Microwave Spectroscopy

BY J. N. MACDONALD AND J. SHERIDAN

1 Introduction

We have retained a general continuity with Volume 3, and regarded work in Chemical Titles before NO. 7 of 1974 as normally covered earlier. For timeliness, however, we have included as many as possible of the papers appearing up to the manuscript stage. Inevitably, some recent studies will be considered in the next Report. Subject to limitations through inconsistencies in titling and keyword listing, a d through the widening of fields which are closely related to microwave (MW) spectroscopy, we have covered finalized publications to September 1975.

While much work remains in what may now be called classical MW spectroscopy, an increasing proportion concerns newer methods and areas, notably double resonance (DR) involving i.r. and u.v.-visible radiation, and studies of time-dependent effects. After considering techniques, in which we include chemical analytical procedures and some purely analytical applications, we deal with some generalities of the derivation of molecular information from spectra and proceed to the discussion of predominantly structural studies through a convenient empirical classification of the molecules concerned, chosen to group together structures with their present MW interest in common. We treat separately the MW spectroscopy of molecules in space, and work primarily concerned with time-dependence and collisional effects.

The flow of new studies towards formal publication is, as always, valuably indicated in the proceedings of conferences, notably the Third European MW Spectroscopy Conference at Venice in 1974, the Fourth Colloquium on High Resolution Molecular Spectroscopy at Tours in 1975, and the 29th and 30th Symposia on Molecular Structure and Spectroscopy at Columbus, Ohio, in 1974 and 1975.

Only in a few randomly chosen examples have we been able to illustrate the strong interdependence of MW spectroscopy and fields such as paramagnetic resonance spectroscopy, laser spectroscopy and molecular beam spectroscopy. The e.p.r. spectroscopy of gaseous free radicals, and related MW absorption studies, have been reviewed. The interrelation of MW, laser and e.p.r. spectroscopies is well shown by the analysis of the laser magnetic resonance spectrum of HO2 in terms of rotational constants. Molecular beam spectroscopy at MW frequencies has yielded striking information on loosely bound molecular complexes; a review has appeared, and specific cases are considered in Section 4A(ii).

Trends have continued towards more consistent success in the study of unstable species and of labile chemical systems and reaction mechanisms, and towards richer information on excited states of molecules. If any one achievement is to be singled out, it is the study of a charged species, CO+, for the first time in a direct MW absorption experiment.

Several valuable surveys of the interpretation of MW data and related information have been published as the proceedings of a conference held at Dartmouth College, Hanover, New Hampshire, in 1973.

2 Techniques

A. Single-radiation Methods. — A spectrometer employing source-modulation, usually at 50 kHz, has been described. Phase-sensitive detection at twice the modulation frequency gives the second derivative of the line-shape, and frequencies up to 80GHz can be used. A critical comparison with Stark-effect modulation systems is made, and the convenience of source modulation for high-resolution work on dense spectra is illustrated for the case of CSCl2. Another complete system, in this instance with computer control, maximizes sensitivity with special regard to work on transient species; the data can also be transferred directly to a large computer for processing. This system was used in the work on CO+ already mentioned. Details of a high-resolution cavity spectrometer for Zeeman studies (see Vol. 3, p. 4) have been given. A superheterodyne system is used with a superconducting magnet. While flexibility must be less than when a broad-band cell is placed in the field, this cavity instrument allows field-strengths as great as 65 kG, with consequent advantages for the study of the second-order Zeeman effect. It is shown that the nominal inhomogeneity of the field influences the precision less strongly than might at first appear, and that magnetic susceptibility anisotropies and molecular quadrupole moments can be derived with accuracies comparable with those from beam studies. A pulsed K-band emission spectrometer with a cell inside an interferometer allows high sensitivity with a flexible cellgeometry for work on timedependent effects. Spectrometers using acoustic detectors (Vol. 3, p. 99) in the range 200 — 870 GHz have been further described by Krupnov and his group;lL the use of high source-powers to increase Sensitivity is discussed, as is the theory of the molecular dynamics of acoustic detection with a view to maximizing performance.

