van der Waals binding energies and intermolecular vibrations of carbazole R (R Ne, Ar, Kr, Xe)

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1 van der Waals inding energies and intermolecular virations of carazole R (R Ne, Ar, Kr, Xe) Thierry Droz, Thomas Bürgi, and Samuel Leutwyler Institut für Anorganische, Analytische und Physikalische Chemie, Freiestr.3, 3000 Bern 9, Switzerland Received 6 March 1995; accepted 8 June 1995 Mass-selective ground-state virational spectra of jet-cooled carazole R R Ne, Ar, Kr, and Xe van der Waals complexes were otained y populating ground-state intra- and intermolecular levels via stimulated emission pumping, followed y time delayed resonant two-photon ionization of the virationally hot complex. By tuning the dump laser frequency, S 0 state virational modes were accessed from 200 cm 1 up to the dissociation energy D 0. Upon dumping to ground-state levels aove D 0, efficient virational predissociation of the complexes occurred, allowing us to determine the S 0 state van der Waals inding energies very accurately. The D 0 (S 0 ) values are cm 1 R Ne, cm 1 R Ar, cm 1 R Kr, and cm 1 R Xe. In the S 1 state, the corresponding inding energies are larger y 9% to 12%, eing cm 1, cm 1, cm 1, and cm 1, respectively American Institute of Physics. I. INTRODUCTION Weakly ound van der Waals vdw complexes etween aromatic molecules M and rare-gas atoms R have ecome prototype systems for the investigation of solvation at a microscopic level, especially with respect to spectroscopic properties, 1 3 intermolecular virational redistriution IVR, and virational predissociation VP Especially for the dynamic studies, the weakness of the vdw ond is an essential feature. Despite extensive research on aromatic vdw complexes, these intermolecular inding energies are still not known to high accuracy. Thus for, e.g., enzene R complexes, the inding energies have een at the focus of recent experimental and theoretical research We have recently introduced the stimulated emission pumping/resonant two-photon ionization SEP-R2PI method for the mass-selective determination of ground-state vdw inding energies and vironic spectra of jet-cooled aromatic van der Waals complexes and clusters M R orm R n, where M is an aromatic molecule carazole and R a solvent atom 21,22 or molecule. 23 The results otained so far for carazole Ar Refs. 21 and 22 reveal great potential for the investigation of virational states, inding energies, and dynamics of weakly ound aromatic vdw systems in the electronic ground state. From the point of view of theory, intermolecular interactions in electronic ground states are much more tractale than excited states, and accurate a initio calculations of molecular properties are now possile Experimentally, the ground-state polarizaility and charge distriution of the aromatic molecule are usually characterized much more accurately than for excited states. In the present work, we extend the application of this method to the complexes of carazole with R Ne, Kr, and Xe. SEP-R2PI spectroscopy can e viewed as stimulated emission pumping SEP followed y a R2PI detection step, in which hot complexes or clusters are detected massspecifically. Conventional SEP techniques, in which population losses are monitored i.e., differential signals are recorded, are well estalished. 8,9,24 29 In contrast to these techniques, SEP-R2PI spectroscopy proes only the hot M R S 0 -products resulting from the pump/dump process followed y ground-state IVR. The method is essentially ackground-free, and hence very sensitive, as will e shown elow. Other, conceptually similar pump/proe schemes have een used in studies of complexes of the ground-state virational dynamics of vdw complexes. 8,9 Rotational coherence fluorescence depletion is a related technique for the measurement of rotational constants. 30 Ionization-detected stimulated Raman spectroscopy IDSRS is also closely related, and has een applied y Felker and co-workers for the detection of intra- 31 and intermolecular 32 virational resonances in vdw complexes and clusters. The SEP-R2PI method can also e viewed as a fully resonant Raman variation on the IDSRS method. Pump/proe methods have also een used to determine excited-state IVR rates in aromatic vdw complexes. 33,34 Limits on vdw inding energies have previously een determined y various methods: excited-state dissociation of M R complexes has een detected y oservation of dispersed fluorescence from the are M aromatic molecule, following IVR/dissociation of the vdw complex. 4,5,7,10,12,35 In an extension, picosecond time-resolved decay time measurements coupled to dispersed fluorescence emission techniques give information on the state-to-state IVR energy flow as well as on the dissociation energy in the vdw complex. 13,14 Alternatively, the nonoservance of S 1 state vironic ands in R2PI spectroscopy indicates virational predissociation of the vdw complex prior to ionization. 11,36 All these techniques proe the excited state and give only upper limits to the inding energies. Conversely, oservation of relaxed fluorescence of the vdw complex following excitation implies that the energy content of the complex is less than the inding energy, and lower limits to vdw inding energies have een so inferred. 7 However in electronically excited states, VP rates usually compete with intramolecular radiative and nonradiative processes fluorescence, intersystem crossing ISC, internal conversion IC, 13 which may intro- This article is copyrighted as indicated in the article. Reuse of AIP content is suject to the terms at: Downloaded to IP: J. Chem. Phys. 103 (10), 8 Septemer /95/103(10)/4035/11/$6.00 On: Fri, 13 Dec :09: American Institute of Physics 4035

