CHAPTER 1
Microwave Spectroscopy
BY J. N. MACDONALD AND J. SHERIDAN
1 Introduction
The literature of microwave spectroscopy has been somewhat less in the period than for several years. There is no general evidence, however, of a reduction in activity. Trends mentioned in previous volumes have continued, particularly those towards wider use of combined techniques such as microwave-optical double resonance. Continued success in studies of relatively unstable species, formed by a variety of reactions, remains a noticeable feature.
A volume has appeared which contains several reviews in this field, including coverage of millimetre and sub-millimetre wave spectroscopy, sub-millimetre wave spectroscopy by methods employing acoustic detectors and forbidden rotational transitions. The least squares fitting of data to molecular properties is also reviewed.
A theoretical discussion has been given of how optical rotation may arise in rotational spectroscopy, predicting the dependence of such effects on the molecular parameters.
2 Techniques
Use of essentially established techniques for the identification and estimation of substances remains active. An automated solid state spectrometer operating in the range 18 to 26 GHz for analysis and process control has been described by workers at the Philips Laboratories at Hamburg. A balanced system of two cells, with their stark-modulations in anti-phase, is used to reduce noise. Tests of aspects of the analytical use of microwave (MW) spectroscopy which have been pointed out in the past are reported, with results which are not without promise. Rinehart has given an up-to-date review of analytical microwave spectroscopy, including references to current developments, not all of which have been fully published. Details of the use of half sine-wave modulation for simplifying spectra for analytical purposes have been given.
Microwave spectroscopy continues to be used with advantage to identify products in complex reaction systems. Bak and co-workers have recently identfied N-methylmethyleneimine in normal and fully deuteriated forms from pyrolysis of dimethylamine and [2H7]dimethylamine at low pressures in a quartz tube. Similar treatment of other substances is reported. Among products being sought is cyanoform, HC(CN)3 [see Section 4A (vi)], the MW spectrum of which has meanwhile been characterized for samples more specifically synthesized." Similar means were used to study MW spectra of cis- and trans-forms of dithioformic acid, HCSSH, formed by pyrolysis of HC(SH)3 (see Section 4C). Several known substances have been identified by MW techniques in the products of the reaction of ozone with vinyl chloride.
Intensity studies have been applied analytically to monitor concentrations of HCN in several vibrational states in the plasma used in the well-known HCN-laser. The total HCN concentration reaches a maximum at very low laser current. As this current increases, the populations of the 10°0 and 00°1 states increase in comparable fashion, the data indicating that the laser action is less critically dependent on metastability in the 10°0 state than has been proposed. The pressure dependences of the populations of these two excited states differ in ways consistent with de-excitation factors which have been thought to limit the operating pressure of this laser.
Isotopic analytical work with deuteriated propenes has been extended by a study of reactions of 1,1-dideuterio propene on Ω-zeolite. The MW analysis of the products gives clear support for an associative mechanism of double-bond shift. Double-bond migration was not detected in 2-cyclopenten-l-one, by such methods, when this substance was treated with deuterium on a nickel catalyst; this is understandable in view of the conjugation in the starting material which such migration would destroy. The isotopic stereochemistry of the resulting deuteriated cyclopentanones was followed by MW spectra and it was found that the predominant dideuterio species has deuterium atoms on the same side of the quasi-plane of the ring at the α- and β-adjacent positions. This predominance is interpreted, perhaps not convincingly, as indicating associative adsorption of the double bond grouping in eclipsed conformation; inversion at one of the carbons is perhaps more strongly excluded than associative adsorption with staggered conformation. In contrast, reduction of 2-cyclopenten-l-one by magnesium in deuteriated acetic acid gave equal deuteriation on both sides of the quasi-plane of the ring.
Beam maser spectroscopy has been extended into the sub-millimetre wave region. Details are given of an instrument in which advantage is taken of the rotational cooling in nozzle beams, sixty-three of which are used in an array with state selectors, directed into a Fabry–Perot cavity. Deuterium hyperfine splittings in D20 and ND3 were measured with linewidths, at half peak intensity, of about 20 kHz.
Several papers deal with the practice and basic theory of double resonance techniques. For MW–MW double resonance, a spectrometer is described in which the pump and signal radiations operate in individual crossed open resonators, extra isolation being achieved by making the electric vectors of the two radiations mutually perpendicular. Up to three watts of pump power in the range 8.2 to 12.4 GHz are applied via a travelling wave amplifier. High effective pump power levels are obtainable and double resonances can be observed with sample pressures as high as 0.5 Torr, while flexibility and stability over large frequency ranges can be maintained. Tests on lines of allyl alcohol indicate that the sensitivity can be raised above that for a conventional Stark modulated system. Such methods point to ways in which double resonance modulation may facilitate the most effective use of cavity cells.
