vacuum ultraviolet photoionization and photodissociation of molecules and clusters || coincidence...
TRANSCRIPT
297
COINCIDENCE STUDIES OF MULTIIONIZED MOLECULES
JOHN H. D. ELAND
Physical Chemistry Laboratory, South Parks Road, Oxford, 0X1 3QZ, U.K.
CONTENTS
1. Introduction 2. Experimental Methods and Theoretical Background
2.1. Formation of Multiply Charged Ions 2.1.1. Double Ionization by Single Photons 2.1.2. Electron Impact Multiionization 2.1.3. Collisional Ionization 2.1.4. Other Forms of Multiple Ionization
2.2. Particle Detection and Analysis 2.2.1. Time-of-Flight Mass Analysis
2.3. Coincidence Techniques 2.3.1. Basic Coincidence Statistics 2.3.2. Measurement of Collection Efficiencies
3. Individual Coincidence Techniques 3.1. Two-Particle Coincidence Experiments
3.1.1. Electron-Electron Coincidences 3.1.2. Electron-Ion Coincidences 3.1.3. Ion-Ion Coincidences 3.1.4. Coincidences with Photons
3.2. Multiparticle Coincidences 3.2.1. Electron-Ion-Ion Coincidences 3.2.2. Fourfold and Higher Coincidences
4. Sample Results 4.1. Mechanism of Near-Threshold Double Photoionization 4.2. Spectroscopy of Doubly Charged Ions 4.3. Mechanisms of Charge Separation
4.3.1. Two-Body Reactions 4.3.2. Three-Body Reactions 4.3.3. Fragment Mass Spectra
5. Future Prospects Acknowledgements References
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1. INTRODUCTION
Only a few molecular multiply charged ions are familiar to most chemists, mainly species such as Hg** and SO4" which are stabilized by solvent interactions in aqueous solution. These particular ions are very rare or non-existent in the gas phase, however, where we find a different set of stable molecular doubly charged ions, well known to mass spectroscopists. Doubly charged molecules are seen in the mass spectra of many compounds, particularly of the aromatic and organometallic families. They also exist (but are usually ignored) as constituents of many natural plasmas including outer planetary atmospheres, comet tails, interstellar clouds and flames, though always in low abundance. Their scarcity can be ascribed in part to the difficulty of formation, since large energies are needed and two separate electrons must be ejected from neutral precursors. This is only part of the reason, however, indeed a small part. In all situations where high energies are available, multiply charged ions are formed in abundance. The reason for their observed rarity is that the vast majority of them break up with charge separation into singly charged and neutral fragments. Coincidence studies are especially important in elucidating the formation of these species and their decays by charge separation, just because so many particles are liberated. A typical double photoionization of an organic molecule can be written symbolically:
m + hp -* [m2+] + 2e" -» m| + m£ + m3 + 2e\ (1.1)
Processes such as this, in which the energy of the incoming photon is shared between five particles in the final state are among the most common forms of double ionization. The fact that double ionization has occurred at all is revealed only if two electrons or two ions are detected in coincidence, and for any detailed study of the mechanism of the reaction it is necessary to pick up more of the products, again in coincidence.
The phrase "in coincidence" may need elucidation at the outset. It simply means that two or more particles from each single ionization event like reaction (1.1), are detected together. In a conventional experiment, ionization might be observed by detecting a random sequence of electrons or of ions or of neutrals, all independently of each other. In a coincidence experiment, by contrast, an electron might be detected first, then the particular ion n^ and the particular neutral m3 formed in the same event that gave birth to the free electron. This obviously allows us to examine correlations between the energies, masses and initial directions of motion of the particles, correlations that are obscured by the averaging process in conventional techniques.
A number of coincidence techniques have been developed to study the formation and reactions of multiply charged ions, and are referred to by acronyms showing what types of particles are detected. Thus PEPICO is photoelectron-photoion coincidence and usually refers to detection of energy-analysed electrons in coincidence with mass-analysed ions. Another form of PEPICO, discussed more fully elsewhere in this book, takes electrons of near-zero energy ("threshold" electrons, hence TPEPICO) and involves scanning the ionizing wavelength, while a third form accepts electrons of all energies without analysis and is a coincidence form of mass spectrometry. PEPECO is photoelectron-photoelectron coincidence, and involves analysis of both electron energies; this is a technique developed specifically to study double photoionization and the spectra
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of doubly charged ions. Likewise PIPICO is photoion-photoion coincidence, and PEPIPICO is a triple coincidence technique in which two mass-analysed ions are detected in coincidence with an electron. Several higher order coincidence experiments are done on higher multiionization, but as the coining of acronyms might get out of hand (PEPIPIPIPICO ?) it seems better to subsume them under the general heading of CSMS, charge separation mass spectrometry, wherever possible. All these techniques are discussed in this chapter.
The plan of the chapter is to go over the experimental and theoretical background before discussing individual techniques, then to consider some significant recent results and finally to look at projections for the future. The chapter is meant as a guide for users or prospective users of the methods discussed, and not primarily as a literature survey. Most published coincidence results on multiply charged ions are included, but many closely related measurements on multiionized molecules by other techniques are not; the reader must be aware that a large related literature, for instance of theoretical works, exists. There is an inevitable bias in the choice of examples towards the author's own work, and several results are presented here for the first time. This field is in an extremely active growth and development phase at present; data being obtained now, as writing is in progress (mid-1990), show that many earlier results need reinterpretation, and new experiments should be planned on different lines from the old.
2. EXPERIMENTAL METHODS AND THEORETICAL BACKGROUND
2.1. Formation of Multiply Charged Ions
Only photoionization and electron impact ionization have been widely used up to now with coincidence techniques to study multiionized molecules. Other means of creating these species have been developed in other fields, however, and we can anticipate that some of them will be of importance in conjunction with coincidence methods in future.
2.1.1. Double Photoionization by Single Photons
For most molecules, photons of at least 30 eV (wavelength less than 41 nm) are required to produce double ionization in useful abundance. By far the best sources of this sort of light are electron or positron storage rings emitting synchrotron radiation1,2, which provide a continuous spectrum of ample intensity extending from the infrared into the hard X-ray region. For double ionization work the radiation must be monochromatized using a grazing incidence spectrometer3 and must also be filtered to remove higher order contamination3. Filtering is essential for experiments on double ionization in the region near the threshold, because the cross-section for double ionization rises by orders of magnitude at the shorter wavelengths where inner-shell processes become possible4. Storage ring synchrotron radiation also has the advantage of being pulsed in typically 1 ns pulses, 100 ns to 1000 ns apart, making many special
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time-of-flight techniques possible. It has the disadvantage of being really conveniently available only to the scientists who work at or near a synchrotron radiation facility.
The only laboratory sources of extreme ultraviolet (XUV) radiation suitable for coincidence work on double ionization are gas discharges in He and Ne. The useful atomic lines emitted by these sources (Fig. 1) can be selected in groups by filters3 or isolated by simple monochromators5'6 and the brightest of them can be comparable in intensity to equivalently monochromatic light from storage rings7. There are several suitable designs of discharge lamp, including the low pressure capillary discharge8, the hollow cathode7,9, the oscillator lamp10 , the magnetically confined discharge11 and the constricted microwave discharge12. Work in the author's laboratory has shown that the spectra of these lamps are very similar when they are operated at low gas pressures, but
Fig. 1. Spectra from low-pressure disharges in helium (above, left) and neon (below, right) at low resolution. The wavelengths (nm) of the main lines are given.
that the capillary discharge is the most intense source for a given discharge power. As a concrete example, a 1 mm x 4 cm capillary discharge in helium at 40 mA current can provide enough light to produce about 106 single ionizations per second by impact of 30.4 nm radiation on neon in the form of an effusive jet at an effective pressure of about 10"4 Ton*. All the lamps suffer from restricted lifetimes due to insulation breakdown caused by sputtering, and it is very well worthwhile to minimize this problem by careful design and the use of low sputtering materials such as titanium. Other lamps reputed to provide even shorter wavelengths include the duoplasmatron13 and the pulsed BRV lamp14, but these have not been used in coincidence work. Another possible laboratory source for multiple ionization work would be an X-ray tube, which can emit not only characteristic X-rays for each anode element but also bremsstrahlung radiation of a continuous spectrum3. It seems probable that high power tubes, possibly with rotating anodes, would be needed to provide practically useful intensities, but this has not yet
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been tried. A modern deterrent to such work is the mass of safety regulations that accompany all X-ray use in many countries.
The mechanism of multiple ionization by single-photon impact is a subject of active research, and it is clear that the dominant mechanism is different in different wavelength regions. We distinguish the principal domains in order of increasing energy as the near-threshold, pre-edge and post-edge regions for each atom or compound, as illustrated in Fig. 2. The "edge" referred to is the minimum energy for ionization from an inner shell.
Fig. 2 . Typical form of the cross-section for double photo ionization. The energy of the first inner-shell edge depends on the atoms present; approximate first edge energies (eV) for some important elements are shown.
In the post-edge region the overwhelmingly dominant mechanism of multiple ionization is initial ejection of a single electron to form a hole in an inner shell, followed by Auger processes in which this core hole is filled and one or more additional electrons are ejected15,16. Every Auger process produces at least double ionization. Auger spectra have been interpreted over many years and show that the doubly charged ions are formed not just in a single state and not in all energetically possible states, but in many selected states, often mainly singlets17. Core holes have very short lifetimes so the uncertainty principle ensures that Auger lines are broad; it is impossible to obtain very high resolution, and ambiguities of interpretation usually remain even after comparison with the best ab initio calculations. The mechanism of triple and higher multiple ionization following core hole formation may involve "simultaneous" ejection of several electrons with a continuous spectrum, or formation of intermediate states of different charges as electrons are ejected "one at a time". This is an area where little is known, and coincidence measurements could be of great value.
In pre-edge regions, atomic and molecular absorption spectra show intense peaks or "resonances", where electrons are excited from inner shells into previously unoccupied orbitals. The decay of these resonances is similar to the Auger effects, except that singly charged ions can be produced as well as multiply charged ones. The dominant form of
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decay is usually the "spectator" Auger process in which the original core electron remains in the orbital to which it was excited while the other electrons relax, filling the inner-shell hole and ejecting one or more electrons18. In cases that have been studied in detail, some by coincidence methods19"21, it seems that doubly charged ions are formed mainly indirectly via intermediate superexcited states of the singly charged ion.
