The discussion of angular momentum coupling in Appendix C focussed on electronic (orbital and spin) angular momenta. Other types of angular momenta may be present in molecules and their coupling to electronic angular momenta can have an important impact in spectroscopy. In this appendix rotational angular momentum is added to the pot and its interaction with electronic angular momenta is considered. The discussion is restricted to linear molecules, and several limiting cases, known as Hund's coupling cases, are briefly described.

Hund's case (a)

Hund's case (a) coupling builds upon the orbital + spin coupling already described in Appendix C. The orbital angular momenta in a molecule are assumed to be coupled to the internuclear axis by an electrostatic interaction and spin–orbit coupling leads to the spin angular momenta also precessing around the same axis. However, the spin–orbit coupling is not too strong to blur the distinction between orbital and spin angular momenta. Rotation in a linear molecule leads to rotational angular momentum and yields a vector R that is oriented perpendicular to the internuclear axis, as shown in Figure G.1.

In Hund's case (a) it is assumed that the interaction between the electronic and rotational angular momenta is weak, and hence the former (the orbital angular momentum L and the spin angular momentum S) continue to precess rapidly around the internuclear axis with projections whose sum is equal to Ω (= Λ + Σ).

This book is concerned with the spectroscopy of molecules, primarily in the gas phase. Broadly speaking, there are two types of gas source that are commonly used in laboratory spectroscopy. One is a thermal source, by which we mean that the ensemble of molecules is close to or at thermal equilibrium with the surroundings. An alternative, and non-equilibrium, source is the supersonic jet. Both are discussed below. Individual molecules can also be investigated in the condensed phase by trapping them in rigid, unreactive solids. This matrix isolation technique will also be briefly described.

Thermal sources

A simple gas cell may suffice for many spectroscopic measurements. This is a leak-tight container that retains the gas sample and allows light to enter and leave. It may be little more than a glass or fused silica container, with windows at either end and one or more valves for gas filling and evacuation. The cell can be filled on a vacuum line after first pumping it free of air (if necessary). If the sample under investigation is a stable and relatively unreactive gas at room temperature, this is a trivial matter.

If the sample is a liquid or solid with a low vapour pressure at room temperature, then the cell may need to be warmed with a heating jacket to achieve a sufficiently high vapour pressure. Residual air, together with volatile impurities that may be trapped in the condensed sample, can be removed using one or more freeze–pump–thaw cycles.

Crucial to any spectroscopic technique is the source of radiation. It is therefore pertinent to begin the discussion of experimental techniques by reviewing available radiation sources. Although there are many different types of light sources, of which some specific examples will be given later, in many spectroscopic techniques lasers are the preferred choice. Indeed some types of spectroscopy are impossible without lasers, and so it is important to be familiar with the properties of these devices. Consequently, before describing some specific spectroscopic methods, a brief account of the underlying principles and capabilities of some of the more important types of lasers is given.

Properties

Since their discovery in 1960, lasers have become widespread in science and technology. Laser light possesses some or all of the following properties:

1. (i) high intensity,

2. (ii) low divergence,

3. (iii) high monochromaticity,

4. (iv) spatial and temporal coherence.

Each of these properties is not unique to lasers, but their combination is most easily realized in a laser. For example, a beam of light of low divergence can be obtained from a lamp by collimation via a series of small apertures, but in the process the intensity of light passing through the final aperture will be very low. On the other hand, lasers naturally produce beams of light with a low divergence and so the original intensity is not compromised.

The quantization of angular momentum is a recurring theme throughout spectroscopy. According to quantum mechanics only certain specific angular momenta are allowed for a rotating body. This applies to electrons orbiting nuclei (orbital angular momentum), electrons or nuclei ‘spinning’ about their own axes (spin angular momentum), and to molecules undergoing end-over-end rotation (rotational angular momentum). Furthermore, one type of angular momentum may influence another, i.e. the angular motions may couple together through electrical or magnetic interactions. In some cases this coupling may be very weak, while in others it may be very strong.

This chapter is restricted to consideration of a single body undergoing angular motion, such as an electron orbiting an atomic nucleus; the case of two coupled angular momenta is covered in Appendix C. In classical mechanics, the orbital angular momentum is represented by a vector, l, pointing in a direction perpendicular to the plane of orbital motion and located at the centre-of-mass. This is illustrated in Figure 3.1. If a cartesian coordinate system of any arbitrary orientation and with the origin at the centre-of-mass is superimposed on this picture, then the angular momentum can be resolved into independent components along the three axes (lx, ly, lz). If the z axis is now chosen such that it coincides with the vector l, then clearly both lx and ly are zero and lz becomes the same as l.

