Vibrational frequency, 367 Table

The changes in geometry (Table 1) and vibrational frequencies (Table 2) of 1 (A = C), as well as the differences in relative energies (Table 3) of isomers 2 and 3 with an increase in the quality of the theoretical method, emphasize the importance of electron correlation and basis set. Although the geometry of the CHj fragment does... 

The vibrational spectra of all of the known actinide element hexafluorides can be interpreted on the basis of the structure of a regular octahedron. Malm et al. (56) have measured the infrared spectra of NpF and PuFe and have deduced the fundamental vibration frequencies (Table VI). 

Certain difficulties arise when using water as a solvent in infrared spectroscopy. The infrared modes of water are very intense and may overlap with the sample modes of interest. This problem may be overcome by substituting water with deuterium oxide (D2O), The infrared modes of D2O occur at different frequencies to those observed for water because of the mass dependence of the vibrational frequency. Table 3.2b lists the characteristic bands observed for both H2O and D2O. 

Anion 3 has longer C=0 and P=0 bonds than the neutral compounds 2,4, and 5. This is reflected in the lower vibrational frequencies (Table 2), and is accompanied by minor shortening of the C—P bond in anion 3. 

The vibrational spectra of alkali fluorometallates have been examined in considerable detail. In the hexafluorometallates Li2ZrFe and M2MF6 (M = Rb or Cs M = Zr or Hf) the octahedral [MFe] " anion occupies a site of Dsd symmetry, and consequently the triply degenerate normal modes [V3 V4 V5 (f2g) and (t2u) in Oh] are split into a and e components. Vibrational frequencies (Table 19) have been assigned on the basis of polarized Raman and polarized IR reflectance spectra of single crystals, and assignments have been confirmed by normal coordinate analyses. 

The valence and symmetry force constants of benzene calculated using density functional theory were first reported by us [10c,d]. These results are summarized in this section. We discuss the vibrational frequencies (Table 5), isotopic shifts, and absorption intensities (Table 6). Selected force constants in symmetry-coordinate representations are listed and compared to the fields due to the Pulay [10b] et al. as well as OG [10a] in Table 7. 

Molecular descriptors must then be computed. Any numerical value that describes the molecule could be used. Many descriptors are obtained from molecular mechanics or semiempirical calculations. Energies, population analysis, and vibrational frequency analysis with its associated thermodynamic quantities are often obtained this way. Ah initio results can be used reliably, but are often avoided due to the large amount of computation necessary. The largest percentage of descriptors are easily determined values, such as molecular weights, topological indexes, moments of inertia, and so on. Table 30.1 lists some of the descriptors that have been found to be useful in previous studies. These are discussed in more detail in the review articles listed in the bibliography. 

The vibration frequencies of C-H bond are noticeably higher for gaseous thiazole than for its dilute solutions in carbon tetrachloride or tor liquid samples (Table 1-27). The molar extinction coefficient and especially the integrated intensity of the same peaks decrease dramatically with dilution (203). Inversely, the y(C(2jH) and y(C(5(H) frequencies are lower for gaseous thiazole than for its solutions, and still lower than for liquid samples (cf. Table 1-27). 

Finally, the S(CH) bending frequencies are practically independant of the physical state of the sample as are the nuclear vibration modes (Table 1-27). 

Table 1-28 lists the mean vibration frequencies characteristic of CH bonds (t/CH, 5CH, yCH) as a function of the substitution pattern. For the v(CH) vibrations, the highest frequency peak disappears in the spectra of 5-substituted derivatives, whereas it is unchanged by substitution at the 2-or 4-positions. This band has been assigned to the v(CH) vibration connected with the CH bond at the 5-position (173). 

The skeleton vibrations. C3NSX, CjNSXj. C NSXY, or C NSXj (where X or Y is the monoatomic substituent or the atom of the substituent which is bonded to the ring for polyatomic substituents), have been classified into suites, numbered I to X. A suite is a set of absorption bands or diffusion lines assigned, to a first approximation, to a same mode of vibration for the different molecules. Suites I to VIII concern bands assigned to A symmetry vibrations, while suites IX and X describe bands assigned to A" symmetry vibrations. For each of these suites, the analysis of the various published works gives the limits of the observed frequencies (Table 1-29). 

Table 20 Fundamental Vibrational Frequencies (in cm of Parent Heterocycles...

A kinetic isotope effect that is a result of the breaking of the bond to the isotopic atom is called a primary kinetic isotope effect. Equation (6-88) is, therefore, a very simple and approximate relationship for the maximum primary kinetic isotope effect in a reaction in which only bond cleavage occurs. Table 6-5 shows the results obtained when typical vibrational frequencies are used in Eq. (6-88). Evidently the maximum isotope effect is predicted to be very substantial. 

The HF vibrational frequencies are too high by about 7% relative to the experimental harmonic values, and by 10-13% relative to the anharmonic values. This overestimation is due to the incorrect dissociation and the corresponding bond lengths being too short (Table 11.1), and is consequently quite general. Vibrational frequencies at the HF level are therefore often scaled by 0.9 to partly compensate for these systematic errors. 

Inclusion of electron correlation normally lowers the force constants, since the correlation energy increases as a function of bond length. This usually means that vibrational frequencies decrease, although there are exceptions (vibrational frequencies also depend on off-diagonal force constants). The values calculated at the MP2 and CCSD(T) levels are shown in Tables 11.14 and 11.15. 

The effect of core-electron correlation is small, as shown in Table 11.16. It should be noted that the valence and core correlation energy per electron pair is of the same magnitude, however, the core correlation is almost constant over the whole energy surface and consequently contributes very little to properties depending on relative energies, like vibrational frequencies. It should be noted that relativistic corrections for the frequencies are expected to be of the order of 1 cm" or less. ... 

Table 1.4 Vibrational frequencies in MXjj species (cm ) (M = Ru, Os X = halogen)...

Many of the compounds in higher oxidation states are reactive, and for moisture-sensitive solids that cannot be crystallized, some of the bond lengths quoted in Table 2.1 are from EXAFS measurements [24], Raman spectroscopy is likewise well suited to studying such reactive compounds, and vibrational data for halometallates are given in Table 2.2 trends illustrated include the decrease in frequency as the oxidation state of the metal decreases, and similarly a decrease in vibrational frequency, for a given oxidation state, with increasing mass of the halogen. 

They have square planar structures corresponding bond lengths and vibrational frequencies are given in Table 3.3. 

Table 10.2 Fundamental vibrational frequencies of some common molecules.

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