Laser Magnetic Resonance Spectroscopy

BY D. K. RUSSELL

1 Introduction

The topic of Laser Magnetic Resonance, or LMR, spectroscopy, has received passing attention in these pages previously, but its growing importance as a method for obtaining structural and chemical information about free radicals has now prompted this Report. After an introduction, we shall consider in some detail the theory of the method, with particular emphasis on the extraction of significant molecular parameters from observed spectra. This will be followed by a discussion of some experimental aspects of the technique, after which an appraisal of some of the more important rec2nt results will lead onto a consideration of some likely future developments.

The development of spectroscopic techniques in the region between the traditional microwave region, with a high limit of about 300 GHz or 10 cm-1, and grating infra-red spectroscopy, with a low limit of about 6000 GHz or 200 cm-1, has been hampered by the lack of high-power tunable sources (for a discussion of this point, and recent attempts to bridge this gap, see reference 2). The first really versatile sources of radiation in this region were the far infrared lasers, discovered in 1964. These lasers operated on the rotational transitions of small molecules such as H2O, D2O or HCN excited in an electric discharge, and produced up to 0.1 watts of continuous coherent radiation in the 100 cm-1 region. The drawback of these lasers was, of course, that they were not tunable by more than the linewidth of the lasing transition, at first sight severely limiting the possibility of observing the rotational transitions of many important molecules in this region. However, since many of these species are free radicals, and hence paramagnetic, the energy levels of the molecules themselves may be tuned into resonance with the fixed frequency source. In a pioneering experiment in 1968, Evenson and his co-workers succeeded in demonstrating the feasibility of this technique when they detected a weak rotational transition in O2 using the HCN laser as a source. The obvious similarity between this technique and the well known electron para-magnetic resonance led to the title "Laser Electron Paramagnetic Resonance"; this description, perhaps on the grounds of its unfortunate acronym, was soon replaced by "Laser Magnetic Resonance".

After this initial observation, progress was swift. The sensitivity of the technique was improved by several orders of magnitude by placing the spectroscopic absorption region within the laser cavity, and the spectra of other stable magnetic molecules in this frequency range were observed. The high sensitivity and exciting potential of the new technique were amply demonstrated in 1971 by the detection of rotational spectra of the hitherto elusive CH radical in oxygen-acetylene flames. The frequency range was extended further into the infra-red by the use of CO2 and CO lasers in the detection of vibrational transitions of free radicals, and the number of laser frequencies available in the far infra-red region was dramatically increased by the discovery of optically pumped far infra-red lasers.

The more than 200 publications in the last decade in the area of LMR include a great many spectroscopic "firsts", as well as applications of considerable importance in areas as diverse as chemical kinetics, atmospheric chemistry, reaction mechanisms and astro-physics. This activity, which as yet shows little sign of falling off, amply attests the versatility and power of this spectroscopic technique.

2 Theory of the Method

This review is concerned exclusively with the use of LMR spectroscopy as a technique for the detection and monitoring of short-lived atomic and molecular species in the gas phase. While there are undoubtedly many important potential applications in condensed phases, to the author's knowledge little has been done to explore this aspect of the technique. In this section we shall examine the basic theory of the method, in particular its relation to the better-known technique of electron spin resonance (and especially gas phase electron resonance), and then consider the types of information available from observed spectra in relation to the Hamiltonian used to describe the energy levels of the system.

In condensed phases, the major source of angular momentum, and hence paramagnetism, is the spin of unpaired electrons, with generally smaller contributions from such orbital angular momentum as remains unquenched, and also magnetic nuclei. This situation contrasts strongly with the gas phase, where, in addition to the effects of unquenched orbital angular momentum, those of molecular rotation (and in some cases, vibration) also play a vital role in determining the overall behaviour of the system in a magnetic field. As a result, whereas the behaviour of atoms in states of zero orbital angular momentum (such as H in its 1 2S ground state) is broadly similar in both gaseous and condensed phases, that of atoms in non-S states and all molecules is quite different.

