Microwave Spectroscopy

BY A. C. LEGON AND D. J. MILLEN

1 Introduction

This chapter preserves continuity with the Report in Volume 2. It covers papers included in Chemical Titles for the period from April 1973 to March 1974 inclusive, and follows the general pattern used in previous years. During the year under review a new structural parameter rm has been introduced (see ref. 274). The new parameter can be calculated solely from ground-state data, making use of 'mass-dependence' of rotational constants of isotopically substituted molecules, and leads to values close to re values. An advance in understanding electrical properties of molecules has been made by the combined use of i.r. intensities and the dependence of Stark effects on both vibrational state and isotopic substitution to evaluate a molecular dipole moment function (see ref. 20). For molecules with internal rotation, where V3 terms in the barrier hindering rotation have now been evaluated for many molecules, the significance of values of V6 terms which are beginning to be obtained has been called into question (see ref. 129–133). For some large molecules it has been shown how low-resolution microwave spectroscopy can now be applied to conformational problems (see ref. 275).

A further attempt has been made to settle the difficult question of the equilibrium structure of formamide (see ref. 108). It is concluded from a careful analysis of microwave and i.r. spectra that the lowest-lying vibrational mode, the NH2 wag, is governed by a single minimum potential function and that therefore the atoms are coplanar at equilibrium. Rotational spectra of two formally non-polar molecules, allene and methane, have been reported. For the weakly polar species H2C[??]C[??]CD2 ground-state transitions have been detected by conventional techniques (see ref. 119), and ΔJ = 0 transitions in the vibronic ground state of CH4 (allowed by the centrifugal distortion dipole moment) have been observed both through double resonance (see refs. 302, 303) and conventionally (see ref. 304). In addition, Mizushima-Venkateswarlu type ΔJ = 0 transitions within the v3 = 1 state of CH4 have succumbed to the double resonance technique (see refs. 333, 334). Double resonance experiments of the microwave-optical variety (see ref. 350), on the other hand, have allowed the accurate measurement of rotational transitions in an electronically excited state of BaO. The first observation of the gas-phase electron magnetic resonance spectrum (see ref. 265) of a non-linear free radical, namely HCO, has been followed by the observation of the pure microwave spectrum (see refs. 266, 268) of the same molecule. This may indicate that the study of triatomic free radicals could follow the pattern already seen in the study of diatomic free radicals where resonance studies have often been followed by microwave studies. For the most part, the parameters evaluated from microwave spectroscopy are molecular parameters, but it has recently been shown that thermodynamic functions can be obtained through the measurement of absolute intensities of transitions (see ref. 273). A new development in molecular beam maser spectroscopy has been the measurement of scattering cross-section for NH3 for two different cases, the first with beam molecules in the upper inversion state, and the second for a coherent superposition state with equal amplitudes of upper and lower inversion states (see ref. 31 1). A significant instrumental development is the spectrometer described by Krupnov et al. (see ref. 396). This has both high sensitivity and the facility for broad-banded operation in the millimetre regions by virtue of an acoustic detector.

2 Diatomic Molecules

A number of new developments have occurred in the study of diatomic molecules. The microwave spectrum of IF has been obtained for the first time and the sign of the dipole moment of ClF reported in Volume 2 has been called into question. Zeeman effect studies have been made for several diatomic molecules, and new observations have been made on rotational spectra of a number of alkali halides.

Nuclear quadrupole hyperfine structure for 39K127I has been measured on the J = 2 <- 1 transition at 7.2 GHz. Observations on vibrational states up to v = 3 lead to the following quadrupole coupling constants: eq0Q(39K)= -4.12 [plus or minus] 0.10 MHz and eqvQ(1271)= [-85.32 - 2.93(v + 1/2) [+ or -] 0.12] MHz. Using a specially designed high-temperature spectrometer for Zeeman effect measurements, Honerjager and Tischer have obtained gJ-factors for CsF, CsCl, CsBr, and CsI. Magnetic susceptibility anisotropies were also obtained for CsF and CsCl. A partial resolution of the J = 1 -> 0 transition of 6Li19F has been achieved by using electric resonance spectroscopy in the millimetre region ; magnetic spin rotation and lithium nuclear quadrupole coupling constants have been obtained. Microwave spectra of AlBr and AlI which were reported for the first time in 1972, have been further examined and nuclear quadrupole coupling constants have been evaluated from measured hyperfine structures of J = 1 <- 0 and J = 2 <- 1 transitions, respectively. The values are collected in Table 1 which also includes values for AlCl obtained by calculation on a reassignment of the spectrum.

For All, the vibrational dependence of the iodine coupling constant was also obtained as was the magnetic spin-rotation coupling for this case. Similar measurements have also been reported for TlF.