2 4036 Droz, Bürgi, and Leutwyler: Binding energies of carazole R duce uncertainties in the determination of the inding energy. Recently Krause et al. 37 applied mass-selective threshold pulsed field ionization to otain information on the photodissociation process of cluster ions. By monitoring oth the cluster-ion M R and product-ion M channel, lower and upper limits to the ion-state dissociation energy ecome accessile. Adding the ionization potential shift IP of M R relative to M results in lower and upper limits for the electronic ground-state inding energy. Therefore, with respect to the measurement of inding energies, this technique is a complementary scheme to the SEP-R2PI method descried in this work. A detailed description of the experimental setup is given in Sec. II. In Sec. III we present and discuss the S 0 and S 1 state inding energies as well as the intermolecular virational level structure oserved for carazole R R Ne, Ar, Kr, and Xe, and also correlate and compare the D 0 values of the different vdw complexes. Section IV contains the conclusions. II. EXPERIMENT A. Principle of the SEP-R2PI method A scheme of the method 21,22 is displayed in Fig. 1. Supersonically cooled M R complexes are pumped at the S 0 S and, shown as step 1 in Fig. 1. A very small fraction typically 0.1% of the generated S 1 -state complexes asors a second photon at the pump laser frequency, and is directly ionized, see Fig. 1. In the dump step, induced y a second tunale laser 2 or 2, a large fraction typically 30% 40% of the excited-state population is transferred ack to a specific intra- or intermolecular S 0 virational level, at an excitation energy E relative to the virationless ground state. The comination of pump 1 and dump 2 / 2 steps, which are synchronized to within 2 ns, define the SEP process. The population transfer efficiency achieved in the SEP process depends on several factors, including laser powers for the pump and dump steps, oscillator strength ( f ), Franck Condon factors FC s, IC as well as ISC rates in the S 1 state and dynamics in the S 0 state. By tuning the dump laser a wide range of ground state virational states can e accessed. Following the SEP process, the vdw complex is left to evolve on the ground-state hypersurface, and can e proed for delay times ranging from 50 ns to 15 s, see Sec. II B. Initially, rapid relaxation occurs out of the prepared S 0 -set of mixed eigenstates; in the limit of high vdw mode densities, rapid dissipative IVR occurs. If E D 0 (S 0 ), this is followed y virational predissociation VP typically on a longer time scale than IVR. 7 9,14 Due to sustantial anharmonicities of the intermolecular potential energy surface PES and the high virational level density, which are oth very typical for vdw complexes and clusters, 38,39 virational relaxation processes occur already at modest excitation energies of a few 100 cm 1. The relaxation products are proed in the proe step step 3 in Fig. 1 using single-color R2PI. We distinguish two cases: 1 If the complex has not dissociated during, i.e., FIG. 1. Schematic level diagram of the stimulated-emission-pumping resonant two-photon ionization SEP-R2PI experiment, as applied to a M R vdw complex. The vertical axis indicates virational and/or electronic energy in the M R complex, the horizontal axis indicates time. In the pump step 1, the M R complex is excited from S 0 to S 1, usually via the electronic origin. In the dump step 2, vironic transitions from the S 1 zeropoint level are stimulated down to intra- or intermolecular virational levels in the S 0 state, which lie elow the M R vdw inding energy D 0. The system evolves in S 0 during a variale time 50 ns to 15 s. During this time, IVR leads to population of hot vdw levels. Alternatively, in step 2, the dump photon populates levels aove D 0, leading to virational predissociation VP during. The population increase or decrease in hot vdw levels is then proed y 1 1 resonant two-photon ionization R2PI via vdw sequence ands, using photons 3 3. E D 0 (S 0 ), the product M R complex can e proed via hot ands or sequence ands. By scanning the dump laser 2 and monitoring the ion signal from the proe laser 3, the ground-state virations with energies elow the dissociation energy are mapped out; this will e denoted dump spectrum. Alternatively, if the dump and pump laser are held fixed, and the frequency of the proe laser is varied, S 0 S 1 vironic spectra of selectively heated complexes are otained, denoted proe spectra. Since the dump laser is tuned to a single vironic transition, all the complexes are generated with defined total internal virational energy y the dump process, i.e., are microcanonically hot systems. The energy definition disregards the rotational energy spread, which is however low, typically T rot 2 K in the eam. 2 If the M R species has dissociated that is E D 0 within the time, the hot ground-state population originating from the SEP process has vanished, hence S 0 virations are no longer recorded as positive signals in the proe step. Under certain conditions discussed in more detail in Sec. III C it is possile to oserve ground-state vira- J. Chem. Phys., Vol. 103, No. 10, 8 Septemer 1995 This article is copyrighted as indicated in the article. 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3 Droz, Bürgi, and Leutwyler: Binding energies of carazole R 4037 FIG. 2. Proe spectra of the carazole Xe complex following the SEP process, using 1 1 resonant two-photon ionization. In trace a the pump laser 1 in Fig. 1 is on, the dump laser 2 is locked. In, oth pump and dump lasers are on, dumping occurs to the 14 3 intramolecular comination and at cm 1, elow the vdw ond energy D 0 (S 0 ); note the large increase in road ackground in the spectrum. In trace c, the part of the spectrum due to remaining cold carazole Xe population in the eam is sutracted c 0.7 a. Hence, c is the spectrum of hot S 0 state complexes generated y the pump/dump steps. Note that the residual sharp ands are lue-shifted with respect to spectrum a. tions lying aove D 0 (S 0 ) as negative peaks. Thus, D 0 (S 0 ) is racketed y the last positively oserved and the first negatively or nonoserved S 0 virational level. Figure 2 a shows a proe laser spectrum of the carazole Xe vdw complex in the vicinity of the electronic origin (S 0 S 1 ); for