A study of the inner-valence ionization region in HCl and DCl

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1 See discussions, stats, and author profiles for this publication at: A study of the inner-valence ionization region in HCl and DCl Article in Journal of Physics B Atomic Molecular and Optical Physics March 2004 Impact Factor: 1.98 DOI: / /37/6/003 CITATIONS 4 READS authors, including: Michael Martins University of Hamburg 152 PUBLICATIONS 2,744 CITATIONS Stacey L Sorensen Lund University 178 PUBLICATIONS 3,131 CITATIONS SEE PROFILE SEE PROFILE Olle Björneholm Uppsala University 230 PUBLICATIONS 4,646 CITATIONS Raimund Feifel University of Gothenburg 180 PUBLICATIONS 2,483 CITATIONS SEE PROFILE SEE PROFILE Available from: L Mauritz Andersson Retrieved on: 12 May 2016

2 INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS J. Phys. B: At. Mol. Opt. Phys. 37 (2004) PII: S (04) A study of the inner-valence ionization region in HCl and DCl F Burmeister 1,8, L M Andersson 2, G Öhrwall 1, T Richter 3, P Zimmermann 3, K Godehusen 4, M Martins 5, H O Karlsson 2, S L Sorensen 6, O Björneholm 1, R Feifel 1,9, K Wiesner 1, O Goscinski 2, L Karlsson 1, S Svensson 1 and A J Yencha 7 1 Department of Physics, Uppsala University, Box 530, S Uppsala, Sweden 2 Department of Quantum Chemistry, Uppsala University, Box 518, S Uppsala, Sweden 3 TU-Berlin, Institut für Atomare Physik, Hardenbergstrasse 36, D Berlin, Germany 4 BESSY GmbH, Albert-Einstein-Strasse 15, D Berlin, Germany 5 Institut für Experimentalphysik, Luruper Chaussee 149, D Hamburg, Germany 6 SLF, Institute of Physics, University of Lund, Box 118, S Lund, Sweden 7 Department of Chemistry, State University of New York at Albany, Albany, NY 12222, USA yencha@albany.edu Received 6 November 2003 Published 2 March 2004 Online at stacks.iop.org/jphysb/37/1173 (DOI: / /37/6/003) Abstract An in-depth photoionization study of the inner-valence electrons in HCl and DCl has been performed using synchrotron radiation. A series of photoelectron spectra of HCl were obtained at a resolution of 23 mev over the binding energy range ev at various excitation energies and at two different electron collection angles relative to the plane of polarization of the undulator radiation. In addition, photoelectron spectra of DCl were recorded at two different excitation energies. These spectra were compared directly with the threshold photoelectron spectra of HCl and DCl that were recorded previously under similar resolution conditions ( 30 mev). This comparative study reveals new information on the nature of the numerous band systems observed in this binding energy region. In addition, we present the experimental confirmation of the theoretical prediction given by Andersson et al (2001 Phys. Rev. A ) that a vibrational progression showing interference structure would appear in the main inner-valence ionization band in the photoelectron spectrum of DCl at a resolution of 10 mev. 8 Present address: BESSY GmbH, Albert-Einstein-Strasse 15, D Berlin, Germany. 9 Present address: Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, UK /04/ $ IOP Publishing Ltd Printed in the UK 1173

