Microwave spectroscopy rotational constants

Van der Waals complexes can be observed spectroscopically by a variety of different teclmiques, including microwave, infrared and ultraviolet/visible spectroscopy. Their existence is perhaps the simplest and most direct demonstration that there are attractive forces between stable molecules. Indeed the spectroscopic properties of Van der Waals complexes provide one of the most detailed sources of infonnation available on intennolecular forces, especially in the region around the potential minimum. The measured rotational constants of Van der Waals complexes provide infonnation on intennolecular distances and orientations, and the frequencies of bending and stretching vibrations provide infonnation on how easily the complex can be distorted from its equilibrium confonnation. In favourable cases, the whole of the potential well can be mapped out from spectroscopic data. 

Microwave studies in molecular beams are usually limited to studying the ground vibrational state of the complex. For complexes made up of two molecules (as opposed to atoms), the intennolecular vibrations are usually of relatively low amplitude (though there are some notable exceptions to this, such as the ammonia dimer). Under these circumstances, the methods of classical microwave spectroscopy can be used to detennine the stmcture of the complex. The principal quantities obtained from a microwave spectmm are the rotational constants of the complex, which are conventionally designated A, B and C in decreasing order of magnitude there is one rotational constant 5 for a linear complex, two constants (A and B or B and C) for a complex that is a symmetric top and tliree constants (A, B and C) for an... 

Similar operational definitions have to be taken into account for every experimental tool of structural chemistry to define the meaning of the observables that it provides6. In microwave spectroscopy, for example, structural information is obtained from the rotational constants... 

In microwave spectroscopy, the situation is characterized by the fact that the number of independent pieces of observable data is often restricted to three rotational constants, while the number of degrees of freedom—3N-6 or 3N-5, where N is the number of atoms—can be significantly larger. The number of independent experimental rotational constants can be effectively increased by recording the spectra of isotopically substituted species, but that is not always possible. Thus, structural studies by microwave spectroscopy are often seriously underdetermined and extraneous information is useful in aiding the spectroscopic assignment. 

Due to the characteristics of the technique, comparisons of -parameters in microwave spectroscopy are not meaningful within 0.01 A6, particularly if one or several atoms are close to a principal axis of rotation. When restructures are determined from three rotational constants for a species with more than three degrees of freedom, no estimate is possible of the significance of the results. 

Table 2 Rotational constants, bond lengths and bond angles of 1,2,3-trioxolane, obtained by microwave spectroscopy.

Trioxolanes remain the most studied ring system by microwave spectroscopy and recently, 1,2,4-trithiolane also became the subject of attention. In all cases, isotopically labelled derivatives were made which have very different rotational constants. These aid assignment of structures and also provide useful tools for looking at the mechanism of the ozonolysis reaction. Rotational constants for the parent compounds and their calculated dipole moments are given in Table 3. 

Rotational Raman spectroscopy is a powerful tool to determine the structures of molecules. In particular, besides electron diffraction, it is the only method that can probe molecules that exhibit no electric dipole moment for which microwave or infrared data do not exist. Although rotational constants can be extracted from vibrational spectra via combination differences or by known correction factors of deuterated species the method is the only one that yields directly the rotational constant B0. However for cyclopropane, the rotational microwave spectrum, recording the weak AK=3 transitions could be measured by Brupacher [20],... 

A significant application of microwave spectroscopy is in the determination of barriers to internal rotation of one part of a molecule relative to another. Internal rotation is a vibrational motion, but has effects observable in the pure-rotation spectrum. If the barrier to internal rotation is very high, then the internal torsion is just like any other vibrational mode, and the rotational constants are affected in the usual way Bv = Be —... 

