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.

Modern spectroscopic techniques such as laser-induced fluorescence, resonance-enhanced multiphoton ionization (REMPI), cavity ringdown, and ZEKE are important tools in the physical and chemical sciences. These, and other techniques in electronic and photoelectron spectroscopy, can provide extraordinarily detailed information on the properties of molecules in the gas phase and see widespread use in laboratories across the world. Applications extend beyond spectroscopy into important areas such as chemical dynamics, kinetics, and analysis of complicated chemical systems such as plasmas and the Earth's atmosphere. This book aims to provide the reader with a firm grounding in the basic principles and experimental techniques employed in modern electronic and photoelectron spectroscopy. It is aimed particularly at advanced undergraduate and graduate level students studying courses in spectroscopy. However, we hope it will also be more broadly useful for the many graduate students in physical chemistry, theoretical chemistry, and chemical physics who encounter electronic and/or photoelectron spectroscopy at some point during their research and who wish to find out more.

There are already many books available describing the principles, experimental techniques, and applications of spectroscopy. However, our aim has been to produce a book that tackles the subject in a rather different way from predecessors. Students at the advanced undergraduate and early graduate levels should be in a position to develop their knowledge and understanding of spectroscopy through contact with the research literature.

A severe restriction of conventional photoelectron spectroscopy is its low resolution. The main limitation is instrumental resolution, particularly that caused by the electron energy analyser, as was discussed in Chapter 12. Resolving rotational structure is not a realistic prospect for conventional photoelectron spectroscopy but even vibrational structure may be difficult to resolve. In addition to the instrumental resolution must be added other factors such as rotational and Doppler broadening which, if they could be dramatically reduced, might make a sufficient difference to improve many photoelectron spectra. A potential solution is to combine conventional photoelectron spectroscopy with supersonic molecular beams. Supersonic expansions can produce dramatic cooling of rotational degrees of freedom and, if part of the expansion is skimmed into a second vacuum chamber, can be converted to a beam with a very narrow range of velocities. This is precisely the approach adopted by Wang et al. [1], the molecular beam being crossed at right angles by HeI VUV radiation (58.4 nm) to produce a near Doppler-free photoelectron spectrum. The resolution achieved is in the region of 12 meV (100 cm-1).

The ultraviolet photoelectron spectra of CO2, OCS, and CS2 in molecular beams are discussed here. These illustrate some of the important concepts involved in the interpretation of the photoelectron spectra of polyatomic molecules.

Molecular symmetry is of great importance in the discussion of spectroscopy. It helps to simplify the explanation of complex phenomena, such as molecular vibrations, and is an important aid in the derivation of electronic states and transition selection rules. It also simplifies the application of molecular orbital theory, which is often applied to assign or predict electronic spectra. In many cases, it provides strikingly simple answers to complicated questions.

In its original form, group theory is a rigorous mathematical subject. No attempt will be made here to be rigorous – the aim is simply to summarize the basics as they apply to symmetry, in light of which the spectroscopic applications of the theory can become clearer. Although the concepts introduced here might be valid for any object with symmetry elements, we will apply these only to molecules. This appendix is not intended to be a comprehensive account of point group symmetry and group theory. Instead the intention is to review some of the key principles required for applications in electronic spectroscopy. A newcomer to the subject of symmetry and group theory is first advised to consult an appropriate textbook on this topic, such as one of those listed in the Further Reading at the end of this appendix.

Symmetry elements and operations

We begin with two fundamental concepts, symmetry operations and symmetry elements. Symmetry operations are transformations that move the molecule such that it is indistinguishable from its initial position and orientation.

As described in Chapter 11, laser-induced fluorescence (LIF) spectroscopy is one of the simplest and yet most powerful tools for obtaining high resolution spectra. Its high sensitivity is particularly convenient for the investigation of extremely reactive molecules, such as free radicals and ions. In this Case Study we illustrate how LIF spectroscopy can be used to obtain important information on a small carbon cluster, the C3 molecule. The spectra presented were originally obtained by Rohlfing [1], who produced C3 by pulsed laser ablation of graphite. This is a violent method for vaporizing a solid and the plasma formed above the graphite surface will undoubtedly contain carbon atoms, clusters such as C2, C3, and various cations and anions. To reduce spectral congestion, the laser ablation source was combined with a supersonic nozzle to produce a cooled sample for spectroscopic probing.

The LIF spectrum was obtained by crossing the supersonic jet with a tunable pulsed laser beam and measuring the intensity of fluorescence as a function of laser wavelength. As discussed in Section 11.2, an LIF excitation spectrum is similar to an absorption spectrum but the signal intensity depends not only on the absorption probability, but also the fluorescence quantum yield of the upper state.

The photoelectron spectroscopy of anions is, in many respects, directly analogous to the photoelectron spectroscopy of neutral molecules. However, an important difference is that an electron in the valence shell of an anion is much more weakly bound than in a neutral molecule. In fact there are some molecules, such as N2, that are unable to bind an additional electron at all. The binding energy of an electron in an anion, which is known as the electron affinity (EA), is the energy difference between the neutral molecule and the anion. The electron affinity is defined as a positive quantity if the anion possesses a lower energy than the neutral molecule, i.e. the electron is bound to the molecule and energy must be added to remove it.

The photoelectron spectrum of an anion, also known as the photodetachment spectrum, can provide information on both the anion and the neutral molecule. A good example of this is the photoelectron spectrum of, which was first recorded by Ervin, Ho, and Lineberger [1].

The experiment

The most common method for generating anions in the gas phase is an electrical discharge. Ervin et al. produced by a microwave (ac) discharge through a helium/air mixture. A variety of neutral and charged species would be expected under such conditions, including several possible anions and cations.

The Born–Oppenheimer approximation is an essential element without which the very notion of a potential energy surface would not exist (1). It also provides an example of how different coordinates can often be treated independently as a first approximation. This approach has far-reaching consequences, since it greatly simplifies the construction of partition functions in statistical mechanics. The approximation involves neglect of terms that couple together the electronic and nuclear degrees of freedom. The nuclear motion is then governed entirely by a single PES for each electronic state because the Schrödinger equation can be separated into independent nuclear and electronic parts. The simplest approach to the nuclear dynamics then leads to the normal mode approximation via successive coordinate transformations. These developments are treated in some detail, partly because the results are used extensively in subsequent chapters, and partly because they highlight important general principles, which can easily be extended to other situations. The consequences of breakdown in the Born–Oppenheimer approximation, and treatments of dynamics beyond the normal mode approach, are discussed in Section 2.4 and Section 2.5, respectively.

Independent degrees of freedom

The Schrödinger equation that we normally wish to solve in order to identify wavefunctions and energy levels is a partial differential equation if more than one coordinate is involved. The most common method of solution for such equations involves separation of variables (2).