Depending on the resolution, a spectrum may consist of well-resolved discrete peaks, each of which is attributable to a single specific transition, or it may consist of broader bands that are actually composed of several unresolved transitions. In either case, the intensities will depend on a number of factors. The sensitivity of the spectrometer is crucial. So too is the concentration of the absorbing or emitting species. However, our interest in the remainder of this chapter is with the intrinsic transition probability, i.e. the part that is determined solely by the specific properties of the molecule. The key to understanding this is the concept of the transition moment.

Transition moments

Consider two pairs of energy levels, one pair in molecule A and one pair in a completely different molecule B. Assume for the sake of simplicity that the energy separation between the pair of levels is exactly (and fortuitously) the same for both molecules. Suppose that a sample of A is illuminated by a stream of monochromatic photons with the correct energy to excite A from its lower to its upper energy level. There will be a certain probability that a molecule is excited per unit time. Now suppose sample A is replaced with B, keeping the concentration and all other experimental conditions unchanged. In general the probability of photon absorption per unit time for B would be different from A, perhaps by a very large amount.

The study of molecular complexes in the gas phase provides important information on intermolecular forces and spectroscopy has played a vital role in this field. As an illustration, the complex formed between an aluminium atom and a water molecule is described here.

To obtain Al(H2O), it is necessary to bring together aluminium atoms and water molecules. Getting water into the gas phase is easy, but aluminium poses more of a problem since at ordinary temperatures the solid has a very low vapour pressure. An obvious solution is to heat the aluminium in an oven. However, the high temperature has a concomitant downside; if water is passed through (or near) the oven the high temperature will almost certainly prevent the formation of a weakly bound complex such as Al(H2O). Instead, the heat may allow the activation barriers to be exceeded for other reactions, leading to products such as the insertion species HAlOH.

A solution to this apparent quandary is to make Al(H2O) by the laser ablation–supersonic jet method, which was mentioned briefly in Chapter 8 (see Section 8.2.3). Any involatile solid, including metals, can be vaporized by focussing a high intensity pulsed laser beam onto the surface of the solid.

Laser-induced fluorescence, resonance-enhanced multiphoton ionization, and cavity ringdown spectroscopic techniques offer ways of detecting electronic transitions without directly measuring light absorption. An alternative approach is possible if the excitation process leads to fragmentation of the original molecule. By monitoring one of the photofragments as a function of laser wavelength, a spectrum can be recorded. This is the basic idea behind photodissociation spectroscopy.

There are limitations to this approach. If photodissociation is slow, then the absorbed energy may be dissipated by other mechanisms, making photodissociation spectroscopy ineffective. It is also possible that some rovibrational energy levels in the excited electronic state will lead to fast photofragmentation whereas others will not. In this case there will be missing or very weak lines in the spectrum which, in a conventional absorption spectrum, may have been strong. Fast photofragmentation is clearly desirable on the one hand, but it can also be a severe disadvantage if it is too fast, since it may lead to serious lifetime broadening in the spectrum (see Section 9.1).

Despite the above limitations, photodissociation spectroscopy can provide important information. This is particularly true for relatively weakly bound molecules and complexes, since these have a greater propensity for dissociating. In this and the subsequent example the capabilities of photodissociation spectroscopy are illustrated by considering weakly bound complexes formed between a metal cation, Mg+, and rare (noble) gas (group 18) atoms.

This Case Study demonstrates some of the subtle arguments that can be employed in assigning vibrational features in electronic spectra. It also provides an illustration of how important structural information on a fairly complex molecule can be extracted. The original work was carried out by Gordon and Hollas using both direct absorption spectroscopy of 1,4-benzodioxan vapour and laser-induced fluorescence (LIF) spectroscopy in a supersonic jet [1]. The direct absorption spectra were of a room temperature sample and were therefore more congested than the jet-cooled LIF spectra. Nevertheless, the direct absorption data provided important information, as will be seen shortly. For the LIF experiments, both excitation and dispersed fluorescence methods were employed (see Section 11.2 for experimental details). Only a few selected aspects of the work by Gordon and Hollas are discussed here; the interested reader should consult the original papers for a more comprehensive account [1, 2].

Possible structures of 1,4-benzodioxan are shown in Figure 18.1. Assuming planarity of the benzene ring, there are three feasible structures that differ in the conformation of the dioxan ring. One possibility is that both C O bonds are displaced above (or equivalently below) the plane of the benzene ring yielding a folded structure with only a plane of symmetry (Cs point group symmetry).

Carbon monoxide was one of the first molecules studied by ultraviolet photoelectron spectroscopy [1]. A typical HeI spectrum is shown in Figure 13.1. The spectrum appears to be clustered into three band systems. The starting point for interpreting this spectrum is to consider the molecular orbitals of CO and the possible electronic states of the cation formed when an electron is removed.

Electronic structures of CO and CO+

Any student familiar with chemical bonding will almost certainly be able to construct a qualitative molecular orbital diagram for a diatomic molecule composed of first row atoms. Such a diagram is shown for CO in Figure 13.2. The orbital occupancy corresponds to the ground electronic configuration 1σ22σ23σ24σ21π45σ2. The σ MOs actually have σ+ symmetry but it is not uncommon to see the superscript omitted. Since all occupied orbitals are fully occupied, the ground state is therefore a 1Σ+ state and, since it is the lowest electronic state of CO, it is given the prefix X, i.e. X1Σ+, to distinguish it from higher energy 1Σ+ states of CO.

Consider the electronic states of the cation formed by removing an electron. If the electron is removed from the highest occupied molecular orbital (HOMO), the 5 orbital, then the cation will be in a 2Σ+ state.

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.