Selection rules microwave

The methyl iodide molecule is studied using microwave (pure rotational) spectroscopy. The following integral governs the rotational selection rules for transitions labeled J, M, K... 

In Equation (6) ge is the electronic g tensor, yn is the nuclear g factor (dimensionless), fln is the nuclear magneton in erg/G (or J/T), In is the nuclear spin angular momentum operator, An is the electron-nuclear hyperfine tensor in Hz, and Qn (non-zero for fn > 1) is the quadrupole interaction tensor in Hz. The first two terms in the Hamiltonian are the electron and nuclear Zeeman interactions, respectively the third term is the electron-nuclear hyperfine interaction and the last term is the nuclear quadrupole interaction. For the usual systems with an odd number of unpaired electrons, the transition moment is finite only for a magnetic dipole moment operator oriented perpendicular to the static magnetic field direction. In an ESR resonator in which the sample is placed, the microwave magnetic field must be therefore perpendicular to the external static magnetic field. The selection rules for the electron spin transitions are given in Equation (7)... 

The dipole and polarization selection rules of microwave and infrared spectroscopy place a restriction on the utility of these techniques in the study of molecular structure. However, there are complementary techniques that can be used to obtain rotational and vibrational spectrum for many other molecules as well. The most useful is Raman spectroscopy. 

Spectroscopic techniques look at the way photons of light are absorbed quantum mechanically. X-ray photons excite inner-shell electrons, ultra-violet and visible-light photons excite outer-shell (valence) electrons. Infrared photons are less energetic, and induce bond vibrations. Microwaves are less energetic still, and induce molecular rotation. Spectroscopic selection rules are analysed from within the context of optical transitions, including charge-transfer interactions The absorbed photon may be subsequently emitted through one of several different pathways, such as fluorescence or phosphorescence. Other photon emission processes, such as incandescence, are also discussed. 

As illustrated in Fig. 41 (see p. 84), the number of observed Cu-ENDOR lines (63Cu enriched sample217 ) does not follow the usual ENDOR selection rules for EPR observers with resolved hfs (two transitions for EPR observers with mi = I, four transitions for EPR observers with - I < n < I Sect. 3.2). This may be due to transfer of microwave saturation to EPR transitions other than the one which is used as an observer. A corresponding effect has been observed in Co-ENDOR spectra of Co(acacen)61. ... 

Infrared, Raman, microwave, and double resonance techniques turn out to offer nicely complementary tools, which usually can and have to be complemented by quantum chemical calculations. In both experiment and theory, progress over the last 10 years has been enormous. The relationship between theory and experiment is symbiotic, as the elementary systems represent benchmarks for rigorous quantum treatments of clear-cut observables. Even the simplest cases such as methanol dimer still present challenges, which can only be met by high-level electron correlation and nuclear motion approaches in many dimensions. On the experimental side, infrared spectroscopy is most powerful for the O—H stretching dynamics, whereas double resonance techniques offer selectivity and Raman scattering profits from other selection rules. A few challenges for accurate theoretical treatments in this field are listed in Table I. 

Symmetric tops with no dipole moment have no microwave spectrum. For example, planar symmetric-top molecules have a C axis and a ak symmetry plane such molecules cannot have a dipole moment. Thus benzene has no microwave spectrum. For a symmetric top with a permanent electric dipole moment, the selection rules for pure-rotation transitions are... 

Transitions due to a nonvanishing dipole-moment component da are called cr-type transitions. The selection rules for Kpr and Koh for the three kinds of asymmetric-top microwave transitions are... 

For a symmetric top, the selection rules are such that we can determine only B0 [see (5.85)]. Knowledge of Ib°, the moment of inertia about a principal axis perpendicular to the symmetry axis, is not sufficient to determine the molecular structure, except for a diatomic molecule. To get added information, the microwave spectra of isotopically substituted spe-... 

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.)... 

ESR transitions are due to the interaction of the electron s spin magnetic moment fis with the oscillating field of the incident microwave radiation. The experimental setup is such that B, is perpendicular to B0, so that the selection rules are determined by the integral... 

The central problem is to calculate the field required to drive the n — n + 1 transition via an electric dipole transition. In the presence of an electric field, static or microwave, the natural states to use are the parabolic Stark states. While there is no selection rule as strict as the M = 1 selection rule for angular momentum eigenstates, it is in general true that each n Stark state has strong dipole matrix elements to only the one or two n + 1 Stark states which have approximately the same first order Stark shifts. Red states are coupled to red states, and blue to blue. Explicit expressions for these matrix elements between parabolic states have been worked out,25 and, as pointed out by Bardsley et al.26, the largest matrix elements are those between the extreme red or blue Stark states. These matrix elements are given by (n z n + 1) = n2/3.26... 

