CHAPTER 1
Microwave Spectroscopy
BY J. N. MACDONALD AND J. SHERIDAN
1 Introduction
We have continued the system employed in Volume 4 to summarize a continued flow of work on the many facets of this field.
A marked feature has been the continuance of successful attacks on the microwave (MW) spectroscopy of unstable species and energetically unfavourable conformations of molecules. The charged species HCO+ and HN+2, previously regarded as sources of microwave emissions from space, have now been studied in the laboratory, and the isomer of hydrogen cyanide (HNC), also present in space, has been investigated in great detail. A second conformer has been shown to be present in as familiar a substance as formic acid, and details of its structure have been established. The scope, power, and reliability of the techniques are clearly increasing to a point where some long-standing gaps in our knowledge of simple molecules in the gas phase are being rapidly filled. The range of molecules studied is similar to that in former years. The astrophysical aspects of the subject continue very active, and may receive further incentive from the commissioning of the new 300GHz radio-telescope near Amhurst, Massachusetts.
Few reviews have appeared, but Sutter and Flygare have given a comprehensive account of the theory and practice of MW Zeeman spectroscopy. Work with molecular beam maws has been reviewed by Lainé and by Dymanus. The related field of spectroscopy with coherent laser sources has been surveyed by Shimim. The spectroscopy of van der Waals molecules, including the important contributions of MW work, has been reviewed.
2 Techniques
A. Single-radiation Methods. — A notable publication describes details of a pulsed system for Fourier transform MW spectroscopy (Vol. 4, p. 68), with systematic discussion of the factors and procedures which can allow measurements in the time domain to give considerable improvements in signal-to-noise ratio and in resolution due to the absence of power broadening. The system developed, which is tested at rather low frequencies, some 4 — 6 GHz, uses a 4 m length of 'empty' C-band guide as a cell. Data confirming the advantages and promise of the methods are presented for lines of CH2O and CD2O.
In this connection, we may note the use of Fourier-transform methods in the lower resolution study of spectra of water vapour at 168 — 189 GHz, with use of harmonic radiation from IMPATT diode oscillators.
Details of a spectrometer using a cell of the usual Stark effect waveguide type, but tuned to resonance for selected absorptions, have been given. While the sensitivity here claimed is not exceptional, this type of cell is that described by others (Vol. 4, p. 5) as especially suited to analytical work at extreme sensitivities.
B. Multiple-radiation Methods. — Two papers by Stiefvater describe in detail techniques of MW-MW double resonance modulation spectroscopy developed as a standard laboratory method which has already demonstrated its value in the detection and assignment of complex spectra, including many lines due to weakly populated states and rare isotopic species (see Vol. 4, pp. 3 and 45). In the first paper the general principles, including the use of double resonance 'maps', are developed and it is noted that the ready detection of resonances when the pump frequency is some way from its exact resonance value allows 'double search' procedures in which signal and pump frequencies are swept. In a second part, the lineshapes and their integrated intensities are considered: there are two readily distinguished lineshapes which allow deductions to be made about the location of the energy level common to the two transitions and so facilitate spectral assignments. The integrated intensities of lines can be found by procedures which do not require knowledge of the absolute values of the pump power.
In the above work the pump frequency is modulated in and out of resonance at 100kHz through a square-wave voltage applied to the reflector of the pump klystron. In a description of a related instrument the Zurich group have employed also an amplitude modulation of the pump power at 30 kHz with a PIN diode and, in describing the instrument, have made interesting comparisons of the frequency and amplitude modulation options in terms of leakage signals and other electronic difficulties. The two types of lineshape are also considered and compared, in examples, with calculated shapes.
A double resonance spectrometer of essentially conventional Stark effect modulated type, but with the attractive facility to sweep the pump frequency automatically over the whole of the 8–12.4 GHz band, has been described. Double resonance connections between transitions in this band and selected signal transitions may then be readily found.
The Kiel group have reported further on RF–MW double resonance, in which the 'RF' frequency applied as pump radiation to the Stark effect electrode (see Vol. 3, p. 3) can be as high as 4 GHz and so enter the low MW range. The signal frequencies have also been extended to 160 GHz. Experimental details are given and many examples of resonances are quoted, with particular reference to CH3OCl and CD3OCl, which illustrate the value of the methods in allowing high sensitivities in the measurement of rotational transitions at very low frequencies.
Double resonances involving MW with i.r. or higher frequency radiation from lasers continue to be widely reported, and the use of lasers for DR work has been reviewed. Takami has developed the theory of such cases, with both MW detection and optical detection. Lineshapes and peak values of the DR signals are considered, as are the effects of varying optical saturation on such observations; circumstances which may lead to anomalous line-shapes are indicated.
