K-quantum number

Mode specificity has also been observed for HOCl—>Cl+OH dissociation [92, 93 and 94]- For this system, many of the states are highly mixed and unassignable (see below). However, resonance states with most of the energy in the OH bond, e.g. = 6, are assignable and have nnimolecnlar rate constants orders of magnitude smaller than the RRKM prediction [92, 93 and 94]- The lifetimes of these resonances have a very strong dependence on the J and K quantum numbers of HOCl. 

The rotational eigenfunctions and energy levels of a molecule for which all three principal moments of inertia are distinct (a so-called asymmetric top) can not easily be expressed in terms of the angular momentum eigenstates and the J, M, and K quantum numbers. However, given the three principal moments of inertia la, Ib, and Ic, a matrix representation of each of the three contributions to the rotational Hamiltonian... 

When the above analysis is applied to a diatomic species such as HCl, only k = 0 is present since the only vibration present in such a molecule is the bond stretching vibration, which has a symmetry. Moreover, the rotational functions are spherical harmonics (which can be viewed as D l, m, K (Q,< >,X) functions with K = 0), so the K and K quantum numbers are identically zero. As a result, the product of 3-j symbols... 

The K quantum number ean not ehange beeause the dipole moment lies along the moleeule s C3 axis and the light s eleetrie field thus ean exert no torque that twists the moleeule about this axis. As a result, the light ean not induee transitions that exeite the moleeule s spinning motion about this axis. 

To discover smaller specific effects on the intramolecular dynamics after attachment of an Ar atom to the benzene molecule, we performed lifetime measurements of single rovibronic states in the 6q band of the benzene-Ar and the benzene-84 Kr complex. No dependence of the lifetime on the J K> quantum number within one vibronic band was found [38]. This is in line with the results in the bare molecule and points to a nonradiative process in the statistical limit produced by a coupling to a quasi-continuum, for example, the triplet manifold. 

Symmetrical tops are of two types. A prolate spheroid (football shape) in which /A < /b, and an oblate spheroid (pancake shape) in which /A > /b. Again, there are 2J + 1 sets of energy levels for each J, but they are no longer degenerate, as can be seen from equation (A6.9), which includes both the J and K quantum number. 

Asymmetric top rotational states are labelled by the value of J (or N if S 0), with subscripts Ka,Kc, where the latter correlate with the K = k quantum number about the a and c axes in the prolate and oblate symmetric top limits respectively. 

A succession of levels like those of a linear molecule can be calculated for each quantum number K, which in this case describes the quantized component of the angular momentum about the unique a-axis. K cannot exceed 7, the quantum number for the total angular momentum, i.e., K = 0, 1,... dz7. For an oblate symmetric top the rotational constant A j has to be replaced by Q ]. In relation to the case of A" = 0, other K quantum numbers allowed will thus result in lower energies Ejk, which is in contrast to the prolate top with a positive term of (A[ j - 6 ]). Evidently, all rotational levels with 0 are doubly degenerate. It should be noted that each level still possesses an M-degeneracy of (27 -f 1) as discussed in connection with the linear molecule. This is due to space quantization. 

Each K quantum number in the lower vibrational state with the exception of A = 0, gives rise to two subbands. The subband origins can be calculated according to... 

The allowed dipole transitions between the states of the complex can be deduced from an analysis of the expression for the transition intensity, and it follows easily that the observed dipole transitions must obey the following rigorous selection rules AJ = 1, Aa = 0 or AJ = 0, Aquantum number is nearly conserved, an additional approximate selection rule should hold AK = 0,1. 

The rotationless vibrational levels of formaldehyde can each be assigned a set of normal mode quantum numbers and fit to Eq. (2.65) up to 9,300 cm" above the zero-point level (Reisner et al., 1984). At higher J and K values the spectra become more complex as a result of rotation-induced mixing of anharmonic vibrational basis functions, which compromises the goodness of both vibrational and K quantum numbers (Dai et al., 1985a). However, the mixing between zero-order basis functions is not... 

A second rotational effect comes into play when rotations are strongly coupled to the vibrations, via, for instance, coriolis interactions. In that case, the projection of the principle rotational quantum number, the K quantum number in symmetric top molecules, is no longer conserved. The energy associated with this quantum number then gets mixed in with the molecule s vibrational energy, thereby increasing the density and sums of states. When this happens we say that the A -rotor is active. If the T-rotor does not couple with the vibrations, it is inactive. We first discuss what happens when a diatom dissociates and follow that with the dissociation of polyatomic molecules. 

Many nonlinear molecules can be treated as symmetric top rotors in which two of the moments of inertia are equal. The moment of inertia about the synunetiy axis is 7, while the two other moments of inertia are 7 = ly A symmetric top can be visualized as a rotating cylinder. For a given J, the cylinder can rotate in a total of 27 -I- 1 orientations, each with a different K quantum number which determines its projection along the symmetry axis. Figure 7.9 shows the case of prolate and oblate tops rotating with K J and K = 0. 

The rotational PEDs for the dissociation of state-selected NO2 have been measured and analyzed using both the prior model and PST (Robie et al., 1992 Hunter et al., 1993). A convenient approximation is to assume that the product energy distributions are independent of the NO2 M and K quantum numbers. Three product angular momenta, 7no> - o> and must be combined to add up to the total angular momentum, convenience, the NO ii value is included in the Jj q term thereby adding either 0.5 or 1.5 to the rotational quantum number. The angular momenta are combined in two steps. The intermediate J is introduced which is defined by the vector addition J = Jno + that... 

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