Microwave magnetic resonance

Electron spin resonance (e.s.r.) spectroscopy, applied to free radicals in condensed phases, is a long established technique with several commercially available spectrometers. The gas phase applications we will describe have httle in common with condensed phase studies, and are much more a part of rotational spectroscopy. However, the experimental methods nsed for condensed phase studies can be applied to the study of gases with rather httle change, so it is appropriate first to describe a typical microwave magnetic resonance spectrometer, as illustrated schematically in figure 9.1. 

Most e.s.r. spectrometers operate in the so-called X-band microwave frequency range 9.5 GHz is a typical operating frequency, and it is convenient because the magnetic fields required for resonance are in the range accessible to conventional electromagnets. Spectrometers operating up to 40 GHz have been used but they are less suitable for gas phase studies, mainly because of the smaller size of the resonant cavity. 

Conventional condensed phase e.s.r. studies usually employ a rectangular cavity, but most gas phase studies have been made using cylindrical cavities operating in the so-called TEon mode. In a TE u mode, TE stand for transverse electric , the integer m represents the number ofE field maxima in a 180° angle measured in a plane perpendicular to the axis of the cylinder, n represents the number of E field maxima betweeu the ceutre and the wall, and p is the number of E field maxima along the axis 

In order to see how these principles are put into practice we now describe a cavity designed by Carrington, Levy and Miller [3] specifically for gas phase studies of free radicals it is illustrated in figure 9.3. It operates in the cylindrical TEon mode and 

Several different methods have been used successfully to generate a detectable concentration of short-lived free radicals inside the resonant cavity. The simplest method is a microwave discharge in the flowing gas, located upstream of the resonant cavity discharges in water vapour, for example, yield readily detectable concentrations of OH radicals. Shorter lived species have been produced by atom abstraction reactions inside the cavity, for example, by mixing fluorine atoms, produced by a microwave discharge in CF4, with a suitable secondary gas. Reaction of F atoms with OCS, for example, prodnces detectable concentrations of the SF radical [4]. 

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Beringer, R. and Castle, J.G. Jr. 1951. Microwave magnetic resonance spectrum of oxygen. Physical Review 81 82-88. 

The development of the effective Hamiltonian has been due to many authors. In condensed phase electron spin magnetic resonance the so-called spin Hamiltonian [20,21] is an example of an effective Hamiltonian, as is the nuclear spin Hamiltonian [22] used in liquid phase nuclear magnetic resonance. In gas phase studies, the first investigation of a free radical by microwave spectroscopy [23] introduced the ideas of the effective Hamiltonian, as also did the first microwave magnetic resonance study [24], Miller [25] was one of the first to develop the more formal aspects of the subject, particularly so far as gas phase studies are concerned, and Carrington, Levy and Miller [26] have reviewed the theory of microwave magnetic resonance, and the use of the effective Hamiltonian. 

The hydroxyl radical, OH, occupies an extremely important position in spectroscopy, in free radical laboratory chemistry, and in atmospheric, cometary and interstellar chemistry. Its ultraviolet electronic spectrum has been described in many papers published over the past seventy years. It was the first short lived gaseous free radical to be studied by microwave spectroscopy, described in a classic paper by Dousmanis, Sanders and Townes [121] in 1955. The details of this work are presented in chapter 10. It was the first free radical to be studied by microwave magnetic resonance, in pioneering work by Radford [141] the microwave and far-infrared laser magnetic resonance studies are... 

Figure 9.1. Block diagram of a microwave magnetic resonance spectrometer. 

Figure 9.5. Observed microwave magnetic resonance spectra of A 02 (top) and1A SO (bottom). The microwave frequency was close to 10 GHz in both cases. The top spectrum is obtained by magnetic field modulation, the bottom by electric field modulation.

Figure 9.7. Microwave magnetic resonance spectrum of1A NF (J = 2) recorded at a frequency of 9320 MHz [16],...

It is probably true that the majority of free radicals which have been studied by microwave magnetic resonance have 2 n ground states. In part this might be because... 

Figure 9.9. Microwave magnetic resonance spectra of top) CIO [20] and (bottom) BrO [21], both in their J = 3/2, 2n3/2 states.

The main conclusion from these results is that the observed hyperfine splitting is determined primarily by a linear combination of the hyperfine constants corresponding to the three separate interactions. The spectrum depends upon the axial component ofthe total magnetic hyperfine interaction, which we designate / 3/2 (= a + (1 /2)(b + 2c/3)), and in a good case (a) system it is not usually possible to separate the individual contributions from the microwave magnetic resonance spectrum alone. The solution to the problem lies in the combination of these studies with pure rotational spectroscopy, as we shall see later in this chapter. 

Historically the first open shell molecule to be studied by magnetic resonance methods was nitric oxide, NO. The 2n1/2 fine-structure component is lower in energy than the 2n3/2 component by 123 cm 1 and is only weakly magnetic. However, the 2n3/2 component is substantially populated at room temperature and its microwave magnetic resonance spectrum is readily recorded. Spectra of the lowest rotational level,... 

Figure 9.12. Microwave magnetic resonance spectra of NO in the J = 3/2 level of the 2n3/2 component, recorded by Brown and Radford [37]. Part (a) shows the 15N160 spectrum, with a very small A-doublet splitting, a larger second-order Zeeman splitting of the three AM/ = 1 components, and a doublet splitting from the 15N nucleus, which has I = 1/2. Part (b) shows the 14N160 spectrum, which is similar to that shown in (a), except that there is now a triplet splitting from the 14N nucleus, which has 7 = 1. The microwave frequency was 2879.9 MHz.

Figure 9.16. Recording of the A-doublet microwave magnetic resonance spectrum of OH in the J = 3/2 F2 (2 n 1/2) rotational level [7]. The assignment of the lines is given in the text. The resonant microwave frequency was 9200 MHz.

The microwave magnetic resonance spectrum of SO was recorded at a resonance frequency of 8762 MHz and involved Zeeman components of rotational transitions between the N = 1 and 2 rotational levels. We first describe the effective Hamiltonian and its matrix elements, and then the observed spectrum and its analysis. 

In their analysis of the SO microwave magnetic resonance spectrum, Carrington, Levy and Miller [56] set up and diagonalised a series of matrices of size up to 22 x 22, one for each Mj value, which alone remains a good quantum number. They included rotational levels from N = 0 to 7, but to illustrate the nature of the problem we will set up the 9 x 9 matrix for N = 0 to 3, for Mj = 1 in practice one includes levels of N value high enough to avoid truncation errors. The individual matrix elements for our... 

Figure 9.26. Left lower rotational levels of SO 3 in zero magnetic field, and the transitions observed (see chapter 10). Right microwave magnetic resonance transitions observed in SO at 8762 MHz [56].

An unusual example of a microwave spectrometer which uses superheterodyne detection and molecular modulation is a tunable-cavity spectrometer designed and built by Radford [13]. Microwave cavities were described in chapter 9, where they form the heart of a microwave magnetic resonance spectrometer. Compared with... 

There can be no question that the most important species with a 3 E ground state is molecular oxygen and, not surprisingly, it was one of the first molecules to be studied in detail when microwave and millimetre-wave techniques were first developed. It was also one of the first molecules to be studied by microwave magnetic resonance, notably by Beringer and Castle [118]. In this section we concentrate on the field-free rotational spectrum, but note at the outset that this is an atypical system O2 is a homonuclear diatomic molecule in its predominant isotopomer, 160160, and as such does not possess an electric dipole moment. Spectroscopic transitions must necessarily be magnetic dipole only. 

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