Diatomic oxides and sulphides of some Group IV elements have been further investigated. Wollrab and Rasmussen have investigated the lifetime of gas-phase carbon monosulphide by monitoring the J = 1 <- 0 transition of CS produced by a discharge through carbon disulphide. Half-lifetimes have been obtained as a function of the initial pressure of carbon disulphide and the mechanism of decay of carbon monosulphide has been considered. Measurements of the Zeeman effect have been made for Ge0, SiS, Sn0, and Pb0. The gJ-factors and magnetic susceptibility anisotropies [??]T have been obtained and are collected in Tables 2 and 3.

Molecular quadrupole moments and asymmetries of electronic charge distributions in these two molecules have also been evaluated. Two papers on the oxygen molecule have appeared. One clears up a discrepancy concerning the optical and microwave values of B0 and D0 for 16O2. The other reports the observation and analysis of the millimetre and sub-millimetre wave spectrum of 18O2. Among the data obtained are Be = 38 518.6 MHz and re = 1.20743 Å, the latter agreeing well with the value obtained from 16O2.

Interesting work on interhalogen diatomic molecules has been reported. The sign of the dipole moment of ClF, as -ClF+ has been re-examined and the microwave spectrum of IF has been observed for the first time. A theoretical calculation l1 of the properties of the ClF molecule has been made using Hartree-Fock wave-functions and the calculated spectroscopic constants (re, D0, ωe, ωexe, Be and αe) are found to be in moderate agreement with experiment, except for the dipole moment polarity which is found to be +ClF- with μ = 1.099 D. Flygare and his co-workers l2 have re-examined their previous data and analysis on ClF which led to the sign of the dipole as -ClF+ and found no errors. They have also reported new experimental results on ClF with emphasis on the determination of the sign of the dipole moment, and these results agree with the earlier work. At the same time they have summarized the applications that have been made of the molecular Zeeman method to the determination of the sign of electric dipole moments and conclude that the validity of the method is firmly established. This leads to the conclusion that if the result for CIF is incorrect it is not due to the method but to a pecularity in the J = 1 <- 0 transition for CIF. In summary the present position appears to be that the sign of the dipole moment as obtained from the theoretical calculations is -ClF+ whereas the Zeeman method leads to +ClF-, though it is recognized that the marginal nature of the experimental result, μ = -(2.1 [+ or -] 1.4 D), calls for measurement at higher resolution.

Two separate papers have reported on the microwave spectrum of IF. The analyses lead to good agreement for the ground-state rotational constant and the iodine nuclear quadrupole coupling constant : B0 = 8357.41 87 and 8357.35 MHz, with eq0Q(l27l) = -3438.15 and -3437.7 MHz. Analysis of the spectrum for the v = 1 state leads to Y01, = 8385.520 MHz. Values of Y11, Y2l, and Y02 have also been reported and the magnetic spin-rotation coupling constant has been evaluated. Radiofrequency spectra of both HF and H35Cl in an external electric and magnetic field have been measured using a high-resolution molecular beam electron-resonance spectrometer, and magnetic properties of the molecules evaluated. Molecular electric quadrupole moments have also been evaluated and found to be in good agreement with values obtained theoretically and from microwave line- broadening experiments.

Other work on diatomic molecules includes the derivation of theoretical expressions for intensities of rotational and rotation–vibration spectra of asymmetrically isotopically substituted diatomic molecules. Semi-classical formulae have been obtained for the centrifugal distortion constants Dv and Hv and a numerical procedure developed for computing these constants from RKR turning points.

3 Triatomic Molecules

The OCS molecule continues to play its role as spectroscopic guinea-pig. New microwave measurements on 13C and 18O species have been reported in an attempt to provide multiple means of determining equilibrium distances to check the consistency of results. It is also among the molecules chosen to test the use of a new structural parameter rm (see Section 7). A method for determining the signs of dipole moment derivatives has been tested on OCS, as has a high-resolution microwave spectrometer for accurate determination of molecular magnetic properties and electric quadrupole moments.

New isotopic measurements on carbonyl sulphide give rotational constants for 16O13C32S and 18O12C32S in several vibrational states and also some new information for the species 18O13C32S, 18O13C34S, 18O12C34S. Equilibrium internuclear distances, calculated for six choices of pairs of isotopic species, differ by amounts larger than the experimental uncertainties. The discrepancy is attributed to omission of weak resonances and the γij rotational constants.

The dipole moment function of a molecule is a concept that has been widely used but even for triatomic molecules knowledge about such functions has been very restricted. The signs of such dipole moments themselves have become known only during the past five years or so. For the OCS molecule the ground-state moment is +0.715 D (1 D = 3.336 × 10-30 Cm), the positive sign meaning by convention that the dipole moment has a positive direction from O to S, i.e. it corresponds to a net negative charge on the oxygen and a positive charge on the sulphur. The change in the dipole moment as the molecule is distorted is directly reflected in the intensity of i.r. bands and these provide a good source of accurate information about dipole moment derivatives, but since, the dipole derivative depends on the square root of the intensity the direction and sign of dipole moment derivatives remain indeterminate. Foord and Whiffen have made use of additional information provided by measurement, through the Stark effect, of dipole moments of molecules in excited states and of isotopically substituted molecules. The smallness of change means that such information is of low accuracy but the important feature is that it does contain information about the sign. By combining both kinds of information the seven parameters in the parallel component of the dipole moment function given below have been evaluated.