The near-threshold region is defined as being too low in energy for any inner-shell excitations or ejections. Thought about double ionization in this region has been dominated for decades by a theory of direct (that is, single step) two-electron ejection, the Wannier theory22 and its extensions23. This theory, which can also be applied to multiple-electron ejection, predicts that the double photoionization cross-section should rise from zero at threshold as the 1.056 power of the excess energy, that the electron spectrum should be flat and that certain states of the doubly charged ion should be favoured and others disfavoured on symmetry grounds. The range of energies over which the theory should apply has not been unanimously predicted theoretically, but experiments seem to indicate a range of a few electronvolts. The predictions of the theory are apparently confirmed in this range for the double photoionizations of He24,25 and H226'27, the only cases where there is but a single final state. For all complex atoms and molecules so far studied the cross-sections for double photoionization are roughly linear functions of excess energy, but the other predictions are not upheld (unless at energies very near threshold). This is a domain in which major advances are being made by the PEPECO technique, and further details are given later in this chapter.
2.1.2. Electron Impact
It is so easy to generate electrons of any energy in any desired abundance that electron impact might seem to be the ideal tool for routine use in the study of multiply charged ions. Indeed, electrons were used in the first pioneering coincidence work on molecular multiple ionization28, and in the first modern revival of the ion-ion coincidence technique29 and have been used again recently30. Nevertheless, they have drawbacks, which arise mainly from their ease of deflection in an electric field. For state selective experiments photoionization, with its input energy of hv per photon, is far easier than electron impact, where coincidences with electrons of known energy loss must be measured. In coincidence experiments needing good mass analysis of the ions (PIPICO, PEPIPICO, CSMS), ion formation should take place in a region of strong uniform electric field that draws the ions out as they are formed. A typical field of several hundred volts per centimetre will strongly deflect an incident electron beam, unless its energy is high. For this reason it is relatively easy to use electrons of 500 eV energy or above, but much more difficult to use low energy electrons. At this high energy, inner-shell processes take place and molecules undergo triple and quadruple ionization30
as well as double ionization. The contributions of the different degrees of ionization are difficult to sort out in simple ion-ion coincidence experiments and spectra for n-fold ionization may be contaminated by residues of (w-f-l)-fold ionization. Experiments involving coincidences with primary electrons which have lost a measured amount of energy31 solve the problem of uncontrolled initial energy transfer by electron impact, but are technically extremely demanding.
Formation of an mn+ cation by electron impact leaves n+1 free electrons to share any
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excess energy and according to the classical theory of direct processes the cross-section should increase as the (approximately) nth power of the excess energy23. While this may have some truth in it, particularly just near threshold, there is absolutely no reason to think that a direct process is the main means of multiionization at high electron energies. Experimental cross-sections for producing stable molecular and atomic multiply charged ions32 generally rise from zero at threshold to maxima at energies of one or a few hundred electronvolts. There is no theory, body of experimental results or even prospect of experimental results to guide the enquirer on what states a multiply charged ion is left in after formation by electron impact. The convenience of electron generation is paid for, as in normal mass spectrometry, by rather profound ignorance of the energy deposition function. One positive point is that electron energy loss spectra33'34 can demonstrate the extent of core hole formation (pre- and post-edge); once a core hole or resonance is formed its fate is the same (neglecting the subtle effects of post-collision interactions35'36) whether formation was by photon or electron impact.
2.1.3. Collisional lonization
Collisions of high energy ions with neutral target species can produce double ionization of either the projectile or the target. In charge stripping a singly charged cation loses an electron, becoming doubly charged:
p+ 4- T -» p2+ + T + e\ (2.1)
For the process to be efficient the projectile needs an energy of several kiloelectronvolts, and the target should be chosen carefully; 02, N02 and NO have been found to be particularly effective37"39. Reaction (2.1) has been used and studied widely in tandem mass spectrometry40, but not yet by coincidence methods. The breakdown products of doubly charged ions formed by charge stripping often distinguish between isomeric ions where more conventional mass spectrometric techniques do not41; this may be the result of some selectivity among the parent monocations between those that undergo the high energy charge stripping and those that dissociate at lower energies.
If the velocity of the doubly charged product ions is measured within a very small angle of the original projectile direction the second ionization potential of the projectile can be determined, since the energy needed for ionization of the ion comes from the relative translational energy. Many second ionization potentials have been measured in this way for species which support a long-lived doubly charged ion42. They are an extremely valuable resource as they represent vertical transitions at the geometry of the singly charged ions rather than at that of the neutral molecules, and can provide access to the most stable regions of the potential energy surfaces of doubly charged ions.
Double ionization of the target can occur by double charge transfer:
p+ + T -* p" + T2+. (2.2)
Cross-sections for reactions of this sort are very small, and their importance stems from their use to measure spectra of doubly charged ions which do not exist as stable species. Again, if the negative ions p" are detected within a small angle of the original projectile
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direction the energy needed for double ionization (with allowance for the electron affinity of the projectile) can be deduced from the observed change in velocity43,44. It has recently been shown that by choice of projectile the range of strongly populated excited states of the doubly charged target ion can be varied45,46. Another advantage of the method is that when protons are used as projectiles the choice of doubly charged ion states populated in the product is governed by strict selection rules, which simplify the interpretation of the spectra44.
An extreme form of collisional multiple ionization is used in the coulomb explosion technique47. Positive or negative ions with MeV energies are made to impinge on a thin (ca. 50 A) foil, which they traverse in a time very short compared with normal nuclear motion in the molecule. In passage through the foil so many of the outer electrons of the projectile are stripped off that on emergence the molecular ion undergoes a veritable explosion driven by electrostatic repulsion, every single atom having become positively charged. The greatest interest of this technique in the present context is that its exponents have developed highly sophisticated multiparticle coincidence detectors48 and accompanying data handling methods that push the art of coincidence spectroscopy to new heights. In principle they are able to determine the geometric structures of molecular ions directly by extrapolating the trajectories of the many product ions detected in coincidence back to the instant of the explosion. The structures of several ions, including H3
+ and CH5+, were determined experimentally for the first time by this
method43.
2.1.4. Other Forms of Multiple Ionization
The ionization of singly charged ions by photons with energy analysis of the photoelectrons would constitute the Holy Grail of doubly charged ion spectroscopy, the photoelectron spectroscopy of cations. It would provide an ideal source of energy-selected doubly charged ions for coincidence experiments on their properties; sadly this ideal is not yet realizable because of limits on the density of ion beams (space charge effects) and on the intensity of light sources energetic enough to ionize ions. Ionization of ions in beams by electrons is, however, a well-established technique for atomic multiionization49,50, which could possibly be extended to molecules using techniques similar to those currently in place for charge stripping experiments.
Multiple photon multiple ionization by intense pulsed lasers is a much more accessible means of creating doubly and multiply charged ions. Its disadvantages are that the actual number of photons involved is usually not known, and any fluence sufficient to cause multiple ionization also causes abundant single ionization, excitation and fragmentation at the same time. Because many ions in different charge states are liable to be created on each laser pulse, coincidence methods of the sort discussed in this chapter are not suitable. A different data handling technique, covariance mapping, has been developed to overcome this difficulty51,52.
Recent developments in the analytical mass spectrometry of very large molecules have thrown up several new techniques which produce multiply charged ions. In plasma desorption mass spectrometry53 (PDMS) and fast atom bombardment54 (FAB) pre-existing ions are desorbed from polar matrices such as glycerol solution into the gas phase. Under certain conditions abundant stable multiply charged ions are found55, and it is not
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yet known whether they also undergo charge separation. In electrospray ionization and thermospray ionization mass spectrometry56'57 extraordinarily highly charged ions are observed; an example is the ion (M+56H)56+ from bovine serum albumin58. Gas phase ions of this sort have been reported particularly for peptides and small proteins, and again it is entirely unknown whether or not they dissociate in the mass spectrometer, and if so whether charge separation occurs. Multiply charged cluster ions formed by electron impact on gas phase clusters certainly do dissociate59,60, but their reactions have not yet been examined by coincidence methods.
2.2. Particle Detection and Analysis
The foremost requirement of all methods of particle analysis and detection for use in coincidence experiments is high collection efficiency. This always conflicts with the need for high resolution in energy or mass, but as no coincidence signals may be observable at all above the noise level without high collection efficiency, resolution usually has to be sacrificed. The best solution is to use multiplex analysis techniques wherever possible, so that particles of all energies and all masses are measured continuously and simultaneously. The second requirement of coincidence experiments is good time resolution for all particles, to which end the detectors must have fast response and any time spread during analysis must be minimized. The third requirement is the lowest possible background count. These requirements essentially dictate the basic form of many coincidence experiments.
For detection of photons there is as yet no practical alternative to an efficient photomultiplier tube; quantum efficiencies of 25% are attained in some wavelength regions for light reaching the photocathode. To ensure that a large fraction of the light emitted in a reaction does reach the photocathode a lens or mirror system of low f-number is needed, and wavelength analysis must usually be done at low resolution using filters.
For detection of uncharged atomic or molecular fragments any electron multiplier can be used, provided the neutral particles have enough kinetic energy to produce secondary electrons on impact. Energies of 300 eV and above are sufficient for light molecules, but there are no quantitative studies known to the author. The detection efficiency will normally be mass dependent and different from the efficiency for ions of the same energy because the neutrals do not respond to electric fields near the detector surface.
Electrons are detected with high efficiency when they impinge on multipliers of the discrete dynode, channeltron or multichannel plate configurations with energies of a few hundred electron volts. Energy analysis may be done using any one of the many forms of electron spectrometer61, but those that accept electrons in a large solid angle, such as the spherical retarding field62, the elliptical mirror analyser63 or the magnetic bottle64
should have a decided advantage. Several of the dispersive analysers can be made multiplex by the use of a position-sensitive detector65 in the focal plane, and such a combination would have great advantages in coincidence measurements. The magnetic bottle analyser, being a time-of-flight device, is fully multiplex in energy as well as possessing high collection efficiency; this makes it exceptionally advantageous if the light source is pulsed, as illustrated in the first measurement of a complete PEPECO
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spectrum19. Positive and also negative ions are detected in the same way as electrons when they
strike the sensitive dynode surface of an electron multiplier with sufficient kinetic energy. The efficiency of the detection process depends for all particles on the kinetic energy66,67
and detection efficiencies of 100% have been claimed68. The author's experience is that efficiencies measured by coincidence methods (Section 2.3.2, below) are usually in the range of 20% to 40%, and it is probably wise to use these more conservative estimates in the design of experiments. For mass analysis of ions69 in coincidence both magnetic sectors and quadrupole analysers have also been used, but the time-of-flight method is so especially suitable for coincidence work that it is used much more often than any other method, and its characteristics deserve a more detailed description.