3 1174 F Burmeister et al 1. Introduction The study of ionization of atoms and molecules has led to a significant good understanding of the electronic structures of both neutral and ionic species and has paved the way for a theoretical interpretation of numerous physical properties. One such property is that of electron correlation in ionization, i.e. where the ejection of an electron induces a correlated reaction of other electrons within the system. Such correlation effects are well known in the ionization of core electrons in most atomic and molecular systems. On the other hand, correlation effects are largely absent in the ionization of outer-valence electrons. The electronic nature of inner-valence states is intermediate between core and outer-valence states and theory and experiment often do not agree. Even in the rare gases, correlation effects are found to be important in inner-valence ionization [1]. In general, the inner-valence region of cations consists of numerous discrete states that can be described as either single or multiple hole states. One method of studying these states is photoelectron spectroscopy (PES), whereby a monochromatic photon source, of energy in excess of the ionization potential of the molecule, is used to achieve ionization. The spectrum shows rovibronic band systems related to the final ionic states formed. The great utility of PES lies in the fact that, in the absence of resonance states coinciding with the photon energy, the ionization process can be viewed as a direct ionization event controlled by the Franck Condon (FC) principle and the sudden approximation, whereby electron ejection occurs on a time scale very much faster than nuclear motion. The allied field of threshold photoelectron spectroscopy (TPES) provides similar information with regard to direct ionization in molecules but in addition affords information on indirect autoionization processes. In TPES, ionization is accomplished by scanning the photon energy (usually synchrotron radiation) through the energy range of interest. The resulting TPE spectrum, obtained by collecting only electrons of almost zero kinetic energy, reveals the rovibronic band systems that are related to the final ionic states of the molecule created at their threshold energies. These band systems are often found to be significantly different from those observed in the PE spectrum. Because of the complementary nature of these two types of spectroscopies, more information can be gained about the ionization behaviour of molecules through comparative studies. In this report, we focus on the photoionization of the inner-valence electrons in HCl and DCl by the methods of PES and TPES. Numerous previous reports on studies of the inner-valence ionization of these molecules have appeared using the methods of PES [2] and TPES [3, 4], but to our knowledge no direct comparative study has yet been performed. 2. Experimental details The PE spectra of HCl and DCl reported here were recorded at several locations and under different conditions. These are detailed below. A series of PE spectra of HCl was recorded using a Scienta SES-200 hemispherical electron energy analyser at the photon excitation energies of 40, 50 and 60 ev measured at the magic angle of 54.7 relative to the polarization vector of the synchrotron light on the undulator beamline at the advanced light source (ALS) facility in Berkeley, CA. In addition, another PE spectrum was recorded using an excitation energy of 50 ev at an angle of 90 relative to the polarization vector of the synchrotron light. The photoelectron linewidths (FWHM) were determined to be 23 mev. The HCl sample gas was degassed at liquid-nitrogen temperature just prior to use to ensure the complete removal of any hydrogen gas that may

4 A study of the inner-valence ionization region in HCl and DCl 1175 have been present due to the decomposition of the sample within the storage cylinder. HCl was obtained from the Aldrich Chemical Co. (Milwaukee, WI) with a stated purity of 99+%. The high-resolution DCl PE spectrum presented in this paper was measured at the undulator beamline U125/2-SGM (BUS-beamline) [5] at Berliner Elektronenspeicherring für Synchrotronstrahlung, BESSY, using a hemispherical electron analyser Scienta SES-2002 at the magic angle of 54.7 relative to the polarization vector of the synchrotron radiation. The spectrum was smoothed using a Gaussian function with a FWHM of 3 mev. The photon energy used was 40 ev. The photoelectron linewidth (FWHM) of the spectrum was determined to be 10 mev. Another DCl PE spectrum presented here was obtained at the undulator beamline I411 [6] connected to the third-generation electron storage ring MAX II at MAX-Lab in Lund, Sweden using a hemispherical electron analyser Scienta SES-200 at the magic angle of 54.7 relative to the polarization vector of the synchrotron radiation. The photon energy used was 64 ev. The photoelectron linewidth (FWHM) of the spectrum was determined to be 30 mev. In both DCl experiments, the PE spectra were obtained using a crossed-beam configuration. The DCl used in these studies was produced by reacting D 2 SO 4 with NaCl. The TPE spectra of HCl and DCl given here for comparative purposes were taken from the work of Yencha et al [4]. The spectra were recorded on beamline 3.2 of the synchrotron radiation source of the Daresbury laboratory. Photons emanating from the electron storage ring were dispersed by a 5 m McPherson monochromator prior to entering the experimental apparatus. A penetrating-field electron spectrometer [7, 8] was tuned to accept near threshold electrons (<20 mev, although 95% of the electrons were within 3 mev of threshold). The energy resolution obtained was 30 mev. The energy scale of all the presented HCl and DCl spectra was established by aligning the H 1, v + = 0, peak position in the respective isotopomer using the absolute energy values established in [4]. These peaks are identified with an asterisk ( ) in table 1 and in figures 1 4. The purity of all gases used was carefully controlled by measuring the outer-valence electron spectra. All spectra presented were recorded at the ambient room temperature. 3. Results and discussion 3.1. PES/TPES In figure 1 the inner-valence photoionization bands are shown for HCl and DCl. Spectra (b, d and e) were recorded using PES with the spectrometer set to the magic angle (54.7 ). TPES was used to obtain spectra (a and c) taken from Yencha et al [4]. Spectrum (e) (hυ = 64 ev) was published previously [9] in partial form. All the PES spectra are dominated by the broad-band system between binding energies 25.2 and 27.5 ev, that is associated with a continuum electronic state. Furthermore, several vibrational progressions appear in the spectra. These are labelled with notations F-L, according to the convention used in the previous TPES study of HCl and DCl [4], with some slight modifications. The peak energy positions of these features for HCl + and DCl + are given in table 1 for both TPES and PES studies. Vibrational progression G 2 in the PE spectra (b, d and e) exhibits a peculiar interference pattern with the broad-band system between 26 and 27 ev. This has recently been shown to be due to non-adiabatic coupling between a bound and a repulsive electronic state [9, 10]. (Vibrational progressions G 2 and H 1 are denoted as A and B, respectively, in these references.) The TPE spectra (a and c) show both the continuum band system and the vibrational progression G 2, but the interference pattern is absent. Also, this progression is as prominent in the DCl + spectrum (c) as it is in the HCl + spectrum (a). In contrast, in