this spectrum the pump laser was on, ut the dump laser was off, and 750 ns. In trace, the second laser dumps Car Xe complex population to an S 0 intramolecular comination and at cm 1 ; the proe laser covers the same spectrum as in trace a. A manifold of hot ands and sequence ands appears as a relatively unstructured ackground spectrum; superimposed on this is the spectrum of the remaining cold Car Xe complexes which did not undergo the SEP process. In Fig. 2 c, sutraction of the cold spectrum a from reveals the spectrum of microcanonically hot carazole Xe at an internal energy of 845 cm 1. Note that the vironic ands still present in c are wider and less intense than in trace a, and are lue-shifted y nearly 3 cm 1. On the other hand the road ackground in the cm 1 range without sharp structure reflects the statistical energy redistriution y IVR at a relatively high density of states. For the dump spectra, the sensitivity depends on the choice of the proe laser frequency. The arrow in Fig. 2 c marks an optimum position for the proe laser proe cm 1, as the fraction of hot complexes detected at this frequency is relatively large, and the ackground of cold clusters present without dump laser Fig. 2 a is minimal. The proe-laser frequencies used for the other complexes are given in Sec. III. The and intensities of the dump spectra depend on i the Franck Condon factors for the S 1 S 0 transition; ii the S 0 IVR rates from the optically accessed or right state to the ackground states; iii optical saturation: in order to achieve a reasonale downward population transfer, the dump laser intensity was usually high enough to saturate the stronger vironic transitions, leading to an overestimate of the weaker ands; iv the frequency of the proe laser. This effect is most pronounced at low dump frequencies excess energies, since the mode density is still low and virational interstate couplings may e level-dependent. At low excitation energies, the proe spectra are structured, i.e., distinct sequence ands are oserved, as was previously shown for Car Ar Ref. 21 after dumping to 3 a 1 at 215 cm 1. Since in the dump spectra the proe laser is fixed at a certain frequency, modes for a sequence or hot and that happens to lie at the proe laser frequency are enhanced y the proe step. At higher frequencies, the proe laser spectra are road and unstructured, ut the shape of the proe spectrum can change systematically with excitation energy. For example in Car Xe, where the proe spectrum is road and unstructured aove 420 cm 1 excitation energy, the maximum of the road spectrum shifts to higher energy when exciting higher virational levels. B. Experimental details 1. Cluster synthesis Car R R Ne, Ar, Kr, and Xe clusters were synthesized and cooled in pulsed, seeded supersonic expansions. A magnetically actuated pulsed valve was employed, with a circular nozzle of diameter D 0.4 mm and wall thickness 0.2 mm. Gas pulsewidths were s. Carazole Fluka AG Switzerland, 99% purity was heated to 120 C, giving a vapor pressure of 1 mar, and seeded into either pure neon or mixtures of 2% argon, krypton or xenon in 98% neon carrier gas at a acking pressure p ar. The skimmed molecular eam was proed at a distance x/d 400. Details of the molecular eam machine and the linear time-of-flight mass spectrometer system are essentially identical to that of our previous work Laser system Three independently tunale nanosecond UV lasers are employed in the experiment. The pump and dump laser pulses step 1 and 2 or 2 in Fig. 1 were provided y two frequency douled dye lasers FL2002, FL3002, DCM dye, pumped y the same 532 nm output of a Nd:YAG laser Quanta Ray GCR3. Typical pulse energies were 200 J and 1 mj for pump and dump laser pulses, respectively. Both eams were mutually overlapped in space and time, and crossed the molecular eam perpendicularly within the ion source. The frequency douled UV output of a third pulse dye laser FL3002, DCM dye, pumped y a sec- J. Chem. Phys., Vol. 103, No. 10, 8 Septemer 1995 This article is copyrighted as indicated in the article. Reuse of AIP content is suject to the terms at: Downloaded to IP:

4 4038 Droz, Bürgi, and Leutwyler: Binding energies of carazole R ond Nd:YAG laser Quanta Ray GCR 170 was used for the proe. The Q-switches of the two Nd:YAG lasers were synchronized with a digital delay generator Stanford Research DG 535. The crossing point of the proe laser with the molecular eam could e varied from 0 to 13 mm downstream of the pump/dump eams. This is possile due to the relatively large acceptance diameter of the TOF mass spectrometer. With Ne carrier gas, this corresponds to a time delay up to 15 s. The minimum delay time that could e usefully employed was 50 ns, roughly twice the fluorescence lifetime of the Car Ar complex. 40 Typical proe laser pulse energy was 300 J. All three laser eams were unfocused, and the eam profiles at the molecular eam were approximately 2 2 mm. 3. Fluorescence lifetimes Carazole or Car R complexes R R Ne, Ar, Kr, and Xe were excited at their respective electronic origins, at x/d 15. The resulting fluorescence was collected with a quartz lens and detected y a RCA 7265 photomultiplier. The fluorescence decay curves were recorded with a Tektronix DSA GHz digitizer and averaged over 1000 laser shots. The data were corrected for the laser pulsewidth and instrument response function via deconvolution. All five decay curves were exponential to within experimental accuracy. III. RESULTS AND DISCUSSION A. Carazole Kr 1. S 0 ground-state virations We first discuss the intra- and intermolecular virational levels of Car Kr in the frequency range cm 1. For all dump spectra the proe frequency was proe cm 1,64cm 1 to the lue of the S 0 S 1 origin transition. An overview spectrum is shown in Fig. 3, and two spectrally expanded regions in Fig. 4. The intramolecular modes are classified in the C 2v point group symmetry of are carazole, although the complex has lower symmetry. The S 0 (A 1 ) S 1 (A 1 ) transition is in-plane and short-axis yaxis polarized. The assignment of S 0 intramolecular ands in the Car Kr SEP-R2PI dump spectrum is ased on previous work in molecular eams and low-temperature crystals 41,42 as well as a initio calculations. 