Rotation constants, selected 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. 

Over the last years we have explored several advanced techniques for high-resolution rotational coherence spectroscopy (RCS [1]) in order to study the structures of molecules and clusters in the gas phase [2]. We have provided spectroscopic examples demonstrating (i) mass-selectivity (Fig. 1, [3]), (ii) that the rotational constants of the ground and electronic excited states can be obtained independently with high precision (lO MO"5, [4]), (iii) that the transition dipole moment alignment, (iv) centrifugal distortion constants, and (v) information on the polarizability tensor can be obtained (Fig.l, [5]). Here we review results pertaining to points (i), (ii), (iv) and (v) [2,3,5],... 

Recall that homonuclear diatomic molecules have no vibration-rotation or pure-rotation spectra due to the vanishing of the permanent electric dipole moment. For electronic transitions, the transition-moment integral (7.4) does not involve the dipole moment d hence electric-dipole electronic transitions are allowed for homonuclear diatomic molecules, subject to the above selection rules, of course. [The electric dipole moment d is given by (1.289), and should be distinguished from the electric dipole-moment operator d, which is given by (1.286).] Analysis of the vibrational and rotational structure of an electronic transition in a homonuclear diatomic molecule allows the determination of the vibrational and rotational constants of the electronic states involved, which is information that cannot be provided by IR or microwave spectroscopy. (Raman spectroscopy can also furnish information on the constants of the ground electronic state of a homonuclear diatomic molecule.)... 

Theory provides calculated values of absolute shieldings, that is, the shielding relative to a bare nucleus with no electrons. As we see in Section 4.3, experimental measurements provide information on shieldings relative to some selected standard. For comparison between theory and experiment, additional data are needed. For example, it can be shown that trP calculated with the gauge origin at a particular nucleus in a small molecule is proportional to the molecular spin—rotation constant of that nucleus, which can be independently measured by microwave spectroscopy, because crD can be calculated precisely, this combination permits the establishment of an absolute experimental shielding scale for various nuclei. For hydrogen, simultaneous measurements of NMR and the electronic... 

The resulting spectrum represents a weighted average over the rotational states and a careful analysis of it yields the nuclear quadrupole coupling constant. Molecular beam electric resonance is complementary to pure rotational spectroscopy since transitions between the Stark levels of the rotational states (AJ = 0) are observed (sometimes AJ= 1 transitions are also studied). Specially constructed maser spectrometers55 that can detect transitions of rotationally selected molecules have been used to determine very small coupling constants, such as those for deuterium compounds. Again, molecular beam resonance is currently limited to the study of small molecules. 

The molecule PH3 (C3V symmetry) is an oblate symmetric top (Crotational constants C (refers to rotation around the C3 axis) and B (perpendicular to C3). Since the permanent electric dipole moment is pointed parallel to the C3 axis, only pure rotational transitions with the selection rule AK=0 are allowed (K is the quantum number of the component about the C3 axis of the total angular momentum J). Their analysis leads to the parameters B, Dj, Djk, and Hjk. From the perturbation-allowed transitions AK= 3n (n=1,2,...), which become weakly allowed by centrifugal distortion effects (inducing a small dipole moment of about 8x10 D perpendicular to the C3 axis [1, 2, 3]), the K-related constants (C, Dk, Hk) were obtained see, e.g. [1, 3, 4]. 

This variety in rotational selection rules, coupled with our natural endowment of molecules with diverse rotational constants, leads to wide variations in the rotational fine structure exhibited by symmetric and near-symmetric tops. For definiteness, we consider a prolate symmetric top whose rotational energy levels are given in Eq. 5.26. Rotational lines will be found at the frequencies... 

TABLE 9.2 Rotational constants (cm ) for selected polyatomic molecules. 

Any homonuclear diatomic molecule has no permanent dipole moment and therefore no allowed rotational spectrum. Because the dipole moment remains zero as the bond stretches, homonuclear diatomics also have no allowed vibrational spectrum. Only electronic spectroscopy in homonuclear diatomics is allowed by electric dipole selection rules, and high precision measurements of the rotational and vibrational constants in molecules as simple as H2 and N2 can be quite difficult. 

TABLE 14.2 Rotational constants B and centrifugal distortion constants Dj for selected diatomic molecules ... 

---