CHAPTER 1
Photoelectron Spectroscopy
BY A. HAMNETT AND A. F. ORCHARD
There has been intense activity in the general field of photoelectron (p.e.) spectroscopy, especially as regards the low-energy aspect of the technique which normally involves photoionisation in the vapour phase using u.v. radiation sources. A very important book on u.v.–p.e. spectroscopy by Turner et al. has appeared, the fruit of many years research by the pioneering Imperial College-Oxford group. P.e. spectroscopy using X-ray sources (X–p.e. spectroscopy or ESCA*) has in the past been almost entirely confined to the solid state, but in late 1969 an authoritative monograph by Siegbahn et al. on the X–p.e. spectroscopy of gases was published. The proceedings of a Royal Society discussion on p.e. spectroscopy held in February 1969 has now appeared in print : this provides a most interesting variety of articles on both u.v.–p.e. and X–p.e. studies. A very useful recent review by Brundle' should also be mentioned.
We report on u.v.–p.e. and X–p.e. spectroscopy in separate sections below. But first of all, a brief review of theoretical work on photoelectron emission is appropriate.
1 The Theory of Photoelectron Emission from Atoms and Molecules
Theoretical work on gas-phase phenomena falls naturally into two categories : (i) the angular distribution of photoelectrons and (ii) the calculation of total photoionisation cross-sections. Photoelectrons show an intensity variation with angle of emission because the plane of polarisation of the exciting radiation defines an axis of quantisation. For unpolarised radiation the direction of the photon beam provides such an axis. It has been known for many years that the angular dependence for electric-dipole induced transitions obeys the general law
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where x is the axis of polarisation, φx is the angle between the momentum vector of the ejected electron and this axis. and β is the asymmetry parameter which has been defined in various ways. P2(cos φ) is the second Legendre polynomial and is given by the expression 1/2(3 cos2 φ - 1).
Peshkin has shown how the above equation may be derived from quite general considerations of symmetry and has elaborated the theory to cover cross-pole and multipole ionisations. The assumptions underlying his derivation may be listed as:
(a) the target atoms are oriented at random,
(b) the influence of external fields is neglected,
(c) when more than one electron is emitted, the direction of emission of the
An expression for the asymmetry parameter β was first given by Bethe for the hydrogen atom and generalised recently by Cooper and Zare and also by Berry et al. to many-electron atoms, a central spherical potential field and LS coupling being assumed. Calculations using this formula have been made for the inert gases by Manson and Cooper, who show how β varies with the energy of the exciting radiation. Buckingham et al. have extended equation (1) to the case of diatomic molecules and have found that its form is unaltered save that the value of β will depend on the specific Hund coupling case involved. The equation derived by Cooper and Zare can be seen as a special case of the more general expression given by Buckingham et al. Sichel has extended this work to the situation where rotational fine structure can be resolved.
Experimental verification of the general form of equation (1) is difficult since, in normal photoelectron work, the ionising radiation is unpolarised. The corresponding expression for unpolarised radiation is given by Peshkin as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where φ, is now the angle between the trajectory of the ejected electron and the photon beam. This formula has been shown to hold for argon by Morgenstern et al., for argon, xenon and various small molecules by Vilesov and Lopetin, and for zinc and cadmium atoms (in an atomic beam) by Harrison. Samson has discussed the form of the equation for partially polarised radiation (obtained from a grating) and has measured values of the asymmetry parameter β for argon and molecular nitrogen. He finds that β is very nearly 2 for helium, indicating that at an observation angle φ, given by cos φ = [square root of 2/3] the troublesome selfabsorption by helium in He" spectra might be eliminated.
The calculation of photoionisation cross-sections poses many problems, not least of which is the fact that the true forms of the continuum wavefunctions are not known for polyelectronic species. It is usually assumed that continuum functions for many-electron atoms differ from those of the hydrogen atom simply by a phase factor, δ, which can be shown theoretically to relate to the quantum defect, obtainable from Rydberg analysis of atomic spectra, extrapolating to positive energy. However, this information is not available for most molecules, nor indeed has the theory been shown to hold in the molecular (non-spherically symmetrical) case. Another major problem concerns the accuracy with which the ground state of the neutral atom or molecule is described. To evaluate properly the scope of the theory the best wavefunctions to hand should of course be used : but this is easier said than done, and most workers have been forced to compromise this requirement by using rather inaccurate wavefunctions. Tuckwell has, with some measure of success, calculated photoionisation cross-sections for molecular N2 and 02, making use of a transformation into prolate spheroidal co-ordinates: in the case of O2, however, the quantum defect data were not available so that only relative cross-sections could be estimated. Similar calculations have been performed for atoms by Henry and also by McGinn, while a more empirical approach has been described by Zilitis. Perhaps the most sophisticated many-electron treatment was reported by Brown, who has computed ab initio photoionisation cross-sections for the helium atom, using a correlated atomic wavefunction. The agreement with experimental data was disappointingly poor at high photon energies.