5 1176 F Burmeister et al Table 1. Peak energy positions (in ev) for the inner-valence ionization region of hydrogen chloride and deuterium chloride from figure 1. The asterisk ( ) peak is the reference peak for the absolute energy calibration. The peaks marked with a dagger ( ) are features whose energy value was obtained using the 90 PE spectrum in figure 2. Band HCl + DCl + Band HCl + DCl + system v +a PES b TPES c PES b TPES c system v +a PES b TPES c PES b TPES c F H F H I G J G K L H a Vibrational quantum numbers refer to present work. b Present work. c [4]. the DCl PE spectrum (e) this progression is much weaker than in the HCl PE spectrum (b). The weakness of this progression in DCl has recently been attributed to a combination of lower resonance intensity and a limited experimental resolution requiring higher resolution conditions to be observed [10]. The reason that this interference is not observed in the TPE spectra is likely due to the dominance of autoionization effects (to be discussed further in section 3.5). For higher binding energies, the energy positions of the band systems shown in figure 1 of the PE and TPE spectra are similar (see table 1), but the intensities differ significantly with the latter being generally more intense. This is, again, most likely due to autoionization contributions to the TPE spectra. On the lower-binding energy side of the broadband around 26 ev, the TPE spectra show structured features (labelled F 1 and F 2 in spectra (a and c)) that do not appear in the PE spectra (b, d and e). These additional features in the TPE spectra cannot be solely due to autoionization effects because the same structure appears in the

6 A study of the inner-valence ionization region in HCl and DCl 1177 Figure 1. Inner-valence photoionization bands of HCl and DCl measured by either threshold photoelectron spectroscopy (TPES) or photoelectron spectroscopy (PES) as indicated in the panels. The asterisk ( ) peak is the reference peak for absolute energy calibration. Figure 2. Expanded-view comparison of the hυ = 50 ev PE spectra of HCl measured at 54.7 and 90 with respect to the plane of the polarization of the undulator radiation. The spectra were intensity normalized to the continuum band system at 26 ev. The asterisk ( ) peak is the reference peak for absolute energy calibration. hυ = 50 ev PE spectrum of HCl measured at 90 with respect to the plane of polarization of the undulator radiation as shown in figure 2. Rather this suggests the presence of additional states. Furthermore, a second vibrational progression, denoted as G 1, appears on the higherbinding energy side of the broadband for the 90 PE spectrum. Interestingly, the bands in the

7 1178 F Burmeister et al Figure 3. Angle-resolved hυ = 50 ev PE spectra of HCl in the inner-valence photoionization region recorded at the magic angle (54.7 ) and at 90 with respect to the plane of polarization of the undulator radiation. The spectra were intensity normalized with respect to the background at high binding energies. The asterisk ( ) peak is the reference peak for absolute energy calibration. vibrational progression G 1 in the PE spectrum show Fano-type profiles. This suggests that the origin of the interference is similar to those observed in the G 2 vibrational progression discussed above, i.e. the non-adiabatic coupling between a bound and repulsive electronic state. From the closeness of the energy positions of these interferences in the G 1 and G 2 vibrational progressions, it can be inferred that the same repulsive state is involved in both systems Angle-dependent PES In figure 3, the full, angular-resolved PE spectra of the inner-valence bands of HCl + are shown. As can be seen, essentially all vibrational features in the 54.7 PE spectrum are enhanced relative to the 90 PE spectrum. This indicates that the anisotropy in the angular distribution of the photoelectrons is very strong with a large asymmetry parameter β [2]. This suggests that all the features in the spectra have a common element present in their electronic structure, namely one involving the (4σ ) 1 ionization. Since the 4σ orbital is composed mainly of the Cl 3s atomic orbital, it is expected that the formation of ionic states having a substantial component of the 4σ orbital will exhibit a large β value. The spectra were intensity normalized to the background at high binding energies. We are aware that the background signal cannot in general be expected to have an isotropic angular distribution. The background signal originates from shake-off electrons, which typically have a small, positive beta value [11, 12]. The qualitative discussion above is, however, valid even if we consider such a correction to the β value. Due to the uncertainty of the normalization of the spectra, we do not attempt to present a quantitative interpretation Energy-dependent PES In figure 4 we present the excitation-energy-dependent PE spectra of HCl and DCl. As can be seen, few differences can be noted in the band systems observed indicating that the photoionization cross sections for all systems have similar energy dependences. We do note,

