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** Calculation of vibrational frequencies **

Theoretical prediction of vibrational frequencies serves as an aid to experiment for the characterization of chemical species. When experimental observation is difficult or impossible, theoretical approaches are able to offer useful information. The calculated vibrational frequencies can be used to verify whether a molecular structure is a genuine minimum, or is a transition state structure. The vibrational frequencies of a molecule are all real for a true minimum, and should have a single imaginary frequency for a saddle point. The characterization of transition state structures can only be achieved accurately by theoretical methods. [Pg.670]

Fig. 5.10. The theoretical calculation of the time trace of transient absorption (TRABS) for a one-mode system. The energy gap is 20 cm-1 and the vibrational mode is 420 cm-1. The dark curve is the reactant TRABS and the light-gray curve is the product TRABS. The probing frequency is set at respective peak positions of the induced absorption spectra of both reactant state and product state. For discussion see text. |

Theoretical Calculations. The vibrational frequencies and infrared and Raman intensities can be calculated for benzene using programs such as Gaussian/Gaussview and HyperChem. These programs also permit animated visualization of the normal modes such as the symmetric CC and CH stretches studied in this experiment. [Pg.414]

From the theoretical point of view the work of Leszczynski and collaborators159, should be mentioned, where the calculated harmonic vibrational frequencies of thioformaldehyde were compared with those of formaldehyde and selenoformaldehyde. The largest discrepancy (120 cm-1) between calculated and experimental vibrational frequencies was found for the aforementioned CH2 in-plane deformation. [Pg.1393]

The H local vibrational mode at 3096 cm has been assigned to N-H centers. This assignment is consistent with a recent theoretical investigation by Van de Walle who calculated a vibrational frequency of approximately 3100 cm for the N-H center. It is interesting to note that this frequency deviates by about 10 % from the value observed for the N-H vibration in ammonia molecules. [Pg.149]

The theoretical basis for a full valence force field treatment of extended lattices lies with the work of Kleinman and Spitzer published in 1962. ° These authors, who developed their force field to calculate the vibrational frequencies of quartz, felt that the most accurate way to represent the vibrational motion in a quartz crystal was to include the relative motion of oxygen and silicon atoms. The valence force field was the most effective method for treating this localized picture. [Pg.130]

No characteristic IR data were reported for pyrrolizines or dihydropyrrolizines. An almost complete set of vibrational frequencies was deduced by combining an infrared (IR) and a Raman spectrum of pyrrolizinone 2 <2001J(P2)2195>. The experimental values thus obtained were used to scale the theoretical complete set of vibrational frequencies of 2. Using the same scaling constant, the authors proposed a set of calculated vibrational frequencies for dihydropyrrolizinone 3. [Pg.6]

This review has summarize the applications of neutron inelastic scattering to the study of pol3uners. The technique has proven useful for measuring and characterizii low-frequency intramolecular and inter-molecular vibrations, particularly for three systems, such as polyethylene and the n-paraffins, for which theoretical calculations of phase-frequency relations are available. More calculations of this type, and extension of them to include the effects of departures of chain conformations from their ideal transplanar or helical configurations, are needed for an optimum application of the method. [Pg.25]

Figure 15 Tj (p, T) vs. temperature for the solvent carbon dioxide at the critical density and the theoretically calculated curve. The frequency u> and the hard sphere diameters are the same as those used in the fit of the 33°C data. The theory is scaled to match the data at 33°C and the critical density, 10.6 mol/L. Unlike ethane at the critical density, there is no inverted region, and the vibrational lifetime decreases nearly linearly with temperature. The theory does not quantitatively fit the data, but it does show the correct general behavior. Most importantly, the hydrodynamic/thermodynamic theory shows the existence of the inverted region in ethane and the lack of one in carbon dioxide. |

Similar sorts of conclusions apply to the frequencies. A systematic study " found that a DZP basis set yields vibrational frequencies within about 9% of experimental (harmonic) values. The discrepancy diminishes to 4% when correlation is included via CISD and to 2% with a coupled cluster treatment. Another set of calculations confirmed the eost-effec-tiveness of the MP2 treatment of vibrational frequencies, indicating better agreement with experiment than MP3 on some oceasions. Certain types of modes can be more sensitive to the level of theoretical treatment than others. For example, out-of-plane bending motions for it-bonded systems can require triple- plus two sets of polarization functions, as well as a set of/-functions in the basis set . [Pg.143]

The entropy difference A5tot between the HS and the LS states of an iron(II) SCO complex is the driving force for thermally induced spin transition [97], About one quarter of AStot is due to the multiplicity of the HS state, whereas the remaining three quarters are due to a shift of vibrational frequencies upon SCO. The part that arises from the spin multiplicity can easily be calculated. However, the vibrational contribution AS ib is less readily accessible, either experimentally or theoretically, because the vibrational spectrum of a SCO complex, such as [Fe(phen)2(NCS)2] (with 147 normal modes for the free molecule) is rather complex. Therefore, a reasonably complete assignment of modes can be achieved only by a combination of complementary spectroscopic techniques in conjunction with appropriate calculations. [Pg.526]

** Calculation of vibrational frequencies **

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