Experimental Technique Microwave Spectroscopy

Consider a heteronuclear diatomic molecule such as HCl or CO. The rotational motion of such a molecule can be described by a simple model called the rigid rotor. A rigid rotor consists of two point masses (ffij and m2) that are connected by a massless, but rigid, bar of length R. In this model the masses correspond to the two atoms of the diatomic molecule and the bar (R) represents a bond of length R between them  

The Schrddinger equation corresponding to the rotations of this rigid rotor can be solved exactly to obtain the following quantized rotational energies  

if the Unes of the microwave spectrum are known, then the value of 5 can be determined, from which we can calculate the moment of inertia and, thus, the bond distance r. 

It is important to note that because the moment of inertia depends upon the masses of the atoms in the molecule, the microwave spectrum of a diatomic molecule will be sensitive to the isotopic composition of the molecule. The structure of polyatomic molecules can also be studied using microwave spectroscopy, although the procedure is more complicated than that considered here for diatomic molecules. 

Electromagnetic radiation can only affect the rotation of a diatomic molecule if the two ends of the molecule are oppositely charged (see the figure). Thus, only diatomic molecules with polar bonds (such as HCl, CO, HE) will absorb micro-wave radiation. Molecules with nonpolar bonds (N2, O2) cannot be studied in this way. 

---

The interaction of dihalogen molecules XY with different acceptors B quite often leads to vicious chemical reactions. In most cases, the 1 1 complexes are extremely short-lived. To investigate these prereactive complexes experimentally in a collision-free environment, pulsed-nozzle, Fourier-transform microwave spectroscopy has turned out to be the ideal technique. Legon and coworkers prepared a large number of these complexes and performed detailed rotational spectroscopic analyses. Several series of simple molecules... 

As stated above, CNDO formalism was able to predict for many methyl derivatives (containing numerous hydrogen atoms) preferred conformations fully identical to those obtained by the most appropriate experimental techniques, electron diffraction and microwave spectroscopy. This was the case, for example, for each term of the (CH3)2M (14) and (CH3)3M (15) series. This quantum approach appeared likely to help experimentalists to locate accurately, and in a simpler way than usual, the light atoms - mainly hydrogen — in a molecule. 

The theoretical conformational analysis of a molecule, whatever the quantum technique used, provides quantities related to the free molecule at 0°K and within ideal standard entropy conditions. It follows that such results must be compared with experimental results obtained in conditions as close as possible to these. Obviously, any study in the gas phase will be preferable to corresponding ones performed on liquid or solid states. The most suitable experimental approaches will thus be electron diffraction and microwave spectroscopy. 

The purpose of this brief survey was to demonstrate that, despite the criticisms which may be made of the use of any semi-empirical quantum technique for structural and conformational studies, the CNDO/2 and Extended CNDO/2 formalisms are definitely reliable tools for theoretical conformational analyses in inorganic and coordination chemistry. Moreover, if these tools are combined with the most suitable experimental techniques (i.e. microwave spectroscopy and electron diffraction) in that field, many problems of geometry and conformation can be solved in a way that neither of these approaches could have accomplished alone. 

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. 

Equilibrium geometries for upwards of four thousand small molecules have been determined experimentally in the gas phase, primarily by microwave spectroscopy and electron diffraction. In the best cases, the experimental techniques are able to provide bond lengths and angles to within a few thousandths of an A and a few tenths of a degree, respectively. For larger systems, lack of data usually prohibits complete stmcture determination, and some geometrical variables may have been assumed in the reported stmcture. 

Experimental gas-phase structures of charged species are virtually non-existent. It is impossible to establish sufficiently high concentrations for conventional spectroscopy. Also, microwave spectroscopy, the principal technique for accurate structure determinations, cannot be applied to charged species. 

Experimental assessments of the concentration of the minor hydroxy tautomer of 2-pyridone and substituted derivatives in cyclohexane and acetonitrile solution may be carried out by the use of fluorescence spectroscopy (85JCS(P2)1423). For the parent compound, the pyridinol component in cyclohexane is estimated to be 4% and in acetonitrile 1.2% this preference for the hydroxy form in the former over the latter solvent is maintained over a fair range of variously substituted pyridones. Ab initio calculations (85JA7569) on 4-hydroxypyridine, the minor tautomer in aqueous solution, include 92 water molecules in the estimations, and thus give a very detailed picture of the solvated molecule, while the experimental technique of microwave spectroscopy not only gives an accurate estimation of the 2-hydroxypyridine / 2-pyridone ratio of 3 1 in the gas phase but also reveals that the former isomer is predominantly in the (Z)-form (80) and that both isomers are planar (93JPC46). 

Townes, C. H., and A. L. Schawlow, Microwave Spectroscopy, McGraw-Hill, New York, 1955. Comprehensive discussions of theory and experimental techniques useful appendices for calculating asymmetric-top energy levels. For internal rotation, however, consult Sugden and Kenney or Wollrab. 

