Ab initio calculations of vibrational frequencies

P. Botschwina, in Structure and Dynamics of Weakly Bound Molecular Complexes. A. Weber, Ed., Reidel, Dordrecht, 1987, p. 181. Ab Initio Calculations of Vibrational Frequencies and Infrared Intensities for the Hydrogen-Bonded Complex HCN —HF. 

Once internal modes are defined, it is also possible to define the infrared intensity of these modes. For a normal mode, the infrared intensity is calculated with the help of the dipole moment derivatives. The dipole derivatives 3p/5x with regard to Cartesian coordinates can be determined in the course of an ab initio calculation of vibrational frequencies. The corresponding dipole derivatives with regard to normal coordinates are obtained by the transformation... 

Although the ab initio calculation of vibrational frequencies of molecular systems is a well-known practice, it is not so common in the case of crystalline systems. However, quantum-mechanical calculation of lattice vibrations and phonon spectra has become a subject of increasing interest and effective methods have been developed and implemented. In this respect, a recent review by Baroni et al. gives a detailed overview of the state of the art of ab initio calculation of vibrations and related properties for crystalline materials. Most of the current implementations are based on DFPT and use either plane waves or localized functions as a basis set. " As an example, calculated and experimental vibration frequencies at T are reported in Table 18 for... 

Although simple, this molecule presents some interesting conformational properties and is a good example to illustrate both (i) ab initio molecular geometry optimization of minima and transition structures (which may be located by symmetry analysis), and (ii) ab initio calculations of vibrational frequencies. 

Mincu, I., Hillebrand, M., AUouche, A., Cossu, M., Verlaque, R, Aycard, J.R, and Pourcin, J., Photolysis of the dichlorocyclobutenedione in rare gas at 10 K. Infrared spectral analysis and ab initio calculations of vibrational frequencies. First identification of two new species (dichloro-substituted bisketene and dichloropropadienone). Kinetics and reaction mechanism, /. Phys. Chem., 100, 16045, 1996. 

From the vibrational structure in the photoelectron spectrum of the PH3 frequencies of the symmetric out-of-plane (inversion) vibration of the ion, V2=450 [16], 500 20 [17, 18], and 530 80 cm [5], were obtained. The so-called frequency halving (compared to V2 900 cm" for PH3) can be explained by a double minimum potential with a low inversion barrier which allows the left and right vibrational energy levels to interact and to split into equally spaced doublets see e.g. [18]. Ab initio calculated harmonic vibrational frequencies were reported [7]. 

There are, however, indications for a phase transition in formic acid around 208 K jl10,111. Which kind of structural change actu ally occurs, a transition to structure IV, an order-disorder transition involving structures I and IV, or a significant change in interchain orientation or -distances is still an open question lll-113. An ab initio calculation of vibrational spectra of formic acid chains is currently out of reach. We compiled therefore available Raman results on 0-H frequencies in isolated formic acid, in the cyclic dimer and in the crystal in table 11 in order to enable a comparison with the previously discussed cases of hydrogen fluoride and hydrogen cyanide. 

The entropy of N2H-" at 298 K, S° = 200 2 [3] and 202 J-mol K" [14], was calculated using statistical mechanics. Ab initio values of vibrational frequencies were used in the latter calculation [14]. Vibrational contributions to the entropy were neglected in the former calculation [3]. 

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... 

An informative IR spectrum of the t-butyl radical, containing 18 bands, has been recorded after freezing of the products of vacuum pyrolysis of azoisobutane [110] and 2-nitrosoisobutane [111] in an argon matrix at 10 K (Pacansky and Chang, 1981). This spectrum is in agreement with a pyramidal structure of the radical (CH3)3C (symmetry C3v) which has elongated CH bonds in positions trans to the radical centre. On the basis of experimental vibrational frequencies and ab initio calculations of the radical geometry the enthalpy value [// (300)] of its formation has been calculated as 44 kJ moP. ... 

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

Recently, the assignment of the band at 980 cm to 28 has been doubted based on new calculations (this band is shifted to 976 cm if 28 is generated from 1,4-diiodobenzene (37), which is not unusual in the presence of iodine atoms. This shift may also be attributable to the change of the matrix host from argon to neon). ° On the other hand, ab initio calculations of the IR spectrum of 28 are complicated by the existence of orbital instabilities, the effect of which may (often) be negligible for first order properties (such as geometry and energy), but can result in severe deviations for second-order properties (vibrational frequencies, IR intensities). 

Ab initio calculations of the normal vibrational frequencies for the primary and secondary ozonides of ethylene allowed making a few modifications of the earlier assignments, and will serve for assisting in assigning vibrational bands of larger ozonides <1996SAA1479>. 

Tucker SC, Truhlar DG, Ab initio calculations of the transition-state geometry and vibrational frequencies of the SN2 reaction of chloride with chloromethane, J Phys Chem 93, 8138-8142 (1989), and refs therein... 

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