2.2.7. Time-of-Flight Mass Analysis
In the most useful form of time-of-flight (TOF) mass spectrometer, ions are created at time t=0 in a uniform electric field which immediately accelerates them along the spectrometer axis. No slits intervene before the ion detector so collection efficiency is very high, and the apparatus is always sensitive to ions of all masses. There have been many developments of the basic TOF principle for higher mass resolution69, and most of these are applicable to coincidence work. For fundamental studies of ion reaction dynamics the two-field Wiley and Maclaren design70 and some forms of reflectron71 are especially appropriate, and we concentrate on them here.
In all TOF instruments the flight time of an ion is proportional to the square root of its mass-to-charge ratio. By proper adjustment it can be made independent of the
Fig. 3 . Scheme of a simple TOF mass spectrometer. The nominal and actual ionization positions are indicated by asterisks.
position in the source where ionization occurs, and linearly proportional, within a small range, to any component of the ion's initial momentum along the flight axis. This principle is so important that it is worth demonstrating, and we shall take the simplest case of a spectrometer consisting of a source region with field E and a field-free drift space of length D, as illustrated in Fig. 3. Let the standard distance traversed in the
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source be s0, any extra distance actually traversed there be x, the initial velocity component along the axis towards the detector be w0 and let acceleration of the ion of mass m be a. The time spent in the source, ts, is then
ts = {(v02+2as0+2ax)1/2 -v0}/a (2.3)
and the time spent in the drift space, tD, is given by
tD = D(v02+2as0+2ax)-1/2. (2.4)
Introducing the standard times in the two regions ^ and t0D which apply when x and v0 are zero in Eqs. (2.3) and (2.4) and the times u, defined as vja and tx defined ds (2x/af2
we obtain the total time v.
t = tjl + tf+t,2)/^2}1'2 + t0D{l + (U2+t?)/t(2Ym-U . (2.5)
It follows from this that the flight time becomes independent of x to a good approximation if the standard times t0D and ^ are equal. This is also the condition that the flight time is linearly proportional to rv, and as the acceleration is just E/m, tv equals p/E where p is the initial momentum component along the axis which can be positive, negative or zero. The flight time under these focus conditions is thus 2^ - p/E. Both this expression and Eqn. (2.3) reflect the fact that an ion with an initial velocity directed away from the detector must be decelerated to a stop by the field and then reaccelerated to its initial velocity in the opposite direction. The time needed for this, 2tv is called the turnaround time, and its maximum value, where the initial velocity is away from the detector, is equal to the width of the resulting mass spectral peak.
The focus condition demonstrated above holds good in all TOF mass spectrometers of the Wiley and Maclaren or reflectron type. It is probably valid in all instruments using only static electric fields, though no formal proof of this conjecture is to hand. Reflectron mass spectrometers, which contain an additional stage where ions are reflected to the detector by an electrostatic field, have more flexible focusing properties. They can be operated under different focus conditions for different purposes; with surface ionization, for instance, there are no initially backward-flying ions and x may also be zero, so conditions which eliminate forward velocity dependence of the flight time are chosen. In gas phase work, however, the turnaround time is an unavoidable limitation on mass resolution. Where mass resolution is the major objective it can be optimized by using the highest possible source field, since ty is inversely proportional to E.
From the width of a TOF peak, 2rv, the mean initial velocity can be derived; from the shape of the peak we can often obtain the full kinetic energy release distribution (KERD). The principle of peak shape analysis72 is that if all ions are detected irrespective of their sideways velocity components, then each single initial speed, v0, produces a flat-topped peak of width 2V<z to contribute to the overall peak shape73. The initial speed distribution can thus be obtained by differentiation of the peak sides, or in practice by fitting to a simulated peak shape which makes allowance for the thermal velocity distribution. This principle is not valid, however, unless the velocity release is isotropic in the spectrometer coordinates. An angular distribution which favours dissociation along
ts = {(v02+2as0+2ax)1/2 -v0}/a (2.3)
tD = D(v02+2as0+2ax)'1/2. (2.4)
t = tJl + (tv2+tS)/t0s
2}1/2 + t0Jl + (tv2+^^^^^ (2.5) p+
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the spectrometer axis produces a hollow dished shape with peaks at the extremities, while a distribution favouring sideways decay produces a conical shape even for a single-valued initial velocity. Even electron impact ionization and photoionization with unpolarized light produce some ions with strongly anisotropic distributions74"76, though the majority of dissociative ionization reactions are probably almost isotropic. Where parent ions have time to rotate before dissociating, any initial anisotropy is greatly reduced77, so strong anisotropy is expected only for very rapid unimolecular reactions. The process of ionization or the selection of ions by electron detection in one direction can sometimes produce forward-backward asymmetry in which the early or late part of a TOF peak is emphasized75,78; as apparatus discrimination produces the same effect such cases must be scrutinized carefully. Samples of different TOF peak shapes are shown later (Fig. 20).
Ion dissociations which occur on a timescale comparable to the ions' flight time through the apparatus produce characteristic signatures in all forms of mass spectrum, and both the ions and the signals they engender in the mass spectum are generally called "metastables". In simple TOF instruments (not reflectrons) they produce tails towards the low mass side of parent ion peaks (dissociations before final acceleration) and also tails on the high mass side of daughter ion peaks (dissociations in the source field). The intensites and shapes of the metastables can sometimes be interpreted to yield dissociation rate constants79, but great care must be taken because the lifetime distributions are unknown and unlikely in most cases to be exponential. The field-free drift space provides the greatest opportunity for late dissociation, but unless a further electric field precedes the detector, neutral fragments and daughter ions formed in this zone continue at the velocity of the parent ion and strike the detector simultaneously. If any kinetic energy release accompanies the dissociation, however, the ion and neutral fragment will be spread apart in time to either side of the normal parent ion arrival time. In many instruments neutral fragments formed in this way have enough kinetic energy to be detected as easily as ions; metastable decays of this sort are thus an important source of unexpected coincidences in experiments where pairs of ion signals are looked for.
In TOF mass spectrometers which include reflectors or acceleration zones after the field-free region, slow decays produce metastable peaks at non-integer masses. The formula relating the apparent mass to parent and daughter ion masses must be evaluated separately for each instrument: in one reflectron mass spectrometer specifically designed for coicidence studies, for instance, a reaction in the drift space according to
m+ -> m | + n (2.6)
produces a diffuse peak at an apparent mass m between m and w;:
m = (m + bmj)2/[m(l + b)2]. (2.7)
Here b is the fraction of the total flight time that a normal ion spends in the reflector. The apparatus has a "straight through" detector as well as a detector for ions reflected by the applied field. This allows coincidences to be recorded between fast neutral fragments, which strike the straight-through detector, and ionic fragments30,80, reflected to the ion detector. Coincidence signals of this sort help to identify the origins of
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metastable peaks by removing ambiguity about the parent mass. Unfortunately the mass resolution is not high for the neutrals because even small kinetic energy releases in dissociations at the start of the drift space have a strong influence on their total flight time, spreading the peaks out.
2.3. Coincidence Techniques
2.3.1. Basic Coincidence Statistics
All coincidence experiments have the same purpose, to selectively observe particles born together in single primary events. The time taken by each particle to travel from its birthplace to its detector is controlled and monitored by the experimenter, who can then distinguish between correlated groups of particle arrival signals, where a fixed time relationship between members of the group exists, and uncorrrelated signals which arrive randomly. In all real experiments there are some uncorrelated signals which nevertheless mimic true coincidences; these false coincidences either must be made negligibly weak by suitable choice of conditions or must be calculated and subtracted later.
In order to describe the various signals in coincidence experiments we use a notation in which the total number of detectable events (ionizations, for instance) is N. The fraction of these events which are of the desired sort is g and the overall collection and detection efficiency (henceforth "collection efficiency") for particle./ is fj. The rate C at which true coincidences are registered in a simple twofold coincidence experiment is
C = gNffa, (2.8)
where a is an overlap factor. This factor expresses the fact that if neither/; nor/2 is unity the primary events observed by the two channels as particles 1 and 2 may not be the same events. Usually a represents a lack of spatial overlap; if the nature of the particles 1 and 2 is different, electrons and ions for instance, the regions of space from which they are efficiently extracted may not coincide.
Even if there is no other source of background signals, any deviation of the values °f fi> f2or a fr°m u m t v ls sufficient to produce false coincidences. At the first detector the observed count rate is Nfl9 and each count may be considered to open a coincidence gate for a time r, giving a total open time of Nfr seconds per second. The number of false coincidences registered during this open time depends on the form of the electronic system in use. If there is a time-to-amplitude converter (TAC) or time-to-digital converter (TDC) with a single "stop" input to accept the second particle signals, only one coincidence, true or false, can be registered for each opening. The background of false coincidences which builds up in the multichannel analyser will then be stronger for short delay times than for long, and will be a complex function of both channel number and channel contents. Detailed analysis and numerical prescriptions for subtracting the background accurately have been given81. If the background is very weak it may be essentially flat and easily subtracted. In many modern experiments the electronic system can register several particle arrivals after each start signal, so both true and false coincidences can be recorded for a single start. In this case, of all Nf2 signals at the
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second detector the ones not recorded as true coincidences may be seen during the gate open time as false coincidences. The false coincidence count rate F is thus
F = N2fj2(\-fia)T. (2.9)
If the signal is recorded in a multichannel analyser each channel will have a time width r and will gather false coincidences independently at the rate given by Eqn. (2.9). Because the true coincidence signal will normally spread over several channels, say m, the ratio of true to false coincidences in this case is given by
C/F = ag/{mNT(l-4i)}. (2.10)
In most real experiments the collection efficiencies are significantly less than unity, and the expression reduces to ag/mNr. This is very much simplified, but does demonstrate some vital characteristics of coincidence experiments. First, the ratio is inversely proportional to the event rate, N. If no signal is seen, as often happens when a new experiment is attempted, the first recourse is to reduce the event rate by reducing the gas pressure or radiation intensity. Lack of signal may also be due to too wide a peak or, more likely, to poor overlap. Although the magnitude of a is of great importance logically and physically, it is not usually possible to determine it experimentally, and it will not be included in later equations. To ensure that it is near unity is one of the experimenter's most vital tasks in setting up a coincidence experiment, and we must assume that he or she has succeeded.