8 A study of the inner-valence ionization region in HCl and DCl 1179 Figure 4. Photoelectron spectra of HCl and DCl in the inner-valence photoionization region recorded at different photon excitation energies. The asterisk ( ) peak is the reference peak for absolute energy calibration. however, that the (hυ = 40 ev) PE spectrum of HCl exhibits a rising background for high binding energies (i.e. lower electron kinetic energies). The reason for this behaviour is probably due to the scattering of low-energy electrons. In the (hυ = 60 ev) PE spectrum of HCl a new broad feature appears between 27.8 and 28.1 ev binding energy, for which we have no explanation Avoided crossing In figure 5, the PE spectra of the main inner-valence photoionization band denoted as (4σ ) 1 are presented in detail for the DCl and HCl molecules. The broad profile of this band system is due to the steep ionic-state potential energy curve in the Franck Condon region. Within this continuum band system, two vibrational progressions denoted as G 2 and H 1 appear, reflecting the existence of two bound states in the energy region of the continuum state. Vibrational progression H 1 is suggested to correspond to the electronic configuration (4σ ) 2 (5σ ) 2 (2π) 2 (1δ) 1, i.e. a 2h1p state with two holes in the 2π orbital and one particle in a δ Rydberg orbital [4, 13]. It consists of a series of Lorentzian-type peaks that lie on the high-energy tail of the band system corresponding to the continuum state. Since no interference features are observed we conclude that the Fano parameters are large. This means that the interaction between this state and the continuum state is weak or non-existent. No potential curve has been found in the literature that can be assigned to the vibrational progression H 1. Vibrational progression G 2 on the other hand exhibits Fano-like interference in the spectra, as shown in figure 5 and in the papers by Burmeister et al [9] and Andersson et al [10]. There are two main differences between the vibrational progression G 2 in DCl + and HCl +, namely a factor 1/ 2 smaller energy separation between the vibrational bands in DCl + due to difference in reduced mass

9 1180 F Burmeister et al Figure 5. The major inner-valence photoionization bands (4σ ) 1 of DCl and HCl are shown as dotted data points. A broad band corresponding to a dissociative electronic state dominates the region. Two vibrational progressions G 2 and H 1 are indicated. The peaks in vibrational progression H 1 have symmetric line shapes, whereas vibrational progression G 2 exhibits an interference pattern. The solid curves correspond to theoretical simulations. and the weaker and narrower shape of the Fano profiles for DCl +. The latter will be discussed below. Also included in figure 5 are theoretical simulations of the spectra convoluted with Gaussian functions to represent the experimental resolution of 10 mev FWHM for DCl + and 23 mev FWHM for HCl +. The simulations were carried out as in the previous work by Andersson et al [10], which in short consists of solving the time-dependent Schrödinger equation for the nuclear dynamics on two coupled potential curves. The autocorrelation function for an initial state derived from the neutral molecule vibrational ground state is Fourier transformed to produce the photoionization spectra. The assumption for the simulations is that the outgoing electron does not interact with the rest of the molecules. For the ionicstate potential energy curves, we assume a Morse potential for the bound diabatic curve (1h in figure 6) and a repulsive exponential for the unbound diabatic curve (2h1p in figure 6) with a position independent coupling [9, 10, 14]. With experimental dissociation limits five free parameters remain. The potentials used in the simulations are shown in figure 6 and were determined from a fit to the previous lower resolution HCl spectrum [9, 10]. The same potentials are now used for the present higher resolution spectra for HCl and DCl. A table containing the Fano parameters as well as a detailed description of the potential energy curves used can be found in the paper by Andersson et al [10]. An understanding of the weaker and narrower shape of the Fano resonances in the DCl + spectrum shown in figure 5 is based upon the potential curve scheme shown in figure 6.

