Rotational spectra quantized rotation

Birnbaum G. Quantized rotational motion in liquids Far infrared rotational spectrum of HF and NH3 in liquid SF6, Mol. Phys. 25, 241-5 (1973). 

Infrared radiation of frequencies less than about 100 cm-1 is absorbed and converted by an organic molecule into energy of molecular rotation. This absorption is quantized thus a molecular rotation spectrum consists of discrete lines. 

The spectrum of C02 physically adsorbed on Cabosil has also been used to study the question of rotation in physically adsorbed molecules 24). Figure 27 is due to C02 physically adsorbed on Cabosil at 30° C. with surface coverage, 0, less than 0.01. The half-width of this band is 14 cm.-1. This is less than one-half of the 30 cm.-1 that would be expected for rotation about a fixed axis at room temperature. These results indicate that there is no free rotation of any kind in this case. This does not mean that the molecule is locked in one position. Free rotation as used here refers to a quantized rotation. The type of movement in which the molecule rotates in short irregular spurts is not ruled out. 

There is a clear difference between microwave spectroscopy and microwave dielectric heating effects. Thus, in microwave spectroscopy, molecules are examined in the gas phase and the microwave spectrum for a molecule exhibits many sharp bands [15] over the frequency range 3-60 GHz. Such sharp bands arise from transitions between quantized rotational states of the molecules. Microwave spectroscopy provides an excellent fingerprinting method for identifying molecules in a gas phase and has been used, for example, to confirm the presence of a wide range of molecules in outer space. 

Elsewhere, in the mid-IR, photon energy is sufficient to modify the quantized terms vib and iJjo in expression 10.2. This is therefore a vibration-rotation spectrum, that is, several tens of rotational transitions accompany each vibrational transition. For the simplest molecules it is possible to interpret particular aspects of the absorption bands. Experience and theory have enabled rules of the permitted transitions to be drawn up. Small molecules as carbon monoxide and hydrogen chloride (Figure 10.5) have been intensely studied from this point of view. 

In the rest of this section we discuss our analysis (10,11) of the accurate cumulative reaction probabilities for the halogen-hydrogen halide systems that were published by Schatz (17-19). The CRPs were digitized with an optical scanner, which introduces negligible error. The accurate N°(E) was fit with cubic splines and convoluted using Eq. (20). Our analysis is based on the observation that the calculated CRPs of Schatz for Cl + HC1,1 + HI, and I + DI appeared to have an overall steplike structure reminiscent of that associated with quantized transition states, underlying the narrower features associated with trapped-state resonances and rotational thresholds. Our conclusion that quantized transition states exert broad control of the chemical reactivity for these reactions is not inconsistent with Schatz s description of the narrow trapped-state resonance and rotational threshold features. These different sorts of dynamical features represent different time scales, with the shorter-time (broader) features being more closely related to the traditional concern of chemical kinetics, i.e., reactivity, as discussed below Eq. (23). The relationship of features in the CRP to features in the photoelectron spectrum is not fully worked out yet. 

In transition state theory it is assumed that a dynamical bottleneck in the interaction region controls chemical reactivity. Transition state theory relates the rate of a chemical reaction in a microcanonical ensemble to the number of energetically accessible vibrational-rotational levels of the interacting particles at the dynamical bottleneck. In spite of the success of transition state theory, direct evidence for a quantized spectrum of the transition state has been found only recently, and this evidence was found first in accurate quantum mechanical reactive scattering calculations. Quantized transition states have now been identified in accurate three-dimensional quantal calculations for 12 reactive atom-diatom systems. The systems are H + H2, D + H2, O + H2, Cl + H2, H + 02, F + H2, Cl + HC1, I + HI, I 4- DI, He + H2, Ne + H2, and O + HC1. 

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