Rotational absorption, pure transitions

Second, due to the nonzero matrix elements of the operator of the dipole moment, transitions between the rotational sublevels of the same vibronic level with the change of the projection K by unity (AA = 1) are possible. In the work of Child and Longuet-Higgins (1961) it is noted that the possible vibronic pure rotational absorption spectrum within the same vibronic level is somewhat similar to the pure rotational spectrum in the excited degenerate dipolar-type state of harmonic oscillators predicted by Mizushima and Venkatesvarlu (1953). 

For a certain diatomic molecnle, two of the pure-rotational absorption lines are at 806.65 GHz and 921.84 GHz, where 1 GHz = 10 Hz, and there are no pure-rotational lines between these two lines. Find the initial 7 value for each of these transitions and find the molecular rotational constant B. 

The overall OD vibrational distribution from the HOD photodissociation resembles that from the D2O photodissociation. Similarly, the OH vibrational distribution from the HOD photodissociation is similar to that from the H2O photodissociation. There are, however, notable differences for the OD products from HOD and D2O, similarly for the OH products from HOD and H2O. It is also clear that rotational temperatures are all quite cold for all OH (OD) products. From the above experimental results, the branching ratio of the H and D product channels from the HOD photodissociation can be estimated, since the mixed sample of H2O and D2O with 1 1 ratio can quickly reach equilibrium with the exact ratios of H2O, HOD and D2O known to be 1 2 1. Because the absorption spectrum of H2O at 157nm is a broadband transition, we can reasonably assume that the absorption cross-sections are the same for the three water isotopomer molecules. It is also quite obvious that the quantum yield of these molecules at 157 nm excitation should be unity since the A1B surface is purely repulsive and is not coupled to any other electronic surfaces. From the above measurement of the H-atom products from the mixed sample, the ratio of the H-atom products from HOD and H2O is determined to be 1.27. If we assume the quantum yield for H2O at 157 is unity, the quantum yield for the H production should be 0.64 (i.e. 1.27 divided by 2) since the HOD concentration is twice that of H2O in the mixed sample. Similarly, from the above measurement of the D-atom product from the mixed sample, we can actually determine the ratio of the D-atom products from HOD and D2O to be 0.52. Using the same assumption that the quantum yield of the D2O photodissociation at 157 nm is unity, the quantum yield of the D-atom production from the HOD photodissociation at 157 nm is determined to be 0.26. Therefore the total quantum yield for the H and D products from HOD is 0.64 + 0.26 = 0.90. This is a little bit smaller ( 10%) than 1 since the total quantum yield of the H and D productions from the HOD photodissociation should be unity because no other dissociation channel is present for the HOD photodissociation other than the H and D atom elimination processes. There are a couple of sources of error, however, in this estimation (a) the assumption that the absorption cross-sections of all three water isotopomers at 157 nm are exactly the same, and (b) the accuracy of the volume mixture in the... 

Upon absorption of light of an appropriate wavelength, a diatomic molecule can undergo an electronic transition, along with simultaneous vibrational and rotational transitions. In this case, there is no restriction on Au. That is, the selection rule Av = +1 valid for purely vibrational and vibrational-rotational transitions no longer applies thus numerous vibrational transitions can occur. If the molecule is at room temperature, it will normally be in its lower state, v" = 0 hence transitions corresponding to v" = 0 to v = 0,... 

A translational line like the one seen above in rare gas mixtures is relatively weak but discernible in pure hydrogen at low frequencies (<230 cm-1), Fig. 3.10. However, if a(v)/[l —exp (—hcv/kT)] is plotted instead of a(v), the line at zero frequency is prominent, Fig. 3.11 the 6o(l) line that corresponds to an orientational transition of ortho-H2. Other absorption lines are prominent, Fig. 3.10. Especially at low temperatures, strong but diffuse So(0) and So(l) lines appear near the rotational transition frequencies at 354 and 587 cm-1, respectively. These rotational transitions of H2 are, of course, well known from Raman studies and correspond to J = 0 -> 2 and J = 1 — 3 transitions J designates the rotational quantum number. These transitions are infrared inactive in the isolated molecule. At higher temperatures, rotational lines So(J) with J > 1 are also discernible these may be seen more clearly in mixtures of hydrogen with the heavier rare gases, see for example Fig. 3.14 below. 

H2-X where X is a molecule. If a molecule other than H2 is chosen as the collision al partner X, new absorption bands appear at the rotovi-brational bands of that molecule. As an example, Fig. 3.17 shows the rototranslational enhancement spectra [46] of H2-CH4 for the temperature of 195 K. At the higher frequencies (v > 250 cm-1), these look much like the H2-Ar spectrum of Fig. 3.10 the H2 So(J) lines at 354, 587, and 815 cm-1 are clearly discernible. Besides these H2 rotational lines, a strong low-frequency spectrum is apparent which corresponds to the (unresolved) induced rotational transitions of the CH4 molecule these in turn look like the envelope of the rotational spectra seen in pure methane, Fig. 3.22. This is evident in the decomposition of the spectrum, Fig. 3.17, into its main components [46] the CH4 octopole (dashed curve) and hex-adecapole (dot-dashed curve) components that resemble the CH4-CH4 spectrum of Fig. 3.22, and the H2 quadrupole-induced component (dotted curve) which resembles the H2-Ar spectrum, Fig. 3.14. The superposition (heavy curve) models the measurement (big dots) closely. Similar spectra are known for systems like H2-N2 [58]. 