10 A study of the inner-valence ionization region in HCl and DCl 1181 Figure 6. Potential energy curves for the electronic states of interest for the interference patterns shown in figure 5. The associated adiabatic (diabatic) states with assignments are shown as solid (dashed) lines. The Franck Condon region between 1.16 and 1.39 Å is shown. The avoided crossing influences the adiabatic states around R C = 1.6 Å. The potential energy curve associated with vibrational progression H 1 in figure 5 is not included here. On the left-hand side of the figure, the HCl and DCl spectra are included in a Franck Condon projection scheme. The broad band is associated with the adiabatic dissociative electronic state 3 2 +, whereas the vibrational progression denoted as G 2 in figure 5 is associated with the adiabatic bound electronic state whose vibrational levels are shown here for HCl +. Here, four potential curves are plotted. The adiabatic curves and (solid-line curves) stem from the work of Hiyama and Iwata [14]. The dashed-line curves represent the related diabatic potential curves, corresponding to the electronic configurations (4σ ) 1 (one hole: 1h) and (5σ ) 2 (6σ ) 1 (two holes one particle: 2h1p). The potential curve representing the vibrational progression H 1, see figure 5, is not included. The vibrational progression G 2 is associated with the adiabatic potential curve 4 2 +, as shown in the Franck Condon projection scheme in figure 6 for HCl +. Both HCl + and DCl + clearly exhibit Fano-type interference patterns (see figures 5 and 6) but they are weaker and narrower in the case of DCl +. The reason for these effects is as follows [9, 10]. The bound adiabatic electronic state is populated more so in HCl + than in DCl + because of its lighter mass, and consequently its higher nuclear velocity allows for a more favourable non-avoided crossing behaviour, according to a Landau Zener type approach, see, e.g., [15]. In the paper by Andersson et al [10], simulations demonstrate the appearance of vibrational progression G 2 in DCl + at higher resolution, and the prediction was made that the structure would appear at an experimental resolution of 10 mev. The DCl + spectrum presented in figure 5 clearly confirms that prediction Origin of inner-valence vibrational band systems Now we address the origin of the vibrational band systems shown in figure 1 (F-L). In the binding energy range between 25 and 30.5 ev there are minimally 11 vibrational systems identified, most of which show well-defined patterns. In the recent papers by Burmeister et al [9] and Andersson et al [10], it was assumed that the bound state responsible for the vibrational structure of system G 2 in figure 1 (spectra (b and e)) was mainly due to the innervalence adiabatic state as described above. This was based on the assignment given by Hiyama and Iwata [14] in their ab initio calculations of the adiabatic potential energy curves for HCl +. However, we note that in these calculations the authors intentionally did not include Rydberg configurations in their basis set. According to the ab initio calculations of von Niessen et al [13], who did include many Rydberg-type functions in their basis sets, all

