Vibrational force field

Rauhut, G., Pulay, P., 1995, Transferable Scaling Factors for Density Functional Derived Vibrational Force Fields , J. Phys. Chem., 99, 3093. 

Conformation of a System of Three Linked Peptide Units. Biopol. 6, 1425-1436. von Carlowitz, S., H. Oberhammer, H. Willner, and J. E. Boggs. 1986. Structural Determination of a Recalcitrant Molecule (S2F4). J. Mol. Struct. 100,161-177. von Carlowitz, S., W. Zeil, P. Pulay, and J. E. Boggs. 1982. The Molecular Structure, Vibrational Force Field, Spectral Frequencies, and Infrared Intensities of CH3POF2. J. Mol. Struct. (Theochem) 87, 113-124. 

FIGURE 1. Number of publications (per year) relating to force fields and dealing with amines, nitro or nitroso compounds, during the years 1968-1994. Most of the works, prior to 1975, are connected with vibrational force fields... 

As will be shown further on, the most interesting isotope effects are quantum effects. Since the most important quantized motions in molecules are vibrations it makes sense that isotope effects yield information about the isotope independent surface (the vibrational force field) on which these quantized motions take place. 

This model has the advantage that the atomic polar tensor elements can be determined at the equilibrium geometry from a single molecular orbital calculation. Coupled with a set of trajectories (3R /3G)o obtained from a normal coordinate analysis, the IR and VCD intensities of all the normal modes of a molecule can be obtained in one calculation. In contrast, the other MO models require a separate MO calculation for each normal mode, since the (3p,/3G)o contributions for each unit are determined by finite displacement of the molecule along each normal coordinate. Both the APT and FPC models are useful in readily assessing how changes in geometry or refinements in the vibrational force field affect the frequencies and intensities of all the vibrational modes of a molecule. 

In the case of cyclopropane, the vibrational force field and infrared intensities have been examined in some detail both experimentally and via calculation. One of the more interesting observations is that the dipole moment derivatives for the C-H stretching modes are relatively small (corresponding to their low intensities). There is a relationship between the derivatives and the bond dipoles The low value for cyclopropane is a reflection of the smaller than normal electron population at its hydrogens (Table 3). 

A. Allouche and J. Pourcin, Spectrchim. Acta, 49A, 571 (1993). Ab Initio Calculation of Vibrational Force Fields Determination of Non-Redundant Symmetry Coordinates by Least-Square Component Analysis. 

The vibrational spectrum of a molecule is determined by its three-dimensional structure and its vibrational force field. An analysis of this [usually infrared (IR) and Raman] spectrum can therefore provide information on the structure and on intramolecular and intermolecular interactions. The more probing the analysis, the more detailed is the information that can be obtained. 

Bands are observed in the IR and Raman spectra of a molecule that correspond to normal modes of vibration of that particular structure. These normal modes can be calculated from knowledge of the three-dimensional structure of the molecule and of its vibrational force field. If a reliable force field is available, it is therefore possible to predict the vibrational frequencies of a known or hypothesized structure, and to draw significant structural conclusions on the basis of comparisons with observed IR and Raman bands. 

P.W. LoefTen, R.F. Pettifer, F. Fillaux G.J. Kearley (1995). J. Chem. Phys., 103, 8444—8455. Vibrational force field of solid imidazole from inelastic neutron scattering. 

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