Microwave spectrometer, 219-221 Microwave spectroscopy, 130, 219-231 compilations of results of, 231 dipole-moment measurements in, 225 experimental procedures in, 219-221 frequency measurements in, 220 and molecular structure, 221-225 and rotational barriers, 226-228 and vibrational frequencies, 225-226 Mid infrared, 261 MINDO method, 71,76 and force constants, 245 and ionization potentials, 318-319 Minimal basis set, 65 Minor, 14 Modal matrix, 106 Molecular orbitals for diatomics, 58 and group theory, 418-427 for polyatomics, 66... 

The primary significance of microwave spectroscopy for chemistry is in determination of molecular structure. Assignment of microwave spectral lines to transitions between specific rotational levels allows determination of the rotational constants A0, B0, and C0, and the corresponding moments of inertia. The moments of inertia are dependent on the molecular bond distances and bond angles. 

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.)... 

Brown and coworkers105 used microwave spectroscopy to determine the structure of propadienethione H2C=C=C=S (16) through the analysis of the rotational constants for several of its isotopomers (obtained by pyrolysis of cyclopenteno-l,2,3-thiadiazole and deuterated derivatives). The main structural parameters are shown in Scheme 3a. A most remarkable (and yet unexplained) feature is the fact that this molecule has a C2V geometry, while propadienone, H2C=C=C=0 (17) is kinked 105, as shown in Scheme 3b. 

When rotation occurs about a bond there are two sources of strain energy. The first arises from the nonbonded interactions between the atoms attached to the two atoms of the bond (1,4-interactions) and these interactions are automatically included in most molecular mechanics models. The second source arises from reorganization of the electron density about the bonded atoms, which alters the degree of orbital overlap. The values for the force constants can be determined if a frequency for rotation about a bond in a model compound can be determined. For instance, the bond rotation frequencies of ethane and ethylamine have been determined by microwave spectroscopy. From the temperature dependence of the frequencies, the barriers to rotation have been determined as 12.1 and 8.28 kJ mol-1, respectively1243. The contribution to this barrier that arises from the nonbonded 1,4-interactions is then calculated using the potential functions to be employed in the force field. 

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. 

One of our rare incursions into the field of microwave spectroscopy concerns 1-nitropyrazole (162, X = N02). MP2/6-31G calculations reproduce very well the experimental geometry [172,173] and the calculated rotational constants of a series of pyrazoles (in MHz) were reported (155, X = H, BH2, BH3 , CH3, CHO, CF3, NH2, N02, OH, A1H2, SiH3, PH2, S02H, A-oxide). Our other contributions deal with simple molecules [174],... 

No newer studies using microwave spectroscopy have been published for the parent system. The previous edition of CHEC(1984) should be consulted for ground state rotational constants and dipole moments. 

Krugh and Gold in an early study determined the rotational constants and dipole moment of the parent tetrazole by means of microwave spectroscopy in the gas phase A 10667.3, B 10310.9, C 5240.4 MHz, dipole moment 2.19 D <1974JSP423>. The results of calculations carried out by Fausto and co-workers using the B3LYP/6-31G method are only consistent with the data for the 277-tautomer of tetrazole confirming the prevalence of exactly this form of the compound in the gas phase <2001PCP3541>. 

In order to assign the Zeeman patterns for the three lowest rotational levels quantitatively, one must determine the spacings between the rotational levels, and the values of g/and gr-In the simplest model which neglects centrifugal distortion, the rotation spacings are simply B0. /(./ + 1) this approximation was used by Brown and Uehara [10], who used the rotational constant B0 = 21295 MHz obtained by Saito [12] from pure microwave rotational spectroscopy (see later in the next chapter). The values of the g-factors were found to be g L = 0.999 82, gr = —(1.35) x 10-4. Note that because of the off-diagonal matrix elements (9.6), the Zeeman matrices (one for each value of Mj) are actually infinite in size and must be truncated at some point to achieve the desired level of accuracy. In subsequent work Miller [14] observed the spectrum of A33 SO in natural abundance 33 S has a nuclear spin of 3/2 and from the hyperfine structure Miller was able to determine the magnetic hyperfine constant a (see below for the definition of this constant). 

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... 

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