Vibration-rotational spectra

Papousek D and Aliev M R 1982 Molecular Vibrational-Rotational Spectra (Amsterdam Elsevier)... 

A. Abragam and M.H.L. Pryce, Proc. Roy. Soc. (London) A205, 135 (1951). D. Papousek and M.R. Aliev, Molecular Vibrational-Rotational Spectra. Elsevier. Amsterdam (1982). 

Emission or absorption spectra are produced when molecules undergo transitions between quantum states that correspond to two different internal energies. The energy difference AE between the states is related to the frequency of the radiation emitted or absorbed by the equation DE = hn. Infrared frequencies in the wavelength range 1-50 mm are associated with molecular vibration and vibration-rotation spectra. 

The vibrational-rotational spectra are not exhibited by homonuclear molecules because they have no permanent dipoles. 

Lathouwers, L., Van Leuven, P., Deumens, E., and Ohm, Y. (1987), Applications of the Generator Coordinate Approximation to Diatomic Systems. II. Dunham Analysis of Vibration-Rotation Spectra, /. Chem. Phys. 86, 6352. 

Papousek, D., and Aliev, M. R. (1982), Molecular Vibrational-Rotational Spectra, Elsevier, Amsterdam. 

Hydrogen is the most abundant chemical element in the universe, and in its various atomic and molecular forms furnishes a sensitive test of all of experimental, theoretical and computational methods. Vibration-rotational spectra of dihydrogen in six isotopic variants constituting all binary combinations of H, D and T have nevertheless been recorded in Raman scattering, in either spontaneous or coherent processes, and spectra of HD have been recorded in absorption. Despite the widely variable precision of these measurements, the quality of some data for small values of vibrational quantum number is still superior to that of data from electronic spectra [106], almost necessarily measured in the ultraviolet region with its concomitant large widths of spectral lines. After collecting 420... 

S.P.A. Sauer, J. Oddershede, J.F. Ogilvie, Evaluation of parameters in radial functions from rotational and vibration-rotational spectra and calculation of rotational and vibrational g... 

Computational spectrometry, which implies an interaction between quantum chemistry and analysis of molecular spectra to derive accurate information about molecular properties, is needed for the analysis of the pure rotational and vibration-rotational spectra of HeH in four isotopic variants to obtain precise values of equilibrium intemuclear distance and force coefficient. For this purpose, we have calculated the electronic energy, rotational and vibrational g factors, the electric dipolar moment, and adiabatic corrections for both He and H atomic centres for intemuclear distances over a large range 10 °m [0.3, 10]. Based on these results we have generated radial functions for atomic contributions for g g,... 

Low energy photons in the far IR can only modify the term ERol. This leads to pure rotational spectra that can be easily studied for small diatomic gases. However, in the mid IR, photons have sufficient energy to modify Vib and Fr,. This leads to vibrational-rotational spectra (Fig. 10.6). Each vibrational transition is accompanied by tens of individual rotational transitions. The molecule becomes an oscillating rotor for which energy VR approximately corresponds to the following values, where 7 (./ = 0, 1, 2, 3,...) and V (V = 0, 1, 2) are the rotational and vibrational quantum numbers, respectively. 

We now consider radiative transitions foi which both v and J change, but the electronic state does not these transitions give the vibration-rotation spectra of diatomic molecules. The selection rules for these transitions were found in Section 4.4 to be ( 2 states only)... 

We previously found the selection rule A7 = 1 for a 2 diatomic-molecule vibration-rotation or pure-rotation transition. The rule (4.138) forbids A/ = 1 for homonuclear diatomics this gives us no new information as far as vibration-rotation spectra are concerned, since the absence of a dipole moment insures the absence of a vibration-rotation or pure-rotation spectrum, anyway. 

We saw that homonuclear diatomic molecules exhibit no pure-rotation or vibration-rotation spectra, because they have zero electric dipole moment for all internuclear separations. The Raman effect depends on the polarizability and not the electric dipole moment homonuclear diatomic molecules do have a nonzero polarizability which varies with varying internuclear separation. Hence they exhibit pure-rotation and vibration-rotation Raman spectra. Raman spectroscopy provides information on the vibrational and rotational constants of homonuclear diatomic molecules. 

Second, we consider the diffuseness in gas-phase spectra.74- 78 An account of those aspects of gas-phase spectra that relate to electronic relaxation is only possible if the other causes of diffuseness are first made clear. We therefore summarize some of the characteristics of vibration-rotation spectra with special reference to a molecule like naphthalene at a vapor pressure of 1 mm76 The Doppler width of each line is 0.022 cm-1 the rotational line spacing can be as small as 0.0004 cm-1, or 50 lines per Doppler width the length of a sequence is 300 cm 1 and the average sequence spacing is 5 cm-1 for anthracene the average sequence spacing... 

Spectral lineshapes were first expressed in terms of autocorrelation functions by Foley39 and Anderson.40 Van Kranendonk gave an extensive review of this and attempted to compute the dipolar correlation function for vibration-rotation spectra in the semi-classical approximation.2 The general formalism in its present form is due to Kubo.11 Van Hove related the cross section for thermal neutron scattering to a density autocorrelation function.18 Singwi et al.41 have applied this kind of formalism to the shape of Mossbauer lines, and recently Gordon15 has rederived the formula for the infrared bandshapes and has constructed a physical model for rotational diffusion. There also exists an extensive literature in magnetic resonance where time-correlation functions have been used for more than two decades.8... 

This chapter is devoted to tunneling effects observed in vibration-rotation spectra of isolated molecules and dimers. The relative simplicity of these systems permits one to treat them in terms of multidimensional PES s and even to construct these PES s by using the spectroscopic data. Modern experimental techniques permit the study of these simple systems at superlow temperatures where tunneling prevails over thermal activation. The presence of large-amplitude anharmonic motions in these systems, associated with weak (e.g., van der Waals) forces, requires the full power of quantitative multidimensional tunneling theory. 

Structural Parameters for Electronic States of Carbenes from Electronic and Vibration-Rotation Spectra... 

D. Searles and E. von Nagy-Felsobuki, Ab Initio Variational Calculations of Molecular Vibrational-Rotational Spectra, Springer, Berlin, 1993. 

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