As a simple first example, let us consider the behaviour of the 0 atom in the gas phase in a magnetic field: this will also serve as an introduction to the LMR method. The electronic configuration of the ground state of O is (ls)2 (2s)2 (2p)4, with a resultant syrrunetry of 3P in its lowest energy state. The coupling of spin and orbital angular momentum leads to levels of total angular momentum J=O, 1 or 2, with energies as shown at the left-hand side of Figure 1. In a magnetic field, these levels split into (2J + l) components labelled by mJ quantum numbers: it is between these components that transitions may be induced by microwave radiation of the correct frequency in the gas phase electron resonance experiment, as is illustrated by the six shorter vertical lines in Figure 1. Higher order effects of the magnetic field cause a slight curvature of the levels, and as a result the six transitions occur at slightly different fields, as illustrated by the typical spectrum of Figure 2. The positions of these six transitions depend strongly on the parameters describing the interaction of the spin and orbital magnetic moments with the external magnetic field, and to a lesser extent on the separation of the 3 P components, so that an analysis of the observed spectrum has led to accurate values of these quantities.

As is illustrated in Figure 1, it is also possible to induce transitions between the magnetic components of different spin-orbit levels. Since the maximum energy shift available from magnetic field tuning amounts to some 2 cm-1, the frequency of the source must clearly lie within this limit of the zero-field splittings of about 69 cm-1 (3P0 - 3P1) or 158 cm-1 (3P1 - 3P2). Such frequencies are available from far infra-red lasers, and the tuning of the transitions into resonance with the fixed frequency of the laser constitutes the LMR experiment. LMR spectra due to both fine structure transitions have been observed, leading to very accurate measurements of these fine structure intervals. The resolution of the technique is such that the shift of about 10 MHz in fine structure spacing when 16O is replaced by 18O is easily observed. Similar measurements have been carried out on the fine structure of Hg, C, and Cl, and excited states in several inert gases. In some of these cases, the transitions occur in the mid infra-red region, where the higher powers available from CO2 and CO lasers can be used to provide even higher resolution by the techniques of non-linear or saturation spectroscopy.

We now consider the case of a molecule where orbital angular momentum is the only source of paramagnetism: an example of this type is the metastable excited a 1Δ state of the radical PH. This species may be generated (along with a number of others) simply by passing the products of a microwave discharge in H 2 over red phosphorus. The rotational energies of such a molecule closely resemble those of a molecule in a closed shell state (i.e.1[summation]) with the exception that the lowest J=O and 1 levels are missing, and that the paramagnetism arising from the orbital motion of the electrons permits considerable magnetic tuning of the levels. Data from optical spectroscopy shows that the J=5 [left arrow] 4 transition lies very close to the water vapour discharge laser frequency at 84.323402 cm-1. In Figure 3 is shown the behaviour of the J=4 and 5 rotational levels as a function of applied magnetic field: in this Figure, the higher J=5 rotational level has been shifted down in energy by the laser resonant frequency. The advantage of this method of presentation is that spectroscopic transitions now appear as crossings of appropriate pairs of energy levels, eliminating the need for identifying them in the manner of Figure 1. In Figure 3, two types of transition are identified by open or closed circles: an examination of the levels involved in these two types will show that the former corresponds to transitions where ΔmJ = ± 1, and the latter where ΔmJ = 0. Since most LMR molecular transitions are electric dipole in origin, (unlike those in condensed phase ESR, which are magnetic dipole), these two types are easily distinguished experimentally by observing their behaviour as a function of the relative orientation of the plane of polarisation of the laser radiation and that of the magnetic field. The observed LMR spectrum of PH (a 1Δ) has been analysed to yield an accurate value of the bond length; in addition, the spectrum shows hyperfine structure due to both 3 1 P and 1 H nuclei, so that the electronic distribution in this molecule may be accurately determined.