22,43 Due to Herzerg Teller coupling to the S 2 ( 2 ) electronic state, 2 virations also occur with moderate intensities. 41 Note that a 2 1 comination ands are also of 2 symmetry. Beside a 1 and 2 virations, such comination ands are oserved in the Car Kr spectrum at cm 1 [ 2 (a 2 ) 4 ( 1 )], cm 1 [ 5 (a 2 ) 6 ( 1 )] and cm 1 [ 2 (a 2 ) 3 (a 1 ) 6 ( 1 )]. Between 200 cm 1 and 700 cm 1 the spectrum Fig. 3 consists of three clumps of ands centered at 240 cm 1, 440 cm 1, and 650 cm 1, respectively. Within the first group, shown in Fig. 4 a, are the strong intramolecular virations and 3 a 1. The most prominent ands in the second group are assigned to 7 a 1 and 2 3 a 1, whereas in the third group, presented in Fig. 4, 14 2 and 15 a 1 have largest intensity. Tale I compiles the oserved S 0 virational frequencies and intensities. FIG. 3. SEP-R2PI ground-state spectra of carazole R R Ne, Ar, Kr, and Xe otained y tuning the dump laser frequency step 2, 2 in Fig. 1. The scale is given in wave numers relative to the respective origins 0 0 0, see text. Many comination ands of intra- with intermolecular virations are also oserved in the dump spectra. The derived intermolecular virational frequencies are also listed in Tale I. From these, average values of intermolecular frequencies averaged over all oserved comination ands are listed in Tale II. Virational fundamentals of the y and z vdw modes appear in the spectrum, at 23.4 cm 1 and 38.8 cm 1, respectively. Assignments are ased on earlier work on Car Ar Ref. 44 and Car Kr; 36 y is the in-plane or ending viration along the short axis of carazole and z is the outof-plane or stretching viration. Both modes are totally symmetric a in the complex point group C s. Earlier determination of these frequencies y dispersed fluorescence emission spectroscopy 36 gave y 22.7 cm 1 and z 39.0 cm 1, in good agreement with the present results. The y mode usually yields the strongest intermolecular comination ands, ut the first overtone 2 y as well as the z fundamental are also often oserved in comination with strong and moderately strong intramolecular ands. In comination with 3 a 1, which is especially intense, even the second overtone 3 y and the intermolecular comination z y are oserved. Here, the inter- plus intramolecular comination and 3 (a 1 ) y is even stronger than the intramolecular fundamental 3 a 1 as seen in Figs. 3 and 4 a. 2. Binding energy The ground-state vdw inding energy D 0 (S 0 ) of Car Kr was accurately determined y a racketing measurement. The highest virational level which gives a positive dump J. Chem. Phys., Vol. 103, No. 10, 8 Septemer 1995 This article is copyrighted as indicated in the article. Reuse of AIP content is suject to the terms at: Downloaded to IP:

5 Droz, Bürgi, and Leutwyler: Binding energies of carazole R 4039 FIG. 4. Expanded regions of the dump spectrum of carazole Kr see Fig. 3, showing intermolecular vdw modes y and z in comination with the intramolecular levels 3 trace a and 15 trace, respectively. In order to ring out the missing transitions in trace, the two intramolecular transitions 3 and 15 are horizontally aligned. The scale is relative to the origin of carazole Kr at cm 1. spectrum signal lies at cm 1, shown in Fig. 4. This and corresponds to the 2 (a 2 ) 3 (a 1 ) 6 ( 1 ) comination level, oserved at 682 cm 1 in are carazole. This level determines the lower limit of the vdw inding energy. The following virational levels expected, ut not oserved, are indicated in Fig. 4; the dotted lines indicate the oserved positions of the vdw comination ands of 3 a 1 in Fig. 4 a, and point to the expected positions of the analogous comination ands of 15 a 1 in the lower half of Fig. 4. One such and is the intra- plus intermolecular comination 15 z, expected at cm cm 1. We note that the 15 y and is strong, ut the higher intermolecular comination virations, i.e., the z, the 2 y, and the y z are clearly missing. Another missing or very weak comination and corresponds to the level 14 y z, expected at cm 1. Neither of these, nor any other levels are oserved to higher frequency, implying all levels cm 1 lie aove the dissociation limit of the vdw ond. Comination of these two limits racket the ground-state inding energy of Car Kr as D 0 (S 0 ) cm Delay time dependence and dissociation rates TABLE I. Intra- and intermolecular virational frequencies and and intensities for ground-state carazole Kr, in the cm 1 range. Intermolecular frequencies are derived from comination ands with intramolecular modes. Assignment Wave numer/cm 1 Interm./cm 1 Intensity/% a y y z z y y y z y z y y z z y y y y y z y y a Percentage intensity, relative to strongest and. Tentative assignment. Weer and Rice have performed time-resolved experiments on vdw complexes s-tetrazine R R Ar, Kr, Xe in the electronic ground state, which gave lower limits to virational redistriution lifetimes of 4 15 ns, depending on the rare gas and the excess energy. 8 This indicates that groundstate IVR/VP processes might e quite slow, for yet unknown reasons. Also, the VP rate decreases as the dissociation limit D 0 is approached from aove. For either of these reasons, one might argue that during the delay time 400 TABLE II. Experimental intermolecular virational frequencies in cm 1 for carazole R R Ar, Kr, and Xe in the S 0 and S 1 state. a Viration Ar Kr Xe S 0 state y x y z y z y y z 83.4 S 1 state y x y z y z y 77.2 a Values refer to and maxima; experimental error 0.2 cm 1. Tentative assignment. J. Chem. Phys., Vol. 103, No. 10, 8 Septemer 1995 This article is copyrighted as indicated in the article. Reuse of AIP content is suject to the terms at: Downloaded to IP:

