Transition frequencies, vibrational spectra

Shur, M. S., 1966a. Change of low-frequency vibration spectrum of KH2PO4 during phase transition. Fiz. Tverd. Tela 8 1267. 

Experimental. The vibrational spectrum of an ideal harmonic oscillator would consist of one line at frequency v corresponding to A = hv, where A is the distance between levels on the vertical energy axis in Fig. 10-la. In the harmonic oscillator, AE is the same for a transition from one energy level to an adjacent level. A selection rule An = 1, where n is the vibrational quantum number, requires that the transition be to an adjacent level. 

Another conventional simplification is replacing the whole vibration spectrum by a single harmonic vibration with an effective frequency co. In doing so one has to leave the reversibility problem out of consideration. It is again the model of an active oscillator mentioned in section 2.2 and, in fact, it is friction in the active mode that renders the transition irreversible. Such an approach leads to the well known Kubo-Toyozawa problem [Kubo and Toyozava 1955], in which the Franck-Condon factor FC depends on two parameters, the order of multiphonon process N and the coupling parameter S... 

RAIRS spectra contain absorption band structures related to electronic transitions and vibrations of the bulk, the surface, or adsorbed molecules. In reflectance spectroscopy the ahsorhance is usually determined hy calculating -log(Rs/Ro), where Rs represents the reflectance from the adsorhate-covered substrate and Rq is the reflectance from the bare substrate. For thin films with strong dipole oscillators, the Berre-man effect, which can lead to an additional feature in the reflectance spectrum, must also be considered (Sect. 4.9 Ellipsometry). The frequencies, intensities, full widths at half maximum, and band line-shapes in the absorption spectrum yield information about adsorption states, chemical environment, ordering effects, and vibrational coupling. 

Here te, tc are the correlation times of rotational and vibrational frequency shifts. The isotropic scattering spectrum corresponding to Eq. (3.15) is the Lorentzian line of width Acoi/2 = w0 + ydp- Its maximum is shifted from the vibrational transition frequency by the quantity coq due to the collapse of rotational structure and by the quantity A due to the displacement of the vibrational levels in a medium. 

Ifourth(fd, 2 Q) was multiplied with a window function and then converted to a frequency-domain spectrum via Fourier transformation. The window function determined the wavenumber resolution of the transformed spectrum. Figure 6.3c presents the spectrum transformed with a resolution of 6cm as the fwhm. Negative, symmetrically shaped bands are present at 534, 558, 594, 620, and 683 cm in the real part, together with dispersive shaped bands in the imaginary part at the corresponding wavenumbers. The band shapes indicate the phase of the fourth-order field c() to be n. Cosine-like coherence was generated in the five vibrational modes by an impulsive stimulated Raman transition resonant to an electronic excitation. 

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. 

In the case when the vibrational spectrum of the system spreads out in the quantum region and the vibrational frequencies of the reaction complex are unchanged in the course of the transition, the following approximate formula can be obtained instead of Eqs. (9)... 

Included in Table III is the comparison of the transition frequencies calculated from the energies obtained in our calculations with the experimental transition frequencies of Dabrowski [125]. To convert theoretical frequencies into wavenumbers, we used the factor of 1 hartree = 219474.63137 cm . For all the frequencies our results are either within or very close to the experimental error bracket of 0.1 cm . We hope that the advances in high-resolution spectroscopy will inspire remeasurements of the vibrational spectrum of H2 with the accuracy lower than 0.1 cm. With such high-precision results, it would be possible to verify whether the larger differences between the calculated and the experimental frequencies for higher excitation levels, which now appear, are due to the relativistic and radiative effects. 

Thulium displays in minerals an intense UV and blue visible luminescence with a line spectrum near 360 and 450 nm, correspondingly. They are connected with electron transitions from different excited levels D2 and at 360-365 and 450-455 nm. The liuninescence of Tm " is more easily detected in time-resolved spectra with a narrow gate, because it usually has a relatively short decay time. The UV Hne usually has a much shorter decay time compared with the blue line. Different decay times from these levels are evidently connected with nonradiative relaxation due to the presence of high frequency vibrations in the lattice. The best excitation is at 355 nm, which is connected with transition... 

Above it was pointed out that in unmixed rare gases binary absorption does not exist because of the inversion symmetry of like pairs. For like molecular pairs inversion symmetry does in general not exist because of the anisotropic structure and vibrational excitations of the individual molecules. In Chapter 5, we will show that in pure hydrogen gas, for example, the translational spectrum arises mainly from orientational ( magnetic ) transitions the translational spectrum of H2-H2 is discernible in Fig. 3.10 at low frequencies (0 < v < 250 cm-1). The translational peak is weak if compared to the strong So(J) lines near 354 and 587 cm-1, but its strength is comparable to those of the dissimilar rare gas pairs, Fig. 3.1. The translational H2-He pair spectra are somewhat stronger, Fig. 3.12,... 

Aside from the possession of a permanent dipole moment and sufficient volatility, a molecule must be reasonably small for its microwave spectrum to be profitably studied. Large molecules have many low-frequency vibrational modes these modes will be appreciably populated at room temperature, giving many strong pure-rotation transitions between levels with nonzero vibrational quantum numbers. The microwave spectrum of a large molecule will thus have so many lines that assignment of the lines will be virtually impossible. 

It is well known that the v, band of liquid acetonitrile is significantly asymmetric due to an overlap of hot band transitions in the low frequency side. A study of gas phase rotation-vibration spectrum [19] showed that the hot band transition from the first exited state of the degenerated C-C = N bending v8 mode, v hl = v + v8 - vs, has its center at 4.944 cm 1 lower than that of the fundamental transition, v,. Also the presence of v,h2 = v, + 2v8 - 2v8 transition is expected. The careful study on the v band of liquid acetonitrile by Hashimoto et al [20] provided the reorientational and vibrational relaxation times of liquid acetonitrile molecule. They corrected the contribution by the hot band transition using the Boltzmann population law and approximated the v , v,hl, 2h2, and v, + v4 bands by Lorentzian curves. 

The molecule HI has a bond stretching force constant of 314 N m I. Calculate for both H127I and 2D127I, (a) the classical vibrational frequency v in hertz, and (b) the wavenumber of photons corresponding to the n - 0 to n = 1 transition in the vibrational spectrum. 

The carboxylic acid dimers are quite heavy, with rotational constants typically around 1 GHz, and the microwave absorption experiments are conducted at high temperatures of 200-300 K. The resulting large number of rotation-vibration states populated, coupled with low dimer number densities, on the order of 5 x 1014 mole-cules/cm3, makes complete resolution of the rotational spectrum not feasible. However, virtually all dimers are prolate rotors with only moderate asymmetry. Thus, AJ = 1 transitions (a-type) with the same initial and final quantum numbers, but otherwise of different asymmetric rotor state or different vibrational state, will have the same frequency within about 50 MHz for moderate J values e.g. for J < 5 and for transition frequencies less than 50 GHz. At this level of resolution, isotope shifts are not discernible, and the resulting spectra (Fig. 1) yield one rotational constant, (B + C)/2, with an accuracy of about 0.5 %. 

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