MICROWAVE AND RADIO-FREQUENCY SPECTROSCOPY GENERAL INTRODUCTORY PAPER BY H. C. LONGUET-HIGGINS University Chemical Laboratory, Cambridge 1. INTRODUCTION The intention of the Faraday Society in holding this discussion is to catalyze the employment by chemists of the new techniques of microwave and radio- frequency spectroscopy recently developed by physicists. These techniques have enabled us to probe into h e details of atomic and molecular structure which would have been thought inaccessible to observation as little as 15 years ago. The least recent and most extensively applied of these new developments is the microwave spectroscopy of gases, but this subject represents only one of the five topics which are to be discussed at this conference. These topics are : (1) the microwave spectroscopy of gases : (2) the absorption of microwave power by ionized gases, particularly flames ; (3) paramagnetic resonance spectroscopy ; (4) nuclear magnetic resonance spectroscopy ; (5) nuclear quadrupole spectroscopy. In this list the second heading covers a topic which differs somewhat from the others in that the absorption of microwave power in flames is not associated with quantized transitions.What is measured is essentially the electrical conduc- tivity of the flame as a function of temperature and composition. This con& ductivity, which arises almost entirely from the free electrons, is determined by their concentration and their collision frequency with the molecular species present. The method therefore enables one to measure both these quantities separately, and in some cases to determine ionization potentials, electron affinities, and equilibrium constants.Our first topic of discussion, the microwave spectroscopy of gases, is a subject already thoroughly familiar to physical chemists. Suffice it to say that the transitions responsible for microwave absorption lines are usually due either to changes in rotational quantum number or to changes in internal configuration- for example, the inversion of ammonia and the hindered rotation of methanol. Microwave spectroscopy provides, in fact, the most accurate method for deter- mining the geometry of simple molecules, and is becoming increasingly useful as a tool for measuring barriers to internal rotation. There is, however, one aspect of microwave spectroscopy which promises to provide detailed information also about the electronic structures of simple molecules, namely, the study of hyperfine structure.This hyperhe structure arises from the different possible orientations of certain nuclei in the molecule, and provides both qualitative information about the molecular symmetry and quantitative information as to the electrical envison- ment of the nuclei in question. As the last three subjects in this discussion are also closely concerned with nuclear effects it may be as well at this point to digress at some length on the properties of nuclei which are relevant to low-frequency spectroscopy. 910 GENERAL INTRODUCTION 2. THE ELECTROMAGNETIC PROPERTIES OF THE NUCLEUS For most chemical purposes it is sufficient to regard the nucleus as having only three properties, position r, mass M, and charge Ze.However, in order to interpret the low-energy transitions which arise in radio-frequency spectroscopy, it is necessary to take into account three more properties, namely, spin I, magnetic moment p , and electric quadrupole moment Q. The spin of the nucleus determines its total angular momentum, which is given by the expression h - 271. - Z/I(I + i). If I differs from zero the nucleus can take up any one of 21 + 1 orientations with respect to a given axis in space. These orientations may differ in energy for either of two quite different reasons. First, a nucleus with spin greater than zero in- variably possess a magnetic moment p ; that is to say, the nucleus behaves as a little magnet whose axis coincides with the axis of spin.Hence if the nucleus is placed in a magnetic field H there will be an additional contribution to the potential energy equal to pNcos 8. When this potential is added to the Hamiltonian it turns out that each (214 1)-fold degenerate level is split into a set of 2 1 3 1 sublevels between which it may be possible to induce transitions by the application of a fluctuating magnetic field of suitable frequency. FIG. 1. (a) Nucleus of magnetic dipole moment p in magnetic field H. Magnetic potential energy = pH cos 8. Splitting of levels in (b) Nucleus of electric quadrupole moment Q in inhomogeneous electric field E = V V. If field is axially symmetrical, quadrupole q = 32V,W. Splitting of levels in pure pure magnetic field when I = 2: energy = teQq(3 cos2 6 - 1) where electric field when I = 4 : Secondly, if the nuclear spin I is greater than 3, the nucleus will possess an electric quadrupole moment Q.What this means is that the positive charge in the nucleus is not spherically distributed, but that the nucleus is rather to be thought of as elongated (Q > 0) or flattened (Q < 0), while still retaining its symmetry about the axis of spin. Such deviations from spherical symmetry make no difference to the energy, provided that the electric field at the nucleus is uniform; however, if the electric lines of force are not parallel in the neighbourhood of the nucleus then the electrical energy of the nucleus will depend on its orientationH. C. LONGUET-HIGGINS 11 relative to the line of force which passes through it.This may be expressed by adding to the Hamiltonian a potential-energy term of the form QeQq (3 C O S ~ 8 - I), where 4 represents the inhomogeneity of the electric field arising from all the other charges (electron and nuclei included) in the rest of the molecule.