The partitioning of electrons into molecular orbitals (MOs) provides a useful, albeit not exact, model of the electronic structure in a molecule. The MO picture makes it possible to understand what happens to the individual electrons in a molecule. Taking the electronic structure as a whole, a molecule has a certain set of quantized electronic states available. Electronic spectroscopy is the study of transitions between these electronic states induced by the absorption or emission of radiation. Within the MO model an electronic transition involves an electron moving from one MO to another, but the concept of quantized electronic states applies even if the MO model breaks down.

Different electronic states are distinguished by labelling schemes which, at first sight, can seem rather mysterious. However, understanding such labels is not a difficult task once a few examples have been encountered. We begin by considering the more familiar case of atoms, before moving on to molecules.

Atoms

If we accept the orbital approximation, then the starting point for establishing the electronic state of an atom is the distribution of the electrons amongst the orbitals. In other words the electronic configuration must be determined. Individual atomic orbitals are given quantum numbers to distinguish one from another, leading to labels such as 1s, 3p, 4f, and so on. The number in each of these labels specifies the principal quantum number, which can run from 1 to infinity.

The lowering of symmetry in moving from benzene (D6h) to chlorobenzene (C2v) results in the removal of molecular orbital degeneracies. A convenient way of investigating this effect is through conventional photoelectron spectroscopy, and indeed Ruščić et al. studied this degeneracy breaking in 1981 using both HeI and HeII photoelectron spectroscopy [1]. The spectra obtained are shown in Figure 27.1, with the upper trace being that recorded using HeI radiation and the lower trace using HeII radiation.

The first two bands have similar ionization energies (maxima at 9.07 and 9.54 eV) and almost identical intensities. These bands correlate with the two components of the e1g HOMO in benzene, which is a pair of π bonding orbitals (see Chapter 25) but which have split into two distinct orbitals in chlorobenzene owing to the lowering of the symmetry. Note that these two bands, and indeed most other bands in the spectra, are relatively broad. The next highest bands again form a pair, but these have considerably sharper profiles and correspond to ionization from lone pairs on the Cl atom.

The low resolution in conventional photoelectron spectroscopy restricts the amount of information that can be extracted. In this Case Study we consider alternative techniques that provide additional information about the chlorobenzene cation. This builds upon the material encountered in the previous two Case Studies.

The Pauli exclusion principle states that no two electrons in an atom or molecule can share entirely the same set of quantum numbers. This requirement follows from the nature of electronic wavefunctions, which must be antisymmetric with respect to the exchange of any identical electrons. This has an impact in the determination of the electronic states possible from a given electronic configuration.

Atoms

Consider, for example, the carbon atom, which has a ground electronic configuration 1s22s22p2. Suppose that one of the 2p electrons is excited to a 3p orbital. To determine the electronic states that are possible from this configuration, the process described in Section 4.1 can be followed. The 1s and 2s orbitals are full and so we can focus on the p electrons only. The possible values of the total orbital angular momentum quantum number L are 2, 1 or 0. Similarly, the total spin quantum number must be 1 or 0 and so the possible electronic states that result from the 1s22s22p13p1 configuration are 3D, 1D, 3P, 1P, 3S, and 1S. It is therefore initially tempting to propose that electronic states of the same spatial and spin symmetry arise from the ground electronic configuration. Such an assumption would be wrong because it ignores the Pauli principle.

This Case Study follows on from the previous one. However, rotationally resolved photodissociation spectra are the focus here, specifically for Mg+–Ne and Mg+–Ar. Although these ions are diatomic species, their rotationally resolved spectra are not trivial to analyse. The reason for this is the presence of an unpaired electron, which gives rise to a net spin angular momentum which can interact with the overall rotation of the complex (spin–rotation coupling). In addition, in some electronic states there may also be a net orbital angular momentum, and this can interact both directly with the molecular rotation (giving rise to the phenomenon known as Λ doubling) and with the electron spin. The latter is much the strongest of these angular momentum interactions and its effect can be readily seen in the rotationally resolved spectra, as will be discussed below.

Duncan and co-workers have recorded partly rotationally resolved electronic spectra for the A2Π˗ X2Σ+ transitions of Mg+–Ne and Mg+–Ar, and these form the basis of the Case Study described here [1, 2]. A photodissociation technique was employed as detailed in Chapter 23. Before describing the spectra and their analysis, the expected rotational energy level structure for the X2Σ+ and A2Π electronic states is considered. Much of this description is similar to that met for NO in Chapter 22.

Modern electronic spectroscopy is a broad and constantly expanding field. A detailed description of the experimental techniques available for this one area of spectroscopy could fill several books of this size. This part is therefore restricted to giving an introduction to some of the underlying principles of experimental spectroscopy, together with brief descriptions of some of the more widely used and easily understood methods employed in electronic spectroscopy.