A further complicating factor, in the theory of molecular photoionisation, is the variation of cross-section with energy over the vibrational structure of a photoelectron band. The calculation of the Franck–Condon factors continues to interest many workers. In particular, Tuckwell has shown for O2, that similar cross-sections are obtained by direct integration, without separation of the electronic and vibrational problems, and also by independent calculation of Franck–Condon factors. This provides justification for the customary use of the Franck–Condon principle in molecular photoelectron spectroscopy.
Relative cross-sections can be dealt with at a more general level. By assuming Orchard have rationalised the simple notion that the relative intensity of a photoelectron band reflects the degeneracy of the subshell ionised, and have extended the idea to the case of open-shell species.
Serious deviations from simple intensity expectations may arise in the event of a transition to an autoionising state. Blake et al. have calculated Franck–Condon factors for a model autoionising transition and have shown how very complicated band profiles may result. A more complex theory is proposed by Smith who invokes the Fano–Mies theory of configuration interaction and finds an experimental example in the neon-excited photoelectron spectrum of O2 measured by Branton et al. (Figure 1)
Relative photoionisation cross-sections may also be significantly affected by configuration interaction effects : many-electron transitions that are forbidden in the simple theory which uses the Hartree–Fock approximation become partially allowed when electron correlation is properly included. The 'mechanism' can be especially important in the case of open-shell molecules and a formally forbidden ionisation process (producing the C2Πu, state of O+2) has indeed been detected by Edqvist et al. in the O2 He photoelectron spectrum. This followed a suggestion by Dixon and Hull that the transition to the C2Πu state, nominally inaccessible by a simple one-electron process, could borrow sufficient intensity through configuration interaction to become observable when, correspondingly, the allowed A2ΠU photoelectron band should diminish in intensity from the expected value. Similar calculations have been reported for N2O by Lorquet and Cadet.
Much of the above theory can be applied directly to ESCA studies on gases but the corresponding theory for the solid state is still at an early stage of development. Siegbahn et al. have measured the angular distribution of electrons photoemitted from a single crystal of sodium chloride and have shown it to be a very complex function of φ, for which phenomenon the theory of Deswames and Hall can give only a qualitative account. Angular distribution in gas-phase ESCA work has been discussed explicitly by Rao and Parthasaradhi. Theories relating to 'shake-up' and 'shake-off' processes are discussed below, but we note here that Krause has shown that the simple 'sudden perturbation' approach is not quantitatively accurate. Various correlations with chemical shift are also discussed below but mention may be made of the calculation of the exchange splitting of the nitrogen and oxygen levels in nitric oxide. This fine structure arises from interaction with the unpaired electron in the highest occupied orbital (27π) which generates two states differing in energy by twice the relevant exchange integral.
2 Ultraviolet Molecular Photoelectron Spectroscopy
Gas-phase u.v.–p.e. spectroscopy continues to develop at a considerable rate, both with respect to very detailed fundamental investigations of small molecules and also as regards the application of the technique to the study of larger molecules, inorganic and organic. We have already mentioned the major work of Turner et al., which contains a wealth of hitherto unpublished u.v.–p.e. spectra (though mainly of organic compounds) and extensive discussion of the problems of interpretation. There has also been a large number of review article, It appears that He p.e. spectroscopy is now over its initial 'teething' period, the major instrumental and interpretative difficulties having been resolved. It is to be hoped, therefore, that an increasing proportion of future work will relate more to the problems of chemical, as opposed to spectroscopic or purely theoretical interest.
U.v.–p.e. spectroscopy can provide a variety of information concerning molecular energy levels. For sufficiently small stable molecular species, high (or even medium) resolution measurements permit the study of vibrational motions and of vibronic and spin–orbit interactions in different states of the molecular ions: data on molecular ions are otherwise only very occasionally available from conventional U.V. emission spectroscopy. Where vibrational and other detail is not resolved, a u.v.–p.e. spectrum still yields the relative energies of certain states of the molecular ion, and in general these states are different from those sometimes observable in U.V. emission work. But the ion states studied in u.v.–p.e. spectroscopy always correspond to states that are inferable from U.V. Rydberg absorption work.
