Frequencies and Force Constants

Species ) Quantity Anharmonic value Corrected (harmonic) value ) 

All data refer to CCI4 as solvent unless stated otherwise. 

8) Anharmonic parameters from (27) harmonic parameters evaluated for these using the corrections of (56). 

1 ) These data refer to hydrocarbon solution, in which frequencies are (27) 2134.0 (vi), 2000.8 (fa), 2079.0 (vg), 2050.0 (ris). The effects of solvent shift are clearly far smaller than those of the approximations under discussion. 

The energy factored force field for carbonyls contains interaction parameters as well as stretching parameters. Such parameters are invariably required to be positive, for CO groups attached to the same metal, by the experimental finding that symmetric combinations of the individual CO vibrations occur at higher frequencies than similar antisymmetric combinations. 

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Schultz H, Lehmann H, Rein M, Hanack M (1991) Phthalocyaninatometal and Related Complexes with Special Electrical and Optical Properties. 74 41-146 Schutte CJH (1971) The Ab-Initio Calculation of Molecular Vibrational Frequencies and Force Constants. 9 213-263... 

Table 2.10 Vibrational Stretching Frequencies and Force Constants...

Schutte, C.J.H. The Ab-Initio Calculation of Molecular Vibrational Frequencies and Force Constants. Vol. 9, pp. 213—263. 

Our development has assumed temperature independent force constants. In real liquids, however, there is a small temperature dependence of frequencies and force constants due to anharmonicities, lattice expansion, etc. The incorporation of these effects into the theory is treated in later sections. 

Stretching frequencies and force constants for the M=P bond have been derived from Raman spectroscopic data for compounds [(N3N)Mo=P] (4a) and [(N3N)W=P] (4b), as well as for related nitrido and arsenido complexes [30]. For W=E (E = N, P, As), force constants were shown to decrease with increasing M=E bond length, while for each respective pnicogenido ligand E, the force constant for the W complex was greater than that of the Mo complex, a trend also reflected in literature data for transition metal nitrido and 0X0 complexes [20]. 

Molecular electronic spectroscopy can provide information on vibrational parameters (frequencies and force constants), rotational parameters (moments of inertia and therefore molecular geometries), electronic excitation energies, ionization potentials, and dissociation energies for ground and excited electronic states. Moreover, a knowledge of excited electronic states is important in understanding the course of photochemically induced reactions. 

The vibrational overlap integrals play a key role in electron transfer. A region of vibrational overlap defines values of the normal coordinate where a finite probability exists for finding coordinates appropriate for both reactants and products. The greater the overlap, the greater the transition rate. The vibrational overlap integrals can be evaluated explicitly for harmonic oscillator wavefunctions. An example is shown in equation (26) for the overlap between an initial level with vibrational quantum number v = 0 to a level v = v where the frequency (and force constant) are taken to be the same before and after electron transfer. 

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.

Vibrational Frequencies and Force Constants for the Triatomic Halogen Cations... 

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