For laser-MW double resonance work, H. Jones has described two types of cell which allow ready detection of resonances and two-photon transitions when optical detection is used in conjunction with wide scanning of the microwave radiation in such cells within the laser cavity. Scan rates of 1 GHz min-1 were possible, with MW pumping power densities down to a few mW cm-2. The use of such an arrangement to measure 30 transitions in the v2 band of ammonia with high accuracy, through two-photon transitions, is also described.
Further theoretical work on optical-MW double resonance deals with the case where the optical frequency is off-resonance. Line shapes for fixed optical and variable MW frequencies are calculated for a variety of saturation conditions and for both MW and optical detection. This unified treatment of two-photon transitions and the optical Stark effect relates directly to several areas of current work. A model for the optical detection of MW transitions is described by Wormsbecher, Harris, and Wicke. This treatment includes the possibility of large laser powers and deals with intensities and line widths as functions of the radiation powers, collisions and spontaneous emission. There is good agreement with experiment for BaO and NO2. The treatment may be applied to ground or excited state resonances and should serve as a guide to the selection of systems from the many which may respond to these powerful means of study.
3 Derivation of Molecular Information
Several new papers have dealt with sextic centrifugal distortion constants and general aspects of this area are reviewed by Watson. In an extension of an earlier approach by van Eijk, Typke has shown that a suitable choice of reduced Hamiltonian allows more satisfactory analysis in terms of sextic constants than in previous treatments, particularly for near-symmetric tops. Georghiou using third- and fourth-order perturbation theory has derived expressions for sextic constants for a general polyatomic molecule, and has shown that such constants so calculated agree well with experiment in simple cases, giving promise that the observed sextic constants can be used more in the future to obtain information about anharmonic force fields. Watson has derived a relationship involving only rotational constants and quartic and sextic centrifugal distortion constants which should hold for any planar molecule. Strictly, the constants should have their equilibrium values, but the relationship remains useful as a constraint in fitting procedures. The relationship is checked with data for several symmetric bent triatomic molecules and possible limitations due to truncation of the Hamiltonian at the sextic terms are pointed out.
Two papers are of interest with reference to Stark effects. Following Stark effect studies of the highly polar linear molecule HCN···HF it is pointed out that large deviations occur from predictions of second or even fourth order perturbation theory. If the constant B for a linear molecule is sufficiently small, and the dipole sufliciently large, the perturbation expansion converges only slowly. The percentage deviation of the second order findings from those obtained by diagonalizing the energy matrix is tabulated for use in other cases as a function of μE/B (E = electric field) for all MJ components of transitions up to J = 5 <- 4. In a continuation of their work on isometric groups of non-rigid molecules, the Zürich workers have considered Stark effects in detail. A most interesting feature is the possibility of establishing the signs of products of dipole components in such cases and hence allocating unequivocally a line of action to the total dipole moment. Results for acetaldehyde show convincingly that the product μaμb, has a sign consistent only with a total dipole in the approximate direction of the C=0 bond.
A new iteration procedure for determination of rs geometric parameters from arrays of constants for isotopic forms of a molecule has been described. This differs in some respects from similar procedures described previously (in this series, Vol. 4, p. 7). The iteration is carried out in Cartesian co-ordinates, rather than internal ones. Moments of inertia and their differences are included, multiple isotopic substitutions being also covered. Some advantages are claimed for the new method, such as in cases where the number of isotopic forms is minimal, or where there is sign ambiguity in a small co-ordinate. A comparison of the results applied to ethylene oxide is made with the earlier work of Hirose (in this series, Vol. 4, p. 43).
A test of the rm procedure for structure determination (in this series, Vol. 3, p. 77) is reported by Smith and Watson for OCS. Values of Bo for fourteen isotopic species are computed from a recent detailed treatment of the force field 33 and the rm distances shown to differ from the re values by significant amounts. Good agreement between rm and re is obtained by extrapolation to the case of vanishingly small mass changes. It is shown that the errors in atomic co-ordinates are comparable in the rm and rs methods, except where the number of parameters is equal to the number of moments of inertia of a single isotopic form, where the rm and re structures agree well. This paper contains a useful discussion of fundamental aspects of determination of geometric parameters at its present state of refinement.
