Introduction

The dynamics of chemical reactions can be probed in detail by employing a method of experimentation that is sensitive to both reactant and product internal state energy distributions and velocities and correlations between these quantities. Two main scattering techniques have emerged to study bimolecular reactions of the form A+BC → AB+C.

One is the crossed molecular beam technique [1], in which molecular beams of the reactants A and BC, with well-defined beam velocities, are intersected at some angle. The AB and/or C product velocity and angular distributions are then measured with a form of universal ionization (such as electron impact ionization) and time-of-flight mass spectrometry (TOF–MS). The universal ionization step is used because the product densities are usually too small to allow a form of state selection, such as that of laser ionization, which provides small detection volumes.

Another method is a single beam technique [2,3], in which reactants or their precursors are premixed and co-expanded through a pulsed nozzle thus forming a single molecular beam. A photolysis laser is used to generate hot-atom reactants that subsequently react with other molecules in the beam. After a suitable time delay (typically 50–500 ns) that allows a sufficient density of products to build up, a second (probe) laser is used to state-selectively probe the reaction products, which are then detected with a velocity-sensitive technique (either TOF–MS, or Doppler spectrometry).

The field of molecular reaction dynamics has made enormous progress since the pioneering experiments of Yuan Lee, Dudley Herschbach and John Polanyi. The intervening years have seen numerous developments in both experimental techniques and theoretical methods. For the authors of this book one of the most exciting of these advances was the introduction of charged particle imaging by Dave Chandler and Paul Houston described in their 1987 paper ‘Two-dimensional imaging of state selected photodissociation products detected by multiphoton ionization’ published in the Journal of Chemical Physics.

I was extremely fortunate to be able to join Paul Houston in Ithaca in 1988/89 where we constructed the second imaging machine (Dave Chandler's original machine in Sandia having been temporarily put out of action in an unfortunate accident that Paul describes in the first chapter). It was an extraordinarily exciting experience to be involved in those earlier experiments and I am extremely grateful to Paul for the opportunity. The early data showed the power of the technique to provide graphic insight into chemical mechanism but it was difficult to obtain quantitative information because of instrumental problems to do with the arrangement of the ion optics. These were overcome by André Eppink and Dave Parker working in Nijmegen.

Introduction

As we have seen in the previous chapters inversion algorithms are required in conjunction with two-dimensional (2-D) detection methods in order to reconstruct the velocity (speed and angle) distributions of the products of photodissociation processes. Since these generally need to make certain assumptions about the symmetry of the measured distributions it would be desirable to measure the velocity distribution directly by making a simultaneous measurement of the position and arrival time of each of the photoproducts. In the previous chapter we saw how two charge-coupled device (CCD) cameras can be used in conjunction to make such a measurement. The present chapter develops this idea further by describing a newly developed three-dimensional (3-D) photofragment imaging technique. In this context the term ‘3-D imaging’ refers to the simultaneous measurement of all three coordinates of a single particle, which are defined by the spatial position in the 2-D surface of the position-sensitive detector (PSD) and by the time of arrival at the detector (the third dimension) of the ionized product of a photodissociation process. The transverse velocity components (vx, vy) of the initial velocity of the product are determined from the measured 2-D impact position on the PSD surface, while the measured time of arrival gives the longitudinal component (vz) of the velocity. Hereafter the laboratory axes X, Y, and Z are directed along the laser beam, the molecular beam, and the accelerating electric field, respectively (Fig. 6.1).

A book whose title refers to the spectroscopy of diatomic molecules is, inevitably, going to be compared with the classic book written by G. Herzberg under the title Spectroscopy of Diatomic Molecules. This book was published in 1950, and it dealt almost entirely with electronic spectroscopy in the gas phase, studied by the classic spectrographic techniques employing photographic plates. The spectroscopic resolution at that time was limited to around 0.1 cm−1 by the Doppler effect; this meant that the vibrational and rotational structure of electronic absorption or emission band systems could be easily resolved in most systems. The diatomic molecules studied by 1950 included conventional closed shell systems, and a large number of open shell electronic states of molecules in both their ground and excited states. Herzberg presented a beautiful and detailed summary of the principles underlying the analysis of such spectra. The theory of the rotational levels of both closed and open shell diatomic molecules was already well developed by 1950, and the correlation of experimental and theoretical results was one of the major achievements of Herzberg's book. It is a matter of deep regret to us both that we cannot present our book to ‘GH’ for, hopefully, his approval. On the other hand, we were both privileged to spend time working in the laboratory in Ottawa directed by GH, and to have known him as a colleague, mentor and friend.

Introduction

A molecule is an assembly of positively charged nuclei and negatively charged electrons that forms a stable entity through the electrostatic forces which hold it all together. Since all the particles which make up the molecule are moving relative to each other, a full mechanical description of the molecule is very complicated, even when treated classically. Fortunately, the overall motion of the molecule can be broken down into various types of motion, namely, translational, rotational, vibrational and electronic. To a good approximation, each of these motions can be considered on its own. The basis of this classification was established in a ground-breaking paper written by Born and Oppenheimer in 1927, just one year after the introduction of wave mechanics. The main objective of their paper was the separation of electronic and nuclear motions in a molecule. The physical basis of this separation is quite simple. Both electrons and nuclei experience similar forces in a molecular system, since they arise from a mutual electrostatic interaction. However, the mass of the electron, m, is about four orders-of-magnitude smaller than the mass of the nucleus M. Consequently, the electrons are accelerated at a much greater rate and move much more quickly than the nuclei. On a very short time scale (less than 10−16 s), the electrons will move but the nuclei will barely do so; as a first approximation, the nuclei can be regarded as being fixed in space.