6 4040 Droz, Bürgi, and Leutwyler: Binding energies of carazole R TABLE III. Dissociation energies D 0 in cm 1 for the S 0 and S 1 state of carazole R R Ne, Ar, Kr, and Xe. R D 0 (S 0 ) a D 0 (S 1 ) Increase Ne Ar % Kr % Xe % a Spectral shifts are relative to the carazole and at cm 1. Value from Ref. 51. FIG. 5. SEP-R2PI spectra of carazole Kr otained y scanning the dump laser in the vicinity of the ground-state dissociation limit D 0 (S 0 ). The delay times etween SEP process and R2PI detection step, are a 90 ns, 400 ns, and c ns. Within experimental accuracy, all traces show identical and positions and relative intensities. ns employed for the dump spectra in Fig. 4 the vdw complex did not dissociate to an appreciale extent. If S 0 -state VP dynamics would indeed extend into this time range, the intensities of ands corresponding to levels lying aove D 0 should e delay time dependent. Also, since the VP rate increases with increasing excess energy E (E E D 0 ), ands corresponding to different levels aove D 0 should disappear at different rates with increasing delay time. In order to investigate this, dump spectra were measured over a spectral range of 100 cm 1 in the vicinity of the dissociation limit, with the proe laser delayed y 90 ns, 400 ns, and 12 s, covering more than two orders of delay time. As Fig. 5 shows, the spectra show no delay time dependence whatsoever etween 90 ns to 12 s, even small details of the relative and intensities eing conserved. From this we conclude that i even at the lowest excess energy E, corresponding to the 15 (a 1 ) z level, the VP lifetime must e 40 ns, given the delay time of 90 ns, the expected signal intensity, and the noise level, corresponding to a lower limit of the VP rate k VP s 1. ii Since no higherlying levels are oserved, their VP lifetimes must also e 40 ns, indicating no detectale variations in VP rates in this energy range. iii If the cm 1 level were aove the dissociation energy, as postulated aove, its VP lifetime would have to e 30 s, given the 12 s and the similarity of spectrum in Fig. 5 c to that in Fig. 5 a. A difference of almost three orders of magnitude in VP rate over a small energy range is highly improale, and we conclude that the lower experimental limit of D 0 (S 0 ) for Car Kr is indeed cm 1. The VP rate predicted y the RRKM model is given y k VP E N v E, h E where E is the total intra- and intermolecular virational energy, E is the amount of excess virational energy aove the dissociation threshold D 0 see definition aove, the numerator is the sum of virational states exceeding the dissociation energy ut exclusive of the dissociation coordinate, and (E) is the virational density of states at energy E. If we employ the lower limit to the VP rate derived aove and assume that N v (E ) 1, i.e., E is at the first state aove the dissociation energy, a virational density of states 1200/cm 1 is otained at a total energy corresponding to the vdw dissociation energy. Previous estimates of the virational density of states 6,14,15 are one to two orders of magnitude lower than this, indicating that the VP rate predicted y the RRKM model is s 1 just aove the threshold. This is in agreement with the present oservations. The S 1 excited-state inding energy can e determined y adding the spectral red shift of cm 1 to the ground-state inding energy, giving D 0 (S 1 ) cm 1. The measured values for the S 0 ground-state inding energy, the spectral shift and the S 1 excited state inding energy as well as the relative increase of the inding energy upon going from S 0 to S 1 are collected in Tale III for Car R R Ne, Ar, Kr, and Xe. B. Carazole Xe 1. S 0 ground-state virations The dump spectrum of Car Xe in the frequency range cm 1 is shown in Fig. 3, and expanded in Fig. 6. The proe laser was fixed 71 cm 1 to the lue of the and. Tale IV lists the frequencies, intensities, and assignments of the oserved transitions. The relative intensities of the intramolecular virations in the spectra of Car Xe and Car Kr are similar etween 630 cm 1 and 690 cm 1. Intense ands at 632 cm 1 and 653 cm 1 are assigned to the 14 and 15 modes, respectively, whereas consideraly weaker ands assigned to 3 3 a 1 and 2 (a 2 ) 3 (a 1 ) 6 ( 1 ) arise at 643 cm 1 and 684 cm 1, respectively. The frequencies of these intramolecular modes agree to within 0.5 cm 1 for the Kr and Xe complexes. At energies eyond D 0 (S 0 ) of Car Kr, further intramolecular modes have een assigned for Car Xe. The most prominent ands aove 840 cm 1 are cominations of 3 with 14 and 15 at cm 1 and cm 1. Slightly less intense ands arise from 21 2, 5 (a 2 ) 12 ( 1 ) and 22 a 1 modes at cm 1, cm 1 and cm 1, respectively. As for Car Kr, the two intermolecular fundamentals y and z are active and are oserved as cominations with J. Chem. Phys., Vol. 103, No. 10, 8 Septemer 1995 This article is copyrighted as indicated in the article. Reuse of AIP content is suject to the terms at: Downloaded to IP:

7 Droz, Bürgi, and Leutwyler: Binding energies of carazole R 4041 FIG. 6. Expanded regions of the ground-state spectrum of carazole Xe, cf. Fig. 3. The spectral regions corresponding to the intramolecular levels 15 trace a and 3 15 trace, respectively, are shown. In order to point out the ands which are missing in trace, the two intramolecular transitions 15 and 3 15 are horizontally aligned. The scale is relative to the origin of carazole Xe at cm 1. intramolecular modes in the dump spectra. Tale II compiles intermolecular frequencies as derived from comination ands with intramolecular modes. The average S 0 state fundamental frequencies are 24.4 cm 1 and 37.7 cm 1 for y and z, respectively. As for Car Kr, y is oserved in comination with all moderately strong ands in the spectrum, the intensity eing one third to one half of the corresponding intramolecular and intensity. Beside the very intense y and, z,2 y and y z are clearly oserved in comination with 15, as shown in Fig. 6 a. Weaker ands are assigned to 2 y z and 3 y, respectively. 