Modulation devices have been evolved for work on unstable species. A Stark-effect modulator which reverses the field direction in alternate 'field-on' half cycles of square wave avoids charge accumulation on the Stark electrode in the study of discharges. Zeeman effect modulator, either square wave at 1 kHz or sinusoidal at 25 kHz, give high sensitivities for detection of SO and OH, and six weak transitions of the latter are reported for the first time.

In a procedure related to the saturation modulation method (Vol. 3, p. 100) spectra are detected through the difference in cavity resonance curves in the presence and absence of power saturation; this has promise for high frequencies and for cavity studies in which mode-contours require suppression.

The first level-crossing resonances in the MW range have been observed when the levels of the J = 1, K = 1 ->J = 2, K = 1 transition of CH3F are tuned by the Stark effect of a field perpendicular to the electric vector of the radiation. Further theoretical study has been made of the influence of absorption sidebands due to RF Stark fields in level-crossing experiments.

Other specialized technical developments are mentioned in Section 6 in connexion with time-dependent effects. Many relevant background developments are treated in the Proceedings of the 1st International Conference on Sub-millimetre waves and their Applications, at Atlanta in 1974.

B. Multiple-radiation Methods. — The MW–MW double resonance technique is now widely applied. A spectrometer with square-wave amplitude modulation of the X-band pump-power in a PIN diode has been briefly described. The pump radiation is then amplified to 2 watts in a travelling wave tube and harmonics so generated are filtered. Tests with four-level DR effects in ethylene oxide are presented, some signals being ascribed to a modulation through Starkeffect shifts due to the high pump power. In this and other MW–MW–DR systems, a directional coupler matching the main and auxiliary guides for the widely differing frequencies to be combined, has proved valuable. Stiefvater has shown that MW–MW–DR modulation methods can give remarkable sensitivity and specificity in the study of weak spectra among strong absorptions; application to vibrationally excited states and especially to isotopic species in natural abundance, where even deuteriated forms can be studied, emphasizes the wide importance of such developments to chemists.

The solution of matching problems in the valuable technique of RF–MW–DR permits RF frequencies up to 3.4 GHz with a Stark modulated cell, and makes the method contiguous with MW–MW–DR. In interestingly related work the RF is used to pump magnetic dipole transitions in the 7 — 22 MHz range between states of the same parity in OH (J = 9/2, F = 5+ -> 4+; J = 9/2, F = 5- -> 4- and J = 7/2, F = 4- -> 3-). The RF current is applied in a loop containing the plates of a parallel-plate cell. The transitions mentioned were measured precisely and the linked MW transitions determined with improved accuracy.

Multiple resonance combining MW radiation with optical energy, normally from lasers, continues to be very active (Vol. 3, pp. 89 ff.). The work is divisible into i.r.–MW–DR, concerned with vibrational excitations, and u.v./visible–MW–DR, concerned with electronic excitations; MW–optical double resonance (MODR) usually denotes the second of these.

Technical developments in i.r.–MW–DR include particularly that by Redon and Fourrier of a parallel-plate cell for homogeneous DC Stark fields up to 50 kV cm-1. The construction is so precise that remarkably large MW Stark shifts can be followed, a shift of 12.6 GHz being recorded for the M = 9 component of the J = 9, K = 6 inversion line of ammonia, at 28.39 kV cm-1. The large fields are used to tune i.r. lines to exact laser frequencies for i.r. –MW–DR observations; sometimes the transitions so tuned become allowed only in the presence of the field. The removal of M-degeneracies in the MW transitions by the field is also an advantage. Thus, a field of 11.4 kV cm-1 tunes the sa Q (J = 9, K = 6, M = 9)v2 = 0 ->v2 = 1 transition of NH3 into coincidence with the R(30)N20 laser line. With the laser on, depletion of this v2 = 0 level causes the M = 9 Stark component of the NH3J = 9, K = 6 ground-state line to change from absorption to emission; this M-component is then 2.58GHz from its zero-field position.

