Rotation spectroscopy

The simplest vibration-rotation spectra to interpret are those of diatomic molecules. The rotational energy levels of diatomic molecules are characterized by a single rotational quantum number, J. If the molecule is assumed to be a rigid rotor (i.e., its bond length remains constant no matter how rapidly the molecule rotates), the rotational energy is given by 

for a rigid rotor, the pure rotation spectmm would be comprised of a series of lines with equal spacing of 2B cm. For most molecules, B is sufficiently small that the pure rotation spectrum is found in the microwave region of the spectrum however, for light molecules such as HCl, H2O, or CO, rotational transitions absorb in the far infrared. 

Diatomic molecules, X Y, have a single fundamental vibrational mode, of wave-number Vo, which is infrared active only if X Y. For any allowed vibrational transition of a gaseous diatomic molecule, there must be a simultaneous rotational 

the vibration-rotation spectrum of a rigid diatomic molecule consists of a series of equally spaced lines above and below vq that correspond to A7 = +1 and AJ = — 1, respectively. The series of lines below vq AJ = — 1) is known as the P branch of the band, while the lines above vq AJ = +1) are known as the R branch. Because AJ 0, there is no absorption line at Vq.  

there is a strong line in the spectrum, known as the Q branch, corresponding to A7 = 0. The reason that the selection rules are different for these two modes is because different symmetry elements of the linear CO2 molecule are lost during these two vibrations. 

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Electrons, protons and neutrons and all other particles that have s = are known as fennions. Other particles are restricted to s = 0 or 1 and are known as bosons. There are thus profound differences in the quantum-mechanical properties of fennions and bosons, which have important implications in fields ranging from statistical mechanics to spectroscopic selection mles. It can be shown that the spin quantum number S associated with an even number of fennions must be integral, while that for an odd number of them must be half-integral. The resulting composite particles behave collectively like bosons and fennions, respectively, so the wavefunction synnnetry properties associated with bosons can be relevant in chemical physics. One prominent example is the treatment of nuclei, which are typically considered as composite particles rather than interacting protons and neutrons. Nuclei with even atomic number tlierefore behave like individual bosons and those with odd atomic number as fennions, a distinction that plays an important role in rotational spectroscopy of polyatomic molecules. 

Within physical chemistry, the long-lasting interest in IR spectroscopy lies in structural and dynamical characterization. Fligh resolution vibration-rotation spectroscopy in the gas phase reveals bond lengths, bond angles, molecular symmetry and force constants. Time-resolved IR spectroscopy characterizes reaction kinetics, vibrational lifetimes and relaxation processes. 

The methyl iodide molecule is studied using microwave (pure rotational) spectroscopy. The following integral governs the rotational selection rules for transitions labeled J, M, K... 

Brown, J. M. and Carrington, A. (2003) Rotational Spectroscopy of Diatomic Molecules, Cambridge University Press, Cambridge. 

We have seen in Section 5.2.1.4 that there is a stack of rotational energy levels associated with all vibrational levels. In rotational spectroscopy we observe transitions between rotational energy levels associated with the same vibrational level (usually v = 0). In vibration-rotation spectroscopy we observe transitions between stacks of rotational energy levels associated with two different vibrational levels. These transitions accompany all vibrational transitions but, whereas vibrational transitions may be observed even when the sample is in the liquid or solid phase, the rotational transitions may be observed only in the gas phase at low pressure and usually in an absorption process. 

Raman scattering is normally of such very low intensity that gas phase Raman spectroscopy is one of the more difficult techniques. This is particularly the case for vibration-rotation Raman spectroscopy since scattering involving vibrational transitions is much weaker than that involving rotational transitions, which were described in Sections 5.3.3 and 5.3.5. For this reason we shall consider here only the more easily studied infrared vibration-rotation spectroscopy which must also be investigated in the gas phase (or in a supersonic jet, see Section 9.3.8). 

Duxbury, G. (1999) Infrared Vibration-Rotation Spectroscopy, John Wiley, Chichester. 

It is important to realize that electronic spectroscopy provides the fifth method, for heteronuclear diatomic molecules, of obtaining the intemuclear distance in the ground electronic state. The other four arise through the techniques of rotational spectroscopy (microwave, millimetre wave or far-infrared, and Raman) and vibration-rotation spectroscopy (infrared and Raman). In homonuclear diatomics, only the Raman techniques may be used. However, if the molecule is short-lived, as is the case, for example, with CuH and C2, electronic spectroscopy, because of its high sensitivity, is often the only means of determining the ground state intemuclear distance. 

R. Varma and L. W. Hmbesh, Chemical Analysis by Microwave Rotational Spectroscopy,]ohxi Wiley Sons, Inc., New York, 1979. 

The trisulfane molecule exists as two conformers which have been termed as cis- and trans-HzSi. While the trans-form is a helical molecule of C2 symmetry with the motif ++ (or — for the enantiomer), the cfs-form is of Q symmetry with the motif +- (identical to -+). Both forms have been detected by rotational spectroscopy [17, 45, 46]. The motif gives the order of the signs of the torsion angles at the SS bonds. The geometrical parameters [17] are presented in Table 4. The trans-isomer is by only 1 kj mol more stable than the cfs-form but the barrier to internal rotation from tmns to cis is 35 kJ mor [46]. The dipole moments were calculated by ab initio MO theory at the QCISD/TZ+P level as 0.68 D (trans) and 2.02 D (cis) [46]. For geometrical parameters of cis- and trans-trisulfane calculated at the MP2/6-311++G> > level, see [34]. 

The structure of the S2O molecule has been determined by rotational spectroscopy. The internuclear distances d and the bond angles a obtained by two groups are as follows ... 

Finally, for the determination of selection rules for rotational spectroscopy it is necessary to find the wavefimcdons for this problem. This subject will be left for further development as given in numerous texts on molecular spectroscopy. 

Vol. 9 Vibration-Rotational Spectroscopy and Molecular Dynamics ed. D. Papousek... 

Vol. 51 Trace Element Analysis of Geological Materials. By Roger D. Reeves and Robert R. Brooks Vol. 52 Chemical Analysis by Microwave Rotational Spectroscopy. By Ravi Varma and Lawrence... 

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