A photoabsorption, photodissociation and photoelectron spectroscopy study of C6H6 and C6D6

Chemical Physics 229 Ž1998. 107–123

A photoabsorption, photodissociation and photoelectron spectroscopy study of C 6 H 6 and C 6 D6 E.E. Rennie a , C.A.F. Johnson a , J.E. Parker a , D.M.P. Holland M.A. Hayes b a

b,)

, D.A. Shaw b,

Department of Chemistry, Heriot-Watt UniÕersity, Riccarton, Edinburgh, EH14 4AS, UK b Daresbury Laboratory, Daresbury, Warrington, Cheshire, WA4 4AD, UK Received 28 July 1997; in final form 3 December 1997

Abstract The absolute photoabsorption, photoionisation and photodissociation cross-sections and the photoionisation quantum ˚ using a double ion efficiency of benzene and hexadeuterobenzene have been measured from the ionisation threshold to 350 A chamber and monochromated synchrotron radiation. The HeI excited photoelectron spectrum of C 6 D6 has been recorded and the vibrational structure exhibited in the X 2 E 1g , A 2 E 2g , E 2 B1u and F 2A 1g bands has been analysed with the aid of theoretical predictions and by analogy with the recently reported high-resolution photoelectron spectrum of C 6 H 6 . The ˚ and photoabsorption spectrum displays extensive vibrational structure extending from the ionisation threshold to ; 730 A, many of these absorption features have been arranged into Rydberg series. A detailed assignment of the vibrational progressions associated with some Rydberg states has been accomplished by making use of the corresponding photoelectron spectrum. A sum rule analysis has been carried out by combining the present absolute photoabsorption measurements with similar data covering the remaining wavelength regions. q 1998 Elsevier Science B.V.

1. Introduction The interpretation and characterisation of the electronic spectrum of benzene has long served as a benchmark for the development and testing of theoretical approaches designed to describe p-electron systems. As a consequence, numerous experimental and theoretical studies have been carried out on this prototype aromatic molecule, and these investigations have helped improve quantum mechanical theories concerning electronic structure in polyatomic molecules w1–3x. The high symmetry of benzene has

)

Corresponding author.

facilitated studies of the interactions between electronic states of differing symmetries, mixed by spin–orbit or vibronic coupling, and, in particular, the C 6 Hq 6 X state has long been known to be strongly influenced by Jahn–Teller phenomena. Jahn–Teller coupling effects have been predicted and observed in high Rydberg members of series converging onto the 2 C 6 Hq 6 X E 1g ionisation threshold and in the photoelectron spectra of the X 2 E 1g and A 2 E 2g states. The present work focuses on the assignments of the series converging onto the higher ionisation thresholds and on the vibronic structure exhibited within specific Rydberg states. The labelling system given ˚ w4x has been adopted for the by Bieri and Asbrink designation of the ionic states.

0301-0104r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 0 1 - 0 1 0 4 Ž 9 7 . 0 0 3 7 3 - X

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E.E. Rennie et al.r Chemical Physics 229 (1998) 107–123

The single-photon absorption spectrum of the valence shell of benzene and hexadeuterobenzene w5– 25x has been studied over a long period. Four Rydberg series have been observed converging onto the lowest ionisation threshold and at least three more onto higher limits. In addition, transitions into several low-lying valence states have been identified below the ionisation threshold. For many years the conclusive assignment of the Rydberg series converging onto the X 2 E 1g ionisation threshold remained uncertain, but recently significant progress has been achieved through multiphoton ionisation ŽMPI. experiments on cooled molecules w26–42x, and through the development of theoretical approaches which have allowed the accurate calculation of energy levels. As the molecular ground state of benzene is 1A 1g , electric dipole selection rules restrict single-photon transitions into states of ungerade electronic symmetry, although transitions into gerade symmetry states may be vibronically induced. Two- Žor even number. photon absorption allows g–g and u–u transitions to occur. Thus, multiphoton studies have enabled the Rydberg series of gerade symmetry converging onto the X 2 E 1g threshold to be investigated and assigned. Furthermore, threephoton resonant, four-photon ionisation, spectra have allowed the ungerade Rydberg series to be studied. As a result of these MPI studies the assignments of three of the four ungerade Rydberg series Žoriginally labelled R, RX , RY and RZ by Wilkinson w8x. and six gerade Rydberg series converging onto the X 2 E 1g threshold have now been placed on a firm basis. The two lowest lying virtual orbitals are 1e 2u and 1b 2g . Excitation of an electron from the 1e1g orbital into the 1e 2u orbital or the 1b 2g orbital gives rise to 1 B 2u , 1 B1u , 1 E 1u and 1 E 2g states. These singlet valence states have been studied in great detail w3,30x, and the corresponding triplet states have been observed in electron energy-loss spectra w43x. Although the assignments of transitions involving an electron from the 1e1g orbital are now firmly established, the Rydberg and valence transitions resulting from excitation of electrons from the more tightly bound orbitals are not so well characterised. The early photoabsorption spectra w5,10x revealed Rydberg series converging onto ionisation thresholds around 11.48 and 16.84 eV, and these series have been confirmed in more recent studies w13,16,22,25x

using photoelectric detection. It has now been established that the threshold at 11.48 eV corresponds to the removal of an electron from the 3e 2g orbital, and assignments have been proposed w17–19,23,25x for the two strong Rydberg series converging onto this limit based upon an interpretation of the vibronic structure observed in two Rydberg states. In the present study the photoabsorption spectrum encompassing the Rydberg series converging onto the A 2 E 2g ionisation threshold has been remeasured and interpreted with the aid of recently recorded photoelectron spectra of C 6 H 6 w44x, and C 6 D6 reported in this work. This has led to a reassignment of some of the vibrational structure displayed in the absorption spectrum. The valence shell molecular orbital sequence of benzene in its ground state ŽD6h symmetry. may be written as 2 4 2 Ž 2a lg . Ž 2e lu . 4 Ž 2e 2g . Ž 3a lg . Ž 2b lu . 2 Ž lb 2u . 2 Ž 3e lu . 44

4

2 Ž la 2u . Ž 3e 2g . Ž le lg . l A lg .

The HeI excited photoelectron spectrum of C 6 H 6 revealed vibrational structure in the X 2 E 1g , A 2 E 2g , C 2 E 1u , E 2 B 1u and the F 2A 1g bands w44x. The vibronic structure observed in the X 2 E 1g and the A 2 E 2g photoelectron bands is a consequence of dynamical Jahn–Teller effects, and these interactions have been investigated theoretically w45x. Calculations have also been carried out which reproduce the complex structure of the overlapping A 2 E 2g and B 2A 2u photoelectron bands w46x. Theoretical predictions for the energies of many of the discrete ŽRydberg and valence. transitions have been calculated w3,47,48x and the influence of shape resonances w49– 53x has been investigated. The effect of electron correlation on the satellite structure observed in the inner valence region of the photoelectron spectrum has also been examined w44,54x.

2. Experimental apparatus and procedure 2.1. Photoelectron spectroscopy studies The HeI excited photoelectron spectrum of hexadeuterobenzene was recorded using a hemispherical electrostatic energy analyser of 100 mm mean radius.

E.E. Rennie et al.r Chemical Physics 229 (1998) 107–123

Photoionisation takes place in a field-free cage constructed from graphite-coated copper mesh, and electrons ejected in a direction perpendicular to the radiation pass through three-element entrance and exit lenses before being detected with a channeltron. By using a mixture of benzene and argon, and measuring the width of the Ar 3p photoelectron peak, the resolution of the spectrometer during the present work was determined to be 16 meV FWHM. The spectra have not been corrected for the variation in the analyser transmission efficiency as a function of kinetic energy, and the binding energies of the photoelectron bands have been placed on an absolute scale by reference to well-established ionisation potentials w10,32,41,42x. The photoelectron bands corresponding to ionisation from the 1e1g , 3e 2g , 2b1u

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and 3a 1g orbitals were recorded and are shown in Fig. 1, together with the theoretical prediction for the X 2 E 1g state w45x. 2.2. Synchrotron radiation studies The photoabsorption cross-section and the photoionisation quantum efficiency were measured using a double ion chamber and synchrotron radiation emitted from the Daresbury Laboratory storage ring. The 5 m normal incidence monochromator w55x, and the experimental apparatus and procedure w56x have been described in detail previously. The double ion chamber incorporated a set of plates, two of which were used to collect the photoions. At the rear of the chamber the transmitted

Fig. 1. HeI excited photoelectron spectra of the X 2 E 1g , A 2 E 2g , E 2 B1u and F 2A 1g states of hexadeuterobenzene. The theoretical prediction for the X 2 E 1g photoelectron band, shown in the lower right-hand frame, has been taken from Eiding et al. w45x.

E.E. Rennie et al.r Chemical Physics 229 (1998) 107–123

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radiation struck a sodium salicylate screen and the resulting fluorescence was detected with a photomultiplier. This signal was used to deduce the incident photon intensity. Lithium fluoride or indium filters could be inserted into the photon beam between the monochromator exit slit and the entrance to the capillary to suppress higher-order radiation. A photoabsorption spectrum of benzene was measured by scanning the monochromator over the desired wavelength range and recording two electrometer currents, a reading proportional to the photomultiplier signal, and the gas pressure. The entire procedure was then repeated using argon, xenon or nitric oxide. For the inert gases it may be assumed that the photoionisation quantum efficiency is unity, whilst for nitric oxide the values reported by Watanabe et al. w57x were used. Hence the photoionisation quantum efficiency of benzene could be deduced. 3. Results and discussion 3.1. Photoelectron spectrum of C6 D6 An interpretation for some of the dominant features in the C 6 D6q X 2 E 1g and A 2 E 2g photoelectron

bands can be proposed by analogy with the recent high-resolution HeI excited photoelectron spectrum of C 6 H 6 w44x, and through a knowledge of the vibrational energies derived from the two-photon excitation study by Whetten et al. w30x and the laser-excited C 6 Hq X state spectra w31,38,39,42x. 6 The theoretical work concerning the dynamical Jahn–Teller effect in the X 2 E 1g and A 2 E 2g states w45x has also provided essential guidance in the assignment process. Eiding et al. w45x have shown that the vibronic structure in the C 6 Hq X 2 E 1g 6 photoelectron band arises from a three-mode linear Jahn–Teller effect, involving coupling of the y 6 , y 8 and y 9 vibrational modes, together with excitation of the symmetrical C–C stretching mode y 1. For convenience, the vibrational characteristics, symmetries and neutral ground-state energies are summarised in Table 1. For the A 2 E 2g state the dominant vibronic structure has been assigned in terms of a two-mode Žy 6 and y 8 . Jahn–Teller effect and the totally symmetric Žy 1 and y 2 . modes w46x, and the diffuseness of the B 2A 2u photoelectron band has been shown to be due to vibronic mixing with the A 2 E 2g band. For the X 2 E 1g state the first vibrationally excited feature in the experimental spectrum lies 79 meV

Table 1 Symmetries, characteristics and energies of the vibrational modes in the neutral ground states of C 6 H 6 and C 6 D6 w12,58,59x Vibrational mode

Symmetry

Characteristic Žfor C 6 H 6 .

C 6 H 6 vibrational energy ŽmeV.

C 6 D6 vibrational energy ŽmeV.

y1 y2 y3 y4 y5 y6 y7 y8 y9 y 10 y 11 y 12 y 13 y 14 y 15 y 16 y 17 y 18 y 19 y 20

a 1g a 1g a 2g b 2g b 2g e 2g e 2g e 2g e 2g e1g a 2u b1u b1u b 2u b 2u e 2u e 2u e1u e1u e1u

ring stretch CH stretch CH bend ring deformation CH bend ring deformation CH stretch ring stretch CH bend CH bend CH bend ring deformation CH stretch ring stretch CH bend ring deformation CH bend CH bend ring stretch and deformation CH stretch

123.3 395.6 169.4 87.7 122.8 75.4 393.5 199.2 146.0 104.9 83.6 125.2 379.0 162.3 142.5 49.4 119.9 128.7 185.2 394.4

117.4 292.9 131.8 74.3 102.8 72.0 289.1 193.9 107.5 81.8 61.5 120.3 283.3 159.5 102.6 43.1 97.6 101.0 166.4 290.9

E.E. Rennie et al.r Chemical Physics 229 (1998) 107–123

above the adiabatic peak, in exact agreement with the theoretical prediction w45x, and can be assigned to the 6 10 transition. To slightly higher binding energy another peak is observed which is separated from the adiabatic peak by 111 meV, compared to a predicted spacing of 121 meV. This feature probably contains significant contributions from the 9 10 and the 110 transitions, based upon the evidence provided by the more highly resolved laser-excited spectra w31,38,39,42x. In the calculated spectrum the next significant feature appears as a closely spaced doublet, with peaks separated by 199 and 213 meV from the adiabatic peak. The experimental spectrum shows little evidence of this doublet structure, but rather displays a broad peak located 205 meV from the adiabatic peak. This feature probably contains substantial contributions from the 110 6 10 transition, in agreement with the laser-excited studies, and the 6 03 transition. At higher binding energies the theoretical work indicates that the vibronic structure becomes complex and an interpretation in terms of dominant transitions is no longer feasible. Overall, the general agreement between the experimental and calculated spectrum is reasonably good, and most of the significant features have been predicted correctly. It appears that the agreement could be improved by slightly expanding the theoretical binding energy scale. In the experimental spectrum hot bands can be observed at energies below the adiabatic peak, and X state spectrum of by analogy with the C 6 Hq 6 Baltzer et al. w44x, contributions from the 6 10 Ž j s 12 ., 6 11Ž j s 23 . and 1611 transitions are probably present. The C 6 D6q X 2 E 1g photoelectron band has been measured previously w60,61x using HeI and hydrogen Lyman-a excitation sources, and the present results are in good overall agreement with these earlier studies. The only noticeable difference concerns the peak occurring at a binding energy of ; 9.45 eV which exhibits a weak doublet structure in the spectrum recorded with Lyman-a radiation. Unfortunately there is no theoretical prediction for the A 2 E 2g photoelectron band. The experimental spectrum shows two peaks lying 76 and 105 meV above the adiabatic peak, and these features probably contain significant contributions from the 6 10 Ž j s 12 . and the 9 10 transitions, respectively. Again, by analogy with the laser-excited spectra, the feature occurring 182 meV above the vibrationless peak probably

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encompasses the 8 10 , 110 6 10 and 6 03 transitions. However, a proper interpretation of the structure exhibited in the A 2 E 2g photoelectron band is not feasible without theoretical guidance. Recently, Goode et al. w42x have investigated the A 2 E 2g state, with vibrational resolution, by means of photoinduced Rydberg ionisation spectroscopy, and the results have been used to assess the Jahn–Teller and pseudo Jahn– Teller interactions. The vibrational structure associated with the C 6 D6q E 2 B1u photoelectron band is very similar to that in the corresponding band in C 6 H 6 and consists of several broad peaks. However, these peaks do not form a regular vibrational progression and their interpretation is not straightforward. Baltzer et al. w44x have suggested that there are two separate progressions in the y 2 mode, as shown in Fig. 1, with the second progression containing an additional excitation of some other vibrational mode, possibly y 1 w44x. An analysis of the present spectrum yields a value of 200 meV for y 2 . Baltzer et al. w44x have shown that the C 6 Hq 6 2 F A 1g photoelectron band can be interpreted in terms of a dominant progression in the y 1 mode, together with a second progression, also involving the excitation of y 1 , but with an additional single excitation of y 2 . The present spectrum gives values of 111 and ; 262 meV for the y 1 and y 2 modes, respectively. Baker et al. w60x give a value of 115 meV for y 1. 3.2. Photoabsorption studies of C6 H6 and C6 D6 3.2.1. OÕerall spectrum Figs. 2 and 3 show the absolute photoabsorption cross-sections and the photoionisation quantum efficiencies of C 6 H 6 and C 6 D6 , together with the thresholds for various ionic states. The present values of the cross-section for C 6 H 6 are in general accordance with those in the study reported by Person and Nicole w15x, but consistently higher than those given by Person w11x and Yoshino et al. w14x. The data recorded by Bunch et al. w9x are too scattered to allow a meaningful comparison. The double ionisation threshold of benzene occurs around 24.6 eV w62x and corresponds to the formation of the 3A 2g state. It appears unlikely that the present data display any features attributable to doubly ionised phenomena.

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Fig. 2. The absolute photoabsorption cross-section and photoionisation quantum efficiency of C 6 H 6 . The cross-section is referenced to the right-hand scale and the efficiency to the left-hand scale. Key for photoionisation quantum efficiency measurements: Ž — . present data, Ž,. Person w11x, Žn. Yoshino et al. w14x, Ž`. Rebbert and Ausloos w73x.

3.2.2. Rydberg series conÕerging onto the X 2 E1g ionisation threshold Grubb et al. w34x have summarised the ungerade and gerade Rydberg series converging onto the lowest ionisation threshold, excited in single- and multi-

photon studies. These series have not been investigated in the present work. However, they are of relevance, because, lacking any theoretical predictions for the quantum defects of Rydberg series converging onto the higher ionisation thresholds, the

Fig. 3. The absolute photoabsorption cross-section and photoionisation quantum efficiency of C 6 D6 . The cross-section is referenced to the right-hand scale and the efficiency to the left-hand scale. Key for photoionisation quantum efficiency measurements: Ž — . present data, Ž,. Person w11x.

E.E. Rennie et al.r Chemical Physics 229 (1998) 107–123

quantum defects observed for series converging onto the lowest ionisation threshold can be used as guidance in assigning the higher Rydberg series. In particular, Grubb et al. w32x have reported the variation, as a function of principal quantum number, in the quantum defects of ten Rydberg series converging onto the X 2 E 1g ionisation threshold. 3.2.3. Rydberg series conÕerging onto the A 2 E2 g ionisation threshold The absolute photoabsorption cross-sections of C 6 H 6 and C 6 D6 , between the ionisation threshold ˚ are shown in Figs. 4–6. This waveand 1050 A, length range encompasses Rydberg states belonging to series converging onto the A 2 E 2g ionisation threshold and two strong series, both of which have been observed previously w5,10,13,16,22,25x are marked. Dipole selection rules allow excitation of an electron from the 3e 2g orbital to form npŽe 1u . E 1u , nfŽe 1u . E 1u , nfŽe 2u . A 2u , nfŽb 1u . E 1u and nfŽb 2u . E 1u Rydberg series. An analysis of the present data for C 6 H 6 gives quantum defects of 0.29 and 0.47 for the two series, in good agreement with earlier investigations. It appears to be well established for benzene w32x, that a quantum defect of 0.46 should be associated with an npŽe 1u . series, and therefore this

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strong series has been assigned in previous work as 3e g ™ npŽe 1u . 1 E 1u . However, the designation of the other strong series is less certain. Rydberg series converging onto the second ionisation threshold of benzene and several isotopically substituted benzenes have been discussed by Itah et al. w17–19x. Based upon an analysis of vibronic structure and intensity patterns, they correlated the Rydberg series having d s 0.3 with 3e 2g ™ nfŽb 1u , b 2u , e 1u , e 2u . excitations. The present spectra allow the series with d s 0.29 and 0.47 to be observed up to n s 12 and n s 8, respectively. The n s 4 members of these series are fairly well separated from overlapping structure and Fig. 5 indicates that most of the features can be assigned by analogy with the A 2 E 2g state photoelectron spectrum of C 6 H 6 w40x and C 6 D6 Žpresent study.. The n s 6 members ˚ have been discussed in detail located around 1120 A w17–19x, and in the C 6 H 6 absorption spectrum recorded by Itah et al. four features were discernible. ˚ together A main peak was observed at 1119.6 A, with two additional features displaced by 640 and 920 cmy1 to higher energy, and another feature displaced by 240 cmy1 to lower energy. The first three of these features were attributed to one electronic state with the main peak representing the 0–0

Fig. 4. The absolute photoabsorption cross-section of C 6 H 6 , referenced to the left-hand scale, and C 6 D6 , referenced to the right-hand scale, ˚ All the assignments shown in the figure refer to the C 6 H 6 spectrum. in the wavelength range between the ionisation thresholds and 1210 A.

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Fig. 5. The absolute photoabsorption cross-section of C 6 H 6 , referenced to the left-hand scale, and C 6 D6 , referenced to the right-hand scale, ˚ in the wavelength range between 1145 and 1220 A.

transition and the peaks displaced by 640 and 920 cmy1 corresponding to transitions involving excitation of the y6 Že 2g . and the y 1Ža 1g . vibrational modes.

Itah et al. w19x observed similar structure in the absorption spectrum of C 6 D6 , where the corresponding additional peaks were displaced by 600 and 880

Fig. 6. The absolute photoabsorption cross-section of C 6 H 6 , referenced to the left-hand scale, and C 6 D6 , referenced to the right-hand scale, ˚ All the assignments shown in the figure refer to the C 6 H 6 spectrum. in the wavelength range between 1050 and 1150 A.

E.E. Rennie et al.r Chemical Physics 229 (1998) 107–123

cmy1 to higher energies. An inspection of Fig. 6 allows the features identified by Itah et al. as vibronic structure belonging to the d s 0.3, n s 6 Rydberg state to be reinterpreted. In the present spec˚ and is assigned as the trum a peak occurs at 1119.7 A adiabatic transition of the d s 0.3, n s 6 Rydberg state. The two features displaced by 640 and 920 cmy1 to higher energy are actually the 0–0 transitions of the n s 7, d s 0.47 and d s 0.29 Rydberg states, and the feature occurring ; 240 cmy1 to lower energy is the 0–0 transition associated with the n s 6 member of the d s 0.47 series. Thus we are left assigning the Rydberg series with a quantum defect of 0.29 as an nf series, ˚ beginning with the n s 4 member around 1180 A. Although d s 0.3 is rather large for an f term, Price et al. w63x have argued that such a value may be acceptable in a large molecule, such as benzene, where the quantum defect depends on the local atomic environment as well as on core penetration. Close inspection of the C 6 H 6 photoabsorption spectrum reveals two weak peaks located at 1225.7 ˚ Similar features are discernible in the and 1235.1 A. C 6 D6 spectrum but are slightly less prominent. The energy separation between the two peaks in C 6 H 6 is ; 77 meV, which could correspond to a single quantum of the y6 vibrational mode. Although transitions into the npŽa 2u . Rydberg series converging onto the A 2 E 2g ionisation threshold are dipole forbidden, it is conceivable that such transitions could be vibronically induced. Although such a proposal is speculative, it is possible that the two observed peaks form part of a vibrational progression belonging to the 3pŽa 2u . state. If it is assumed that the peak at ˚ corresponds to the second Žat least. mem1235.1 A ber of the vibrational progression, since the adiabatic transition would not be observed, then the Rydberg state located in this region would have a quantum defect of ; 0.05. Although this value is low compared to that for similar npŽa 2u . series in benzene w32,34x, it does provide a possible interpretation of the structure. The possibility of assigning the two peaks occur˚ in the photoabsorption ring at 1225.7 and 1235.1 A spectrum of C 6 H 6 as part of the vibrational progression associated with a Rydberg state belonging to a series converging onto the C 2 E 1u ionisation threshold was considered. For an n s 3 state this proposal

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results in a quantum defect of slightly greater than unity. Although this value lies within the range generally accepted for an s-type state, it is significantly larger than that found for other s-type Rydberg series in benzene where, typically, d f 0.8. Therefore this interpretation has been discounted. Clearly, additional experimental and theoretical work is required to resolve this issue.

3.2.4. Rydberg series conÕerging onto the B 2A 2 u ionisation threshold The photoelectron band corresponding to ionisation from the 1a 2u orbital shows no vibrational structure and has a vertical binding energy of 12.3 eV w44x. The theoretical work of Koppel et al. w46x ¨ predicts that the lowest lying line of A 2u symmetry occurs at a binding energy of ; 11.6 eV, and that the first few lines of this symmetry form a fairly simple pattern. These lines are A 2u vibronic levels of the 2 E 2g electronic state which gain their spectral strength by vibronic intensity borrowing from the higher 2A 2u electronic state. The vibronic levels lying above ; 12 eV form an essentially structureless quasicontinuum. In the photoelectron spectrum of benzene the B 2A 2u state band has a fairly high intensity, and therefore it appears reasonable to expect Rydberg states converging onto this threshold to be observed in the photoabsorption spectrum. Both ns and nd Rydberg series are dipole allowed following the excitation of an electron from the 1a 2u orbital. In the vicinity of the ionisation threshold there appears to be more continuum absorption than can be attributed solely to the 3e 2g ™ 3pŽe 1u . 1 E 1u transition and, from energetic considerations, it seems that some of this background intensity may be ascribed to the 1a 2u ™ 3sŽa 1g . 1A 2u transition. In the photoabsorption spectrum of C 6 D6 a prominent peak occurs around ˚ If it is assumed that the 3s Rydberg state 1320 A. ˚ then a quantum defect of 0.84 is occurs at 1320 A, obtained. Inserting this value into the Rydberg formula suggests that the n s 4 and 5 states should ˚ respectively. Thus it occur around 1134 and 1077 A, appears that 1a 2u ™ ns excitations may be responsible for some of the underlying spectral intensity in the vicinity of the ionisation threshold and in the ˚ Although this region between 1050 and 1150 A.

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latter region encompasses Rydberg states converging onto the A 2 E 2g ionisation limit, it appears that 1a 2u ™ 4s and 5s transitions contribute towards the general rise in cross-section. These proposals are in reasonable accordance with those of Koch and Otto w13x who tentatively assigned an ns series with d s 0.77 and an nd series with d s 0.16. It should be noted that since the absorption features associated with excitation from the 1a 2u orbital are structureless and broad, the quantum defect values derived from the present data are somewhat approximate. 3.2.5. Rydberg series conÕerging onto the C 2 E1u ionisation threshold Ionisation from the 3e 1u and 1b 2u orbitals gives rise to overlapping bands falling in the 13.6–15.3 eV binding energy range of the photoelectron spectrum w44x. The band associated with the C 2 E 1u state shows weak vibrational features with energy spacings of ; 78 meV, suggesting excitation of the y6 mode. In addition, the C 2 E 1u state is influenced by Jahn–Teller interactions and this results in two broad peaks with maxima occurring around 14.0 and 14.5 eV. Excitation of an electron from the 3e1u orbital may lead to the formation of ns and nd Rydberg series. The experimentally deduced quantum defects

will depend on the value chosen for the ionisation threshold, and the complex shape of the C 2 E 1u state photoelectron band makes this choice rather difficult. In the following discussion it has been assumed that the Rydberg series converge onto an ionisation threshold at 13.95 eV. The large peaks at 1019 and ˚ can be identified as the n s 3 and n s 4 949 A members of the nd series, with d s 0.24 and 0.08, respectively. Koch and Otto w13x give a quantum defect of 0.28 for this series. The broad peak under˚ can be lying the vibrational structure around 1117 A ˚ attributed to the 3s member, and the peak at 983.3 A to the 4s member. An analysis using the 4s peak position yields d s 0.82 for the ns series. Both series appear to die out for higher members; a possible explanation being the presence of a shape resonance modifying the overall intensity in this region Žsee Section 3.2.8.. Close inspection of the photoabsorption spectrum reveals several weak fea˚ which could be due to the higher tures around 920 A members, as shown in Fig. 7. The projected positions of the n s 5, 6 and 7 members of the d series and the 6s member approximately coincide with some of these features. The position of the 5s peak is less obvious and there appears to be some additional structure in the vicinity of the projected peak posi-

Fig. 7. The absolute photoabsorption cross-section of C 6 H 6 , referenced to the left-hand scale, and C 6 D6 , referenced to the right-hand scale, ˚ in the wavelength range between 870 and 1040 A.

E.E. Rennie et al.r Chemical Physics 229 (1998) 107–123

tion. Note also the presence of weak, vibrational like, structure on the 4s peak. The alternative explanation that the small peaks ˚ are due to vibrational levels is unlikely around 920 A as there is no obvious candidate for a Rydberg state with vibrational structure in this region. 3.2.6. Rydberg series conÕerging onto the E 2 B1u ionisation threshold The photoelectron spectrum of the E 2 B 1u band displays a complicated vibrational structure w44x which has yet to be unambiguously identified. Dipole selection rules allow the formation of only nd Rydberg states following excitation from the 2b1u orbital. The E 2 B 1u ionisation threshold occurs at ˚ w44x, and if we assume a quantum defect of 801.3 A 0.1, the location of the 3d Rydberg state would be ˚ Thus it is possible that the 2b1u ™ 3d around 895 A. ˚ transition contributes to the broad feature at 892 A. 3.2.7. Rydberg series conÕerging onto the F 2A 1g ionisation threshold A Rydberg series converging onto the F 2A 1g ionisation threshold has been observed previously w10,16x but the present study ŽFig. 8. enables the vibrational structure associated with the n s 3–6

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states to be examined in greater detail. Several vibrational members are discernible in each progression. For the n s 3 and n s 4 states, the vibrational spacings in C 6 H 6 are 116 and 120 meV, respectively, with the corresponding values in C 6 D6 being 115 and 120 meV. The present results for C 6 H 6 are in good agreement with those reported by El-Sayed et al. w10x. The vibrational structure observed in the absorption spectrum is similar to that displayed in the corresponding photoelectron band w44x and may be associated with excitation of the y 1 mode. An analysis of the Rydberg series converging onto the F 2A 1g ionisation threshold yields a quantum defect of 0.47, which suggests that this series should be assigned as npŽe 1u . 1 E 1u . 3.2.8. The influence of shape resonances on the photoabsorption cross-section Horsley et al. w49x have performed an experimental and theoretical investigation on the influence of shape resonances in the K-shell photoabsorption spectrum of benzene. Their multiple scattering X a calculations predict shape resonantly enhanced transitions into the 1e 2u Ž p ) . and 1b 2g Ž p ) . orbitals located 5.5 and 1.8 eV below the K-shell ionisation threshold with relative intensities of 1.0 and 0.43,

Fig. 8. The absolute photoabsorption cross-section of C 6 H 6 , referenced to the left-hand scale, and C 6 D6 , referenced to the right-hand scale, ˚ in the wavelength range between 720 and 870 A.

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respectively. Above threshold, shape resonantly enhanced transitions into the 4e 1u Ž s ) ., 4e 2g Ž s ) . and 1a 2g Ž s ) . orbitals are calculated to occur at 2.4, 6.8 and 10.3 eV above the ionisation limit with relative intensities of 1.54, 0.05 and 0.35, respectively. In regard to valence shell excitation, dipole selection rules allow shape resonantly enhanced transitions from the 1e 1g , 3e 2g and 3a 1g orbitals into the 4e 1u orbital. Taking into account the tendency for the positions of shape resonances involving valence shell excitation to move a few eV towards higher energy compared to K-shell locations, it is possible that the 1e 1g ™ 4e 1u and 3e 2g ™ 4e1u shape resonantly enhanced transitions might contribute to the general rise in absorption cross-section between 950 and ˚ and that the 3a 1g ™ 4e1u transition could oc800 A, ˚ Two cur around the intensity maximum at 700 A. very broad and weak features are discernible around ˚ It is possible that excitations from 515 and 600 A. ungerade symmetry valence orbitals into the 4e 2g and 1a 2g orbitals might contribute to these features. However, the calculations predict that the relative intensities of these transitions are weak. 3.3. Oscillator strength moments and sum rules The use of oscillator strength moments and sum rules to evaluate photoabsorption and photoionisa-

tion cross-sections has been reviewed by Berkowitz w64x. The generalised formula for the moments may be expressed as SŽ p. s

Ž 4 p a0ra 0 . pa 02 a0

p

l0

H0

s Ž l . lyŽ pq2. d l ,

where a 0 is the Bohr radius and a 0 is the fine structure constant. The integration extends from the absorption threshold l0 . SŽ0. is equal to the number of electrons in the molecule. SŽy2. is related to the electric dipole polarisability, a N , by a N s 4 a30 SŽy2.. Although benzene is a remarkably popular molecule for experimental study, surprisingly few measurements of the absolute photoabsorption cross-section have been reported, and, to the best of our knowledge, only two previous investigations have been carried out on C 6 D6 w11,22x. At excitation energies below the ionisation threshold, the best measurements appear to be those obtained by Pantos et al. w20x who reported the absolute cross-section ˚ The present measurebetween 1347 and 2700 A. ˚ ments extend to a short-wavelength limit of 350 A, but, as far as we are aware, the only absolute measurements at shorter wavelengths have been carried out over a very limited range in the vicinity of the carbon K-shell edge w65,66x. Consequently the atomic

Fig. 9. The absolute photoabsorption cross-section of C 6 H 6 .

E.E. Rennie et al.r Chemical Physics 229 (1998) 107–123

X-ray absorption data of Henke et al. w67x have had to be employed in several regions. Unfortunately, the C 6 H 6 absorption cross-section derived using the values of Henke et al. does not join smoothly onto the ˚ Therefore, we have used the present results at 350 A. ˚ and then inserted a data of Henke et al. to 250 A straight line. Another difficulty concerns the K-shell measurements w65,66x which exhibit significant differences in magnitude. As we are not in the position to judge which is the better measurement, we have carried out sum rule analyses using each set. A composite cross-section has been compiled using the data of Henke et al. w67x, Akimov et al. w65x, Pantos et al. w20x, together with the present results, and is shown in Fig. 9. The results of our sum rule analysis are given in Table 2. The electric dipole polarisability can be calculated from SŽy2., and yields a N s 9.81 = 10y2 4 cm3, in comparison with the direct experimental value w68x of 10.4 = 10y2 4 cm3. Berkowitz has defined a parameter Si Žy1. as the ionisation component of SŽy1.. This parameter has ˚ and the ionisation been evaluated between 350 A threshold from the product of the photoionisation quantum efficiency and the absolute photoabsorption cross-section measured in the present study, and yields a value of 13.54. For shorter wavelengths we have assumed that the photoabsorption and photoionisation cross-sections are equivalent and use the photoabsorption cross-section. We obtain Si Žy1. s ˚ and 15.99 for the wavelength range between 1.25 A threshold. Rieke and Prepejchal w69x have reported a directly measured value of 17.54. Table 2 Results of sum rule analysis Wavelength range ˚. ŽA

SŽy1. 2.445a 2.107 b

SŽy2.

1.25–350

18.623 a 19.278 b

350–1345

20.669

14.871

11.826

1345–2698

1.182

2.230

4.240

40.474 a 41.129 b

19.546 a 19.208 b

16.555a 16.556 b

Total a

SŽ0.

0.489 a 0.490 b

Si Žy1. 2.445a 2.107 b 13.541

15.986 a 15.648 b

Results obtained using Henke et al. w67x and Akimov et al. w65x. Results obtained using Henke et al. w67x and McLaren et al. Žcited in Piancastelli et al. w66x..

b

119

3.4. Photoionisation quantum efficiency When a molecule is excited into a neutral state lying above the ionisation threshold, the photoionisation quantum efficiency, defined as the ratio of the number of ions created to the number of photons absorbed, may be less than unity. Under such circumstances the excited state may decay either by fluorescence from the parent molecule or by dissociation into neutral fragments. The probability of fluorescence decay from the excited parent molecule is small enough to be neglected. However, neutral photodissociation cross-sections often remain significant for several electron volts above the ionisation threshold w70,71x, and may be composed of contributions from direct and indirect processes. The indirect processes are due to transitions into Rydberg states which subsequently predissociate to form neutral fragments. Such processes lead to the occurrence of prominent structure in the photodissociation crosssection w72x. Alternatively, the excited state may decay by autoionisation resulting in the creation of an ion. The competition between predissociation and autoionisation reveals itself directly as a variation in the photoionisation quantum efficiency. Figs. 2 and 3 show the photoionisation quantum efficiencies for C 6 H 6 and C 6 D6 , respectively, together with previous measurements. The agreement between the various sets of results is reasonable. However, the detailed structure discernible only in the present data illustrates the advantage of being able to vary the excitation wavelength in a continuous manner. Close inspection reveals that peaks in the absorption spectrum coincide with local minima in the photoionisation quantum efficiency, indicating that predissociation into neutral products competes successfully with autoionisation in the decay of these excited states. Both g H and g D increase quite rapidly from their ionisation thresholds and reach a value of ; 0.65 ˚ and then pass through a broad miniaround 1200 A, ˚ This minimum in g mum between 1050 and 1120 A. appears to coincide with a broad structured maximum in the photoabsorption spectrum. At shorter wavelengths, two additional minima in the photoionisation quantum efficiency occur around 900 and ˚ Although the minimum at 950 A˚ seems to 950 A. coincide with the prominent peak in the absorption

120

E.E. Rennie et al.r Chemical Physics 229 (1998) 107–123

spectrum attributed to the 3e1u ™ 5s and the 3e1u ™ ˚ 4d transitions, the significant dip in g around 900 A does not appear to correlate with a particularly strong discrete transition. It is noticeable that the two fea˚ in the C 6 H 6 tures located at 1225.7 and 1235.1 A absorption spectrum, and the corresponding features in the C 6 D6 spectrum, coincide with local minima in their respective photoionisation quantum efficiencies. Although these features are clearly observable in the absorption spectra they are barely discernible in their photoionisation cross-sections. Very similar characteristics were observed recently for two peaks occur˚ in the ethylene photoabsorption ring around 1100 A spectrum w71x. Staib and Domcke w74x have carried out a theoretical study of Jahn–Teller coupling effects in the doubly degenerate Rydberg series converging onto the X 2 E 1g ionisation threshold. Photoionisation and photoabsorption cross-sections have been calculated ˚ and the from the ionisation threshold to ; 1306 A, decay of high-n Rydberg states converging onto vibrationally excited states of the ion has been examined. In particular the competition between vibrational autoionisation and predissociation into neutral products has been considered. The results show that vibrational autoionisation is strongly quenched by competing radiationless-decay channels, and, further-

more, that autoionisation of the np 1A 2u series is much stronger than that of the np 1 E 2u series. Unfortunately, it is not feasible to carry out a meaningful comparison between these theoretical predictions and the present experimental results, because in the relevant wavelength region the 3e 2g ™ 3pŽe 1u . transition gives rise to several intense features which overshadow the effects due to excitation of the 1e 1g electron to high n states. However, the future development of this approach to include electronic autoionisation would be of great interest because this decay mechanism exerts a major influence in the wavelength range under investigation. Measurements of the photoionisation quantum efficiency, which directly reflect the competition between electronic autoionisation and neutral predissociation, could then be used to assess the theoretical predictions. 3.5. Photoionisation and photodissociation crosssections Figs. 10 and 11 show the absolute photoionisation, and the absolute photodissociation, cross-sections for C 6 H 6 and C 6 D6 , respectively. The photoionisation cross-section has been obtained from the present measurements by the product of the absolute photoabsorption cross-section and the photoionisa-

Fig. 10. The absolute photoionisation cross-section, referenced to the left-hand scale, and the absolute photodissociation cross-section, referenced to the right-hand scale, of C 6 H 6 .

E.E. Rennie et al.r Chemical Physics 229 (1998) 107–123

121

Fig. 11. The absolute photoionisation cross-section, referenced to the left-hand scale, and the absolute photodissociation cross-section, referenced to the right-hand scale, of C 6 D6 .

tion quantum efficiency. The absolute photodissociation cross-section is then given by the difference between the photoabsorption and photoionisation cross-sections, assuming that fluorescence decay can be neglected. Relative photoionisation yield curves of the benzene parent and fragment ions have been measured previously w75–78x, and the data indicate that the proportion of fragment ions is small for wavelengths ˚ Hence between the ionisation longer than ; 900 A. ˚ threshold and 900 A the C 6 Hq 6 yield curve should be similar to the absolute photoionisation cross-section, and comparisons between the spectra reported by Dibeler and Reese w75x and Akopyan and Vilesov w76x, and the present data, show that this is the case. Several step-like features, associated with vibrational excitation, can be discerned close to threshold in the photoionisation spectrum. The absolute photoionisation cross-section of benzene has been calculated by Kilcoyne et al. w52x. A comparison between the theoretical curves and the present results reveals some similarities, in particular, the prominent maxi˚ but a detailed comparison is, as mum around 700 A, yet, not possible. The photodissociation cross-sections for C 6 H 6 and C 6 D6 remain significant several electron volts above the ionisation threshold and both exhibit a ˚ and a weaker substantial peak centred around 1100 A ˚ feature around 900 A. In this respect the photodisso-

ciation spectrum of benzene is very similar to that of ethylene w71x which displays a prominent feature ˚ and a secondary maximum around around 1025 A ˚ 875 A.

Acknowledgements We thank the EPSRC for financial support and a CASE Studentship ŽEER., and the staff of Daresbury Laboratory for their efficient operation of the storage ring.

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