2. Binding energies An accurate ground-state van der Waals inding energy D 0 (S 0 ) was also otained for Car Xe. In Fig. 6 the relevant part of the spectrum is expanded; the last oserved level, at cm 1, corresponds to the intra- plus intermolecular comination level 5 12 y. The next expected level 3 15 y at cm cm 1 is not oserved. Therefore, the racketing measurement is very accurate, giving a ground-state inding energy of D 0 (S 0 ) cm 1. In Fig. 6 a, the 15 a 1 viration at cm 1 serves as an example for the typical pattern of intra- plus intermolecular virations. In Fig. 6 the dotted lines indicate the corresponding line positions for cominations with the 3 15 mode, which are clearly missing. If the dissociation limit were cm 1, the 3 15 y and should have comparale intensity as the last oserved and, TABLE IV. Intra- and intermolecular virational frequencies and relative intensities for ground-state carazole Xe, in the frequency range cm 1. Intermolecular frequencies are derived from comination ands with intramolecular modes. Assignment Wave numer/cm 1 Interm./cm 1 Intensity % a y y z y y z y z y y y y z y z y y y y y a Percentage intensity, relative to strongest and. Tentative assignment. since oth levels correspond to comination ands of an intramolecular viration with y and the two intramolecular ands are of similar intensity. Addition of the spectral shift of cm 1 yields a dissociation energy in the S 1 first excited state of D 0 (S 1 ) cm 1 see also Tale III. C. Carazole Ar 1. S 0 ground-state virations A rief discussion of intramolecular and vdw virations of Car Ar, as shown in Fig. 3, was given in Ref. 21. The same intramolecular modes as for Car Kr are oserved for Car Ar with similar relative intensities. The two strong ands at cm 1 and cm 1 correspond to intramolecular virations 3 and 2 1. Further ands in the spectrum elow the dissociation limit are oserved at cm 1, cm 1, and cm 1 corresponding to intramolecular virations 2 4, 7, and 2 3. Comination ands with intermolecular virations are consideraly less intense for J. Chem. Phys., Vol. 103, No. 10, 8 Septemer 1995 This article is copyrighted as indicated in the article. Reuse of AIP content is suject to the terms at: Downloaded to IP:

8 4042 Droz, Bürgi, and Leutwyler: Binding energies of carazole R Car Ar than for Car Kr and Car Xe, reflecting smaller FC factors in the former case. The strongest vdw and is the y transition, corresponding to a frequency of 22.9 cm 1 for the short-axis y mode. A weaker level occurs closely aove this transition, and is tentatively interpreted as a Fermi resonance of the y fundamental with the fifth overtone of the long-axis in-plane mode, e.g., x. The z comination is also strong, yielding a frequency of 50.0 cm 1 for the out-of-plane z fundamental. A weak and at cm 1 is tentatively assigned as the y transition. The experimentally oserved intermolecular frequencies in the S 0 and S 1 electronic states are collected in Tale II. TABLE V. Fluorescence lifetimes of carazole and carazole/rare gas complexes measured at the respective ands. Species Lifetime ns carazole 38 2 a 38 2 carazole Ne 35 2 a carazole Ar 26 2 a 26 2 carazole Kr 8 1 a carazole Xe 6 a a This work. Reference Binding energies The original racketing measurements for this complex were previously presented in Ref. 21 and the corresponding dump spectrum is shown in Fig. 3. In contrast to Car Kr and Car Xe, virations aove the dissociation limit are oserved as negative signals in all dump spectra of this complex. This oservation is rationalized as follows: The fluorescence quantum yield of Car Ar is fl 0.61 see elow. Ifthe dump laser is not present or not resonant with any vironic transition, the S 1 state population fluoresces to a large collection of levels according to the FC factors. That part of the population which fluoresces to ground-state levels elow D 0 (S 0 ) creates a hot complex population, resulting in a constant ackground signal in the dump spectra. If the dump laser is resonant, a much larger fraction of the excited-state population will e dumped to one specific S 0 state virational level, since the stimulated emission rate is much higher than spontaneous emission, given the laser intensities used in our experiments. Hence, in the dump spectrum the ackground signal from hot complexes produced y fluorescence is decreased. This is overcompensated y an increase of signal from the population transferred to S 0, if this level is elow D 0. The overall effect is an increase of signal and therefore a positive and is oserved in the spectrum. If the dumped virational level is aove D 0, where the excited population dissociates, the decrease of hot population generated y spontaneous emission processes is not compensated, resulting in an overall decrease of signal and a negative and in the spectrum. Negative ands in the dump spectra will only arise if the fluorescence quantum yield is high enough to generate a sustantial ackground signal. As can e seen from Fig. 3, negative signals were oserved for complexes with Ne and Ar, while for Kr and Xe no negative ands could e oserved. This explanation is in agreement with the measured fluorescence lifetimes of Car R R Ne, Ar, Kr, Xe complexes given in Tale V. The measured S 1 lifetimes decrease in the series from Ne to Xe. Based on fluorescence lifetimes and quantum yield measurements of carazole in hexane solution y Bolman, 45 we estimate a fluorescence quantum yield fl 0.9 for gas phase carazole. From the measured S 1 lifetimes we calculate fluorescence quantum yields of 0.83, 0.61, 0.19, and 0.14 for the Car R R Ne, Ar, Kr, and Xe complexes, respectively. Thus, the quantum yield fl of the Kr and Xe complexes is more than three times smaller than for the lighter adatoms, implying that other processes must compete with fluorescence emission. It seems reasonale that the ISC rate strongly increases when going from the Ne to the Xe complex, since spin orit coupling increases with Z 4. Figure 3 shows that D 0 (S 0 ) falls into a spectral region which is relatively devoid of vironic transitions, therefore the accuracy of the racketing measurement is much lower than for the two heavier rare gases. From the spectrum in Fig. 3 the inding energy of Car Ar was determined as D 0 (S 0 ) cm 1 in Ref. 21. In susequent work, we were ale to detect virationally hot carazole released as a product from the VP process. 