The shifts of frequency of MW lines in the presence of a non-resonant laser field have been used, following earlier theory, to determine i.r. transition frequencies with accuracies, in the case of NH3, similar to those obtainable with Stark laser spectroscopy .
C. Techniques for Chemical Analysis. — A further review of analytical MW spectroscopy has been published by Lovas. Most aspects referred to have been frequently discussed in the past (e.g. Vol. 4, p. 5) but there is timely emphasis on the potential of MW methods for the monitoring of complex reactions, including such important areas as pyrolysis processes, catalytic syntheses, such as that of HCN from methane, ammonia and oxygen, and the methanol synthesis. The plea, implicit even in this paper from the United States, for more response from the chemical processing side in pointing to problems in which MW analysis outstrips alternatives will have a familiar ring to old campaigners in this area. More experimental details of the analytical studies by Roussy and his co-workers have been given. Procedures involving peak intensities and line widths, with variations in the usual spectrometer parameters, are described, and mention is made of experimental modifications such as the use of Stark effect modulation fields which are non-uniform in the field on part of the modulation cycle, in order to suppress interferring Stark spectra.
Data banks giving properties of absorptions of molecules for analytical and monitoring use have been accumulating for a long time, particularly at the National Bureau of Standards, and will no doubt find amplification in the listings of numerous lines of astrophysical interest (Section 5). Among contributions of this type we should mention a comprehensive calculation of absorption coefficients for sulphur dioxide lines at frequencies up to 200 GHz and J-values ≤ 50. This paper also describes measurements of intensities and linewidth parameters for a number of lines of this substance, both in a computerized Stark modulation spectrometer with calibration by diode simulation of absorptions, and in a spectrometer using a Fabry–Perot interferometer as cell at 70 GHz.
An encouraging steady level of applications of the MW method to the study of chemical reactions is maintained. Some of the work continues in the easier area of isotopic analysis, where problems of varying linewidth parameters are small. Kemball, Tyler and their co-workers have continued their studies of exchanges and isomerizations in alkenes with work on 1,1-dideuteriopropene, in the absence of hydrogen, over magnesia and rutile. Double-bond shifts and deuterium scrambling were followed. The shift is fast on both catalysts, details indicating that it is mainly intermolecular on magnesia, while an intramolecular process is more significant in the case of rutile. The similar work of Tamaru and his co-workers has been extended to the study of propene–deuterium exchange over films of electron donor–acceptor complexes of polynuclear hydrocarbons with alkali metals, e.g. tetracene2-(Cs+)2. On such catalysts the exchange is thought to proceed via a π-allyl adsorbed species. The isomerization of exo-2,3-dideuteriobicyclo[2,1,O ]pentane to the corresponding endo-form is a similar case of isotopic labelling and has been studied by the MW method between 177 and 202 °C, with derivation of kinetic data. A more limited study of the analogous process involving exo- and endo-2-rnethylbicyclo[2,1,0]pentane belongs strictly to the more complex case where the two substances monitored have different collision properties; although the dipole moments of the exo- and endo-forms (Vol. 4, p. 54) differ considerably, this factor was not thought to contribute a large extra uncertainty in this example. This paper includes a useful discussion of the use of MW analysis in kinetic studies.
Among quantitative studies of concentrations of chemically different reacting species by the MW intensity method, that by Varma and Curl of the equilibria among N2O3, H2O and HNO2 pays particular attention to detail. The energy difference between the cis- and trans-forms of nitrous acid is determined as W(100) cal mol-1 (the trans-form is the more stable) and concentrations of the above three molecules, in both normal and deuteriated forms, were measured to derive data on the equilibria:
N2O3 + D2O [??] 2DNO2
N2O3 + HDO [??] HNO2 + DNO2.
The value of ΔH00 obtained, 1050(300)cal, agrees reasonably with that from recalculations of the thermodynamic properties of HNO2 and application of the third law. Difficulties arising from non-uniform and unsteady cell temperatures in work with cooled cells caused limitations which are clear through the time dependence of intensities of lines due to various species.
Under analytical studies we may include the low resolution MW work in which some 16 carboxylic acids and several amides are tested for their ability to form mixed dimers with trifluoracetic acid. Such mixed dimers, formed in the well-known way with hydrogen-bonded eight-membered ring structures, give low resolution spectra of the usual a-type for prolate rotors and can be identified with some confidence by the agreement of the constants (B + C) from the band spacing with those predicted from models. Mixed dimers were detected for the first time for methyl and cyclic derivatives of acetic acid, for acrylic acid and its 2,2-dimethyl derivative, and for acetamide and propionamide. Monosubstituted acetic acids XCH2CO2H (X = Cl, Br, and CN) did not give evidence of mixed dimer formation, which is possibly in line with the view that trifluoroacetic acid bonds more readily to more weakly acidic partners although a complex has been known to be formed for some time when X = F. Some N-substituted amides gave no observable bimolecule formation, probably for steric reasons; noticeably the cyclic amides HN(CH2)nCO formed a complex with trifluoroacetic acid when n = 3 but not when n = 4. This work is to be correlated with other MW studies of molecular complex formation [Section 4A and Vol. 4, p. 23].