In contrast with the above, the approach of Jones and Kohler to the study of CF3I by i.r.–MW–DR promises that many molecules with dense spectra will obligingly (but arbitrarily) show coincidences with field-free laser lines [Section 4A(v)].

Related to i.r.–MW–DR is the experiment in which the MW spacings between i.r. pure rotational laser lines were measured accurately by mixing the laser frequencies at a metal-to-metal i.r. diode and observing their differences by a beat procedure against a microwave source. The R1 ->R2 separations for OH at total orbital angular momenta (K) of 20 and 21 were obtained as 21.500 GHz and 15.265 GHz respectively, with errors of ≤ 10 MHz and extension to other splittings is clearly possible.

Cases of MW–DR with optical radiation in the u.v.–visible range continue to give MW information about electronically excited states of simple molecules. Application of these methods to metal oxides (Vol. 3, p. 94) has been reviewed.29 Further details of the techniques are given in two studies of the 2B2 state of NO2 [Section 4A(iii)], which may be compared with similar work, although by optical–RF–DR, on the A2Σ+ state of NO. Theoretical considerations of the experimental observables of optical–MW–DR and optical–RF–DR have been described.

C. Techniques for Chemical Analysis. — New approaches to analytical procedures have been made by use of cavity Stark-modulation cells of rectangular cross section. The cells are tuned with plungers to resonate at X-band frequencies in the TE01π ode, when n may reach 20 in a cavity 50 cm long; the resulting large absorption-paths lead to sufficient sensitivity to detect lines with absorption coefficients as small as 6 x 10-13 cm-1. Fine tuning is accomplished with a DC swept Stark voltage, added to the small AC component used in the normal way as modulation, and spectra are presented on a swept Stark voltage scale as different M-states of a transition come into the cavity resonance frequency. Some convenient properties of such a system for work at selected fixed frequencies, including analytical studies, are clear. When car-exhaust gas was directly admitted, at low pressure, to the cell, formaldehyde could be detected at as little as 0.2 p.p.m., which is about 1% of the normal concentration in such gas. For estimation of acrolein from the same source this component was first adsorbed from the dried gas on diatomaceous earth and then desorbed into the cell by heating, but this pre-concentration was inefficient. Concentrations of acrolein above about 1 p.p.m. could be roughly monitored by incorporating the pre-concentration losses into a total calibration procedure. In all these studies, the usual need to eliminate effects of wall-adsorption in the cell was evident.

For example, sulphur dioxide in stack gas, could be estimated in concentrations down to 1 p.p.m. with a conventional X-band spectrometer, after a simple preconcentration process in which pre-filling of the cell for 10 minutes at 100 Torr allowed the preferential cell adsorption of the SO2 to enrich this substance during the subsequent pumping to 50 mTorr. Conventional refinements could considerably extend the sensitivity of this estimation.

We mention here new reviews and general considerations of MW analytical procedures. Applications (Vol. 3, p. 102) to chemical systems continue, especially with regard to mechanism studies through location of D-atoms in hydrocarbon structures. Exchange between deuteriated propene, C3D6, and but-l-ene in the presence of iron or nickel has been followed in this way. Clear evidence was obtained for the dissociative adsorption of α-olefins, as evinced particularly by the dominant appearance of deuterium at the 2-carbon position in the butene. Mechanisms of hydrogen transfer and exchange in propene have been extensively considered and tested by these methods. The D-distributions in products from C3H6 and D2SO4 or D3PO4 show that CH2D — [??]H — CH3 is an intermediate. For contrast and variety, C3H6 treated with D2O and bismuth molybdate gives a distribution indicating a π-allyl intermediate, H2C [??] CH — CH, whereas C3H6 with D2 over C24K deuteriates via a π-ally1 intermediate [MATHEMATICAL EXPRESSION OMITTED]. The spectrometer used was somewhat more sensitive than most conventional instruments and detection of C3H5D and C3H4D2 species at 0.1 % of the total gas allowed considerable precision. Similar work on exchange between propene and D2 or D2O on various oxide catalysts again shows the same variety of mechanisms depending on the catalyst.