22 Analysis of that data yielded additional limits for the inding energy, and comination with the data of Ref. 21 allowed a much more accurate determination. The values determined 22 are D 0 (S 0 ) cm 1 for the S 0 state. Together with the measured spectral shift, 44 yields D 0 (S 1 ) cm 1 for the excited state see Tale III. For the related vdw complex indole Ar, Outhouse et al. have determined an upper limits for the S 0 and S 1 inding energies as D 0 (S 0 ) 502 cm 1 and D 0 (S 1 ) 528 cm This is in qualitative agreement with the present results, since the carazole molecule is larger y one enzene ring, offering an additional stailization interaction in oth states. D. Carazole Ne For this complex, the SEP-R2PI method furnished only an upper limit to the inding energy; in the dump spectra, no positive signals could e oserved, while a negative signal was oserved already at the cm 1 and, as is shown in Fig. 3. The proe frequency was fixed 42 cm 1 to the red of the origin transition. We conclude that the Car Ne dissociation energy is D 0 (S 0 ) cm 1. By adding the spectral shift, D 0 (S 1 ) in the excited state S 1 see Tale III. This clearly demonstrates one of the constraints of the experiment. The dissociation limit can only e racketed if the complex has active modes aove and elow D 0. Also, the determination is more accurate for systems with a high density of active modes around D 0, as for Car Kr and Car Xe. The upper limit to D 0 (S 1 ) given for Car Ne in this work is in qualitative agreement with the excited-state dissociation energy of Ne ound to 2,3-dimethylnaphthalene an aromatic molecule of comparale size to carazole, which was deter- J. Chem. Phys., Vol. 103, No. 10, 8 Septemer 1995 This article is copyrighted as indicated in the article. Reuse of AIP content is suject to the terms at: Downloaded to IP:

9 Droz, Bürgi, and Leutwyler: Binding energies of carazole R 4043 mined from a three-dimensional quantum mechanical fit to the vdw virational level structure as D 0 (S 1 ) cm E. Correlation of results 1. Binding energies Tale III compiles the experimentally determined ground- and excited-state vdw inding energies for Car R R Ne, Ar, Kr, and Xe. With the exception of Car Ne, for which only upper limits were otained, the inding energy measurements are very accurate. The relative errors for R Ar and Xe are of the order of 0.3%, and for R Kr, of the order of 0.7%. The main contriution to the attractive intermolecular interaction of an aromatic molecule with a rare-gas atom are the dispersive interactions. The largest term is the induced dipole-induced dipole, which falls off with R 6, followed y the induced dipole-induced quadrupole contriution, which falls of as R 8. Due to the large dipole moment of carazole 1.9 D, Ref. 36, the dipole-induced dipole interaction, proportional to R 6, is also non-negligile. All of these interactions scale with the rare-gas atomic polarizaility R, aleit with different dependencies on the distance of the atom from the carazole center-of-mass R cm. The distance dependencies are not simple R n functions, due to several factors; i the large size of the aromatic molecule, relative to R cm, the dipole dipole dispersion term etween two interacting atoms falls off with R 6, while for an atom interacting with an infinite surface monolayer, the same atomic interaction term leads to an integrated interaction which is proportional to R 4 ; the dispersive interaction of carazole with a rare gas is an intermediate case; ii the distriution of polarizaility and charge over the molecular frame, which is not homogeneous; iii the summation of attractive terms mentioned aove. Figure 7 a shows the values of D 0 (S 0 ) and D 0 (S 1 ) plotted vs R the polarizailities are from Ref. 47. As expected, D 0 increases with the polarizaility of R, going from Ar to Xe, ut the increase is not linear. The deviation from linear ehavior is significant for large values of R, e.g., R Xe. This is an indication that the distance of the rare gas atom Ar, Kr or Xe, respectively, to carazole, is different and increasing in the aove order. For Car Ne the SEP-R2PI technique yields only upper limits to the vdw dissociation energy of the complex in the ground and first excited state cf. Tale III and Sec. III D.As expressed y the dashed straight lines in Fig. 7 a the upper line is for S 1, the lower for S 0 state, respectively, approximate lower limits can e derived for the Ne case, assuming linear dependence etween D 0 and R for R Ar. The values for Car Ne otained y this procedure are D 0 (S 0 ) 127 cm 1 and D 0 (S 1 ) 139 cm 1, respectively. Figure 7 plots the same D 0 values vs R /R 6 cm. For the R cm, we have chosen to use the values of enzene R determined y Neusser et al. y high resolution electronic spectroscopy 48 and y Brupacher et al. y microwave spectroscopy, 20,49 since this is the most complete set of structural data currently availale for an atom-large molecule FIG. 7. a Experimental dissociation energies D 0 of carazole R R Ne, Ar, Kr, and Xe vs polarizaility R of the rare gas R in the ground S 0 and first excited state S 1, respectively. Dissociation energies D 0 (S 0 ) in cm 1 vs R /R 6 cm. R cm gives the distance of R to the carazole center-ofmass. The error ars give the experimental uncertainties; the numerical values of D 0 are shown in Tale III. For details, see text. complex. As outlined aove, the choice of exponent is aritrary, since there will e attractive contriutions with exponents ranging from n 4 upwards. Despite these uncertainties, the plot of D 0 (S 0 )vs R /R cm for carazole R R Ne, 6 Ar, Kr, and Xe results in an almost perfectly linearity cor- J. Chem. Phys., Vol. 103, No. 10, 8 Septemer 1995 This article is copyrighted as indicated in the article. Reuse of AIP content is suject to the terms at: Downloaded to IP:

