Vibrational force constants for

The infrared spectrum of gaseous HC1 (1H3SC1) shows the v = 0 to v = 1 transition at 2885 cm-1. Calculate the vibrational force constant for the HC1 molecule. 

The negative deviation for the methoxy derivative is also seen in a correlation of log Ki with the vibrational CO force constants obtained from IR measurements the more negative A5° values are further testimony to the deviant behavior of the methoxy derivative. Even though not stated in these terms by Fischer, the most plausible source of the deviations with Z = MeO is the strong 7r-donor effect of the methoxy group (63a) which leads to a substantial stabilization of the carbene complex. The reduced CO vibrational force constants for the methoxy derivative are consistent with this explanation. 

The broad line is easily explained because the width corresponds to a quadrupole coupling constant e qQfh = 88 kHz, which is consistent with the observed infrared vibrational frequency for D in a-Si H,D of 1460 cm . This consistency is obtained through the existence of an empirical scaling relation between the quadrupole coupling constants and the vibrational force constants for hydrogen-bonded systems (Leopold et al,... 

If one wishes to determine the vibrational force constants for a polyatomic molecule, isotopic substitutions are essential. Die general valence force field for a non-linear polyatomic molecule, expressed in internal coordinates, contains a total, of (3N-6)(5N-5) force constants. Some of these may equal others by the symmetry of the molecule, but a maximum of only (3N-6) vibration frequencies may be observed. 

The Raman and infrared spectra for C70 are much more complicated than for Cfio because of the lower symmetry and the large number of Raman-active modes (53) and infrared active modes (31) out of a total of 122 possible vibrational mode frequencies. Nevertheless, well-resolved infrared spectra [88, 103] and Raman spectra have been observed [95, 103, 104]. Using polarization studies and a force constant model calculation [103, 105], an attempt has been made to assign mode symmetries to all the intramolecular modes. Making use of a force constant model based on Ceo and a small perturbation to account for the weakening of the force constants for the belt atoms around the equator, reasonable consistency between the model calculation and the experimentally determined lattice modes [103, 105] has been achieved. 

Kaplan and Thornton (1967) used three different sets of vibrational frequencies to estimate the zero-point energies of the reactants and products of the equilibrium, which provided three different isotope exchange equilibrium constants 1-163, 1-311 and 1-050. The value 1-311 is considered to be most reasonable, whereas the others are rejected as unrealistic for the case in hand. Calculations using the complete theory led to values that varied from 1-086 to 1-774 for different sets of valence-force constants for the compounds involved. 

Changes in observed CH (CD) stretching frequencies on going from reactant to product are found to be too small and in the wrong direction to account for the observed kinetic isotope effect, and the effect is suggested to be due to increased force constants for lower frequency vibrations, such as for bending (Kaplan and Thornton, 1967). This is consistent with a steric explanation. 

According to Eq. (11), the force constant for the normal vibration Q, can be identified with the term in braces and can be negative if the second term, which is positive, exceeds the first term. If the force constant is negative, the energy should be lowered by the nuclear deformation Qi, and the second-order distortion from the symmetrical nuclear arrangement would occur spontaneously. 

The force constant for the vibrations, K = in the harmonic approximation is proportional to oP. Differentiating Equation 24.6 to obtain K and substituting into Equation 24.21, the result is [84,85]... 

The usefulness of quantum-chemical methods varies considerably depending on what sort of force field parameter is to be calculated (for a detailed discussion, see [46]). There are relatively few molecular properties which quantum chemistry can provide in such a way that they can be used directly and profitably in the construction of a force field. Quantum chemistry does very well for molecular bond lengths and bond angles. Even semiempirical methods can do a good job for standard organic molecules. However, in many cases, these are known with sufficient accuracy a C-C single bond is 1.53 A except under exotic circumstances. Similarly, vibrational force constants can often be transferred from similar molecules and need not be recalculated. 

For polyatomic molecules, the stretching force constant for a particular bond cannot in general be obtained in an unambiguous manner because any given vibrational mode generally involves movements of more than two of the atoms, which prevent the expression of the observed frequency in terms of the force constant for just one bond. The vibrational modes of a polyatomic molecule can be analyzed by a method known a normal coordinate analysis to... 

The summations in Eq. (8) and (9) usually extend over all internal parameters, independent and dependent, i.e. the potential constants in these expressions are also not all independent. For example, the nonsymmetric tetrasubstituted methane CRXR2R3R4 possesses five independent force constants for angle deformations at the central carbon atom, whereas in our calculations we sum over the potential energy contributions of the six different angles (only five are independent ) at this atom using six different potential constants for angle deformations. The calculation of the independent force constants, which is necessary for the evaluation of the vibrational frequencies, will be dealt with in Section 2.3. 

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