Overtone bands. The induced first overtone band of H2 is shown in Fig. 3.37 at a variety of temperatures, observed in pure hydrogen gas using long absorption paths. Instead of the three components Q, S(0) and S(l) seen in the fundamental band, we now observe much richer structures, especially at the lower temperatures. This fact suggests that a number of double transitions take place. If one constructs a rotovibrational term scheme of the H2 molecule, like Fig. 3.32, which includes the lowest rotational levels of the v = 2 vibrational state, this is obvious. Various... 

Other systems like H2-H2 feature a small number of bound states. Whenever molecular pairs form bound dimers, spectroscopic structures appear. First and usually most importantly, the continuum of the purely rotational band appears, but various other structures associated with bound-to-free transition usually show up that are harder to model closely. As a rule, the rototranslational absorption spectra of most molecular systems are not as easily modeled as that of H2-He, because of the dimer structures. Of course, in the typical high-pressure laboratory measurements, dimer structures may be broadened to the point where these are hardly discernible. In such a case, the BC and KO model profiles may become adequate again. In any case, the rototranslational spectra of a number of binary systems have been modeled closely over a broad range of temperatures [58], including the (coarse) dimer structures. 

We now consider the pure-rotation spectra of gaseous diatomic molecules. As noted in the previous section, a diatomic molecule with an electric dipole moment can undergo a pure-rotational radiative transition with AJ = +1 or — 1, corresponding to absorption or emission. Rotational spectra are studied as absorption spectra. For a transition with the initial and final rotational quantum numbers J and J+1, respectively, and with no change in electronic or vibrational levels, we find from (4.67)... 

Figure 3.10 The electronic transitions [absorption in (a)] of small molecules show vibrational and rotational lines in addition to the purely electronic spectrum, (b) Luminescence emission is resonance fluorescence (f), and chemical reactions (R) can originate from several excited states...

Most atmospheric visible and DV absorption and emission involves energy transitions of the outer electron shell of the atoms and molecules involved. The infrared spectrum of radiation from these atmospheric constituents is dominated by energy mechanisms associated with the vibration of molecules. The mid-infrared region is rich with molecular fundamental vibration-rotation bands. Many of the overtones of these bands occur in the near infrared. Pure rotation spectra are more often seen in the far infrared. Most polyatomic species found in the atmosphere exhibit strong vibration-rotation bands in the 1 - 25 yin region of the spectrum, which is the region of interest in this paper. The richness of the region for gas analysis... 

Rotational quanta are much smaller than vibrational quanta, and correspond to electromagnetic radiation in the microwave region, typically in the range 103-105MHz (lcm-1 = 3.3 x 104 MHz). Rotational transitions can be excited directly, in microwave absorption spectroscopy (pure rotational spectroscopy), but can also be observed in the rotational fine structure in high-resolution vibrational or electronic spectra. 

Absorption of microwave radiation to excite molecular rotation is allowed only if the molecule has a permanent dipole moment. This restriction is less severe than it may sound, however, because centrifugal distortion can disturb the molecular symmetry enough to allow weak absorption, especially in transitions between the higher rotational states which may appear in the far IR (c. 100cm-1). Microwave spectroscopy can provide a wealth of other molecular data, mostly of interest to physical chemists rather than inorganic chemists. Because of the ways in which molecular rotation is affected by vibration, it is possible to obtain vibrational frequencies from pure rotational spectra, often more accurately than is possible by direct vibrational spectroscopy. 

The pronounced and R branch contours in the first and second overtone spectra of CO (Figures 6.2-1 and 6.2-2) clearly indicate appreciable rotational freedom in dense carbon monoxide. The wavenumbers of maximum absorption in the P and in the / branch, i>/>(max) and i jffmax), of the first overtone (Fig. 6.2-4) and of the second overtone (Fig. 6.2-5) at various temperatures are plotted as a function of the pure carbon monoxide density. As is to be expected, the separation between these two maxima increases with the temperature. In all experimental spectra, the solid line in both figures indicates the arithmetic mean, i> , of the maximum positions of the P and the R branch. slightly decreases with the density but is independent of the temperature. The straight line formed by Urn in Fig. 6.2-4 can be extrapolated to = 4261.9 cm, which is very close to the literature value = 4260.1 cm for the pure vibrational transition in the gas phase (Bouanich et al., 1981). Similarly, extrapolation of the second overtone data in Fig. 6.2-5... 

In the gas phase, the vibrational transitions couple with the rotational ones, giving rise to rotovihrational spectra. The different rotovibrational contours depend on the symmetry of the vibration in relation to the symmetry of the molecule, and on the resolution of the rotational components. In some cases, the energy of the pure vibrational transition corresponds to the minimum of the absorption band ... 

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