* In short, the energy of a nucleus may depend on its orientation either for mag- netic or for electrical reasons, or both. These two situations are illustrated diagrammatically in fig. 1. Table 1 gives the electromagnetic constants of some important nuclei. It may be noticed, as already remarked, that if I = 0 there is no magnetic moment or electric quadrupole moment; if I = -$ there is a magnetic moment but no quadrupole moment and that if I > 3 there is a quadrupole moment also, but that its magnitude varies widely from isotope to isotope.TABLE 1 .-PHYSICAL CONSTANTS OF SOME NUCLEI (from Gordy, Smith and Trambarulo, Microwave Spectroscopy) spin z 1 3 - 1 a I 8 a 0 magnetic moment p (nuclear magnetom) 2.8 0.9 1.8 2.6 0 0.7 0.4 - 0.3 0 0 2.6 3.6 1.1 0 0.6 0.8 0.7 2.1 2.3 2.8 quadrupole moment Q (units of 10-24 cm2) 0 0.003 0.06 0.03 0 0 002 0 0 0 0 0.16 0 0 - 0.08 - 0.08 - 0.06 0.34 0.28 - 0.7 3. PARAMAGNETIC RESONANCE SPECTROSCOPY The phenomenon of paramagnetic resonance, or electron magnetic resonance, as it is sometimes called, is essentially simple in principle. The phenomenon is exhibited only by substances whose molecules possess electronic angular momentum. This angular momentum may arise from the presence of either electrons of uncompensated spin or electrons with finite orbital momentum.In either case the ground state of the molecule will be degenerate in the absence of an external magnetic field. However, we know that both the spin and the orbital angular momentum of an electron give rise to magnetic moments: the spin magnetic moment t is eh/$mnc and its component in a chosen direction may be either & ehl4~mc. Leaving aside the orbital contribution, the theory of which is discussed in later papers, one can see that if a molecule with an unpaired electron * If the field at the nucleus is not axially symmetrical, a more complicated expression -f More accurately, the magnetic moment is 20023 X 4 x eh/4~mc ; this small correction is required.also affects the equation for the resonance frequency.12 GENERAL INTRODUCTION is subjected to a magnetic field H its doublet ground state will be split into two components separated by an energy gap of AE = ehH/2nmc. If now an oscillating magnetic field is applied, transitions will be induced between these two levels If v = eH/2nmc and energy will be absorbed, since at low tem- peratures the lower level will be more highly populated. In practice one keeps v constant and varies H until resonance absorption occurs, but this is only a matter of convenience. The occurrence of absorption is a definite indication of de- generacy in the unperturbed ground state; the interest of the phenomenon, however, lies primarily in the interpretation of the hyperfine structure.Such structure may be observed if the molecule contains nuclei with permanent magnetic moments. The magnetic field of a magnetic nucleus will add to, or subtract from, the external magnetic field in its neighbourhood according to the orientation of the nucleus; hence, if the unpaired electron spends much time near this nucleus it will experience a net magnetic field which depends on the nuclear orientation. This results in a splitting of the resonance lines, and the splitting can be used for determining the extent to which the odd electron is associated with the nucleus in question. I t should be added that more information can be obtained from studies of crystalline materials than from fluid specimens, both because the magnetic field of a nucleus averages to zero if the molecule is rotating rapidly, and because in a crystalline material one can determine the resonance absorption for different directions of the applied fields relative to the crystal axes.4. NUCLEAR MAGNETIC RESONANCE There are two distinct types of measurement which come under the general title of nuclear magnetic resonance. Basically the same phenomenon is observed in both, but rather different types of information are obtained from the two sorts of experiment. In low resolution nuclear magnetic resonance spectroscopy one places a crystal in a permanent magnetic field H and subjects it to an oscillating magnetic field of frequency v. The external field has the effect of splitting the energy levels of the magnetic nuclei in the manner described in 6 2, and the oscillating magnetic field then induces transitions between these levels. If we consider a particular magnetic nucleus, the magnetic field in its neighbourhood may be modified by the magnetic fields of neighbouring nuclei, but there are various possible orientations for each of these