11 1182 F Burmeister et al the ionic states leading up to the double ionization potential in HCl (35.62 ev [16]) contained substantial components of (4σ ) 1 ionization. However, the number of such states calculated is far less than that found experimentally. Nevertheless, we believe that all the states observed experimentally are satellites of (4σ ) 1 ionization with substantial Rydberg character. This is supported by the angle-resolved PE result discussed above. The likely convergence limits of these satellite states are to one or more of the quasi-bound double ionization states with an electron configuration of (4σ ) 2 (5σ ) 2 (2π) 2, i.e. (2π) 2. All these dication states, 3, 1 and 1 +, observed at 35.59, and ev, respectively [17], are quasi-bound with welldefined vibrational levels (see also [16, 18]). Similar energy levels should thus be expected in the Rydberg series converging towards these states. Focussing specifically on the continuum-band region ( ev) in the PE spectra of HCl, it now appears that there are at least six bound (4σ ) 1 satellite states present (see vibrational progressions F 1, F 2, G 1, G 2, H 1 and H 2 in figure 2). Two of these progressions (G 1 and G 2 ) exhibit interference structure from interactions of the corresponding adiabatic bound states with the adiabatic repulsive state. Why no interference structure is observed in the G 2 vibrational progressions in the TPE spectra of HCl and DCl (see spectra (a and c), respectively, in figure 1) can be explained by the primary mechanism for producing these progressions in the TPE spectra. That is, it seems that autoionization is the dominant mechanism whereby Rydberg states lying in this energy region directly populate the adiabatic bound state without going through the adiabatic repulsive state from which interference effects arise. In this regard, we note that in the (5σ ) 1 photoionization of HBr and DBr similar satellite systems are observed in their TPE spectra [19], and it would be interesting to see if interference phenomena can be found in their PE spectra under highresolution conditions ( 20 mev). Clearly, more extensive ab initio calculations, employing much larger basis sets, are needed to account for all the (4σ ) 1 satellite structure observed experimentally in HCl + and DCl Summary Conventional photoelectron (PE) and threshold PE spectra of the inner-valence ionization region are presented and compared for HCl and DCl. The spectra reveal numerous vibrational progressions that consist of satellite band systems associated with (4σ 1 ) ionization. These systems are attributed to ionic Rydberg states converging on one or more of the quasi-bound double ionization states of HCl and DCl. In the binding-energy region ev, a broadband system is found with superimposed vibrational structure. In the case of the PE spectra of HCl, two vibrational progressions are found (one in the PE spectrum of DCl) that exhibit interference structure. As previously described [10], this indicates that there is a non-adiabatic interaction between bound and repulsive states. One of these two vibrational progressions in the PE spectra of HCl was revealed for the first time by means of an angle-dependent study. On the other hand, no interference structure is observed in the TPE spectra of HCl or DCl. This is attributed to the dominance of autoionization effects in the TPE spectra. In the PE spectrum of DCl we have confirmed the prediction made by simulations [10] that the vibrational progression corresponding to the electronic state would appear and exhibit interference structure for an improved experimental resolution of 10 mev. Acknowledgments We thank the staff of the ALS, BESSY and MAX II synchrotron facilities for their assistance in this research. Financial support from the Swedish Foundation for Strategic Research (SSF),

12 A study of the inner-valence ionization region in HCl and DCl 1183 the Swedish Research Council for the Engineering Sciences (TFR), the Swedish Research Council (VR) and the Swedish Foundation for International Cooperation in Research and Higher Education (STINT) is gratefully acknowledged. FB would like to thank Dr R Püttner for valuable discussions. References [1] Becker U and Shirley D A 1996 VUV and Soft X-Ray Photoionization (New York: Plenum) p 144 [2] Hüfner S 1996 Photoelectron Spectroscopy 2nd edn (Berlin: Springer) [3] Yencha A J, McConkey A G, Dawber G, Avaldi L, MacDonald M A, King G C and Hall R I 1995 J. Electron Spectrosc. Relat. Phenom [4] Yencha A J, Cormack A J, Donovan R J, Hopkirk A and King G C 1998 Chem. Phys [5] Martins M, Kaindl G and Schwentner N 1999 J. Electron Spectrosc. Relat. Phenom [6] Bässler M et al 2001 Nucl. Instrum. Methods [7] King G C, Zubek M, Rutter P M and Read F H 1987 J. Phys. E: Sci. Instrum [8] Hall R I, McConkey A, Ellis K, Dawber G, Avaldi L, MacDonald M A and King G C 1992 Meas. Sci. Technol [9] Burmeister F et al 2001 Phys. Rev. A [10] Andersson L M, Burmeister F, Karlsson H O and Goscinski O 2001 Phys. Rev. A [11] Wehlitz R, Heiser F, Hemmers O, Langer B, Menzel A and Becker U 1991 Phys. Rev. Lett [12] Becker U, Hemmers O, Langer A, Menzel A and Wehlitz R 1992 Phys. Rev. A 45 R1295 [13] von Niessen W, Tomasello P, Schirmer J, Cederbaum L S, Cambi R, Tarantelli F and Sgamellotti A 1990 J. Chem. Phys [14] Hiyama M and Iwata S 1993 Chem. Phys. Lett [15] May V and Kühn O 2000 Charge and Energy Transfer Dynamics in Molecular Systems (Berlin: Wiley VCH) [16] Yencha A J, King G C, Lopes M C A, Bozek J D and Berrah N 1999 Chem. Phys. Lett [17] McConkey A G, Dawber G, Avaldi L, MacDonald M A, King G C and Hall R I 1994 J. Phys. B: At. Mol. Opt. Phys [18] Svensson S, Karlsson L, Baltzer P, Keane M P and Wannberg B 1989 Phys. Rev. A [19] Yencha A J, Cormack A J, Donovan R J, Lawley K P, Hopkirk A and King G C 1998 Chem. Phys