As a final, more complex, and perhaps more typical example of the behaviour of the energy levels of gaseous free radicals in a magnetic field, and the resultant LMR spectrum, we consider a second product of the reaction between H atoms and red phosphorus, namely PH2. This species can in fact be produced in somewhat higher concentrations by the reaction of the discharge products of CF4 (largely F atoms, CF2 and CF3) with PH3 at a total pressure of about l mbar. PH2 is an asymmetric rotor of similar dimensions to H2S, and this leads to a complex disposition of rotational energy levels. The spin of the unpaired electron is rather weakly coupled to the molecular framework by a small spin-rotation coupling, so that the energy levels of this molecule show very complex non-linear behaviour as illustrated in Figure 4. This behaviour, together with the increased probability of near coincidences between rotational transitions and laser frequencies, can lead to very rich LMR spectra, as illustrated in Figure 5. The rotational LMR spectra again show hyperfine structure due to all three magnetic nuclei, and a complete analysis of the observed spectra has yielded extensive information about both nuclear and electronic structure. PH2 also provides our first example of a molecule whose vibration-rotation spectrum has been studied using LMR spectroscopy - in this case, vibration-rotation transitions are brought into resonance with a fixed frequency CO2 laser near 1100 cm-1. In this case, complete analysis of the observed spectrum leads to information about both ground and excited vibrational states, and an analysis of the combined far infra-red and mid infra-red data has yielded accurate values for 25 parameters describing these states.

We now turn to a consideration of the Hamiltonian used to describe the observed spectra, paying particular attention to the interpretation of the spectra and the way in which physically meaningful parameters may be extracted from them. As the Zeeman effect in atoms has been well understood for a number of years, little will be said in this respect, except to emphasise the fact that the higher precision of determination of such quantities as fine structure separations may require modification or extension of present theoretical understanding: for example, the isotope shift of the fine structure spacing in O(3P) is dependent on both mass polarisation and relativistic terms. In many cases, the parameters describing the Zeeman effect and the hyperfine interaction with magnetic nuclei can be determined to higher precision using the techniques of gas phase electron resonance or atomic beam radiofrequency spectroscopy.

Since many more of the successes of LMR spectroscopy lie in the field of molecular free radical studies, it is towards an interpretation of the spectra of these species that we will direct our attention. As has been shown by a number of authors, the procedure of using an effective Hamiltonian operating within a single vibrational level of a single electronic state is usually a sufficiently good approximation for the lkHz - lMHz precision of rotational or vibrational spectroscopy, provided the usual molecular parameters are recognized to be functions of the state under discussion: in this way, the results of interactions between such single levels can be considered as contributions to the parameters effective to each level. This approximation may, of course, not be sufficient when individual levels are accidentally close together: an example of this from the field of vibrational LMR spectroscopy occurs in the interpretation of the V2 = 1 [left arrow] 0 transition in DO2, where a satisfactory interpretation was achieved only by inclusion of a Coriolis interaction with the nearby (but unobserved) V1 = l vibrational level. In other cases, the effect of the interactions between such single levels is to introduce new types of term into the effective Hamiltonian: an example of such a term familiar to

ESR spectroscopists is the anisotropic contribution to the 2-tensor, arising from the mixing of excited electronic states the spin-orbit coupling interaction. Here, we will discuss the various terms in the molecular Hamiltonian in their most common form, with particular emphasis on their relation to observed spectra.

The Hamiltonian can be written as

H = HE + HV + HR + HFS + HHF + HZ.... [1]

where each term will be discussed in turn below. HE is taken to represent the contribution to the energy of electronic motion. In molecular LMR spectroscopy, there are as yet no examples of transitions between two electronic states, so that it has not been necessary to include this term: were this the case, no doubt the relative energy of the two electronic states involved could be included as a single determinable parameter.

HV represents the contribution of molecular vibrations to the energy. In only very few cases has more than one vibration energy spacing been observed from LMR spectroscopy, so that unless these data are available from other spectroscopic techniques, it is not possible to determine anything more than the vibrational band centre as an experimentally observable parameter, with the consequent uncertainty arising from anharmonic contributions. In any case, it seems unlikely that the range and precision of data will require anything more sophisticated than the usual series expansion in terms of vibrational quantum numbers for the vibrational energy,

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with the usual modifications to accommodate degenerate vibrations where necessary.

HR represents the contribution to the Hamiltonian arising from molecular rotation. As pointed out above, the effect of operating within a single vibronic state is to introduce effective rotational constants, and also to introduce some new terms. In this case, these new terms are usually interpreted as centrifugal distortion. There have been several representations of the rotational Hamiltonian, but recently the most popular seems to be that of watson, perhaps partly because of the ease with which it can be written into computer programmes:

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