- Rovibrational coupling
Rovibrational coupling is a coupled rotational and vibrational excitation of a
molecule . It is different fromrovibronic coupling , which involves a change in all of electronic, vibrational, and rotational states simultaneously.Rotational-Vibrational Spectroscopy
Generally
vibrational transition s occur in conjunction withrotational transition s. Consequently, it is possible to observe both rotational andvibrational transition s in the vibrational spectrum. Although many methods are available for observing vibrational spectra, the two most common methods areinfrared spectroscopy andRaman spectroscopy .The energy of rotational transitions is on the order of 10^{-21} J/mol whereas vibrational transitions have energies on the order of 10^{-20} J/mol. Therefore, highly-resolved vibrational spectra will contain
fine structure corresponding to the rotational transitions that occur at the same time as a vibrational transition. Although molecular vibrations and rotations do have some effect on one other, this interaction is usually small. Consequently, the rotational and vibrational contributions to the energy of the molecule can be considered independently to a first approximation:E_{vib,rot} = E_{vib} + E_{rot} = left ( n + {1 over 2} ight )h u_0 + hcar B J left ( J + 1 ight )
where n is the vibrational
quantum number , J is the rotationalquantum number , h isPlanck's constant , u_0 is the frequency of the vibration, c is thespeed of light , and ar B is the rotational constant.Evaluating Spectra
The strict selection rule for the adsorption of dipole radiation (the strongest component of light) is that Delta J = 0,pm 1 . This is because of the vector addition properties of quantum mechanical angular momenta, and because light particles (photons) have angular momenta of 1. For linear molecules the most commonly observed case is that only transitions with Delta J = pm 1 are observed. This is only possible when the molecule has a "singlet" ground state, that is there are no unpaired electron spins in the molecule. For molecules that do have unpaired electrons, Q branches (see below) are commonly observed.
The gap between the R- and P-branches is known as the Q-branch. A peak would appear here for a vibrational transition in which the rotational energy did not change (Delta J = 0 ). However, according to the quantum mechanical
rigid rotor model upon which rotational spectroscopy is based, there is a spectroscopicselection rule that requires that Delta J = pm 1 . This selection rule explains why the P- and R-branches are observed, but not the Q-branch (as well as branches for which Delta J = pm 2 , Delta J = pm 3 , etc.).The positions of the peaks in the spectrum can be predicted using the
rigid rotor model. One prediction of therigid rotor model is that the space between each of the peaks should be 2ar B where ar B is the rotational constant for a given molecule. Experimentally, it is observed that the spacing between the R-branch peaks decreases as the frequency increases. Similarly, the spacing between the P-branch peaks increases as the frequency decreases. This variation in the spacing results from the bonds between the atoms in a molecule not being entirely rigid.This variation can be mostly accounted for using a slightly more complex model that takes into account the variation in the rotational constant as the vibrational energy changes. Using this model, the positions of the R-branch peaks are predicted to be at:
ar u_R = u_0 + 2ar B_1 + left ( 3ar B_1 - ar B_0 ight )J + left ( ar B_1 -ar B_0 ight )J^2 qquad J = 0,1,2...
where ar B_0 is the rotational constant for the n = 0 vibrational level and ar B_1 is the rotational constant for the n = 1 vibrational level. Likewise, the P-branch peaks are predicted to be at:
ar u_P = ar u_0 - left ( ar B_1 + ar B_0 ight )J + left ( ar B_1 - ar B_0 ight )J^2 qquad J = 1,2,3...
Rotational-vibrational spectra will also show some fine structure due to the presence of different
isotopes in the spectrum. In the spectrum shown above, all of the rotational peaks are slightly split into two peaks. One peak corresponds to 35Cl and the other to 37Cl. The ratio of the peak intensities corresponds to thenatural abundance of these two isotopes.
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