Rotation angular molecules

The simplest case is a transition in a linear molecule. In this case there is no orbital or spin angular momentum. The total angular momentum, represented by tire quantum number J, is entirely rotational angular momentum. The rotational energy levels of each state approximately fit a simple fomuila ... 

Suppose that W(r,Q) describes the radial (r) and angular (0) motion of a diatomic molecule constrained to move on a planar surface. If an experiment were performed to measure the component of the rotational angular momentum of the diatomic molecule perpendicular to the surface (Lz= -ih d/dQ), only values equal to mh (m=0,1,-1,2,-2,3,-3,...) could be observed, because these are the eigenvalues of ... 

Figure 5.5 The rotational angular momentum vector P for (a) a linear molecule and (b) the prolate symmetric rotor CH3I where is the component along the a axis...

Figure 5.12 shows the J= — 0 transition of the linear molecule cyanodiacetylene (H—C=C—C=C—C=N) observed in emission in Sagittarius B2 (Figure 5.4 shows part of the absorption spectrum in the laboratory). The three hyperfine components into which the transition is split are due to interaction between the rotational angular momentum and the nuclear spin of the nucleus for which 1= 1 (see Table 1.3). The vertical scale is a measure of the change of the temperature of the antenna due to the received signal. 

Various reactions in which the reactants are in particular vibrational and rotational states have been investigated and state-to-state kinetics have been studied. Two procedures have been used in these investigations. Brooks and coworkers first employed the molecular beam method for studying the state-to-state kinetics. The reactants molecules are put into desired vibrational and rotational states by laser excitation and identified the states by their fluorescence. In molecular beam experiments, it is possible to control the translational energy and mutual orientation of the reactants and to determine the degree of polarization of the rotational angular momentum of the product. 

The rotational g factor is the ratio of the rotational magnetic dipole moment of a molecule to its molecular rotational angular momentum [1-5]. Experimentally the rotational g factor was originally determined by measuring the rotational magnetic... 

Molecules for which all three principal moments of inertia (the Ij s) are equal are called spherical tops. For these species, the rotational Hamiltonian can be expressed in terms of the square of the total rotational angular momentum J2 ... 

The first line in this expression describes the rotational structure with color spin-doubling and the hyperflne interaction of the effective electron spin S with the nuclear spin I. B is the rotational constant, J is the electron-rotational angular momentum, A is the o -doubling constant. The second line describes the interaction of the molecule with the external fields B and E, (A is the unit vector directed from the heavy nucleus to the light one). The last line corresponds to the P-odd electromagnetic interaction of the electrons with the anapole moment of the nucleus described by the constant /ca [40], P,T-odd interaction of the electron EDM de with the interamolecular field, and P,T-odd scalar interactions of the electrons with the heavy nucleus [90]. 

These relations are valid only for force laws and potential functions which are functions of die intermolecular separation alone. For an angular dependent potential, the force on molecule is different and, in addition, there is a torque tending to rotate the molecule (Ref 8e, p 22)... 

For nearly all molecules with A = 0, we have case (b) coupling there are also a few molecules with A= 0 that fall in this case. In case (b), the angular momentum A combines with the molecular rotational angular momentum O to give a total angular momentum apart from electronic and nuclear spin, which is called N. The magnitude of N is... 

For a linear polyatomic molecule, there is no rotational angular momentum about the intemuclear axis therefore, the derivatives with respect to chi are absent from (5.40). What are the rotational wave functions for a linear polyatomic molecule ... 

The presence of degenerate vibrational modes affects the rotational energies. In Section 4.11, we saw the effect of electronic angular momentum on the rotational energies of a diatomic molecule. In this section, we shall assume that there is no electronic angular momentum, only nuclear vibrational and rotational angular momentum. If both electronic and... 

The representation 2" of Rz is omitted from Trot because the linear molecule has no rotational angular momentum about the z axis.) Subtraction of the characters of IIg, 2, and IIM from (9.165) gives as the characters of Fvib... 

The angular momentum 0 then combines with the angular momentum O due to the rotation of the molecule to give a total angular momentum (apart from nuclear spin) J. (In the older literature, the rotational angular momentum of the nuclei is called N instead of O.) The magnitude of J is... 

For 2 molecules, we used J as the rotational angular-momentum quantum number since 2 molecules have no electronic spin or orbital angular momentum, J is also the total angular-momentum quantum number, exclusive of nuclear spin, for such molecules. Recall that for atoms J is also used as the total angular-momentum quantum number apart from nuclear spin.) The rotational energy in case (a) is given approximately by... 

The quantum number K gives the rotational angular-momentum component along a molecule-fixed axis of the spherical top. From (5.34) and... 

The interaction between the nuclear electric quadrupole moment and the electrons of the molecule couples the nuclear spin I to the rotational angular momentum J, giving a resultant total angular momentum F, of... 

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