Microwave spectroscopy, among other analytical methods, has been found useful in identifying the array of products from the gas-phase reaction between ethylene and ozone, for which various pathways have been discussed.
We may note the related use of analytical e.s.r. methods at 8.5 GHz to measure gaseous concentrations of F-atoms in kinetic studies of the reaction of these atoms with H2 and with CF3H.
3 Derivation of Molecular Information
Programmes for automatic assignment of spectra by progressive refinements, or rejection, of fits based on provisional assignments continue to be of interest. Russian work in this area has been further described. The procedure, which allows fitting to a non-rigid rotor model with centrifugal constants in addition to A, B, and C, was tested for transitions of SO2 near 300GHz, identified lines having typically J-values from 4 to 15. While a less simple molecule would have provided a more critical evaluation, the facility to incorporate distortion constants is valuable, especially for the higher MW frequencies.
For many purposes, perhaps the publications most relevant to problems of assignment, particularly of weak spectra of asymmetric tops in the presence of many stronger lines, are those already mentioned under double resonance techniques. A note has been published pointing out a simple means of preliminary assignment for planar asymmetric rotors from Q-branch a- or b-type transitions which may be useful in dealing with heavier molecules. Its application to assign 1,2,3,5-tetra-fluorobenzene is mentioned.
There is the usual continued flow of papers dealing in more refined terms with the theory of non-rigid rotors and the derivation of molecular rotation–vibration parameters. At the elementary level of a diatomic molecule, it has been shown that the influence of electronic motion on the rotational Hamiltonian can be considered in a simple manner; the formulation is tested for HCl. A fundamental reconsideration of the derivation of the rotation–vibration Hamiltonian for a polyatomic molecule has been made which is, not least, of interest in relation to the novel suggestions of Wertheimer. Further papers deal in depth with other formulations of the rotation–vibration problem. Extension of the treatment of vibration–rotation through the 'non-rigid bender' Hamiltonian (Vol. 4, p. 14) gives a treatment allowing for two large-amplitude stretching motions in triatomic molecules. Large amplitude effects are shown to be appreciable only if the terminal atoms are heavier than the central one.
Several important papers are concerned mainly with force fields and their relation to parameters derivable from MW work. Whiffen has extended his earlier studies with a different approach to the calculation of rovibrational constants from the force field, discussed with particular reference to OCS. The comparison of predictions with observation forms the basis of a valuable critical appraisal of many features of such work. Aliev and Watson have continued work on sextic centrifugal distortion constants (see Vol. 4, p. 8) in a detail which allows them to indicate omissions and errors in several earlier papers. Predictions are compared with data for SO2, NH3, and CH4 with agreement passing from good to poor in that order. The sextic constants are regarded as ultimately leading to knowledge of cubic anharmonic potential constants. Quartic centrifugal distortion constants have been discussed with special reference to the need for explicit relationships between the results of different mathematical reduction procedures in order that data for various molecules can be compared. The use of vibrational data to define ranges of permitted values of centrifugal distortion constants has been discussed and illustrated for a bent symmetric triatomic molecule such as SO2.
Quasi-linearity has played an increasingly prominent role in the discussion of the energetics of a number of systems, perhaps most notably carbon suboxide and fulminic acid. Yamada and M. Winnewisser have now proposed a single dimensionless parameter as a quantitative measure of quasi-linearity. Since the quasi-linearity results from the loss of validity of the Born–Oppenheimer approximation which requires rotational energy differences to be no more than some 1 per cent of the lowest vibrational energy difference, it was found convenient to define the parameter γ0 as
γ0 = 1 - 4γ
in which γ is the ratio of the rotational to vibrational energy. The value γ0 is close to -1 for well-behaved linear molecules and close to +1 for well behaved bent molecules. Data are depicted for some 50 cases. Most are bent cases, with γ0 between +0.9 and +1.0, while the well-known linear cases CO2, CS2, OCS, N20, C2H2, HCN, and C2N2 show γ0 very close to -1.0. Intermediate cases include HNCO (γ0 = 0-95), HNCS (γ0 = 0.73), C3O2 (yo = -0.28) and HCNO (γ0 = -0.66). Data for CsOH suggest a value of γ0 more negative than -1, corresponding to a quartic contribution of the same sign as the harmonic constribution to the potential energy of bending. The relationships between γ0 and other parameters used in describing spectra of chain-type molecules are also discussed in this most tra of chain-type molecules are also discussed in this most interesting contribution to the overall correlation of a large array of spectral data.