The ratio of true to false coincidences is not often a true measure of the visibility of a coincidence peak. To derive an expression for the actual signal-to-noise (S/N) ratio after a measurement time T we use the fact that both true and false coincidences are random events following Poisson statistics. The S/N ratio is the ratio of the true coincidences in the peak channel to the uncertainty in the sum of accumulated true and false coincidences. Assuming a large number of counts and both,/; and/2 small we obtain
S/N = (ga/m){Nff2T/(ga/m + NT)}1/2. (2.11)
The circumstances where this expression gives useful guidance are those in which a weak signal is being sought; it shows again that every effort must be made to maximize the collection efficiencies as well as the overlap, and to minimize the peak width. Since the dependence on Af is weak a convenient event rate that avoids electronic problems such as dead time or paralysis should be chosen for a long run.
In most real coincidence experiments the statistics are complicated by factors that make analytical expressions for the false coincidence rate in terms of the underlying event rates very unwieldy. Some channels may have significant background count rates, or there may be different types of event contributing different numbers of particles. The collection efficiencies almost always depend on the energies or masses of the particles, and the total coincidence signal may be divided among a known or unknown number of peaks in the spectrum. These complications are not a problem in practice, however, once coincidence signals are seen and can be optimized. For all coincidence experiments, including those involving more than two particles, the true coincidence rates
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can be expressed in terms of collection efficiencies while the false rate can be calculated from observed counting rates and the resolving time. The true w-fold coincidence rate Cn is given by
n
Cn = gnNaIljj. (2.12)
For w-fold ionization in which only one of n electrons is detected the coincidence rate is multiplied by a further factor n if all electrons have an equal chance of detection. The rate of events producing the desired n particles is gnN and a is a common overlap factor. The false coincidence rate is calculated from the observed arrival rate of (n-l)-fold coincidences, the actual rate of signals at the last detector, 7n, and the resolving time r:
K = CnJnr. (2.13)
These expressions are also valid if just two particles are detected and if all are detected at the same detector, but they do assume that the collection efficiencies are small. They conceal a great deal of complexity because both false and true w-fold coincidence rates are functions of at least n-1 parameters, needing at least an n-dimensional space for graphical representation and for such operations as background subtraction.
2.3.2. Measurement of Collection-Detection Efficiencies
Collection-detection efficiencies such as^ and^ which occur constantly in the theory have to be known both in order to estimate the feasibility of coincidence experiments and to deduce relative cross-sections and branching ratios from coincidence results. It is a special feature of the coincidence technique that they can be measured experimentally without any need to know absolute gas pressures or absolute light intensities. The principle of the measurements is best explained by reference to a photoelectron-photoion coincidence experiment; any form of apparatus with separate ion and electron detectors could be used, and it makes no difference whether the electrons are energy analysed or not.
If an atomic gas is ionized at a wavelength where only single ionization is possible the observed count rate of ion-electron coincidences Cu will be
C* = g+Nfmfm), (2.14)
where g+N is the number of single ionizations per second and the ion collection efficiencies are expressed as functions of the electron energy (assumed single valued) and the ion mass respectively. The electron count rate Re will be
Re = g+Nfe(E). (2.15)
The ion collection efficiency is simply equal to the quotient CJRe. This is still true if the electrons are emitted with many different energies, as the reader can quickly verify;
n
C„ = g„Na II fj.
K = CnJnT.
Cu = g+Wc(E)ttm),
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it is essential, however, that any electron background count be subtracted before making the calculation. If a series of atomic gases of different mass such as the rare gases and mercury are admitted, the collection efficiency as a function of mass can be measured, so long as the coincidence signal includes all isotopic ions of each atom. If an electron energy analyser is present a check can be made that exactly the same ion collection efficiency is determined for a given mass, whatever electron energy is selected.
Ions formed in charge separation of multiply charged ions have large initial kinetic energies and may be collected less efficiently than thermal ions. There is no direct method to measure the collection efficiencies for such ions but they should become equal to those of thermal ions of equal mass when the drawout field is sufficiently strong. This condition can be recognized in ion-ion coincidence experiments in two ways. First the ratio of ion-ion coincidences to the pure ion count rate should become independent of drawout field. Secondly, the ion-ion coincidence peak shapes (not widths) become independent of the field and usually become flat-topped when the field is high enough. The peak shapes are perhaps the better test because collection efficiencies for ions of all masses depend to some degree on the total energy with which they strike the detector.
Even in apparatus where there is no energy analysis there is a strong dependence of electron collection efficiency on electron energy, because electrons of more than a certain energy, if they set out initially in a sideways direction, will not be pulled into the detector. The collection efficiency is therefore highest for low energy electrons, lowest for high energy ones and strongly dependent on the drawout field for intermediate energies. In apparatus containing an electron energy analyser, collection efficiency is certainly a function of energy. In either case it can be determined from the coincidence rate (Eqn. 2.14) and the ion count rate Rt given by
R^g+Nfjm). (2.16)
The electron collection efficiency at energy E is the quotient of the coincidence count rate and this ion rate provided the electrons are of a single energy. This can be arranged by choosing helium as the target gas, and changing the energy of the ionizing light to vary the electron energy. For apparatus without energy analysis it is sufficient to use argon, and vary the wavelength in a more convenient region.
Collection efficiencies for ions and electrons are easy to measure in the above way because for a suitable target we know that for every electron we get an ion. It is less easy to determine the collection efficiency for photons or neutral particles, but probably possible. For photons of around 3500 A use can be made of the unit quantum yield of fluorescence and 60 ns lifetime of the B state of the nitrogen molecular ion82, best utilized in an electron-photon coincidence arrangement with electron energy analysis.
3. INDIVIDUAL COINCIDENCE TECHNIQUES
3.1. Two-Particle Coincidence Experiments
We can imagine selecting any two particles from those formed in w-fold ionization, namely n electrons, up to n ions from charge separation, several neutral fragments and
Ki = g*Nfi(m).
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one or more photons from decay of excited species. More than ten possibilities arise from double photoionization alone, but only electron-electron, ion-ion and electron-ion coincidence experiments are of general utility. Some techniques have been used extensively to study single ionization, so only brief descriptions are given here, as little novelty is involved in extending them to multiple ionization.
3.LI. Electron-Electron Coincidences
Electron-electron coincidence spectroscopy in the form of PEPECO with energy analysis of both electrons is the primary means of investigating the mechanism of double photoionization. Its output should ideally be a complete three-dimensional spectrum showing intensity as a function of the two electron energies. The main difficulty, the very low collection efficiency of deflection analysers (0.1 to 1 %), was overcome in the first experiments by selecting one electron of zero energy using an efficient threshold electron collector83, and thus measuring along one edge of the full PEPECO spectrum, as illustrated in Figs. 4 and 5. Such a cut through the PEPECO surface is equivalent
Fig. 4. Simulated PEPECO spectrum showing intensity against two electron energies. This represents the spectrum expected for atomic mercury if photoionization were purely direct, obeying the Wannier theory and its extensions22,23. Of the states of the mercury dication in this energy range only the 3D states should be populated strongly; on grounds of wavefunction symmetry, population of the others should be weak. Each allowed state should give a ridge of constant height at fixed Ej+E2.
to a plot of intensity as a function of the sum of the two electron energies, El + E2, and because of the energy balance equation
£(m2+) = hv-Ej-E2 (3.1)
it is a form of spectrum of the doubly charged ion, an Et +E2 PEPECO spectrum. It has now become clear, however, from data such as those of Fig. 5, that spectra derived from single cuts can be highly misleading8486. The apparatus used to obtain Fig. 5 allows any cut to be measured and has special lenses to improve the collection efficiency84 of the hemispherical analysers as shown in Fig. 6. The false coincidence background
£(m2+) = hv-E1-E2
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Fig. 5. Experimental PEPECO spectrum of mercury ionized by 30.4 nm light synthesized by combining several different cuts through the surface. Note the evident population of the theoretically disfavoured ground state of the mercury dication and the uneven ridges, proof that ionization is at least partly indirect.
spectrum is measured concurrently with the true one by setting a coincidence gate at a time outside the true coincidence zone, and is subtracted afterwards.
The main calibration problem in PEPECO is to determine the collection efficiencies for electrons of different energies in both analysers. If tunable radiation of known intensity is available these can be obtained directly by measuring the electron signals from rare gases, for which the ionization cross-sections and angular distributions are known at many wavelengths4. If only fixed wavelength light is available, calibration is more difficult but can be achieved by measurement of standard photoelectron spectra87.
Fig. 6. PEPECO apparatus developed at Oxford. Target gas is supplied as an effusive jet perpendicular to the light beam.
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In order to obtain complete PEPECO spectra with apparatus of the sort shown in Fig. 6 it is necessary to measure many cuts, both parallel to the axes and on the two diagonal directions, and to interpolate between them. This procedure is extremely time-consuming. One solution would be to make one or both analysers energy multiplex by placing position-sensitive detectors65 in their focal planes. A much more elegant solution, hitherto used only in one study of double ionization following inner-shell electron excitation, is to use electron TOF analysis in a double-ended magnetic bottle, with pulsed synchrotron radiation as the light source19. The collection efficiency can in principle be as high as for electrons without energy analysis (about 25%) since electrons can be gathered from a full hemisphere in both directions. This is undoubtedly the experiment of choice for those with access to a large storage ring. A large ring is best because ideally the period between light pulses, proportional to the circumference of the ring in single-bunch mode, should be longer than the maximum expected electron flight time. The energy resolution depends on the electron energy, the time resolution and the length of the drift paths but can certainly be made adequate for PEPECO studies of double photoionization in the near-threshold region88.
3.1.2. Electron-Ion Coincidences
Electron-ion coincidence spectroscopy in the form of PEPICO, photoelectron ion coincidence, with energy analysis of the electrons is discussed elsewhere in this book, and has been used extensively to study single ionization89. There are two forms of the technique, one using a fixed-energy light source and scanning the electron energy (normal PEPICO) and the other using a variable photon energy and detecting electrons of a fixed energy near zero only (TPEPICO, threshold-PEPICO). Both forms of the technique have been used to acquire photoelectron spectra (or threshold photoelectron spectra) in coincidence with doubly charged ions84'90. Spectra obtained in this way should bear the same relationship to Et +E2 PEPECO spectra as photoionization yield curves bear to regular photoelectron spectra of the same species87. The only doubly charged ions yet examined by TPEPICO have been atoms83'90'91, but a few molecules have been studied in fixed-wavelength PEPICO using the apparatus of Fig. 6 with fields reversed in one hemisphere for ion detection and a small field applied across the source; an example is given later (Fig. 18). There should be marked differences between PEPICO and TPEPICO spectra in coincidence with the same doubly charged ion, which would reflect details of the double ionization mechanism: an experimental comparison has yet to be made.
A different PEPICO experiment on doubly charged ions can be carried out using the Auger effect. Light of any sufficiently short wavelength can eject an inner-shell electron from a molecule, leaving a core hole. The superexcited ion so created then relaxes, usually by the ejection of an Auger electron of definite energy corresponding to the formation of a doubly charged ion in a particular electronic state. Many Auger spectra have been analysed, so the detection of a selected Auger electron often signals formation of a doubly charged ion in a known state; the mass spectrum in coincidence with the electrons shows how ions in that state dissociate, if they do. This form of PEPICO technique has been developed particularly by Eberhardt and his group92"95, and applied to small molecules; an example is shown in Fig. 7.
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Fig. 7. Oxygen Is Auger spectrum of CO on a scale of the binding energy in CO2"1" (left) with PEPICO spectra at electron energies of the first two peaks (right). Note that at the lowest binding energy the doubly charged parent ion is seen, but at the higher energy there are only high velocity atomic ion fragments. The electron energy resolution was reduced in the PEPICO measurement by the field across the source. (Adapted from Eberhardt et al„ Aust. J. Phys., 39, 633 (1986).
Electron-ion coincidence measurements without electron energy analysis provide mass spectra under photon or electron impact in conjunction with PEPIPICO and other coincidence techniques. They can be gathered with very good statistics at each wavelength, and show peak shapes which represent integral kinetic energy release distributions for the various ions. An example of interest in connection with the mechanism of doubly charged ion formation is shown later (Fig. 20).
3.1.3. Ion-Ion Coincidences
Pure ion-ion coincidence experiments, in which just two particles are detected, were first used by Brehm and de Frenes29 in 1978 to study doubly ionized molecules formed by electron impact. Their experiments, and those of Edwards and Wood96 in 1982 with 1 MeV ion impact, used two separate analysers for the two ions detected in coincidence. A modern form of apparatus using a single flight path for both ions97'98 was introduced in 1984, and is depicted in Fig. 8.
Typical PIPICO spectra are illustrated in Fig. 9, showing coincidence counts as a function of the difference in time of arrival of two ion signals at a common detector. Since the individual flight times are proportional to the square roots of the ion masses, the scale is one of difference in the root of the mass. This instantly exposes a weakness of the technique as applied to polyatomic molecules, that all ion pairs of equal mass pile up around zero time difference, whatever the mass may be. For diatomics and many small molecules there is no ambiguity, however, and interest focuses on the shapes of the peaks. In the upper part of Fig. 9 the peaks are flat topped, while in the lower part there are two sharp spikes for each distinct ion pair process. These two forms of spectrum represent two limiting conditions under which PIPICO spectra can be
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Fig. 8. PIPICO apparatus using a single flight path for both ions. A split anode is used behind the multichannel plate particle multiplier to allow ion pairs with very small time separations to be recorded.
Fig. 9. PIPICO spectra of methane and nitrous oxide excited by filtered Hell light. The methane spectrum was recorded under conditions where all ions were detected irrespective of their initial velocity or angle, while for the nitrous oxide spectrum only ions hitting the centre of the detector were registered.
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measured; at high drawout fields or with a large or close detector all ions are detected whatever their initial velocity or direction. At low drawout fields or with a small or distant detector, by contrast, only those ion pairs whose initial velocities lie along the spectrometer axis, directly towards or away from the detector, can be seen. The first quantities to be derived from a PIPICO spectrum are the positions of the peaks, the centres of the flat-topped variety or the mid-points of each pair of spikes. Each position yields the difference of the roots of the masses, and so (hopefully) identifies the pair. Mass resolution can be enhanced by choosing a high drawout field and a long flight path, or by using a reflectron form of TOF mass spectrometer, but it is always very hard to distinguish between different pairs which all have low mass differences.
The second quantity to be extracted is the peak width, or the separation of the two spikes for each pair. The edges of the peaks correspond to ions with initial velocities exactly along the spectrometer axis, forward or backward, and for such ions we know from the analysis in Section 2.2.1 that under correct focus conditions the observed flight times t are
t = t0-p/E, (3.2)
where p is the initial momentum of the ion towards the detector and E is the drawout field strength. The extrema of a PIPICO peak arise from the two possible orientations of an incipient pair along the axis, the heavier ion flying forward and the lighter one backward or vice versa. When a diatomic doubly charged ion dissociates, or when any molecule separates into just two fragments the momenta of the two fragments are equal and opposite to conserve linear momentum. The peak width is therefore 4p/E, and directly reveals the value of the momentum release. The total kinetic energy U can be calculated from the momentum or directly from the width and masses using the convenient formula
U = {wEtfVSSpfm/famJ}, (3.3)
where the units of U, E and w are electron volts, volts per centimetre and nanoseconds respectively and m, m1 and m2 are relative atomic masses of the ions in the reaction
m2+ -* m | + mj. (3.4)
Great care must be taken in deriving widths from experimental spectra for use in this simple formula, however. If the peaks are flat topped (no loss of high energy ions) the full width at half height is suitable, but for any other peak shape, especially the common double-peaked or hollow shapes, the only reliable way is to repeat computer simulations including all known apparatus effects until the peak shape can be accurately fitted. This is necessary because discrimination against off-axis ions is never absolutely complete; the individual wings of a double peak have widths, maxima and centres which arise from a complex summation of factors" including the KERD, the degree of discrimination for each energy and the effect of thermal velocities.
The analysis given so far is valid only for two-fragment dissociations; a great many ion pairs are found to come from reactions with a neutral product, formally
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m2+ -» mt + m£ + m3 . (3.5)
PIPICO peak shapes for such three-body reactions cannot be interpreted in terms of the energy release without further information, despite claims to the contrary in early publications, because the momentum carried by the unobserved neutral particles may be substantial. This has been demonstrated both by PIPICO measurements as a function of wavelength100 and most directly by PEPIPICO peak shapes101, as explained below. All energy releases derived from PIPICO peak widths for three-body reactions need to be re-evaluated, as they nevertheless contain useful, though less simple, information.
Many molecules have been investigated by the PIPICO method, both using laboratory light sources and synchrotron radiation from storage rings, and a fairly full list is given in Table 1. The great majority of the investigations go no further in the analysis of the spectra than the identification of pairs from peak positions, measurement of their relative intensities from peak areas and determination of single-valued energy releases from peak widths. There is theoretically more to be learned from a third aspect of the spectra, the peak shapes.
Peak shapes in PIPICO spectra are affected by three factors, apparatus discrimination, the kinetic energy release distribution (KERD) and the ion angular distributions. A full analysis is possible only for two-body reactions and for cases where apparatus discrimination, which is normally the major factor, has been entirely eliminated. If this is the case the discussion given in Section 2.2.1 for TOF peak shapes applies directly to PIPICO peak shapes. Each single-valued energy release produces a single initial momentum, which if released isotropically in the laboratory frame gives rise to a flat-topped component of the total peak shape, with steep sides broadened by any velocity distribution of the molecule prior to charge separation. The broadening is less in PIPICO than in normal TOF spectra, as the prior velocity is multiplied, in its effect on the peak shape, by a factor (m^m^lm. Anisotropy favouring initial directions of dissociation along the spectrometer axis causes hollow dish-shaped peaks, hard to distinguish from apparatus discrimination effects, while dissociation preferentially perpendicular to the spectrometer axis will cause central peaking indistinguishable from the effect of a KERD containing low energy components. If both anisotropy and more than one single energy release are present they cannot be disentangled without measurements at different angles to the photon beam or to the polarization direction of the light. If it is known (or assumed) that one single energy release is present the angular distribution can be deduced from the peak shape, and conversely the KERD can be deduced123,134 if the angular distribution is known to be isotropic.
Experimental results have so far indicated that the ion pair angular distributions following near-threshold double ionization are essentially isotropic, whether the light is polarized or not. Peak shapes are usually nearly flat topped, as in the examples shown in Fig. 9 except where it is clear that more than one energy release is present, though it must be admitted that few measurements have been made with sufficient precision to set stringent limits on any anisotropy. This behaviour cannot be expected to persist into the pre-edge and post-edge energy regions, however, since the initial steps creating core holes are normal electric dipole transitions with symmetry properties coupled to the molecular axes. At the high energies involved, dissociation must often be faster than molecular rotation. We can thus predict that PIPICO peak shapes for pair production
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TABLE I
References to PIPICO and PEPIPICO measurements
Molecules PIPICO PEPIPICO
H2 43(var) HC1 98(HeII) 02 98, 116(HeII), 136(var) NO 98(HeII) N2 122(var), 123(var) 52(MPI) CO 124(var) 121, 130(MPI) IC1, I2 98(HeII)
H20 116(HeII), 125, 129(var) H2S 98, 116(HeII) HCN 116(HeII) C02 98(HeII), 106, 137(var) N20 98, 116(HeII), 113(var) 107(HeII), 130(MPI) OCS 98(HeII), 128(var) 101(HeII) CS2 98(HeII), 112, 128(var) 101, 107(HeII) N02 116(HeII), 127(var) 101 (Hell) S02 97(var), 98(HeII) 101, 107(HeII), 130(MPI)
NH3 116(HeII), 135(var) 126(var) C2H2 116(HeII)
CH4 121(var), 142(HeII) SiH4 140(var) CH3I 98, 107(HeII), 100(var) 101(HeII) CH3X 116(HeII), 133(var) 134(30.4) CF4 98(HeII) SF6 116(HeII) 101(HeII), 108(var) C2H5Br 132(var) QH6 114(HeII) QF6> CnFm 115, 30(30.4) M(CH3)4 138, 139, 141(var) QHUX 30(30.4) Aromatics 117, 131(var)
The radiation used is shown in parentheses; Hell, filtered Hell; var, various wavelengths; MPI, multiphoton ionization. In formulae, X represents a range of substituents, M stands for Si, Pb or Sn.
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following double ionization by the Auger effect or resonant Auger effect will show strong anisotropy following the same pattern as the angular distributions of the corresponding photoelectrons.
3.1.4. Coincidences with Photons
Electron-photon and ion-photon coincidence experiments, which include the photoionization versions PEFCO102103 and PIFCO82104 (photoelectron or ion-fluorescence coincidence) have been used mainly for singly charged ions, but these techniques are capable of detecting and identifying multiply charged ion emission processes too. So far only two doubly charged ions, N2
2+ and N02+, are known to support optically emitting states10*'105 and one of these was discovered104 by PIFCO. The very high density of electronic states calculated106 to exist in doubly charged ions obtained by ionizing stable molecules makes it unlikely that a great number of emitting species will be found, though this is an open question. Some stable doubly charged ions have structures completely different from those of related neutral molecules, and such ions might well support bound excited states. Emission from excited products of doubly charged ion decay may also occur, and could be detected most sensitively by PIFCO.
3.2. Triple and Higher Coincidence Techniques
Although many new experiments of this sort can be envisaged, the only higher order coincidence experiments so far done on multiple ionization involve detection of one electron, with or without energy analysis, and up to five mass-analysed ions in coincidence.
3.1.1. Electron-lon-lon Coincidence, PEP1PICO
The problem that for ion pairs of equal mass the mass itself cannot be determined by PIPICO is solved if the time of ion formation is known by detection of one or more of the ejected electrons. The times of flight of any number of ions in coincidence with the electron are then measured and reveal the masses. This is the electron-ion-ion coincidence experiment first done by McCulloh, Sharp and Rosenstock28 in 1964, making it by far the most venerable coincidence technique for study of multiionization. It was revived107,108 as PEPIPICO in 1986 using photoionization instead of fast electrons, modern electronic techniques and an apparatus drawn in Fig. 10.
Because the spectra give intensity as a function of two parameters they are three-dimensional (3-D) and a severe problem of presentation arises. Projections of the 3-D figures onto the plane of the paper give an overall impression to the eye, but cannot be interpreted quantitatively. Contour diagrams, colour maps and grey-scale representations of intensity in rectangular coordinate systems are useful where the data set is of good quality. For weak signals, which may be found for minority processes in any data set, dot plots, where a single dot shows each ion pair recorded, are the most honest representation. Where emphasis is on the identity of pairs and their relative intensity, bar diagrams are appropriate; examples of two forms of representation are
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Fig. 10. PEPIPICO apparatus. The time-to-digital converter (TDC) can register up to eight stops for each start signal, timing each one to within a nanosecond.
given in Figs. 11 and 12. References to all published PEPIPICO work from the modern era are gathered in Table 1.
Fig. 11 illustrates many important characteristics of PEPIPICO spectra. First, the two-parameter mass spectrum, for this is what it is, evidently is a new form of molecular fingerprint. Secondly, as a two-parameter spectrum it can be projected in many ways into single-parameter spectra; the spectrum of ions found in pairs is obtained as a summation parallel to one axis; the spectrum of mass differences, related to the PIPICO spectrum, is obtained by summing intensity at constant m2 - ntj for all pairs, while a summation over t2 - tj is almost identical to the PIPICO spectrum. (Any differences between the PIPICO spectrum measured directly and that extracted from the PEPIPICO spectrum arise from selectivity in the electron detector, possibly including angular anisotropy in electron ejection107.) A more interesting new type of spectrum, illustrated in Fig. 13 is a summation over ml + m2, called a pair-sum spectrum, which is a spectrum of doubly charged precursors of the observed cation pairs. This is a spectrum of unstable doubly charged ions, and can be compared with the mass spectra of singly charged ions and of stable doubly charged ions from the same substances recorded by established mass spectrometric techniques109. In fact some of the ions recorded in pairs are secondary decay products from primary charge separation reactions, as explained below, so these spectra are also called apparent precursor spectra.
The preparation of a standard PEPIPICO spectrum such as Fig. 11 from raw data demands two prerequisites; first any background of false coincidences must be eliminated and secondly all distinct processes must be (mass) resolved. If count rates are kept very low the background may be negligible; this is the easy but inefficient method. The false
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Fig. 11. Bar diagram of the PEPIPICO spectrum of perfluorocyclobutane at 30.4 nm.
Fig. 12. Perspective of detail in the 40.7 nm PEPIPICO spectrum of hexane, showing peak shapes for pairs of ions containing two and three carbon atoms. The two strong peaks on the left show masses 27-1-41 and 27+43 , while the peaks on the right are for 29+41 and 29+42. Note that the peaks have the form of ridges inclined at different angles to the orthogonal time axes.
coincidence background is always structured, even if the light spurce is not pulsed, as shown in Fig. 14. It is expressed by Eq. 2.13, since the background intensity at each point is proportional to the electron-ion coincidence rate at that point and to the total ion signal at the detector. The false coincidences build into ridges across the spectrum with relative intensities given by the electron-ion coincidence mass spectrum; the ridges fold back at the diagonal and where they cross their intensities simply add. Because the electron-ion coincidence spectrum is measured concurrently with the PEPIPICO spectrum it is simple to calculate the shape of the two-parameter background spectrum, and to normalize it to the measured PEPIPICO spectrum in a mass region where no real ion pair
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Fig. 13. Spectrum of apparent doubly charged precursors, also called the pair-sum spectrum, derived from the PEPIPICO spectrum of perfluorocyclobutane in Fig. 11. It is compared with the photoionization mass spectrum (PIMS) at 30.4 nm.
Fig. 14. Example of a false coincidence background, measured for perfluorocyclobutane at 58.4 nm. The ridges correspond to peaks in the single-ion mass spectrum (above), while peaks are ion-neutral coincidences.
peaks occur. Subtraction can then be done110 by a suitable Monte Carlo procedure that takes account of the Poisson statistics of the small numbers of counts in many elements of the data array. Because the false coincidence rate (Eq. 2.9) is not linear but quadratic
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in the ionization rate, conditions should remain constant during the run if the subtraction is to work correctly.
In addition to false coincidence ridges, Fig. 14, which was obtained by running PEPIPICO apparatus at a wavelength where no double ionization was possible, contains peaks at the diagonal which are not false coincidences. They are ion-neutral coincidences from metastable decays of singly charged ions in the drift tube. Such peaks are a common feature of raw PEPIPICO spectra, and can be dealt with only by individual recognition. They do not appear in PEPIPICO spectra taken on apparatus based on reflectron TOF mass spectrometers, where neutrals from reactions in the drift tube fail to reach the ion detector.
Mass resolution in PEPIPICO spectra is much better than in PIPICO. Peaks for reactions which produce just two ions and no neutral fragments from a multiply charged parent are shaped as narrow lines when viewed in plots of t2 versus tly those for pairs of singly charged ions being exactly diagonal as shown in Fig. 15. This follows from the conservation of linear momentum and the general expression for the time of flight t under correct focus conditions:
t = t0-pcose/(zE), (3.6)
where 6 is the angle of the dissociation direction to the spectrometer axis and z is the charge of the ion. If one ion starts out with a momentum component towards the detector the other ion must start with an on-axis momentum of opposite direction and identical magnitude. If the ions have the same charge the anticorrelation of their time deviations turns the peak into a line of slope -1. If one ion has a charge of +2 the slope will be -2 or -1/2, depending on whether the doubly charged partner has the lesser or the greater mass-to-charge ratio.
Fig. 15. Detail of the PEPIPICO spectrum of acetone at 30.4 nm on a linear time scale. The two-body peak (upper right) has a slope of exactly -1 , but the peak on the left has a slope -15/14, showing that the primary methyl ion can dissociate by loss of hydrogen. The other peaks have slopes near -1 , suggesting deferred charge separation mechanisms.
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All PEPIPICO spectra of polyatomic molecules contain peaks for many different cation pairs. They can be categorized as two-body peaks, three-body peaks and multibody peaks according to the number of particles into which the nascent doubly charged ion breaks up. The ions of two-body peaks reconstitute the parent molecule when added together, those of a three-body peak reconstitute the parent all but a single atom or a very stable neutral molecule such as CO. All other peaks in the spectrum must be classified as arising from multibody processes unless special evidence to the contrary is forthcoming.
The widths perpendicular to the line-like peaks for two-body reactions arise from random thermal velocities of the molecules before ionization; they are minimized by using target gas in the form of a molecular beam. If a doubly charged ion undergoes three-body decay by the sequential mechanism that has been called deferred charge separation
m2+ -» m2+ + m2
m]+ -* m3+ + m4
+ (3.7)
any kinetic energy release in the first step, ejection of the neutral, has the effect of adding a pseudorandom velocity component to the doubly charged species. After charge separation both ions retain the random velocity components of their immediate parent, but have different random momenta in proportion to their masses. It follows that the peak shape should be a lozenge of unit slope but of greater width than for a two-body reaction, as illustrated in Fig. 16, because after charge separation the heavier partner has a larger random momentum component than the lighter one. If the ions are of nearly equal mass or if the neutral fragment is so light as to carry away almost all the energy release in the first step, the peak shape is more like a sausage than a lozenge, but the slope is always unity as seen in Fig. 15.
A second major mechanism for three-body dissociation is secondary decay in which charge separation happens first
m2+ -> ml + mj
m£ -> m} + m4 (3.8)
and we start by assuming plenty of time for free rotation between the two steps. In this mechanism the momentum from charge separation is passed on to the ion m3 as a velocity. The anti-correlated momentum is thus reduced by the factor m3/m2, and the peak is a line of slope -m3/m2 (or -m2/m3 if m3 ends up lighter than mx), instead of a slope of -1. Any kinetic energy release in the second step gives m3 an added random velocity component to m3 not shared by ml5 so the archetypal peak shape for this mechanism is a lozenge of non-unit slope,- as illustrated in Fig. 16. Examples of the more usual ridges or "sausages" of non-unit slope are seen in Figs. 12 and 15 for hexane and acetone respectively; these arise where the energy release in the second step is relatively small.
If the time between the two steps of either mechanism becomes exceedingly short, or if the dissociation into three fragments is simultaneous there are likely to be correlations
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Fig. 16. Sample peak shapes from four different PEPIPICO spectra, all on linear time scales, (a) H+ + CHO+
from CH3OD, a fat lozenge of slope -1. (b) H+ 4- CH2N+ from methyl cyanide, a fat lozenge of slope -28/40 showing that loss of neutral C from CH2CN+ follows charge separation, (c) CF2
+ + Br+ from CF2ClBr with a twisted shape; the intense part of the peaks is steeper than the less intense part, (d) CF3
+ + I+ from C3F7I where there are probably two distinct mechanisms.
in both magnitude and direction between the momenta taken by the three particles. The resulting peak shapes are characteristic of the directional correlations: if the neutral is ejected mainly along the same line as the two ions an "hourglass" peak shape is found, whereas ejection mainly perpendicular to the ion-ion axis gives an "egg" shaped peak; both have major axes at a slope of -1. In favourable cases the angles between the three initial momentum vectors can be deduced from the peak shape101, but data of very good statistical precision are needed for a reliable result.
Some peak shapes for three-body reactions, with characteristics intermediate between those of the two main cases discussed above may be symptomatic of secondary decay on a femtosecond time scale. The case is still sub-judice, and is discussed further in the section on results.
Peak shapes in PEPIPICO spectra for reactions which involve four or more particles are sometimes similar to the "simple" peak shapes for three-body reactions, but are often more complex. Forms which evoke the names "star", "bone", "fuzzy sausage" and "square" have been seen. The investigation of these peaks has not yet begun in earnest, but many of them seem to come from reaction schemes with alternative pathways or with several consecutive steps. It must be apparent from even this cursory survey that PIPICO peak shapes, which are but one projection of the PEPIPICO data simply do not convey enough information for proper interpretation of any but the two-body reactions.
3.2.2. Fourfold and Higher Coincidences
For triple or higher ionization, radiation with an energy of 60 eV or more is necessary for most molecules. Gas discharge lamps do not provide enough light of such high energy, and laboratory coincidence work using X-ray tubes has not yet begun.
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Multiple ionization is easily accomplished in the laboratory by high energy electron impact, however, as in the pioneering work of McCulloh and coworkers28. Ionization by fast electrons of 500 to 1000 eV energy releases slow secondary electrons in the ionization process, so the apparatus of Fig. 10 is perfectly suitable for coincidence studies of multiply charged ions formed by electron impact, provided precautions are taken to prevent the primary electron beam from impinging on the electron detector30. Multiphoton ionization by giant picosecond laser pulses also causes a high proportion of multiple ionization52, and may provide complementary information.
In 750 eV electron impact on a small range of molecules30 the relative proportions of double, triple, quadruple and quintuple ionization, judged from the yields of charge-separation products, were found to diminish by a factor of about ten for each extra degree of ionization. Thus 100,000 single ionizations are accompanied by 10,000 double ionization events, 1000 triple ionizations and so on. The proportions of higher ionization would certainly be greater in photon impact, particularly at inner-shell excitation wavelengths. The small relative intensity of the higher multiple ionizations, particularly fourfold ionization and beyond, coupled with the inevitable accompaniment of high count rates from lower degrees of ionization, makes false coincidence background subtraction essential. The method given for PEPIPICO spectra can be generalized, but is complex and time consuming. A simpler procedure that removes the great majority of false coincidences is to eliminate from the data set all ion multiplets, any of whose constituents has a flight time not corresponding to an ion known from the mass spectrum. Care must be taken to allow for the greater width of peaks from multiply ionized precursors, because of the increased energies from coulomb repulsion. Apparent precursor spectra for perfluoronaphthalene derived in this way are shown in Fig. 17.
Fig. 17. Apparent precursor spectra for ion pairs and ion triples from perfluoronaphthalene ionized by 750 eV electrons.
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Graphical representation for fourfold or higher coincidence data is a difficult problem; the data taken up to now have been analysed numerically and presented mainly as computer listings. The most useful plots developed so far110 are two-parameter diagrams showing intensity as a function of two sums of times for the ions detected. Thus if the ion flight times are tlt t2, t3 etc. in increasing order, the plot of triples would use t2+t2 and t3 as parameters, that for four-ion groups would use t2+t4 and t2+t3 and so on. These plots have the property that groups of equally charged ions that could reconstitute the parent molecule without mass loss give peaks as diagonal lines of slope -1 because of momentum conservation. The pairwise correlations between individual ions in a triplet or quartet are not forced by conservation laws, however, and reflect the dynamics of the charge separation reaction. A moderately detailed analysis has been done for the triply charged molecules of OCS and S02 separating into three singly charged ions111, and showed non-linear dissociation in both cases. The shapes of other peaks involving unobserved neutrals, which are the majority for polyatomic targets, have not yet been analysed at all either in these diagrams or in the higher dimensional spaces.
The simplest spectra derived from the full multicoincidence data are apparent precursor spectra, showing intensity as a function of the sum of the masses detected in coincidence. An m1+m2+m3 spectrum is illustrated in Fig. 17 for comparison with the ml+m2 precursor spectrum; the evident increase in the extent of fragmentation with increasing charge continues through 4+ and 5+ charge states, and seems to be a general phenomenon30.
4. SAMPLE RESULTS
4.1. Mechanism of Near-Threshold Double Photoionization
PEPECO spectra of atoms, exemplified in Fig. 5, show that photoionization populates electronic states of doubly charged ions indirectly via superexcited states of the singly charged ions. Molecular PEPECO spectra, while still few in number85'110 and not yet fully interpreted, show population of vibrational levels of doubly charged ions outside the Franck-Condon zones expected for direct ionization. The first complete PEPECO spectrum of a molecule, synthesized from several different cuts through the surface, is shown in Fig. 18. The indirect double ionization mechanism is also seen in the PEPICO spectrum in coincidence with doubly charged molecular ions, illustrated in Fig. 19, which corresponds to formation of long-lived molecular dications only. From these observations it is becoming clear that a major fraction of the double photoionization of ordinary molecules at low energy is indirect; the first step is formation of a superexcited singly charged ion, which then autoionizes to the doubly charged final product. We call the mechanism non-resonant autoionization, because the intermediate singly charged ion states can be formed at any high enough photon energy. Some of the superexcited ion states are valence hole states, others are Rydberg states belonging to series converging on the double ionization limits.
The existence of this non-resonant autoionization is of profound importance for the
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Fig. 18. Preliminary PEPECO spectrum of carbon disulphide at 30.4 nm built up by interpolation between different cuts through the surface, measured on the apparatus shown in Fig. 6.
Fig. 19. PEPICO spectrum showing electrons in coincidence with doubly charged CS2 ions produced by 30.4 nm photoionization. If ionization were purely direct the spectrum should be essentially flat. The form of this spectrum is consistent with the observation of satellite peaks in the photoelectron spectrum of CS2 at high photon energy147. It should be identical to an integral of the full PEPECO spectrum, Fig. 18, over stable states of the dication only.
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interpretation of double photoionization experiments on molecules. It means that doubly charged ions can be formed not only in the ranges of nuclear coordinates (or vibrational states) corresponding to the Franck-Condon zone of the neutral ground state but also in other ranges made accessible by the two-step nature of the transition. In other words, double photoionization is not just a vertical Franck-Condon process in the usual sense. Vibrational states of doubly charged ions can probably be populated at every energy, just as intensity is to be found at almost every energy, including the Franck-Condon gaps, in threshold photoelectron spectra. The effect should be greater in double ionization because two electrons are removed, causing large changes in equilibrium geometry. The lowest energy state of a doubly charged molecule may lie outside the Franck-Condon zone, perhaps behind a potential energy barrier, but still be accessible by indirect ionization. Thus photoionization from the ground state molecule can produce doubly charged ions or their fragmentation products at photon energies below the vertical double ionization potential. Appearance potentials in photoionization are therefore not a reliable method for measuring molecular vertical double ionization potentials; results obtained in the past by this method need to be re-evaluated.
To interpret the dissociations and other reactions of multiply charged ions we need to know the distribution of internal energies with which they are formed, called the energy deposition function. For triple and higher ionization by photon impact these are completely unknown, and for the present, unknowable. For double photoionization in the near-threshold region, complete PEPECO spectra could provide the energy deposition functions experimentally as integral E1 + E2 spectra.
4.2. Spectroscopy of Doubly Charged Ions
The hope of obtaining spectra of doubly charged ions was a major impetus to early work using PIPICO and to the development of PEPECO. The new discoveries outlined in the last paragraph mean that the measurements undertaken for that purpose do not give the spectroscopic information that was hoped for, but represent more complex phenomena of equal or greater physical interest.
PIPICO measurements were thought to give spectroscopic information in two ways. First, measured kinetic energy releases in charge separations of diatomic doubly charged ions could be added to the energy of the dissociation asymptotes, known from thermochemistry, to yield apparent energies of the dissociating doubly charged parent ions. Any ambiguity about choice of different assymptotes could be removed by varying the photon energy. Doubly charged ion energies were discovered in this way for dications of diatomic molecules such as 02, N2, CO, NO and I2 and also for those of small polyatomic molecules including C02, OCS, CS2, H20, N20, all listed in Table 1. The results were interpreted as the energies of potential energy curves of the doubly charged ions in the Franck-Condon zones of the corresponding neutral molecules, since double ionization was modelled as a direct, vertical process. This interpretation is at best seriously unsafe. The PEPECO spectra of HI, 02, C02, CS2 and OCS all show110
that because of non-resonant autoionization wider energy ranges than the direct Franck-Condon zones are populated in the dications. A closer study of PIPICO kinetic
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energy releases should confirm this picture; when examined with good statistics and under conditions of small thermal broadening (as shown by narrow PEPIPICO lines) the kinetic energy release distributions should be broader than the expected Franck-Condon zones. Unfortunately the PIPICO results for which the highest kinetic energy resolution is claimed122 have very poor statistics, and KERDs have not been derived. PIPICO data sets with good statistics have been gathered so far only with relatively poor kinetic energy resolution, so the rather broad KERDs that they show may not be definitive.
The second method by which dication spectra have been approached using PIPICO is to plot the yield of ion pairs as a function of photon energy and extrapolate to a threshold for each pair process97,112,122. If different kinetic energy releases can be distinguished the yield of ions of each energy can be followed separately. The cross-section is usually a roughly linear function of excess photon energy above threshold, as expected, and thresholds obtained by linear extrapolation to the noise level are again interpreted as regions where dication potential energy surfaces cross the Franck-Condon zone. This interpretation is also risky, though perhaps less so than the interpretation of kinetic energies, because excitation of the singly charged superexcited states involved in non-resonant autoionization can also lead to ion pair production at photon energies outside the vertical double ionization zone. A clear demonstration of this has been seen in the yield of NO+ -I- N+ ions fron N20 at photon energies well below the normal double ionization energy, with reduced kinetic energy releases113. These data were interpreted at the time as due to transitions in the extreme wings of the Franck-Condon region; in the light of present understanding they are almost certainly due to a two-step process of vertical single ionization to Rydberg states converging on higher states of N202+, followed by autoionization at long internuclear distances. In kinetic terms the doubly charged core of a Rydberg state may start to dissociate, and autoionization may occur as the two particles separate. Instead of autoionization one of the separating ions may capture the excited electron; this leaves one singly charged ion and a neutral species flying apart with the very high kinetic energy normally found for ion pairs. Such high energy ions are indeed seen in exactly the expected photon energy range below double ionization thresholds, as demonstrated by the PEPICO spectra in Fig. 20. They have been seen before143 but have not previously been interpreted in this way or distinguished from the ions produced in dissociative double ionization.