Introduction

Much of the beauty of high-resolution molecular spectroscopy arises from the patterns formed by the fine and hyperfine structure associated with a given transition. All of this structure involves angular momentum in some sense or other and its interpretation depends heavily on the proper description of such motion. Angular momentum theory is very powerful and general. It applies equally to rotations in spin or vibrational coordinate space as to rotations in ordinary three-dimensional space.

All the laws of physics are easier to accept (and even to understand) when the underlying symmetry of the problem is appreciated. For example, classical Euclidean space is isotropic and a physical system is invariant to any rotation in this space. By this we mean that all the measurable properties of the system are unaffected by the rotation. An investigation of the behaviour of a quantum state under such rotations allows the properties of the state to be defined. These properties are most succinctly expressed as quantum numbers. Although quantum numbers are frequently used to label the eigenstates or eigenvalues of a molecule, they really carry information about the symmetry properties of the associated eigenfunctions.

In this chapter we give only a brief description of angular momentum theory, sufficient to introduce the various techniques required for the description of molecular energy levels and the transitions between them.

Introduction and experimental methods

Simple absorption spectrograph

The first direct observations of pure rotational transitions induced by microwave or millimetre-wave radiation date from about 1945. Research during the Second World War, particularly on radiation sources in these wavelength regions, led to rapid developments in this branch of molecular spectroscopy. However, the observation of rotational structure in electronic and vibrational spectra, which had been routine for at least twenty years previously, meant that much was already understood about molecular rotations. Indeed most of the theory was developed in the years immediately following the birth of modern quantum mechanics. We have already described much of this theory in earlier chapters, and we will draw upon the results obtained in this chapter. We have also described molecular beam resonance and maser techniques for studying rotational spectra, but in this chapter we describe somewhat more conventional experiments in which the absorption of microwave radiation by molecules in the bulk gas phase is detected directly. As we will see, some ingenious techniques have been developed in more recent years to enable the study of short-lived transient species, neutral or charged free radicals. Molecular radio astronomy is also, in part, a branch of microwave absorption or emission spectroscopy, and we shall deal with that in subsection 10.1.6. We will also describe, in the next chapter, double resonance experiments in which microwave radiation is combined simultaneously with a second source of radiation of either similar or quite different wavelength.

Introduction

Microwave magnetic resonance, which has often been called ‘gas phase electron resonance’, and far-infrared laser magnetic resonance have been extremely important techniques in the study of free radicals. These techniques depend upon the presence of a large magnetic moment for the species under investigation, because both rely on the ability to tune the energy levels with a magnetic field into resonance with fixed frequency radiation. Although historically the first study of the rotational levels and their fine structure involved fairly conventional swept-frequency microwave spectroscopy, applied to the OH radical, subsequent development of the subject depended initially on the success of magnetic resonance methods. Pure microwave spectroscopy of gaseous free radicals has now become almost routine, and many examples will be described in chapter 10. We have, after some deliberation, decided to present the exciting subject of magnetic resonance with due regard to its historical development. Nevertheless, this and the two following chapters should be taken together for a balanced view. Laser magnetic resonance techniques are still widely used, but microwave magnetic resonance has now been largely superseded by swept-frequency methods, without the presence of an external magnetic field. Zeeman effects can, of course, still be investigated, but they are not an essential part of the detection method.

Experimental methods

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.

Nuclear spins and magnetic moments

In the course of developing a Hamiltonian for diatomic molecules, we have so far introduced and discussed two nuclear properties. We considered at length the nuclear kinetic energy in chapter 2, and in chapter 3 we took account of the nuclear charge in considering the potential energy arising from the electrostatic interaction between electrons and nuclei. With respect to the electrostatic interaction, however, we have implicitly treated the nucleus as an electric monopole, and this assumption is re-examined in section 4.4. First, however, we consider another important property of many nuclei, namely their spin and the important magnetic interactions within a molecule which arise from the property of nuclear spin. The possibility that a nucleus may have a spin and an associated magnetic moment was first postulated by Pauli, following the observation of unexpected structure in atomic spectra. The first quantitative theory of the interaction between a nuclear magnetic moment and the ‘outer’ electrons of an atom was provided by Fermi, Hargreaves, Breit and Doermann and Fermi and Segrè. In the case of diatomic molecules with closed shell electronic states, the magnetic interaction of the nuclear moment with the magnetic angular momentum vector, an I · J coupling, was treated by a number of authors. The interaction between the nuclear electric quadrupole moment and the electronic charges, an interaction which has nothing to do with nuclear spins or magnetic moments, was treated by Bardeen and Townes.