Frequencies and Vibrational Spectra

The calculation of normal-mode frequencies (Section 2.5) is important because  

The frequencies must be calculated to get the zero point energy of the molecule. This is needed for accurate energy comparisons (Section 2.5). 

The normal-mode vibrational frequencies of a molecule correspond, with qualifications, to the bands seen in the infrared (IR) spectrum of the substance. Discrepancies may arise from overtone and combination bands in the experimental IR, and from problems in accurate calculation of relative intensities (less so, probably, from problems in calculation of frequency positions). Thus the IR spectrum of a substance that has never been made can be calculated to serve as a guide for the experimentalist. Unidentified IR bands observed in an experiment can sometimes be assigned to a particular substance on the basis of the calculated spectrum of a suspect if the spectra of the usual suspects are not available from experiment (they might be extremely reactive, transient species), we can calculate them. 

The characterization of stationary points by the number of imaginary frequencies was discussed in Chapter 2, and zero-point energies in Chapter 2 and earlier sections of this chapter. Here we will examine the utility of ab initio calculations for the prediction of IR spectra [235]. It is important to remember that frequencies should be calculated at the same level (e.g. HF/3-210, MP2/6-31G, . ..) as was used for the geometry optimization (Section 2.4). This is because accurate calculation of the curvature of the PES at a stationary point requires that the second derivatives d2E/dqidqjbe found at the same level as was used to create the surface on which the point sits. 

The principle of equating a second derivative with a stretching or bending force constant is not exactly correct. A second derivative d2E/ dq1 would be strictly equal to a force constant only if the energy were a quadratic function of the geometry, i.e. if a graph of E versus q were a parabola. However vibrational curves are not exactly parabolas (Fig. 5.32). For a parabolic Elq relationship, and considering a diatomic molecule for simplicity, we would have  

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A chart for vibration diagnosis is presented in Table 19-9. While this is a general criterion or rough guideline for diagnosis of mechanical problems, it can be developed into a very powerful diagnostic system when specific problems and their associated frequency domain vibration spectra are... 

See introductory remarks in Section I.A.4 of Chapter 7. The IR vibration frequencies of compounds MH4 and MeMH3 were calculated ab initio for the metallic elements of group 14, including M = Sn, and compared with experimental data from various sources105. Many parameters pertaining to rotational and vibrational spectra of compounds... 

Pure rotational spectra only appear for molecules with permanent dipole moments and vibrational spectra require a change of dipole during the motion. However, electronic spectra are observed for all molecules, and changes in the electron distribution in a molecule are always accompanied by dipole changes. As a result even homonuclear molecules (H2 or N2) which have no rotation or vibration spectra, do give electronic spectra with vibrational and rotational structure from which rotational constants and bond vibration frequencies may be derived. 

The physical and spectroscopic properties of a spin-equilibrium complex can appear to be either the average or the superposition of the properties of the separate spin states. Which occurs is dependent on the time scale of the observation relative to the relaxation time of the equilibrium. Thus the electronic and vibrational spectra always appear as a superposition of the two isomers because each spin state possesses a distinctive potential energy surface with its characteristic electronic and vibrational properties. On the other hand, the NMR spectra appear as the average of the spectra of the two spin states, for all but the slowest interconversions, because the frequency of the interconversion is high compared with the frequency differences of the chemical shifts or the inverse of the spin relaxation times of the two isomers. 

As a first test, geometries and vibrational spectra of known complexes such as Ni(C0)4, Fe(C0)5, Cr(C0)6 were optimized and their IR frequencies calculated. Table 1 reports the calculated CO and MC bond lengths and the vco ofNi(CO)5, Cr(C0)6 and Fe(CO)s in comparison with experimental data. 

Equilibrium configurations, total energies, heats of formation, the electronic structure, the self vibrations frequencies and IR spectra of the various possible types of T-junctions are computed by employing of PC Gamess version of semi-empirical PM3-method. The results of our calculations in whole are in a good agreement with published earlier the data of theoretical and experimental researches devoted to the studying of T-junctions. 

In the carbonate minerals, the C03 " group can be regarded as quite well isolated from the counterions, as evidenced by the independence of its properties [such as bond distance (Zemann, 1981), vibrational frequencies, and photoemission spectra] on the nature of the counterions. Thus,... 

Jakobsons, J., J. Gravitis, V. M. Andrianov, J. Dzehne, and V. G. Dashevsku. 1982. Calculation of frequencies of vibrational spectra of model lignin compounds by the method of atom-atom potential functions. I. Calculation of frequencies of the vibrational spectrum of an aromatic ring. Khim. Drev. 1982(5) 52-57. 

Correlations between the structures and vibrational spectra of finite polyphosphate chains have not been widely investigated. The spectra are complex owing to the presence of, and coupling between, bridging PO2 and terminal PO3 groups. As the chain length increases the PO2 group frequencies increase to approach those in catenaphosphates. 

In an Atomic Force Acoustic Microscopy set-up [3-5] either the sample is insonified or the cantilever suspension is excited at ultrasonic frequencies. The vibration spectra of the cantilever depend on the local sample stiffness and hence... 

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