nuclei.From a statistical point of view the magnetic nuclei of a particular type will therefore not all be experiencing the same magnetic field and the ob- served resonance spectrum will be spread out from a line into a fairly wide band. The width of this band will be determined by the distribution of other magnetic nuclei around the nucleus whose re-orientation is being studied, and by making use of this fact one can determine the distances between magnetic nuclei in the molecule. This method has proved particularly valuable for determining the positions of protons in crystalline solids, and proton magnetic resonance provides a useful supplement to X-ray crystallography in this respect.High-resolution nuclear magnetic resonance is a more recent development. In this technique one works with a fluid sample in which each molecule is rotating rapidly in the external magnetic field. As indicated above, this rotation has the effect of averaging out to zero the direct magnetic field of any nucleus at any other nucleus. It might be thought, therefore, that rather little information could be obtained about the molecular structure from the high-resolution method. This, however, is not so for two reasons. First, the average magnetic field at a chosen nucleus is nearly but not exactly equal to the externally applied field.This is because the electrons associated with the nucleus are magnetically susceptible toH. C. LONGUET-HIGGINS 13 the field and their susceptibility has the effect of partially screening the nucleus from the permanent field. The resonance frequency of a nucleus therefore depends slightly on its chemical environment and experience has shown that one can distinguish, for example, protons bonded to oxygen from protons bonded to nitrogen OF carbon. Indeed, the so-called " chemical shifts " in proton resonance can be used as an analytical device in much the same way as infra-red spectroscopy. Secondly, although as just indicated the direct magnetic field of one nucleus at another averages to zero, a given nucleus is not, so to speak, entirely unaware magnetically of its neighbours. This is because the electrons in the bond between two nuclei have the effect of coupling their magnetic moments.The theory of this effect is somewhat complicated but it is quite certain that the resonance fre- quency of a particular nucleus depends slightly on the spin orientations of neigh- bouring magnetic nuclei. This fact enables one to derive from the high-resolution measurements much useful information about the relative disposition of different magnetic nuclei, as later papers in this Discussion fully illustrate. Mention should be made of two more points. First, if a nucleus has a large quadrupole moment, account must be taken of this in the quantitative interpreta- tion of the resonance frequency, though this effect is absent in proton resonance since the proton has no quadrupole moment.Secondly, fine structure can only be resolved if the nucleus in question maintains its position in the molecule for a time substantially greater than l/Av, where Av is the frequency separation of the lines to be resolved. This fact makes it possible to identify mobile protons in hydrogen compounds and even to obtain limits for the rate constants of certain exchange reactions. 5. NUCLEAR QUADRUPOLE SPECTROSCOPY This branch of radiofrequency spectroscopy is somewhat simpler in principle than magnetic resonance spectroscopy. No permanent magnetic field need be applied : the crystalline sample is simply placed in a coil carrying a radiofrequency current and the absorption of energy is measured as a function of frequency.Such absorption will occur if the sample contains one or more nuclei with a permanent electric quadrupole moment. In $ 2 we remarked that the energy of such a nucleus will depend on its orientation in the molecule, if the lines of electric force at the nucleus are not parallel. Such a nucleus can then take up 21 + 1 different orientations whose energies will not be all equal, and one may expect under favourable conditions to observe transitions between these states. Now the nucleus has no electric dipole moment, so an oscillating electric field will be ineffective in inducing such transitions. However, a nucleus with a quadru- pole moment always has a magnetic moment and can be induced to alter its orienta- tion by an oscillating magnetic field of suitable radiofrequency. What one measures, then, is the radiofrequency at which transitions are induced, and this tells one how much energy is needed to re-orient the nucleus in the electric field of the rest of the molecule. Consequently, if one knows the nuclear quadrupole moment Q one can determine the value of q, that is to say, the inhomogeneity of the electric field at the nucleus due to all the other charged particles in the molecule. This measurement of q can in some cases be checked against values obtained from microwave spectra, in which the hyperfine structure also arises from quadrupole effects; it is then a matter for the theoretical chemist to interpret the magnitude of q in terms of the electronic structure of the molecule.