Spherical rotor molecules

The number of spherical rotors, i.e., molecules with three equal moments of inertia, is quite limited. Methane has been the one most extensively studied, and its band contours have been analyzed by a number of workers [ ]. Coriolis perturbations have been observed to occur between the fundamentals V4 at 1306 cm and V2 at 1526 cm-  

If the Coriolis interaction did not split the lines of a spherical rotor, it would be expected that the line structure would be similar to that of a perpendicular vibration of a linear molecule, for which the spacing of the lines is IB, There are no subband designations similar to those discussed for the symmetric rotors. 

Neglecting centrifugal distortion, the rotation term values for a spherical rotor are given by 

This is an identical expression to that for a diatomic or linear polyatomic molecule (Equations 5.11 and 5.12) and, as the rotational selection rule is the same, namely, AJ = 1, the transition wavenumbers or frequencies are given by 

All regular tetrahedral molecules, which belong to the Td point group (Section 4.2.8), may show such a rotational spectrum. However, those spherical rotors that are regular octahedral molecules and that belong to the Oh point group (Section 4.2.9) do not show any such 

2 ROTATIONAL INFRARED, MILLIMETRE WAVE AND MICROWAVE SPECTRA 

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We tend to think of a spherical rotor molecule, such as methane (see Figure 4.12a), as having no permanent dipole moment and, therefore, no infrared, millimetre wave or microwave... 

The Coriolis interaction is found to be larger for degenerate vibrational states than for nondegenerate levels. Thus, for symmetric rotor molecules, the doubly degenerate vibrations may be split so that they differ slightly in energy. The fine-line structure of the absorption band will then show lines due to transitions to both of these levels. For spherical rotor molecules, the Coriolis interaction will cause the triply degenerate frequencies to split. 

Linear, symmetric rotor, spherical rotor and asymmetric rotor molecules... 

As is the case for diatomic molecules, rotational fine structure of electronic spectra of polyatomic molecules is very similar, in principle, to that of their infrared vibrational spectra. For linear, symmetric rotor, spherical rotor and asymmetric rotor molecules the selection mles are the same as those discussed in Sections 6.2.4.1 to 6.2.4.4. The major difference, in practice, is that, as for diatomics, there is likely to be a much larger change of geometry, and therefore of rotational constants, from one electronic state to another than from one vibrational state to another. 

E13.13(b) A molecule must be anisotropically polarizable to show a rotational Raman spectrum all molecules except spherical rotors have this property. So CH2C12, CH3CH3, and N20 can display rotational Raman spectra SF cannot. 

The number of terms (up to five, but only three of them independent) and values of pre-exponential factor A, depend on the fluorophore symmetry and on the orientations of and in the molecule. The rotation correlation times, Tc,i, reflect the main components of the gyration tensor only. For the parallel orientation of both dipole moments, the initial anisotropy in a fluid system has the highest possible value, ro = A = 0.4. In the case of a spherical rotor, fluorescence anisotropy reduces to a single exponential function. For a symmetric rotor, r t) is either single-or double-exponential, depending on the orientation of dipole moments with respect to the long axis. 

D13.3 (I) Rotational Raman spectroscopy. The gross selection rule is that the molecule mustbe anisotropically polarizable, which is to say that its polarizability, or, depends upon the direction of the electric field relative to the molecule. Non-spherical rotors satisfy this condition. Therefore, linear and symmetric rotors are rotationally Raman active. 

P13.23 Refer to the flow chart in Fig. 12.7 in the text. Yes at the first que.stion (linear ) leads to linear point groups and therefore linear rotors. If the molecule is not linear, then yes at the next question (two or more C with n > 2 ) leads to cubic and icosahedral groups and therefore spherical rotors. If the molecule is not a spherical rotor, yes at the next question leads to symmetric rotors if the highest C has > 2 if not. the molecule is an asymmetric rotor. 

If there arc two or more axes of greater than twofold symmetry, the molecule will be a spherical rotor (groups 3, 3a, 3 0, 6a, S). 

Classification of Rotor Type. The solutions of the rotational energy problem are classified according to the rotor type, i.e., according to relations between the principal moments of inertia. A linear molecule ha.s 1% = and 1° = 0 since all atoms lie on the axis. A spherical rotor... 

A, B, C (in decreasing order of magnitude). More symmetrical molecules, e.g. prolate or oblate symmetric rotors, linear molecules, and spherical rotors, have one or more special restrictions on the magnitudes of the rotational constants. Formulae which apply to any rotational constant are described in terms of B. Thus all formulae for B apply equally to A and/or C (if one or both differs from jB), and no implication of molecular symmetry is intended. 

A diatomic molecule such as HCl has three principal moments of inertia. The one about the internuclear axis is practically zero, and the other two, about axes perpendicular to this axis, are equal. A molecule such as CH4 has three principal moments of inertia about the three mutually perpendicular principal axes which are equal, i.e., / = / = /c- Such a molecule with three equal principal moments of inertia is called a spherical rotor (or spherical top) a molecule with two of the three moments equal is called a symmetric top, and one with three unequal principal moments is called an asymmetric rotor (or asymmetric top). For each of these models, a rotational term value equation can be developed. These equations... 

Transitions between the rotational states of a polyatomic molecules can produce a microwave spectrum. We will not discuss the details of the microwave spectra of polyatomic molecules, but make some elementary comments. As with diatomic molecules, we apply the rigid-rotor approximation, assuming that a rotating polyatomic molecule is locked in its equilibrium conformation. Any molecule in its equilibrium conformation must belong to one of four classes linear molecules, spherical top molecules, symmetric top molecules, and asymmetric top molecules. 

This form of the equation is valid for linear molecules and symmetric rotors (for which I corresponds to reorientation of the symmetry axis) and can be used for nondipolar solvents. A somewhat more complicated expression would hold in the absence of axial symmetry. Maroncelli et al. estimated the value tti for AP corresponding to a charge shift of a spherical ion in a continuum model of a polar solvent of dielectric constant s and showed that it increases with increasing solvent polarity and works well when tti is significantly larger than one. 

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