Of paramount interest to the general chemist is the approximate interpretation of u.v.–p.e. energy data using Koopmans' theorem, according to which the observed ionisation energies may be identified with the SCF energies of the various occupied molecular orbitals. The theorem is not accurate, depending as it does on the cancellation of the quite distinct errors arising from the neglect of correlation effects and orbital rescaling terms. Semi-empirical orbital energy sequences inferred from p.e. spectra are nevertheless of value to the chemist and should often prove qualitatively reliable when closely related molecules are compared. A precondition of chemical applications is, however, the unambiguous assignment of the p.e. spectra and it is with this point in mind that, in Section 2C, we choose to discuss many of the recent results in terms of various assignments criteria that are commonly invoked.
The instrumental problems arising in u.v.–p.e. spectroscopy and ESCA are somewhat different in detail. However, all p.e. spectrometers possess a target area from which the electrons emitted are collected and their velocities analysed. The electrons are usually examined at right angles to the direction of the exciting radiation.
A. Instrumental Advances — The main advances during 1970 have been in helium radiation source technology, sample handling, and in the use of electron lenses and dou ble-focusing analysers. The general experimental arrangement necessary has been described by Turner et al. who actually use a 127° deflecting electrostatic analyser of 10 cm radius and a simple d.c. discharge helium lamp, the output of which is mainly the HeI line at 21.22 eV. The majority of the spectra published in their monograph' were obtained with this instrument.
The Light Source. Two methods are used to excite the radiation, the traditional method involving a d.c. discharge between aluminium electrodes and a second method, apparently necessary when very pure helium is used, employing a microwave discharge. Careful analyses of the lines present in a helium discharge have been given by Cairns et al. and by Brundle, from which work it appears that the most common additional lines are the Lyman α hydrogen line and the N lines. Even very pure helium will, however, give a number of satellite lines arising from HeI series, usually denoted HeIβ, Heγ, etc., and lines from transitions in ionised helium, the HeIIα — γ lines. Interestingly, it appears that the extent to which these lines occur depends upon the percentage impurity of other gases in the helium.
HeIβ usually occurs to the extent of about 1% in the lamp output giving a shadow spectrum about 1.88eV to higher kinetic energy. Lloyd has used this component in the radiation to help calibrate the commercial Perkin–Elmer PS 15 spectrometer, while Branton et have made use of it to measure the photoelectron spectrum of neon.
The HeII lines have been obtained to the extent of several percent of the HeI line by several workers using low pressure and high current density. HeIIα radiation has an energy of 40.8 eV and is therefore utilised in exploring the bonding region immediately above 21.2 eV on the ionisation energy scale, the limit of HeIionisations. Massive self-ionisation of helium gas usually occurs at 24.6 eV, leading to a sharp peak in the p.e. spectrum, and at 28–30 eV the HeII spectrum is swamped by the HeI ionisations. Because of the very low intensity of the exciting radiation, the analyser must be adjusted to maximum transmittance with a concomitant loss in resolution. Thus, most published HeII spectra have a resolution of the order of l00mV. In addition, Brundle has pointed out that the HeIIβ radiation may be as much as 5 % of the HeIIα in intensity, so care should be taken to ensure that structure due to this component line is recognised.
Failure to appreciate that such lines are present has led to errors in interpretation, perhaps the most serious case being that of the mercury p.e. spectrum, where a strong line at 20.7 eV, originally assigned to a 5p ionisation, was queried on theoretical grounds. Re-examination of the spectrum showed that the line was in fact the result of a strongly autoionising transition induced by NI radiation. A similar case was noted in the case of benzene by Samson, where the band seen by a number of workers at 20.4eV can be traced to an autoionisation induced by the Lyman α hydrogen line.
It has also been noted by some workers that helium lamps can exhibit slow periodic oscillations in intensity, often of several minutes total period. These fluctuations have been investigated by Asinovskii et al. and are thought to be due to transient effects in the lamp.
Sample Handling. Methods for introducing the sample into the target chamber vary considerably. Branton et al. describe a slow bleed system for gases and volatile liquids whereas Weiss and Lawrence use a fused capillary array to give a molecular beam. Harrison uses an atomic beam generated from a furnace. Jonathan et al., in their measurements on transient species, allow the gas to pass through a silent microwave discharge before introduction into the target chamber.
Electron Analysis. The photoelectrons emitted are usually analysed by a deflecting electrostatic analyser. Branton et al. describe a double-focusing hemispherical design with two electron lenses, one at either end of the analyser, the spectrum being scanned by retardation between analyser and target chamber. Pullen et al. describe a dou ble-focusing device, machined from aluminium, consisting of two concentric spherical sectors. Weiss and Lawrence use a simple deflecting analyser coupled with two lenses.