3 Derivation of Molecular Information

A. Assignment of Spectra. — Computers have occasionally been used in the past to test spectral assignment, for example by exploring the consequences, in predicted transitions, of various choices of assignments of lines which are expected to be included in a group of observations. This idea has been elaborated in a program which can assign an array of up to 200 transitions, from up to 5000 eligible frequencies, for any molecule in any state, provided the spectrum of each state approximates closely to that of a rigid rotor; the best values of the rotational constants are then derived. In principle, all possibilities should be examined, but guide-lines setting limiting properties for a satisfactory assignment are built in. Promising tests are presented for molecules with previously known assignments. Such procedures should have value in speeding the unravelling of dense spectra, especially where no double resonances are available. The method can also increase the data yielded by a spectrum, for example, by defining constants for vibrationally excited states. Unfortunately, the program will not work for those interesting parts of spectra which depart from the rigid rotor form, as in certain cases of large amplitude internal motion, and the neglect of centrifugal distortion demands care in the selection of the keys to an assignment. A second computational procedure with similar objectives has also been described.

Attention continues to be given to the extraction of spectroscopic constants from the 'low resolution' MW spectra first described by Harrington about a decade ago (Vol. 3, p. 79). The rough values of (B + C) from the band-spacings for prolate tops are found to exceed the accurate (B0 + C0) values for the ground states, but the discrepancy is no more than 2% for the nineteen cases quoted, for which the asymmetry parameter, κ, varies from -0.56 to -0.99. Although many factors are involved, this generalization is acceptable from a consideration of changes in spectra when κ is varied for a fixed (B + C). Empirically (B + C)/(B0 + C0) is approximately 1 + 0.025(1 + κ) from which B0 + C0 can be obtained from low-resolution spectra to about one part in 200. A new band type in low resolution spectra reflects transitions of the types J0,J -> (J + l)0,J+1 and J1,J -> (J + 1)1,J+1. Arising from near-degenerate levels in oblate tops, these transitions retain nearly equal frequencies in band MW spectra of quite prolate molecules, and are the strongest a-type R-branch lines. Their frequencies, approximately 2C(J + 1/2) + 1/2(A + B), lead to a spacing of 2C; the frequency divided by the spacing is then J + 1/2 + (A + B)/4C. These bands are illustrated in the spectrum of 1,1-difluorocyclohexane. When available, such bands can be used, with caution, in conjunction with the usual bands, to obtain separate values of B + and C and a rough value of A.

B. Derivation of Molecular Structure Parameters. — Surveys of various types of averaged geometric parameters, and their derivation from MW spectra and related data, have been given by several authorities. More elaborate and systematic treatments of arrays of rotational constants tend to be used to evaluate the statistically most acceptable structures. Hirose has reconsidered the point that correlations among rotational constants should be taken into account, and, following treatment of a similar situation in electron diffraction, a non-diagonal weight matrix is used in the least-squares fitting of constants. The rs-structure of ethylene oxide is treated in this way, with detailed discussion of error estimation. Bond lengths and angles are not changed beyond previous error-bounds by this refinement, but some reduction of standard errors is achieved, particularly compared with results of simple Kraitchman-type calculations for some isotopic combinations. Nösberger, Bauder, and Günthard describe a general procedure to incorporate systematically all ground-state rotational constants and their isotopic changes to obtain the structure in best accord with all measurements. This method, which has been used in several laboratories, is widely applicable and offers a standard justified procedure for treating small isotopic shifts. It is also useful in guiding the acquisition of new data in the course of a study.