That Rydberg series converging on excited states of doubly charged ions are populated by photon impact and decay by autoionization to doubly charged ions is not only required to explain the observations, but is in hindsight clearly predictable. Since the oscillator strength for absorption varies smoothly across any threshold the intensity in these superexcitations must be comparable to the intensity in the direct double ionization itself. Any additional superexcitations by ionization from inner valence levels or core levels, allowing Auger-like processes, are likely to yield double ionization much more abundantly than a direct process. This is dramatically demonstrated in the case of GeH4 by the yield of ion pairs as a function of wavelength, shown in Fig. 21 for comparison with the almost isoelectronic case of CH3Br. A naive extrapolation of the yield curve in this case would certainly give the energy needed to produce a 3d hole rather than any energy to do with the doubly charged ion. While the presence of an inner d-shell is an extreme case, the existence of inner valence levels around the double ionization threshold, which
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is well attested for many molecules by photoelectron spectroscopy, is likely to have a similar, if less dramatic, misleading effect.
Fig. 20. Details of the PEPICO TOF mass spectra of NO ionized at the wavelengths (nm) given on the right. The contributions of ion pairs, determined from the simultaneously measured PEPIPICO spectra, are shown as dotted lines on the spectra at the three shortest wavelengths. Note the abundance of high energy atomic ions not from pairs, even below the double ionization threshold.
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Fig. 21. Relative yields of double and single photoionization in germane and other gases as a function of photon energy, determined from PIPICO measurements with calibration of the collection efficiencies as explained in Section 2.3.2.
4.3. Mechanisms of Charge Separation
4.3.1. Two-Body Reactions
It may seem questionable whether so simple a process as two-body dissociation can have any inner complexity worth calling a mechanism, but we have seen an example of such a thing in the last paragraph. For some ion pairs the formation mechanism is undoubtedly single ionization to a superexcited state followed by dissociation and then autoionization. Proof of this mechanism could come from an electron spectrum characteristic of the intermediate neutral fragment's autoionization as in some singly charged ion decays144, or perhaps from anisotropic ion or electron angular distributions. In an extreme case late autoionization may show a kinetic signature in the PEPIPICO spectrum.
Slow charge separations, where metastable doubly charged parents live for a hundred nanoseconds or so before dissociating, are clearly seen as diagonal ridges in PEPIPICO spectra. Notable examples are the benzene114 and perfluorobenzene115 reactions
C6H62+ -* CH3
+ + C5H3+ (4.1)
C6F62+ -> CF+ + C5F5
+, (4.2)
where the lifetimes observed after ionization at 30.4 nm are of the order of 200 ns.
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Similar slow charge separations are found for several triatomic dications107'116 and for a few dications formed by initial ejection of a neutral fragment from the parent species. For instance the parent dication of methyl thiocyanate, CH3SCN, loses two hydrogen atoms rapidly, whereupon the reaction
CHSCN2* -* CSCN+ + H+ (4.3)
occurs at least partly on a hundred nanosecond time scale. Of course the actual rates of decay always depend on the internal energy content which will often have a broad spread. The fact that dication reactions can be quite slow is also shown by the rearrangements which may precede charge separation. In small species rearrangement processes are usually less important than simple bond cleavage116, but for larger molecules rearrangements may even be dominant at low photon energies117, as is indeed the case for reaction (4.1). A general slowness of charge separation in doubly charged ions is consistent with the observed lack of any strong anisotropy of ion pair products, since the dications can presumably rotate freely before fragmentation.
4.3.2. Three-Body Reactions
The two most clearly delineated mechanisms of three-body reactions were described in Section 3.2.1, namely deferred charge separation and secondary decay of primary charge separation products. In peak shapes for 80 three-body reactions in high quality PEPIPICO spectra of 32 compounds, 31 reactions were found to be secondary110. The other three-body reactions, in a slight majority, are either deferred charge separations or instantaneous explosions. Although it is difficult to make a clear decision between the last two mechanisms unless a metastable signature is visible, we believe that the two-step process is the more common. In double ionization of compounds containing fluorine115
the ejection of a neutral fluorine atom is always a first step of deferred charge separations, whereas hydrogen atoms are seen to be lost by either mechanism. For three-body decay of triply charged ions into three singly charged ions the data base is still small, but in the triatomic cases studied so far111 dissociation seems to be by an instantaneous explosion. Only one reasonably intense four-body dissociation of a quadruply charged ion has been found hitherto, namely
CF2ClBr4+ -*• F+ + CF+ + Cl+ + Br+. (4.4)
As demonstrated in Fig. 17 the more highly charged ions tend to break up with formation of many neutral fragments. This tendency is in accordance with the simplest model of the excess energy content of the parent species, over and above the minimum needed to form singly charged fragments. The minimum excess energy EE can be calculated as
EE = 7n -nlx -(n-l)D, (4.5)
where /„ is the n-fold ionization energy and D is a representative bond dissociation energy. The n-fold ionization energy always increases more rapidly than linearly with n, as shown for instance by Smith's electrostatic model119, so the excess energy increases
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as the degree of ionization increases. It rapidly becomes more than can be contained in the fragments without further bond breaking, so further bonds do indeed break, forming unobserved neutral fragments.
The most intriguing peaks found in PEPIPICO spectra for three-body dissociations of doubly charged ions have a "twisted" shape intermediate between the forms expected for instantaneous explosion and secondary decay. An example is shown in Fig. 16. One interpretation of these peaks, of which many have been found110, is that the product ions may be formed by two concurrent mechanisms. A more interesting possibility is that the secondary decay happens very soon after charge separation, within the coulomb field of the other primary ion. The time needed for such a process to produce peak shapes as observed is in the range 10 fs to 1 ps, a range of great chemical interest. The possibility of determining lifetime distributions for such very fast reactions of the singly charged products of charge separation is under urgent investigation.
Because the PEPIPICO experiments reported hitherto have not involved any energy analysis, let alone analysis of the two ejected electrons in coincidence, the states of the doubly charged ions that set off all the reactions seen in the spectra are entirely unknown. A new form of PEPIPICO with energy selected Auger electrons, now being initiated by Hanson and coworkers120 promises to transform this situation. Because the core hole states intermediate in the Auger effect are of fixed energy, selection of the single Auger electron suffices to define the initial state of the doubly charged ion, opening the way to make PEPIPICO a state-selected technique.
4.3.3. Fragment Ion Mass Spectra
PEPIPICO spectra of a large and rapidly growing number of complex molecules have now been measured30'115117'138'139,141 and there has been one systematic study of charge separation in complex triply and quadruply ionized molecules30 A few general characteristics of the branching in charge separation have emerged, and can be summarized briefly.
First, for all but the most stable compounds such as polynuclear aromatics, the majority of charge separation reactions produce neutral fragments as well as ions. As the size of molecules increases, and as the number of charges increases this tendency becomes more pronounced. The classical coulomb explosion in which every fragment of an individual molecule receives a charge16 does not happen, or is very rare for the large molecules and valence multiionization that have been studied. The tendency to eject neutral fragments is entirely in accord with the excess energy model explained in Section 4.3.2 and elaborated elsewhere115. Even when double ionization is by light of the longest possible wavelength for single photons, PEPIPICO spectra of aliphatic compounds show very few two-body reactions.
Secondly, the ions eventually detected are almost all singly charged and are the characteristic stable light ions well known in ordinary mass spectrometry. Even-electron species are dominant, so a pronounced alternation may be seen in many spectra; for organic molecules containing no nitrogen atoms the mass numbers of ion pairs are most often odd+odd, and there is a corresponding dearth of odd mass numbers in the pair-sum spectra.
Thirdly, multiply charged ions of complex molecules break up in many different
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ways. There are generally more peaks of comparable intensity in the PEPIPICO spectrum than in the mass spectrum of a compound, and even more in the spectra from triple or higher ionization (Fig. 17); whether the many concurrent reactions are truly competing or consecutive is not yet known. Rearrangement products from hydrogen or proton transfers are seen in good abundance from double ionization, so there seems to be some reason to think that these dissociations are slow enough to be described by kinetic theories invoking free energy flow, such as RRKM theory.
5. FUTURE PROSPECTS
Three major directions of advance in the area of coincidence studies of multiple ionization can easily be foreseen. These are first increasingly detailed and precise studies of the processes of ionization and ion decay, secondly increased emphasis on inner-shell ionization and thirdly extension of the work to higher degrees of ionization. At the same time there will probably be an expansion of some of the new techniques into broader areas of chemistry, possibly into analysis121.
Fundamental studies of the physics of multielectron ejection will at first continue to concentrate on atoms, seeking a full description of the multiionization process including angular disributions and angular correlations145 as well as energy distributions of the electrons. These studies will probably engender new techniques which may be even more complex when applied to molecules.
For the spectroscopy of molecular doubly charged ions by coincidence methods the newly appreciated prevalence of indirect ionization seriously changes the outlook. In the near-threshold region full three-dimensional PEPECO spectra are needed , but the best strategy may be to capitalize on indirect pathways by using inner shell ionization. Auger spectra can be simplified, perhaps to the point of full interpretability, by using PEPECO to select Auger spectra from single core hole states. Only one-parameter spectra are needed at a time, and the intensity of the double ionization process is enormously enhanced. While synchrotron radiation would have an advantage here it is worth noting that tunable radiation is not needed to create identifiable core holes; any monochromatic X-rays will do the job.
The mechanisms of multiply charged ion dissociation are a rapid growth area, and there is a good chance that an impact will be made by coincidence studies in the fashionable fields of femtosecond reaction dynamics and vector correlations. The realm of higher charge states is almost virgin territory, but it will be broached quite soon as synchrotron radiation users concentrate on inner shells. The possibility of charge localization effects on fragmentation pathways of multiply charged ions has attracted great interest and some "proof of principle" studies have already shown promise146. If fragmentation can indeed be directed by charge localization, methods based on PEPIPICO should have applications in structural analysis, perhaps to large biologically interesting molecules.
Applications of these coincidence methods in wider areas of chemistry have yet to be clearly demonstrated, though possibilities evidently exist. Some of the new techniques of mass spectrometry such as electrospray ionization and collision induced dissociation can very probably benefit from coincidence detection of the products of multicharged ion
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dissociations, but all such benefits come at a certain cost in experimental complexity. It is up to us, author and readers, to discover the points where the benefits outweigh the costs and to pursue them with vigour. The elegance and power of coincidence techniques to approach fundamental questions of physics and chemistry are rewards in themselves to those who pursue this work, rewards which are freely available to all who care to join us.
ACKNOWLEDGEMENTS
I should like to express my deep gratitude to many colleagues who have worked with me on multiple ionization, and without whom the work would never have reached the stage it has, particularly Pascal Lablanquie and Irene Nenner in Orsay and Steve Price and David Hagan in Oxford. I am also grateful to the SERC who have financially supported the research in Oxford.
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