Pure rotational spectroscopy in the microwave or far IR regions joins electron diffraction as one of the two principal methods for the accurate determination of structural parameters of molecules in the gas phase. The relative merits of the two techniques should therefore be summarised. Microwave spectroscopy usually requires sample partial pressures some two orders of magnitude greater than those needed for electron diffraction, which limits its applicability where substances of low volatility are under scrutiny. Compared with electron diffraction, microwave spectra yield fewer experimental parameters more parameters can be obtained by resort to isotopic substitution, because the replacement of, say, 160 by lsO will affect the rotational constants (unless the O atom is at the centre of the molecule, where the rotational axes coincide) without significantly changing the structural parameters. The microwave spectrum of a very complex molecule of low symmetry may defy complete analysis. But the microwave lines are much sharper than the peaks in the radial distribution function obtained by electron diffraction, so that for a fairly simple molecule whose structure can be determined completely, microwave spectroscopy yields more accurate parameters. Thus internuclear distances can often be measured with uncertainties of the order of 0.001 pm, compared with (at best) 0.1 pm with electron diffraction. If the sample is a mixture of gaseous species (perhaps two or more isomers in equilibrium), it may be possible to unravel the lines due to the different components in the microwave spectrum, but such resolution is more difficult to accomplish with electron diffraction. 

The years from 1960 to 1975 represented a golden era in the radiofrequency and microwave spectroscopy of open shell diatomic molecules. Molecular beam electric resonance was one of the most important experimental approaches, but microwave, far-infrared and magnetic resonance studies of bulk gaseous samples were equally important and our understanding of these open shell species is derived from a combination of different experimental approaches. In this book we have chosen to organise our descriptions according to the experimental techniques employed, but as with any such scheme, we run the risk, which we wish to avoid, of not connecting the results from different types of experiment in a coherent manner. As we shall see, the OH radical is the example par excellence which illustrates the pitfalls of an approach which is technique-oriented, rather than molecule-oriented. 

The basic experimental techniques of structure determination, i.e. microwave spectroscopy (MW) and electron diffraction (ED) for the gas phase and X-ray diffraction (XD) for crystals, as well as the physical meaning of parameters obtained (r, r, r, etc.) are... 

Four different experimental techniques were employed in attempts to elucidate the structure of bicyclobutane. Haller and Srinivasan obtained some structural information from the analysis of partially resolved infrared vibration-rotation bands. However, this method is not expected to give results of high accuracy, especially since some of the fundamental parameters has to be assumed. Meiboom and Snyder used NMR measurements in liquid crystals for structure determination. One limitation of this method is that only ratios of internuclear distances rather than absolute values can be determined. Also, the authors point out that their results should not be considered as final since corrections for vibration were not made. The other two methods successfully employed were electron diffraction and microwave spectroscopy The structural parameters obtained by these methods are collected in Table 1. 

The structures of VdW dimers, considered as weakly bounded complexes in which each monomer maintains its original structure (Buckingham, 1982), are studied at low temperatures by sophisticated experimental techniques, such as far infrared spectra, high-resolution rotational spectroscopy in the microwave region, and molecular beams. Distances Re between the centres of mass and bond strengths De at the VdW minimum for some homodimers of atoms and molecules taken from Literature are collected in Table 4.4. 

There are relatively few experimental techniques for the determination of accurate molecular structures of fiee molecules in their ground states in the gas phase, even considering the subdivisions of spectroscopy microwave, infiared and Raman. The common techniques come under either spectroscopic or electron diffraction methods. 

While microwave spectroscopy must rely on rather indirect means to obtain barrier height information, transitions between energy levels of different n can be directly observed by infrared and Raman studies. Resolution is much poorer in these techniques thus while microwave studies are limited primarily by model errors, the limit to optical studies is to a large extent due to experimental uncertainties. 

The magnitudes of the barriers to rotation of many small organic molecules have been measured. The experimental techniques used to study rotational processes include microwave spectroscopy, electron diffraction, ultrasonic absorption, and infrared spectroscopy. Some representative barriers are listed in Table 2.1. As with ethane, the barriers in methylamine and methanol appear to be dominated by hyperconjugative stabilization of the anti conformation. The barrier decreases (2.9 2.0 1.1) in proportion to the number of anti H-H arrangements (3 2 1). (See Topic 1.1 for further discussion.) ... 

Spectroscopy is the most important experimental source of information on intermolecular interactions. A wide range of spectroscopic techniques is being brought to bear on the problem of weakly bound or van der Waals complexes [94,95]. Molecular beam microwave spectroscopy, pioneered by Klemperer and refined by Flygare, has been used to determine the microwave spectra of a large number of weakly bound complexes and obtain structural information... 

The DQCC values can be experimentally determined from solid - state NMR spectra [12], in NMR experiments with liquid crystal solvents [13] and also by microwave spectroscopy and nuclear double resonance [14]. However, the application of these techniques for transition metal hydrides seems to be problematic for different practical reasons. We show here that the DQCC values can also be determined by T, relaxation experiments on the D - derivatives of transition metal hydrides in solution. It is remarkable thatT, relaxation studies on H nuclei played a great role for the development of the transition metal hydride chemistry and led to the development of excellent methods providing reasonable geometric descriptions of the MH or M(H2) moieties in solution [15, 16]. 

---