants of the GVFF have been calculated reliably, since with decreasing symmetry and with increasing molecular size the number of force constants by far exceeds the number of frequencies. Restrictions to the potential function have therefore been recommended for many problems. 

Infrared spectra are potentially a very useful source of information on cis and trans effects. The frequency of a vibration is determined by the kinetic and potential energies of the nuclei involved (theoretically the whole complex, since all vibrations will couple to a certain extent) and the observed frequencies can be analyzed in terms of a generalized valence force field or some more approximate model to eliminate the kinetic energy and yield force constants (for stretching, bending, twisting, etc.) and interaction constants l iO)... 

At normal temperatures the lattice dynamics involves predominantly low amplitude atomic motions that are well described in a harmonic approximation. Therefore, potential models widely used in the theory of molecular vibration, such as a generalized valence force field (GVFF) model, may be of use for such studies. In a GVFF the potential energy of a system is described with a set... 

FTIR spectra were recorded using a Bruker 113V Fourier transform interferometer. Frequencies are accurate to 1 crn k Solid samples were studied as Nujol mulls (Nujol was previously dried on sodium wire and bubbled with argon). Structural parameters and initial force field were taken from literature [3] and the program used to calculate the generalized valence force field was similar to Schachtschneider s one. [4]... 

A general valence force field for the in-plane motions of N2H2 has been determined from a total of 24 vibrational frequencies of HNNH, HNND, DNND, and the 15N-substituted counterparts.62 The Raman spectra of polycrystalline CH3N=NCH3 and CD3N=NCD3 have been examined at liquid-nitrogen temperatures and a force field has been computed.63... 

Many such model force fields have been discussed in the literature. [For general discussions, see Herzberg (1945), Wilson et al. (1955), Woodward (1972), and Califano (1976). For discussions of the Urey-Bradley force field, see the review by Duncan (1975). For discussions of the entirely different consistent force field approach, see Lifson and Warshel (1968), Warshel et al. (1970), and Burkert and Allinger (1982).] We have chosen to use a simplified general valence force field (SGVFF), which has been defined as one which contains the minimum possible number of interaction constants compatible with a good fit of the spectra (Califano, 1976). Such a force field has been demonstrated to be very effective for hydrocarbons (Schachtschneider and Snyder, 1963). For this form the potential energy of Eq. (63) is written explicitly as... 

C. E. Bloni, L. P. Otto, and C. Altona, Mol. Phys., 32, 1137 (1976). Application of Self-Consistent-Field Ab Initio Calculations to Organic Molecules. III. Equilibrium Structure of Water, Methanol and Dimethylether, General Valence Force Field of Water and Methanol Scaled on Experimental Frequencies. 

Comparing Eqs. 1.154 and 1.149, we obtain the following relations between the force constants of the generalized valence force field and those of the Urey-Bradley force field ... 

If the force constants in terms of the generalized valence force field are selected... 

DFT, density functional theory NCA, normal coordinate analysis GVF, generalized valence force field UBF, Urey-Bradley force field. 

CVF, generalized valence force field UBF, Urey-Bradley force field. 

Si,V] MCM-41 mesoporous MCM-41 material containing both silicon and vanadium in the walls of the pores [350,351] cf. footnote SGVFF simplified generalized valence force field... 

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