Measurements with Na+ ions of energies in the 29-590 e V range, corresponding to v/ve from 0.2 to 0.9, were compared to the diabatic SFI spectra of the Na 28f, 28g, and 28h states observed individually by driving resonant microwave transitions from the 28d state.9 These detailed comparisons show clearly that for high velocity, v/ve 0.9, 59% of the 28d— 28 cross section is to the 28f state, the dipole allowed transition. However, at lower values of v/ve, nondipole processes play a more important role. For example, at v/ve = 0.2, only 37% of the cross section is due to the 28d— 28f transition.9 At high velocities the process is predominantly a dipole M = 1 process, but at low velocities the dipole selection rule breaks down. 

An interesting development in molecular rotational relaxation has been the microwave double-resonance method176-178. The technique permits the exploration of the fine detail of the processes which occur in collisions of polyatomic molecules, and results for a number of symmetric tops have been reported. For example, Oka has described experiments on NH3 in which inversion doublets for selected J values were pumped by high microwave power. Pumping disturbs the population of the inversion doublet, and also that of other doublets which are populated from the original pair by collision processes. By absorption measurements of other inversion doublets with steady state irradiation, Oka has shown that in NH3/NH3 collisions, transitions which are allowed by the electric dipole selection rules (A/ = 0, 1, + - —) are preferred. Oka s analysis indicates that relaxation is most favourable in collision with molecules having similar J values, which are termed rotational resonances (R-R transfer). For example the process... 

Any molecule with a permanent electric dipole moment can interact with an electromagnetic field and increase its rotational energy by absorbing photons. Measuring the separation between rotational levels (for example, by applying a microwave field which can cause transitions between states with different values of /) let us measure the bond length. The selection rule is A/ = +1—the rotational quantum number can only increase by one. So the allowed transition energies are... 

In the microwave ion beam experiments described in this section, it is important to identify the microwave mode corresponding to the resonance line studied in a magnetic field. For a TM mode the microwave electric field along the central axis of the waveguide is parallel to the static magnetic field. We then put p = 0 in equation (10.161) so that the Zeeman components obey the selection rule AMj = 0. Alternatively in a TE mode the microwave electric field is perpendicular to the static magnetic field and the selection rule is A Mj = 1. This is the case for the Zeeman pattern shown in figure 10.73 each J = 3/2 level splits into four Mj components and the six allowed transitions should,... 

The quality of the SOC calculation in O2 can be checked by estimation of the fc Sj" — A3E transition probability. The transition is forbidden by selection rules for electric dipole radiation with account of SOC, and occurs as magnetic dipole spin-current borrowing intensity from microwave transitions between spin-sublevels of the ground state [41]. 

These discoveries could hardly have been brought about without the extensive knowledge of energy levels, selection rules, transition probabilities and spectra assembled by laboratory spectroscopy for a very wide range of molecules. Microwave spectroscopy in the centimeter- and millimeter-wave regions is a well-established research field for further information the reader is referred to the books by Gordy and Cook (1970), and Townes and Schawlow (1955), and to a recent review on millimeter-wave spectroscopy by Winnewisser et al. (1972). Reviews on interstellar molecules are given by Snyder (1972) and Rank etal. (1971). 

Although most lanthanide ions are paramagnetic, because of rapid relaxation effects, spectra can be obtained only at low temperatures (often 4.2 K) in most cases. From the point of view of the chemist, EPR spectra are readily obtained (at room temperature) only from the f Gd +, with its 87/2 ground state. The sublevels of this state are degenerate in the absence of a crystal field (in a free Gd + ion), but are split into four Kramers doublets, with M/-values of 1/2, 3/2, 5/2 and 7/2. The application of a magnetic field removes the degeneracy of each doublet, and transitions can occur on irradiation with microwave radiation, subject to the usual selection rule of AM/ = 1. 

The microwave spectrum of CSFg observed by Kisliuk and Silvey (2 ) shows that the molecule is a symmetric rotor comprised of CFg and SFg groups joined by a C-S bond. The infrared ( i 4) and Raman (4) spectra obey the selection rules predicted for the point group We estimate all structural data except for the C-S bond length by analogy with the CF structure in CgFg... 

Rotational features of almost aU H-bonded complexes in the gaseous phase appear in the microwave region, with wavenumbers less than 10 cm They correspond to transitions between pure rotational levels, pure meaning that vibrations remain unchanged, or no vibrational transition accompanies such rotational transitions. Rotational features, however, also appear in the IR spectra of these H-bonded complexes. IR bands correspond to transitions between various vibrational levels of a molecule. When this molecule is isolated, as in the gas phase, these transitions are always accompanied by transitions between rotational levels that obey the same selection rules as pure rotational transitions detected in microwave spectroscopy. The information conveyed by these rotational features in IR spectra are therefore most similar to those conveyed by microwave spectra, even if the mechanism at the origin of their appearance is different. Their interests lie in the use of an IR spectrometer, a common instrument in many laboratories, instead of a microwave spectrometer, which is a much more specialized instrament. However, the resolution of usual IR spectrometers are lower than that of microwave spectrometers that use Fabry-Perot cavities. This IR technique has been used in the case of simple H-bonded dimers with relatively small moments of inertia, such as, for instance, F-H- -N C-H (3). Such complexes are far from simple to manipulate, but provide particularly simple IR spectra with a limited number of bands that do not show any overlap. 

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