[MATHEMATICAL EXPRESSION OMITTED]

The values of the parameters which show the dependence of the parallel component of the molecular dipole moment on bond stretching and angle distortion are collected in Table 4.

The results indicate that the method of combining Stark effect measurements with i.r. intensity measurements provides a way for determining dipole moment functions of molecules, though it is noted that a good anharmonic force field is required. The physical picture that the results provide is that both oxygen and sulphur become more negatively charged as either bond to carbon is stretched, and this can be understood in terms of the increasing importance of resonance structures such as -O-C[??]S+ when the O-C bond is stretched. It is found that ([partial derivative]2p/[partial derivative]r2CO)e is of opposite sign to ([partial derivative]p/[partial derivative]rCO)e, so eventually a maximum in dipole moment would be reached as the C-O bond is stretched and this would occur at roughly one and a half times the equilibrium C-O bond length.

Zeeman effect studies on linear triatomic molecules include an examination of OCS with a high-resolution Zeeman microwave cavity spectrometer. The method leads to molecular g-value, magnetic susceptibility anisotropy, and electric quadrupole moment, all in close agreement with those obtained by molecular beam techniques. It is suggested that with this technique, microwave spectroscopy provides a useful alternative to beam techniques where high precision results are required. Other molecules for which Zeeman effect studies have recently been made are FCN and BrCN. The determination for FCN of the magnetic susceptibility anisotopy of the molecular g-value leads to a molecular quadrupole moment of (-3.7 [+ or -] 1.0) × 10-26 e.s.u. A similar study for BrCN results in a value of (-6.46 [+ or -] 1.75) × 10-26 e.s.u. in good agreement with a value determined independently and previously reported as (-6.02 [+ or -] 1.1) × 10-26 e.s.u. For HCN, magnetic hyperfine structure has been resolved by use of a millimetre-wave molecular beam maser and the spin-rotation constants obtained for 14N in H12C14N, for H in H12C14N and 13C in D13C14N as + 10.4, -3.7, and + 15.0 kHz, respectively, and these have been used to evaluate paramagnetic shielding factors.

Centrifugal distortion has been investigated in the CF2, SF2, and S20 molecules. For CF2 an additional 35 rotational lines for transitions up to J = 40 have been assigned, in addition to an earlier assignment for transitions up to J = 7. The spectrum has been analysed in terms of a centrifugal distortion model which included seven terms in P6 as well as the five P4 terms. The general valence quadratic force field was calculated from the distortion constants and this has been used to calculate the i.r. fundamentals, which are found to be in good agreement with the observed values. An improved value of the dipole moment of CF2 has also been reported which gives μ = 0.469 [+ or -] 0.026 D. Centrifugal distortion in SF2 has similarly been investigated. In this case some 67 new transitions were assigned and measured with J-values up to 43. Force constants were evaluated and so were the i.r. fundamentals. In this case the i.r. spectrum has so far not been observed, and this provides an example of i.r. fundamentals being predicted within quite close limits from analysis of the microwave spectrum. For both CF2 and SF2 the force fields have been used to calculate average structures from the molecular ground-state rotational constants. A centrifugal distortion analysis for S20 has been made, as a result of a re-examination of the microwave spectrum, on some 70 lines for transitions up to J = 30. Force constants have been evaluated and lend support to the assignment of the i.r. fundamentals.

Cubic potential constants have been obtained for SiF2 from measurement and analysis of microwave transitions for vibrationally excited The present investigation has made a detailed study for states υ1 = 1 and υ3 = 1 and used this with information previously obtained for the ground state and the υ2 = 1 state. The υ1 = 1 and υ3 = 1 states are nearly degenerate, and an extensive analysis has been made of the Coriolis resonance observed in the microwave spectrum for the two states. The υ1 = 1 state is found to be lower than the υ3 = 1 state by 15.395 cm-l, and an intervibrational state microwave transition has been observed, namely υ1 = l,854<- υ3 = l,817. The analysis leads to aA, aB, and αA, αB, and αC for v1, v2, and v3 and from these, third-order force constants have been obtained. The values are in line with the general qualitative pattern that has begun to emerge from the study of a small number of bent XY2 molecules. The third-order terms in Δr1 andΔr2, the bond-stretching co-ordinates, are overwhelmingly important compared with other third-order terms and all third-order terms have negative signs. The equilibrium structure has also been evaluated and leads to the following parameters: re(Si-F) = 1.5901 [+ or -] 0.0001 Å, and θe(F-Si-F) = 100° 46' [+ or -] 1'.