4 Results for Individual Molecules
A. Molecules for which Only One Stable Equilibrium Configuration is Possible or Reasonable. — (i) Diatomic Molecules. The nuclear mass dependence of the Dunham coefficients for a diatomic molecule in Σ ground state has been discussed and a general expression for the coefficients derived taking account of the breakdown of the Born–Oppenheimer approximation. The expression is cast in a form suitable for fitting data on several isotopic species. An approach to the analysis of the Zeeman effect in diatomic molecules by numerical diagonalization of an appropriate secular matrix has been described, the aim being to eliminate the need to use involved perturbation theory to take account of the external field and hyperfine effects. The method yields directly basic molecular g-factors rather than effective ones for each rotational state, the parameters being determined by a least squares fitting procedure to as much relevant spectroscopic data as is available. Results are given for the 2Π ground states of OH and SH as test cases. Analysis of Λ-doubling, hyperfine structure, the pure rotational spectrum, and the A2Σ-X2Π electronic band of OH by numerical diagonalization of the energy matrix of the molecular Hamiltonian is described in a separate publication. Perturbations arising from excited vibrational and/or electronic states are taken into account via a van Vleck transformation and the effects of centrifugal distortion are included. Molecular constants derived by simultaneously fitting microwave, infrared, and electronic line frequencies reproduce the observed data within experimental error. In a third paper the A-doubling spectrum of OH has been re-examined in terms of a model employing an expansion of the fine structure matrix elements in a power series up to the fifth power of J. Predictions are given for, as yet unobserved, transitions originating in states with J< 17/2. A rather unexpected laser oscillation involving certain rotational transitions in the ground electronic, υ = 0 and 1, states of OH has been observed. The pumping mechanism is believed to be a V -> R transfer with ΔJ of the order of 12.
In spite of the fact that the CN radical has been the subject of several thorough studies, including the radioastronomical observation of the N = 1 -> 0 line, its ground state microwave spectrum has, until now, escaped detection principally because of limitations placed on the steady state concentration which can be achieved due to its extreme reactivity. The problems have now been overcome and the N = 1 -> 0 lines of the υ = 0 and 1 states have been studied in glow discharges in N2-cyanogen mixtures using a Zeeman modulated spectrometer described earlier. By combining the results with earlier optical data the equilibrium parameters Be = 56954.100(200) MHz and re = 1.171807(20) Å were derived and analysis of the resolved fine structure has yielded eqQ for nitrogen of - 1.307(27) MHz in close agreement with the astronomical results.
Knowledge of the ClO radical has been advanced through a study of the J = 3/2 <- 1/2 transitions of ClO in the 2π1/2, υ = 1 state. Rotational and quadruple coupling constants have been derived and the equilibrium bond length shown to be 1.56954(5) Å. Some revised data for the υ = 0 state are also reported.
The question of the sign of the dipole moment of ClF has again been the subject of investigation, this time by the MBER techniques. The hyperfine Stark and Zeeman effects have been studied and the dipole moment shown to be 0.85(15) D with sign -FC1+ agreeing in both magnitude and sign with conclusions reached from studies of van der Waals molecules (in this series, Vol. 5, p. 17). Other molecular properties derived include the polarizability anisotropy, molecular quadrupole moment, and the derivative of the Cl quadrupole coupling constant.
The millimetre wave spectrum of CaO in the ground and first excited states of X1Σ+ has been studied. Gas phase CaO was produced by oxidation of the metal vapour with nitrous oxide. The method produces molecules in excited electronic states which subsequently decay with chemiluminescence to the ground state. Rotational and centrifugal distortion constants and various combinations of Dunham coefficients for the υ = 0 and 1 states were deduced and re shown to be 1.82220 Å. Similar work on BaO and SrO together with further discussion of CaO is included in a separate publication. Again the spectra are for the υ = 0 and 1 states of the X1Σ ground states and spectra from isotopic modifications of BaO and SrO have been detected. Amongst the array of constants and molecular parameters derived are re(BaO) = 1.939630(7) Å and re(SrO) = 1.919809(95) Å. The implications for radioastronomical searches for the metal oxides are also discussed. The dipole moment of A1Σ+ BaO has been determined by using the MODR technique employing an Ar laser to pump the A1Σ+ - X1Σ+ (7,O) R(1) transition whilst studying the Stark effect of the J' = 1 4 2 transition. The value of 2.20 (11) D for the A1Σ+state compares with 7.955 D for the X1Σ+, the observed reduction being compatible with the MO description of the bonding in the molecule which effectively predicts electron charge transfer on excitation from an orbital located mainly on oxygen to one located mainly on Ba.
A wide range of vibrational and rotational states of SiO, prepared in the gas phase by heating a mixture of silicon and silicon dioxide to some 1350 °C, has been studied by millimetre wave spectroscopy. The usual molecular parameters and rotational constants have been derived including re = 1.50973(4) Å. Accurate predictions for all transitions likely to be of astrophysical interest are given.