10 4044 Droz, Bürgi, and Leutwyler: Binding energies of carazole R TABLE VI. Zero-point virational energies ZPVE and well depths D e for carazole R R Ar, Kr, and Xe in the S 0 and S 1 state. Property Ar Kr Xe ZPVE S D e (S 0 ) ZPVE S D e (S 1 ) relation, cf. Fig. 7. Upon electronic excitation to the S 1 excited state, all D 0 values increase Tale III. The asolute increase in dissociation energy is experimentally determined y the spectral shifts. Such measurements have een performed for many vdw systems, and it has een known for over a decade that the shifts increase with polarizaility. 50 It is interesting that also the relative increase is larger for the heavier atoms, increasing from 8.8% for Ar to 11.8% for Xe. For carazole-ar a R cm S Å has recently een determined y Sussmann et al.; 51 the corresponding value for the complex with enzene is 3.58 Å. 48 The shorter vdw ond distance reflects the increased interaction strength with carazole. This difference has not een accounted for in the plot of Fig. 7, since only the value for R Ar is known. Up to now, accurate experimental data availale on dissociation energies of aromatic molecule-rare gas vdw complexes are not plentiful, and in many cases the accuracy of the data is not precisely known. Some early references are collected in Ref. 52. For the system Car Kr, Bösiger and Leutwyler 36 previously determined D 0 (S 1 ) and D 0 (S 0 ); in the R2PI spectrum the signal strongly decreased etween two ands at 736 cm 1 and 792 cm 1, and moreover the and at 792 cm 1 was severely roadened. It was concluded that D 0 (S 1 ) is racketed y these two values, resulting in inding energies of D 0 (S 1 ) cm 1 and D 0 (S 0 ) cm 1. This is in good agreement with the value in this work D 0 (S 0 ) cm 1, see Tale III. As for the geometry determinations, many investigations of dissociation energies, some conflicting, have een undertaken for M enzene. Brupacher et al. 20 have deduced the inding energy of enzene Ar and enzene Ne y Fourier transform microwave spectroscopy and predict values of D 0 (S 0 ) 408 cm 1 R Ar and D 0 (S 0 ) 151 cm 1 R Ne, respectively. Neusser et al. 48 predicted a much lower dissociation energy on the asis of an extrapolation of the out-of-plane virational mode. On the other hand, using pulsed field threshold ionization spectroscopy, the same group 37 has determined upper ounds for the ground state D 0 : D 0 enzene Ar 457 cm 1 and D 0 enzene Kr 402 cm 1. Since D 0 enzene Ar must e smaller than D 0 enzene Kr they corrected the upper limit for the inding energy of enzene Ar to D 0 enzene Ar 402 cm 1. This value is in qualitative agreement with the work of Brupacher and co-workers. 20 Given the fact that carazole is larger than enzene, oth values otained for enzene Ar are consistent with the present value for Car Ar D 0 (S 0 ) cm 1, see Tale III. The upper ound for enzene Kr, which is D 0 (S 0 ) 402 cm 1 Ref. 37 is much less than our value for Car Kr of D 0 (S 0 ) cm 1. Assuming that oth values are correct, Kr is ound more than 1.7 times stronger to carazole than to enzene. On the theoretical side, a initio calculations were performed on most enzene R complexes. In a series of papers, Hoza and co-workers have presented ground-state well depths for enzene Ne D e (S 0 ) 99 cm 1, enzene Ar D e (S 0 ) 429 cm 1 D 0 (S 0 ) 380 cm 1, enzene Kr D e (S 0 ) 485 cm 1 D 0 (S 0 ) 450 cm 1 and enzene Xe D e (S 0 ) 601 cm These results were otained using counterpoise corrected MP2 calculations. Klopper 19 and coworkers applied MP2-R12 counterpoise corrected to enzene Ne and enzene Ar and otained ground-state value for D e ; D e (S 0 ) 154 cm 1 R Ne and D e (S 0 ) 553 cm 1 R Ar. There is thus quite a large uncertainty in the a initio results for the strongly studied enzene rare gas complexes; therefore, accurate experimental values are of high interest. 2. Well depths In order to determine the well depths D e, accurate zeropoint virational energies ZPVE are needed. In principle, these are only otainale through knowledge of the exact intermolecular potential, in comination with a threedimensionally exact virational eigenvalue calculation. 53 In the harmonic approximation, the oserved y and z fundamentals yield the zero-point energy contriutions. The zeropoint energy for the x viration is very small, preliminary calculations give frequencies in the range 3 5 cm We have therefore assumed x /2 2.5 cm 1 for the Car Kr and Car Xe complexes while for Car Ar, x /2 was calculated from the oserved and tentatively assigned, cf. Tale II 6 x frequency, assuming harmonic ehavior. Frequency shifts of intramolecular virations upon complexation are neglected, since most frequencies of intramolecular modes are expected to shift very little when forming vdw complexes. The otained zero-point virational energies ZPVE and well depths D e are compiled in Tale VI for the Car Ar, Car Kr, and Car Xe complexes for oth the S 0 and S 1 states. Interestingly, the ZPVE is largest for the Car Ar complex and decreases y 10% for Car Kr and Car Xe. On going to the S 1 electronic state, the ZPVE increases only slightly 1 2 cm 1. The relative difference etween D 0 and D e [(D e D 0 )/D e ] is 6.8% 6.4%, 4.6% 4.4%, and 3.6% 3.4% for Car Ar, Car Kr, and Car Xe in the S 0 S 1 electronic state. IV. CONCLUSIONS The experimental results given in the aove work show that the SEP-R2PI method is a flexile and accurate technique for the determination of the ground-state vdw dissociation energies D 0 (S 0 ) of M R complexes. Very accurate determinations of the D 0 (S 0 ) values are presented for the systems carazole R R Ar, Kr, and Xe, with relative uncertainties of 0.4%. For the complex with Ne an upper limit of D 0 (S 0 ) cm 1 is determined. By taking into account the S 0 /S 1 electronic spectral shifts of the complexes relative to are carazole, excited-state dissociation energies D 0 (S 1 ) were derived with similar precision. J. Chem. Phys., Vol. 103, No. 10, 8 Septemer 1995 This article is copyrighted as indicated in the article. Reuse of AIP content is suject to the terms at: Downloaded to IP: