- Email: [email protected]
Wavepacket dynamics and predissociation of the D1Πu state of Rb2
4 August 2000
Chemical Physics Letters 325 Ž2000. 577–583 www.elsevier.nlrlocatercplett
Wavepacket dynamics and predissociation of the D 1 P u state of Rb 2 Bo Zhang a
a,b
, Lars-Erik Berg a , Tony Hansson
a,b,)
Department of Physics, Section of Atomic and Molecular Physics, Royal Institute of Technology, KTH, SE-100 44 Stockholm, Sweden b Department of Chemistry, Royal Institute of Technology, KTH, SE-100 44 Stockholm, Sweden Received 11 April 2000; in final form 15 June 2000
Abstract We present the first experimental investigation of the real-time dynamics of predissociation in a diatomic molecule involving more than two electronic states – the predissociation of the D 1 P u state of Rb 2 . Our results show that the state is strongly predissociated, t f 5 ps, above a sharp energy threshold. We propose that mainly the Ž1. 3D u state causes the fast predissociation and that the fine-structure components of the products are mixed by coupling among molecular states at large internuclear distances. Furthermore, an outward–inward asymmetry of the wavepacket signal is attributed to autoionisation of the wavepacket evolving in the probe ŽRydberg. state. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction One of the simplest model systems for studies of molecular dynamics at potential energy surface intersections is a diatomic molecule in a predissociating electronically excited state. Consequently, such states have received considerable interest over the years and the basic processes in free molecules seem to be reasonably well understood w1x. The situation is less clear, however, when more than two states interact simultaneously or if there is a cascade of interactions involved, as for the D 1 P u state of Rb 2 . In this case, we cite Spiegelmann et al. w2x, ‘‘ . . . the final answer wregarding the nature of the predissociation mechanismx should only be sought by a dynamical treatment of the predissociation process involving several )
Corresponding author. The Royal Institute of Technology, Physics Department, KTH, SE-100 44 Stockholm, Sweden. Fax: q46-8-200-430; e-mail: [email protected]
states neighbouring or intersecting the predissociated states’’. This statement is in the original context referring to theoretical studies, but it is in our view equally applicable to experiments. A truly dynamical approach inherently requires the application of nuclear wavepacket methods. While the number of experimental studies on the dynamics of bound nuclear wavepackets in diatomic molecules are numerous Žsee, e.g., Ref. w3x for a recent brief review. less than a dozen exist on predissociation dynamics and just for four specific states: NaIŽA. w4–11x, NaBrŽA. w6x, LiIŽA. w6x, and IBrŽB. w12,13x. All of these predissociations are simple in the sense that they represent situations where only two electronic states interact. We present here the first experimental investigation of the real-time dynamics of predissociation involving more than two states – the predissociation of the D 1 P u state of Rb 2 . Breford and Engelke w14x studied this predissociation by monitoring non-time
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 7 3 0 - 2
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B. Zhang et al.r Chemical Physics Letters 325 (2000) 577–583
resolved laser-induced fluorescence ŽLIF. at detection wavelengths corresponding to the molecular D X and atomic D 1 and D 2 transitions, respectively, as a function of excitation wavelength. They attributed the observed main features, an abrupt cutting off of the vibrational progression in the molecular LIF at the short wavelength side of 429.5 nm and a concomitant change in intensity of the atomic LIF lines, to two different predissociation processes taking place. In the lower part of the D state their proposed mechanism invokes a relatively slow predissociation correlated to the 5 2 P3r2 q 5 2 S 1r2 dissociation limit, whereas at wavelengths shorter than 429.5 nm a much faster predissociation correlated to the 4 2 D 3r2 q 5 2 S 1r2 limit sets in. The qualitative features of this mechanism are reproduced in Fig. 1. Very few calculations of the potential energy curves covering the energy interval of the D state exist. Spiegelmann et al. w2x calculated all states correlating to the dissociated atoms limits of RbU Ž7s. q RbŽ5s. and lower and partly investigated the effect of spin–orbit ŽSO. coupling. They tentatively assigned the slow predissociation channel in the D state to a coupling to the Ž4. 3 Sq u state, which adiabatically Želectronically. correlates to the 6 2 S1r2 q 5 2 S 1r2 limit but in a diabatic picture correlates to
™
5 2 P3r2 q 5 2 S 1r2 . Moreover, they suggest that the fast predissociation channel is related to the additional coupling to one or more of the states Ž3. 3 P u , Ž3. 3 Sq Ž .1 q u , and 3 S u . The perturbative relativistic effective core pseudopotential calculations in Ref. w2x were improved upon by Foucrault et al. w15x. They reported on substantially better bonding distances, the bonding distances by Spiegelmann et al. are consistently 2–5% too short, but otherwise verify the qualitative correctness of the older calculations for the limited number of states they account for. Recent high-quality relativistic calculations of the potential energy curves w16x confirm and extend the results by Foucrault et al. Furthermore, they provide a more complete investigation of the SO couplings between the states. In this Letter, we report on the first real-time measurements of the dynamics of the predissociation of the Rb 2 ŽD. state. Our results show that the state is indeed strongly predissociated above a sharp energy threshold at about 430 nm, in which region the D state lifetime is in the range of a few picoseconds. We discuss this finding in terms of the calculations by Spiegelmann et al. w2x and propose a mechanism for the fast predissociation channel. Furthermore, an outward–inward asymmetry of the wavepacket signal is attributed to autoionisation of the wavepacket evolving in the probe ŽRydberg. state.
2. Experimental
Fig. 1. Outline of the pump–probe experiment. The potential energy curves are from Refs. w2,25,26x. The hatched area symbolises the molecular Rydberg states involved in the detection step. Fast and slow denotes the respective schematic predissociation channels.
The Rb 2 molecules were produced by heating solid rubidium in a heat-pipe oven described in Ref. w17x. Typically, the temperature of the oven during the experiments was around 500 K. A flow of argon gas was added to the continuously evacuated oven chamber as to maintain a total pressure of 2 Torr. The optical set-up was a standard pump–probe arrangement. Two independently tunable optical parametric amplifiers ŽTOPAS, Light Conversion. were synchronously pumped ŽCPA-2000, Clark MXR.. The outputs of the TOPAS:es were further non-linearly mixed in BBO crystals, to provide, at the oven, a pump pulse in the range 425–437 nm Ž4 mJ, 3 nm FWHM. and a probe pulse at 630 nm Ž4 mJ, 8 nm FWHM.. The pulses were sent through
B. Zhang et al.r Chemical Physics Letters 325 (2000) 577–583
separate prism-pair compressors, mainly for convenient spectral decomposition of the TOPAS outputs. The FWHM of the nearly Gaussian pump–probe cross-correlation function as measured by sumfrequency generation in a BBO crystal was 210 fs. The relative directions of the linear polarisations of the two pulses was adjusted with a zero-order broadband halfwave plate ŽCoherent. in the pump beam path to make an angle of 54.78, to eliminate orientational contributions to the wavepacket signal Žverified by the absence of rotational anisotropy in the molecular wavepacket signal at zero pulse delay time.. Moreover, the pump beam could be interrupted by means of a computer-controlled shutter. The two light beams were coupled into the heat-pipe oven at a small crossing angle by two f s q500 mm spherical lenses. The fluorescence emanating from the oven was collected in the backwards direction with respect to the light beam propagation direction and dispersed in a small spectrometer operated at a spectral resolution of 2 nm ŽH20IR, Jobin-Yvon.. In the present experiments the spectrometer was set to monitor the 9 2 D5r2,3r2 –5 2 P3r2 atomic transitions at 526 nm. A boxcar integrator ŽSR245, Stanford Research Systems. recorded and averaged the fluorescence signal over 1000 laser shots as a function of pump–probe delay time. The signal was first recorded with both the pump and probe beams on and then with only the probe beam on. Typically, 20 or 40 scans over the covered time-delay range were averaged. All data presented here have been normalised by subtracting from the pump–probe signal the signal with only the probe beam on and dividing by the same.
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induce a partial Ž) 10%. depletion of the fluorescence yield from the higher atomic levels. Setting the detector to monitor any of the probe-induced atomic lines yields the same results as for the chosen one at 526 nm. The recorded fluorescence depletion traces for five different pump wavelengths in the range 425– 437 nm are displayed in Fig. 2. Zero delay time has for each trace been defined to coincide with the point at which the steep slope has reached the value 0.5, and positive time corresponds to the pump pulse arriving at the sample before the probe pulse. All traces except the topmost exhibit a distinct oscillation with a period close to 900 fs, t osc s 890 " 15 fs for l pu s 431.1 nm, that disappears within 8–10 ps. Furthermore, there is a clear asymmetric splitting of the second peak of the oscillations. This feature is not resolved for the subsequent peaks, but all of them are consistently asymmetric. The fast Fourier transform ŽFFT. of the trace for l pu s 431.1 nm is shown in the inset. There are two peaks in the spectrum, which appear at the wave numbers 37 and 76 cmy1 , respectively. The first peak corresponds to our main oscillation period of 890 fs, while the second one apparently is the second harmonic of the
3. Results The pump–probe fluorescence spectrum Žnot shown. consists mainly in atomic lines originating from the 9 2 D levels or lower, with a rapidly decaying tail of the population extending to higher initial levels. The probe-beam-only spectrum is essentially appearing the same, except for a generally higher intensity of the emission lines, whereas the pump beam alone produces atomic lines originating from the 6 2 P and 5 2 P levels. Thus, the main effect of the pump pulse on the probe fluorescence signal is to
Fig. 2. Pump–probe fluorescence depletion signal at the 9 2 D5r 2,3r2 –5 2 P3r2 atomic transition for various pump wavelengths Žindicated next to each trace.. The inset contains the FFT of the signal for l pu s 431.1 nm at positive time delays.
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first. Finally, in the two uppermost traces a fast decay is present with exponential decay constants of 4.3 " 0.2 ps for the upper one and 5.1 " 0.3 ps for the other Žerror limits correspond to the standard error.. The data range for the latter fit was 0.5–10.0 ps, whereas the first fit was restricted to 0.5–6.0 ps, as the decay abruptly becomes non-exponential at 6 ps.
4. Discussion 4.1. WaÕepacket generation and detection We attribute the observed signal traces in Fig. 2 to vibrational wavepacket motion in the Rb 2 ŽD. state. The primary evidences for this assignment are twofold. First, the oscillation period matches the expected vibrational period of the D state. For l pu s 431.1 nm, for instance, we measure t osc s 890 fs, while the calculated vibrational level spacing at the central vibrational quantum number of the wavepacket, 1 yc s 12, corresponds to 870 fs. Second, the sudden appearance of a decay of the signal when the pump photon wavelength passes from the long to short wavelength side of 430 nm coincides with the cut-off wavelength of the molecular fluorescence excitation spectrum of the D state in Ref. w14x. The pump pulse hence creates a wavepacket in the molecular D state. As is clear from Fig. 1, the subsequent absorption of a probe photon brings the 2 q Ž . system to just below or above the Rbq 2 Aq S u ionisation limit, depending on the position of the wavepacket. Now, the presence of a splitting of the first vibrational recurrence and broadening of the subsequent recurrences shows that there exists a well-defined probe position at some distance from a turning point of the wavepacket trajectory. If the detection mechanism of the wavepacket were related to a direct transition to an ionisation continuum, we would not anticipate to see a well-defined probe point like that w18x. The whole Rydberg state manifold converging to the Aq state is accessible, how-
1
All bound–bound transition matrix elements were calculated with the LEVEL 6.1 software package w27x.
ever, and, as the electronic transition dipole moment for excitation of a Rydberg state from a valence state decreases rapidly with the Rydberg states effective principle quantum number w19x, n, to finally converge to the corresponding value for ionisation, transitions to relatively low members of the Rydberg manifold will dominate the probe process w20x. The splitting of the first wavepacket recurrence in the trace for l pu s 431.1 nm is about 275 fs, which would correspond to a probe point either at 4.7 or ˚ ŽWe have shifted the equilibrium distance of 5.5 A. the electronically adiabatic D state potential energy ˚ in order to better curve in Ref. w2x by q0.15 A reproduce the spectrum in Ref. w14x. Our value is very close to that obtained in recent calculations w15,16x.. Fig. 3 shows that the outer of these points falls well into the region of direct ionisation and would thus not offer the required narrow Franck– ˚ on the other Condon window. The point at 4.7 A, hand, corresponds to transitions to Rydberg states with n f 10, which according to the discussion above are likely to be well localised. Hence, we infer that the observed traces stem from a vibrational wavepacket created by the pump pulse at the inner leg of the D state potential energy curve, which is probed at some distance from the inner turning point
Fig. 3. Details of the pump and probe transitions. The hatched area corresponds to the molecular Rydberg states converging to the Aq 2 Sq state shifted down by the energy of one probe u photon. Horizontal lines indicate the centre of the wavepacket energy distribution in the D state for the given photon wavelengths with the corresponding vibrational levels yc given to the right. Vertical lines indicate the approximate initial position of the wavepacket. Ž- - -. difference potential energy curve corresponding Ž . the D 1 P u potento the D 1 P u X 1 Sq g transition. tial energy curve.
§
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by transitions to rather low-n Rydberg states converging to the Aq state. A closer inspection of Fig. 2 reveals that the signal exhibits an outward–inward asymmetry of the wavepacket detection probability. This phenomenon was found in two previous studies w21,22x and was in both cases explained in terms of a detection pathway passing via an intermediate valence state, which has a internuclear separation dependent transition dipole moment for photoionisation. We are in the present experiment too high up in the Rb 2 molecule for such a process to occur. However, if we assume that electronic autoionisation of the probe wavepacket to 2 q y Ž . Rbq is an efficient process, as was 2 Xq Sg q e observed for Na 2 w23x Žalthough the probe state in that case is thought to be a doubly excited non-Rydberg state., then asymmetry follows as a direct consequence of the longer time an inwards moving wavepacket spends in the Rydberg state than an outward–bound one before dissociating andror autoionising into the Aqq ey continuum. This additional time is from classical trajectory calculations 60–100 fs and the magnitude of the asymmetry then yields an upper time limit of about 500 fs for autoionisation of the Rydberg wavepacket to the Xqq ey continuum, which is in compliance with expectations w19x. The last step in the detection process is not unequivocal, as the branching ratio for autoionisation of the dissociating molecular Rydberg state into Aq is unknown. The distinction of the product channels is immaterial in the present case, though, as they are rapidly mixed by collisions in the oven, due to the very large cross-sections for near-resonant electron transfer between highly excited atoms and their ions w19x. The cross-sections for n- and l-changing collisions between similar atomic Rydberg states is even one or two orders of magnitude larger and thus the two-probe photon excited RbU Ž9d. atoms can be efficiently quenched. Autoionisation to bound molecular ions most probably results in a lower quenching efficiency, which explains the smaller fluorescence depletion obtained for this channel.
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the cut-off in the molecular fluorescence excitation spectrum measured by Breford and Engelke w14x. Thus, we confirm their hypothesis that the discontinuity corresponds to a fast predissociation channel opening up at excitation wavelengths shorter than 429.5 nm. The slower decay they conjure for the lower part of the D state is from the lowermost traces in Fig. 2 much too slow to be measured by our pump–probe technique. With absolute values attached to the decay rates at various energies in the D state, we can make a more detailed analysis of the fast predissociation mechanism than was heretofore feasible, and we do so on the basis of the calculations by Spiegelmann et al. To start with, we note that the fast decay energy threshold in Ref. w14x matches the RbU Ž4d. q RbŽ5s. dissociation limit. It hence seems probable that the state mainly responsible for the predissociation correlates with that limit. The possible influence of SO coupling between potential energy curves at large internuclear separations must be considered, however, which means that also states correlating to higher dissociation limits have to be discussed. The electronically adiabatic potential energy curves of all states that cross or come close to D 1 P u at reasonable energies are shown in Fig. 4. In addition to the states mentioned in Ref. w2x, Ž3. 3 P u , Ž3. 3 Sq u , and Ž3. 1 Sq , we found it necessary to include and conu sider the C 1 P u , Ž1. 1D u , Ž1. 3D u , and Ž2. 3 P u states. Ž .1 The two singlet states, Ž3. 1 Sq u and 1 D u , can cause gyroscopic predissociation of the D state through the L-uncoupling operator w24x. This type of interaction is strongly r-dependent in disfavour of large internuclear separations, however, and assuming a typical large value of the electronic part of it, 1 Žunitless., unphysically large total angular momentum values, J, would be required to reproduce the observed fast predissociation rates. Thus, neither one of these singlet states is responsible for the fast predissociation. Of the triplet states in Fig. 4, only Ž1. 3D u has a radial overlap integral of sufficient magnitude to cause fast direct predissociation of the D state by SO coupling. 2 The measured fast predis-
4.2. Fast predissociation dynamics The appearance of a rapid decay of the population in the two uppermost traces in Fig. 2 coincides with
2
All predissociation rates were calculated with the BCONT 1.4 software package w28x.
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Fig. 4. Potential energy curves in proximity of the D 1 P u state. All curves are from Ref. w2x. Bold states are believed to be of major importance to the fast predissociation process.
sociation rates at 2.0 = 10 11 and 2.3 = 10 11 sy1 , respectively, yield an empirical electronic SO coupling constant in the order of 10 cmy1 , which is close to the maximum value Žit is strongly r-dependent. obtained in calculations by Edvardsson et al. w16x. A strict selection rule for SO coupling is D V s 0, and we henceforth only consider V s 1 components, as this is the only possible V value for the D 1 P u state. The Ž1. 3D 1u state correlates to the 4 2 D5r2 q 5 2 S 1r2 dissociation limit, which renders the correct energy threshold. It contradicts the relative atomic fluorescence yields measured in Ref. w14x, though, which indicate a complete transfer of the predissociating molecules to the lower fine-structure component. The Rbq Rby ion-pair curve crosses the Ž1. 3D u ˚ however, and potential energy curve at about 10 A, gives rise to large perturbations of the states in this region. As a consequence, the C 1 P 1u and Ž2. 3 P 1u states correlating to the 4 2 D 3r2 q 5 2 S 1r2 dissociation limit exhibit in the SO diabatic picture several crossings with the Ž1. 3D 1u state that can mix the fine-structure components. We thus find that the Ž1. 3D 1u state is the most likely perturber causing the fast predissociation of the D 1 P 1u state and that the predissociation yield is strongly influenced by SO couplings to ‘lower-lying’ states at large internuclear separation. We must point out, though, that we in addition expect two bound
states to have significant influence on the D state by SO interaction, Ž4. 3 S 1u and Ž3. 3 P 1u . The former state was invoked by Spiegelmann et al. to explain the slow predissociation channel, as it diabatically Želectronically. correlates to the 5 2 P3r2 q 5 2 S 1r2 dissociation limit. We do not expect it to have any significant influence on the timescale of the faster predissociation, however. The Ž3. 3 P 1u state, on the other hand, has a potential energy curve that is very close to and almost identical to that of the D state, which indicates that the states differ just by a single spin–orbital. This means there may exist a strong homogenous perturbation of the D state that spans a large energy interval and is efficient for nearly all J:s simultaneously w24x. Furthermore, the Ž3. 3 P 1u state should be expected to couple as efficiently to Ž1. 3D 1u as the D state does and could thus directly influence the fast predissociation channel. We are currently further investigating the existence of this three-state SO interaction. In conclusion, the here proposed mechanism for the fast predissociation channel of the Rb 2 ŽD 1 P u . state relies on the qualitative correctness of the calculated potential energy curves by Spiegelmann et al. w2x. Higher quality calculations are under way w16x that seem to agree in large with the previous ones, but further experimental and theoretical studies to assess our conjectures and their implications are required and are in progress.
B. Zhang et al.r Chemical Physics Letters 325 (2000) 577–583
Acknowledgements We thank Hans Karlsson, David Edvardsson, and Mauritz Andersson for numerous valuable discussions and comments and for sharing data prior to publication. Stimulating discussions with Nils Elander and Peter van der Meulen are also gratefully acknowledged. Renee ´ Andersson assisted in setting up the experiment. This work was supported by the Swedish Natural Science Research Council ŽNFR..
References w1x H. Kato, ˆ M. Baba, Chem. Rev. 95 Ž1995. 2311. w2x F. Spiegelmann, D. Pavolini, J.-P. Daudey, J. Phys. B: At. Mol. Opt. Phys. 22 Ž1989. 2465. w3x E. Schreiber, Femtosecond Real-Time Spectroscopy of Small Molecules and Clusters, Springer, Berlin, 1998. w4x T.S. Rose, M.J. Rosker, A.H. Zewail, J. Chem. Phys. 88 Ž1988. 6672. w5x M.J. Rosker, M. Dantus, A.H. Zewail, J. Chem. Phys. 89 Ž1988. 6113. w6x T.S. Rose, M.J. Rosker, A.H. Zewail, J. Chem. Phys. 91 Ž1989. 7415. w7x P. Cong, A. Mokhtari, A.H. Zewail, Chem. Phys. Lett. 172 Ž1990. 109. w8x A. Materny, J.L. Herek, P. Cong, A.H. Zewail, J. Phys. Chem. 98 Ž1994. 7415. w9x J.L. Herek, A. Materny, A.H. Zewail, Chem. Phys. Lett. 228 Ž1994. 15. w10x G. Knopp, M. Schmitt, A. Materny, W. Kiefer, J. Phys. Chem. A 101 Ž1997. 4852.
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w11x C. Jouvet, S. Martrenchard, D. Solgadi, C. DedonderLardeux, M. Mons, G. Gregoire, I. Dimicoli, F. Piuzzi, J.P. ´ Visticot, J.M. Mestdagh, P. D’Oliveira, P. Meynadier, M. Perdrix, J. Phys. Chem. A 101 Ž1997. 2555. w12x M.J.J. Vrakking, D.M. Villeneuve, A. Stolow, J. Chem. Phys. 105 Ž1996. 5647. w13x M. Shapiro, M.J.J. Vrakking, A. Stolow, J. Chem. Phys. 110 Ž1999. 2465. w14x E.J. Breford, F. Engelke, Chem. Phys. Lett. 75 Ž1980. 132. w15x M. Foucrault, P. Millie, J.P. Daudey, J. Chem. Phys. 96 Ž1992. 1258. w16x D. Edvardsson, private communication; to be published. w17x L.-E. Berg, M. Beutter, T. Hansson, Chem. Phys. Lett. 253 Ž1996. 327. w18x V. Engel, Chem. Phys. Lett. 178 Ž1991. 130. w19x R.F. Stebbings, F.B. Dunning ŽEds.., Rydberg States of Atoms and Molecules, Cambridge University Press, Cambridge, 1983. w20x R. Andersson, J. Davidsson, T. Hansson, Chem. Phys. Lett. 322 Ž2000. 439. w21x G. Gregoire, M. Mons, I. Dimicoli, F. Piuzzi, E. Charron, C. ´ Dedonder-Lardeux, C. Jouvet, S. Martrenchard, D. Solgadi, A. Suzor-Weiner, Eur. Phys. J. D 1 Ž1998. 187. w22x C. Nicole, M.A. Bouchene, C. Meier, S. Magnier, E. ` Schreiber, B. Girard, J. Chem. Phys. 111 Ž1999. 7857. w23x T. Baumert, B. Buhler, M. Grosser, R. Thalweiser, V. Weiss, ¨ E. Wiedenmann, G. Gerber, J. Phys. Chem. 95 Ž1991. 8103. w24x H. Lefebvre-Brion, R. Fields, Perturbations in the Spectra of Diatomic Molecules, Academic Press, Orlando, FL, 1986. w25x C. Johann, U. Kleinekathofer, K.T. Tang, J.P. Toennies, ¨ Chem. Phys. Lett. 257 Ž1996. 651. w26x C. Amiot, J. Chem. Phys. 93 Ž1990. 8591. w27x R.J. LeRoy, Chemical Physics Research Report CP-555R ŽUniv. of Waterloo, Canada, 1996.. w28x R.J. LeRoy, Chemical Physics Research Report CP-329R3 ŽUniv. of Waterloo, Canada, 1993..
Chemical Physics Letters 325 Ž2000. 577–583 www.elsevier.nlrlocatercplett
Wavepacket dynamics and predissociation of the D 1 P u state of Rb 2 Bo Zhang a
a,b
, Lars-Erik Berg a , Tony Hansson
a,b,)
Department of Physics, Section of Atomic and Molecular Physics, Royal Institute of Technology, KTH, SE-100 44 Stockholm, Sweden b Department of Chemistry, Royal Institute of Technology, KTH, SE-100 44 Stockholm, Sweden Received 11 April 2000; in final form 15 June 2000
Abstract We present the first experimental investigation of the real-time dynamics of predissociation in a diatomic molecule involving more than two electronic states – the predissociation of the D 1 P u state of Rb 2 . Our results show that the state is strongly predissociated, t f 5 ps, above a sharp energy threshold. We propose that mainly the Ž1. 3D u state causes the fast predissociation and that the fine-structure components of the products are mixed by coupling among molecular states at large internuclear distances. Furthermore, an outward–inward asymmetry of the wavepacket signal is attributed to autoionisation of the wavepacket evolving in the probe ŽRydberg. state. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction One of the simplest model systems for studies of molecular dynamics at potential energy surface intersections is a diatomic molecule in a predissociating electronically excited state. Consequently, such states have received considerable interest over the years and the basic processes in free molecules seem to be reasonably well understood w1x. The situation is less clear, however, when more than two states interact simultaneously or if there is a cascade of interactions involved, as for the D 1 P u state of Rb 2 . In this case, we cite Spiegelmann et al. w2x, ‘‘ . . . the final answer wregarding the nature of the predissociation mechanismx should only be sought by a dynamical treatment of the predissociation process involving several )
Corresponding author. The Royal Institute of Technology, Physics Department, KTH, SE-100 44 Stockholm, Sweden. Fax: q46-8-200-430; e-mail: [email protected]
states neighbouring or intersecting the predissociated states’’. This statement is in the original context referring to theoretical studies, but it is in our view equally applicable to experiments. A truly dynamical approach inherently requires the application of nuclear wavepacket methods. While the number of experimental studies on the dynamics of bound nuclear wavepackets in diatomic molecules are numerous Žsee, e.g., Ref. w3x for a recent brief review. less than a dozen exist on predissociation dynamics and just for four specific states: NaIŽA. w4–11x, NaBrŽA. w6x, LiIŽA. w6x, and IBrŽB. w12,13x. All of these predissociations are simple in the sense that they represent situations where only two electronic states interact. We present here the first experimental investigation of the real-time dynamics of predissociation involving more than two states – the predissociation of the D 1 P u state of Rb 2 . Breford and Engelke w14x studied this predissociation by monitoring non-time
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 7 3 0 - 2
578
B. Zhang et al.r Chemical Physics Letters 325 (2000) 577–583
resolved laser-induced fluorescence ŽLIF. at detection wavelengths corresponding to the molecular D X and atomic D 1 and D 2 transitions, respectively, as a function of excitation wavelength. They attributed the observed main features, an abrupt cutting off of the vibrational progression in the molecular LIF at the short wavelength side of 429.5 nm and a concomitant change in intensity of the atomic LIF lines, to two different predissociation processes taking place. In the lower part of the D state their proposed mechanism invokes a relatively slow predissociation correlated to the 5 2 P3r2 q 5 2 S 1r2 dissociation limit, whereas at wavelengths shorter than 429.5 nm a much faster predissociation correlated to the 4 2 D 3r2 q 5 2 S 1r2 limit sets in. The qualitative features of this mechanism are reproduced in Fig. 1. Very few calculations of the potential energy curves covering the energy interval of the D state exist. Spiegelmann et al. w2x calculated all states correlating to the dissociated atoms limits of RbU Ž7s. q RbŽ5s. and lower and partly investigated the effect of spin–orbit ŽSO. coupling. They tentatively assigned the slow predissociation channel in the D state to a coupling to the Ž4. 3 Sq u state, which adiabatically Želectronically. correlates to the 6 2 S1r2 q 5 2 S 1r2 limit but in a diabatic picture correlates to
™
5 2 P3r2 q 5 2 S 1r2 . Moreover, they suggest that the fast predissociation channel is related to the additional coupling to one or more of the states Ž3. 3 P u , Ž3. 3 Sq Ž .1 q u , and 3 S u . The perturbative relativistic effective core pseudopotential calculations in Ref. w2x were improved upon by Foucrault et al. w15x. They reported on substantially better bonding distances, the bonding distances by Spiegelmann et al. are consistently 2–5% too short, but otherwise verify the qualitative correctness of the older calculations for the limited number of states they account for. Recent high-quality relativistic calculations of the potential energy curves w16x confirm and extend the results by Foucrault et al. Furthermore, they provide a more complete investigation of the SO couplings between the states. In this Letter, we report on the first real-time measurements of the dynamics of the predissociation of the Rb 2 ŽD. state. Our results show that the state is indeed strongly predissociated above a sharp energy threshold at about 430 nm, in which region the D state lifetime is in the range of a few picoseconds. We discuss this finding in terms of the calculations by Spiegelmann et al. w2x and propose a mechanism for the fast predissociation channel. Furthermore, an outward–inward asymmetry of the wavepacket signal is attributed to autoionisation of the wavepacket evolving in the probe ŽRydberg. state.
2. Experimental
Fig. 1. Outline of the pump–probe experiment. The potential energy curves are from Refs. w2,25,26x. The hatched area symbolises the molecular Rydberg states involved in the detection step. Fast and slow denotes the respective schematic predissociation channels.
The Rb 2 molecules were produced by heating solid rubidium in a heat-pipe oven described in Ref. w17x. Typically, the temperature of the oven during the experiments was around 500 K. A flow of argon gas was added to the continuously evacuated oven chamber as to maintain a total pressure of 2 Torr. The optical set-up was a standard pump–probe arrangement. Two independently tunable optical parametric amplifiers ŽTOPAS, Light Conversion. were synchronously pumped ŽCPA-2000, Clark MXR.. The outputs of the TOPAS:es were further non-linearly mixed in BBO crystals, to provide, at the oven, a pump pulse in the range 425–437 nm Ž4 mJ, 3 nm FWHM. and a probe pulse at 630 nm Ž4 mJ, 8 nm FWHM.. The pulses were sent through
B. Zhang et al.r Chemical Physics Letters 325 (2000) 577–583
separate prism-pair compressors, mainly for convenient spectral decomposition of the TOPAS outputs. The FWHM of the nearly Gaussian pump–probe cross-correlation function as measured by sumfrequency generation in a BBO crystal was 210 fs. The relative directions of the linear polarisations of the two pulses was adjusted with a zero-order broadband halfwave plate ŽCoherent. in the pump beam path to make an angle of 54.78, to eliminate orientational contributions to the wavepacket signal Žverified by the absence of rotational anisotropy in the molecular wavepacket signal at zero pulse delay time.. Moreover, the pump beam could be interrupted by means of a computer-controlled shutter. The two light beams were coupled into the heat-pipe oven at a small crossing angle by two f s q500 mm spherical lenses. The fluorescence emanating from the oven was collected in the backwards direction with respect to the light beam propagation direction and dispersed in a small spectrometer operated at a spectral resolution of 2 nm ŽH20IR, Jobin-Yvon.. In the present experiments the spectrometer was set to monitor the 9 2 D5r2,3r2 –5 2 P3r2 atomic transitions at 526 nm. A boxcar integrator ŽSR245, Stanford Research Systems. recorded and averaged the fluorescence signal over 1000 laser shots as a function of pump–probe delay time. The signal was first recorded with both the pump and probe beams on and then with only the probe beam on. Typically, 20 or 40 scans over the covered time-delay range were averaged. All data presented here have been normalised by subtracting from the pump–probe signal the signal with only the probe beam on and dividing by the same.
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induce a partial Ž) 10%. depletion of the fluorescence yield from the higher atomic levels. Setting the detector to monitor any of the probe-induced atomic lines yields the same results as for the chosen one at 526 nm. The recorded fluorescence depletion traces for five different pump wavelengths in the range 425– 437 nm are displayed in Fig. 2. Zero delay time has for each trace been defined to coincide with the point at which the steep slope has reached the value 0.5, and positive time corresponds to the pump pulse arriving at the sample before the probe pulse. All traces except the topmost exhibit a distinct oscillation with a period close to 900 fs, t osc s 890 " 15 fs for l pu s 431.1 nm, that disappears within 8–10 ps. Furthermore, there is a clear asymmetric splitting of the second peak of the oscillations. This feature is not resolved for the subsequent peaks, but all of them are consistently asymmetric. The fast Fourier transform ŽFFT. of the trace for l pu s 431.1 nm is shown in the inset. There are two peaks in the spectrum, which appear at the wave numbers 37 and 76 cmy1 , respectively. The first peak corresponds to our main oscillation period of 890 fs, while the second one apparently is the second harmonic of the
3. Results The pump–probe fluorescence spectrum Žnot shown. consists mainly in atomic lines originating from the 9 2 D levels or lower, with a rapidly decaying tail of the population extending to higher initial levels. The probe-beam-only spectrum is essentially appearing the same, except for a generally higher intensity of the emission lines, whereas the pump beam alone produces atomic lines originating from the 6 2 P and 5 2 P levels. Thus, the main effect of the pump pulse on the probe fluorescence signal is to
Fig. 2. Pump–probe fluorescence depletion signal at the 9 2 D5r 2,3r2 –5 2 P3r2 atomic transition for various pump wavelengths Žindicated next to each trace.. The inset contains the FFT of the signal for l pu s 431.1 nm at positive time delays.
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first. Finally, in the two uppermost traces a fast decay is present with exponential decay constants of 4.3 " 0.2 ps for the upper one and 5.1 " 0.3 ps for the other Žerror limits correspond to the standard error.. The data range for the latter fit was 0.5–10.0 ps, whereas the first fit was restricted to 0.5–6.0 ps, as the decay abruptly becomes non-exponential at 6 ps.
4. Discussion 4.1. WaÕepacket generation and detection We attribute the observed signal traces in Fig. 2 to vibrational wavepacket motion in the Rb 2 ŽD. state. The primary evidences for this assignment are twofold. First, the oscillation period matches the expected vibrational period of the D state. For l pu s 431.1 nm, for instance, we measure t osc s 890 fs, while the calculated vibrational level spacing at the central vibrational quantum number of the wavepacket, 1 yc s 12, corresponds to 870 fs. Second, the sudden appearance of a decay of the signal when the pump photon wavelength passes from the long to short wavelength side of 430 nm coincides with the cut-off wavelength of the molecular fluorescence excitation spectrum of the D state in Ref. w14x. The pump pulse hence creates a wavepacket in the molecular D state. As is clear from Fig. 1, the subsequent absorption of a probe photon brings the 2 q Ž . system to just below or above the Rbq 2 Aq S u ionisation limit, depending on the position of the wavepacket. Now, the presence of a splitting of the first vibrational recurrence and broadening of the subsequent recurrences shows that there exists a well-defined probe position at some distance from a turning point of the wavepacket trajectory. If the detection mechanism of the wavepacket were related to a direct transition to an ionisation continuum, we would not anticipate to see a well-defined probe point like that w18x. The whole Rydberg state manifold converging to the Aq state is accessible, how-
1
All bound–bound transition matrix elements were calculated with the LEVEL 6.1 software package w27x.
ever, and, as the electronic transition dipole moment for excitation of a Rydberg state from a valence state decreases rapidly with the Rydberg states effective principle quantum number w19x, n, to finally converge to the corresponding value for ionisation, transitions to relatively low members of the Rydberg manifold will dominate the probe process w20x. The splitting of the first wavepacket recurrence in the trace for l pu s 431.1 nm is about 275 fs, which would correspond to a probe point either at 4.7 or ˚ ŽWe have shifted the equilibrium distance of 5.5 A. the electronically adiabatic D state potential energy ˚ in order to better curve in Ref. w2x by q0.15 A reproduce the spectrum in Ref. w14x. Our value is very close to that obtained in recent calculations w15,16x.. Fig. 3 shows that the outer of these points falls well into the region of direct ionisation and would thus not offer the required narrow Franck– ˚ on the other Condon window. The point at 4.7 A, hand, corresponds to transitions to Rydberg states with n f 10, which according to the discussion above are likely to be well localised. Hence, we infer that the observed traces stem from a vibrational wavepacket created by the pump pulse at the inner leg of the D state potential energy curve, which is probed at some distance from the inner turning point
Fig. 3. Details of the pump and probe transitions. The hatched area corresponds to the molecular Rydberg states converging to the Aq 2 Sq state shifted down by the energy of one probe u photon. Horizontal lines indicate the centre of the wavepacket energy distribution in the D state for the given photon wavelengths with the corresponding vibrational levels yc given to the right. Vertical lines indicate the approximate initial position of the wavepacket. Ž- - -. difference potential energy curve corresponding Ž . the D 1 P u potento the D 1 P u X 1 Sq g transition. tial energy curve.
§
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by transitions to rather low-n Rydberg states converging to the Aq state. A closer inspection of Fig. 2 reveals that the signal exhibits an outward–inward asymmetry of the wavepacket detection probability. This phenomenon was found in two previous studies w21,22x and was in both cases explained in terms of a detection pathway passing via an intermediate valence state, which has a internuclear separation dependent transition dipole moment for photoionisation. We are in the present experiment too high up in the Rb 2 molecule for such a process to occur. However, if we assume that electronic autoionisation of the probe wavepacket to 2 q y Ž . Rbq is an efficient process, as was 2 Xq Sg q e observed for Na 2 w23x Žalthough the probe state in that case is thought to be a doubly excited non-Rydberg state., then asymmetry follows as a direct consequence of the longer time an inwards moving wavepacket spends in the Rydberg state than an outward–bound one before dissociating andror autoionising into the Aqq ey continuum. This additional time is from classical trajectory calculations 60–100 fs and the magnitude of the asymmetry then yields an upper time limit of about 500 fs for autoionisation of the Rydberg wavepacket to the Xqq ey continuum, which is in compliance with expectations w19x. The last step in the detection process is not unequivocal, as the branching ratio for autoionisation of the dissociating molecular Rydberg state into Aq is unknown. The distinction of the product channels is immaterial in the present case, though, as they are rapidly mixed by collisions in the oven, due to the very large cross-sections for near-resonant electron transfer between highly excited atoms and their ions w19x. The cross-sections for n- and l-changing collisions between similar atomic Rydberg states is even one or two orders of magnitude larger and thus the two-probe photon excited RbU Ž9d. atoms can be efficiently quenched. Autoionisation to bound molecular ions most probably results in a lower quenching efficiency, which explains the smaller fluorescence depletion obtained for this channel.
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the cut-off in the molecular fluorescence excitation spectrum measured by Breford and Engelke w14x. Thus, we confirm their hypothesis that the discontinuity corresponds to a fast predissociation channel opening up at excitation wavelengths shorter than 429.5 nm. The slower decay they conjure for the lower part of the D state is from the lowermost traces in Fig. 2 much too slow to be measured by our pump–probe technique. With absolute values attached to the decay rates at various energies in the D state, we can make a more detailed analysis of the fast predissociation mechanism than was heretofore feasible, and we do so on the basis of the calculations by Spiegelmann et al. To start with, we note that the fast decay energy threshold in Ref. w14x matches the RbU Ž4d. q RbŽ5s. dissociation limit. It hence seems probable that the state mainly responsible for the predissociation correlates with that limit. The possible influence of SO coupling between potential energy curves at large internuclear separations must be considered, however, which means that also states correlating to higher dissociation limits have to be discussed. The electronically adiabatic potential energy curves of all states that cross or come close to D 1 P u at reasonable energies are shown in Fig. 4. In addition to the states mentioned in Ref. w2x, Ž3. 3 P u , Ž3. 3 Sq u , and Ž3. 1 Sq , we found it necessary to include and conu sider the C 1 P u , Ž1. 1D u , Ž1. 3D u , and Ž2. 3 P u states. Ž .1 The two singlet states, Ž3. 1 Sq u and 1 D u , can cause gyroscopic predissociation of the D state through the L-uncoupling operator w24x. This type of interaction is strongly r-dependent in disfavour of large internuclear separations, however, and assuming a typical large value of the electronic part of it, 1 Žunitless., unphysically large total angular momentum values, J, would be required to reproduce the observed fast predissociation rates. Thus, neither one of these singlet states is responsible for the fast predissociation. Of the triplet states in Fig. 4, only Ž1. 3D u has a radial overlap integral of sufficient magnitude to cause fast direct predissociation of the D state by SO coupling. 2 The measured fast predis-
4.2. Fast predissociation dynamics The appearance of a rapid decay of the population in the two uppermost traces in Fig. 2 coincides with
2
All predissociation rates were calculated with the BCONT 1.4 software package w28x.
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Fig. 4. Potential energy curves in proximity of the D 1 P u state. All curves are from Ref. w2x. Bold states are believed to be of major importance to the fast predissociation process.
sociation rates at 2.0 = 10 11 and 2.3 = 10 11 sy1 , respectively, yield an empirical electronic SO coupling constant in the order of 10 cmy1 , which is close to the maximum value Žit is strongly r-dependent. obtained in calculations by Edvardsson et al. w16x. A strict selection rule for SO coupling is D V s 0, and we henceforth only consider V s 1 components, as this is the only possible V value for the D 1 P u state. The Ž1. 3D 1u state correlates to the 4 2 D5r2 q 5 2 S 1r2 dissociation limit, which renders the correct energy threshold. It contradicts the relative atomic fluorescence yields measured in Ref. w14x, though, which indicate a complete transfer of the predissociating molecules to the lower fine-structure component. The Rbq Rby ion-pair curve crosses the Ž1. 3D u ˚ however, and potential energy curve at about 10 A, gives rise to large perturbations of the states in this region. As a consequence, the C 1 P 1u and Ž2. 3 P 1u states correlating to the 4 2 D 3r2 q 5 2 S 1r2 dissociation limit exhibit in the SO diabatic picture several crossings with the Ž1. 3D 1u state that can mix the fine-structure components. We thus find that the Ž1. 3D 1u state is the most likely perturber causing the fast predissociation of the D 1 P 1u state and that the predissociation yield is strongly influenced by SO couplings to ‘lower-lying’ states at large internuclear separation. We must point out, though, that we in addition expect two bound
states to have significant influence on the D state by SO interaction, Ž4. 3 S 1u and Ž3. 3 P 1u . The former state was invoked by Spiegelmann et al. to explain the slow predissociation channel, as it diabatically Želectronically. correlates to the 5 2 P3r2 q 5 2 S 1r2 dissociation limit. We do not expect it to have any significant influence on the timescale of the faster predissociation, however. The Ž3. 3 P 1u state, on the other hand, has a potential energy curve that is very close to and almost identical to that of the D state, which indicates that the states differ just by a single spin–orbital. This means there may exist a strong homogenous perturbation of the D state that spans a large energy interval and is efficient for nearly all J:s simultaneously w24x. Furthermore, the Ž3. 3 P 1u state should be expected to couple as efficiently to Ž1. 3D 1u as the D state does and could thus directly influence the fast predissociation channel. We are currently further investigating the existence of this three-state SO interaction. In conclusion, the here proposed mechanism for the fast predissociation channel of the Rb 2 ŽD 1 P u . state relies on the qualitative correctness of the calculated potential energy curves by Spiegelmann et al. w2x. Higher quality calculations are under way w16x that seem to agree in large with the previous ones, but further experimental and theoretical studies to assess our conjectures and their implications are required and are in progress.
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Acknowledgements We thank Hans Karlsson, David Edvardsson, and Mauritz Andersson for numerous valuable discussions and comments and for sharing data prior to publication. Stimulating discussions with Nils Elander and Peter van der Meulen are also gratefully acknowledged. Renee ´ Andersson assisted in setting up the experiment. This work was supported by the Swedish Natural Science Research Council ŽNFR..
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