sures, the solvent was precompressed by cooling the gas in a pressure-resistant cryotrap. The high-pressure cell showed no decrease in pressure during the ...
J Chim Phys (1995) 92, 566-600 © Elsevier, Paris
Solvation ultrafast dynamics of reactions: Vdissociation and atom recombination of iodine in the gas-to-liquid transition region C Lienau*, AHZewail** Arthur Amos Noyes Laboratory of Chemical Physics***, California Institute of Technology, Pasadena CA 91125, USA * Deutsche Forschungsgemeinschaft Postdoctoral Fellow. ** Correspondence and reprints. Contribution No 8989.
Abstract The femtosecond solvation dynamics of an elementary chemical reaction in the gas-to-liquid transition region is examined. The reaction is that of an iodine molecule dissociating and recombining in compressed supercritical rare gases, helium, neon, argon and krypton at pressures between 0 and 2500 bar. This study focuses on four elementary steps in the dis sociation and recombination of iodine in solution: coherence of В state vibrational wave packet motion, solvent-induced В state predissociation, geminate recombination onto ex cited electronic states and subsequent vibrational relaxation. In helium and neon, vibra tional coherence persists for more than 3 ps even at the highest pressures which indicates the importance of vibrational relaxation for the dephasing process. The В state predissociation rate increases with solvent density as suggested by Isolated Binary Collision models and reaches a value of (0.9 ps)-1 in argon at 2500 bar. Geminate recombination in argon at 1600 bar occurs within 2 ps, similar to liquid solvents, while vibrational relaxation into a thermalized A/A' state distribution is slower, occurring at the rate of (13 ps)-1. The geminate re combination yields are strongly dependent on the size of the solvent molecules and the overall pressure dependence of the yields is in agreement with predictions from a diffusionbased theoretical model. The present study exemplifies how variation of the solvent pres sure affects the dynamics of an elementary chemical reaction and presents a unique way of studying the effect of the solvent structure on reaction dynamics in solution. We present a simple model which accounts for these phenomena in different phases: supercritical fluids, liquids, clusters and matrices. Résumé La dynamique femtoseconde de solvatation d'une réaction chimique élémentaire dans la ré gion de transition gaz-liquide est examinée. La réaction est celle d'une molécule d'iode qui se dissocie et se recombine dans les gaz rares hélium, néon, argon et krypton se trouvant dans l'état supercritique sous des pressions comprises entre 0 et 2500 bar. L'étude se con centre sur quatres étapes élémentaires dans la dissociation et la recombinaison de l'iode: la
— 567 — cohérence du mouvement du paquet d'onde vibrationnel dans l'état électronique B, la pré dissociation de l'état électronique B induite par le solvant, la recombinaison géminale dans des états électroniques excités et la relaxation vibrationnelle subséquente. Dans l'hélium et le néon, la cohérence vibrationnelle persiste plus de 3 ps même aux pressions les plus hautes et donne une indication sur l'importance de la relaxation vibrationnelle dans le processus de déphasage. La vitesse de prédissociation de l'état B augmente avec la densité du solvant, comme suggéré par les modèles de collisions binaires isolées, et atteint (0.9 ps)-1 dans l'ar gon à 2500 bar. La recombinaison géminale a lieu dans l'espace de 2 ps dans l'argon à 1600 bar, ce qui est comparable à la vitesse de prédissociation dans les solvants liquides. Par contre, la relaxation vibrationnelle dans les états électroniques A/A’est plus lente: sa vi tesse est celle de (13 ps)-1. Les rendements de la recombinaison géminale dépendent forte ment de la taille des molécules du solvant et la dépendance générale des rendements avec la pression est en accord avec les prédictions théoriques d'un modèle basé sur la diffusion. L'étude actuelle démontre l'effet de la variation de la pression du solvant sur la dynamique d'une réaction chimique élémentaire et présente une methode originale d'étude de l'effet de la structure du solvant sur la dynamique de réaction en solution. Nous proposons un modèle simple qui tient compte de ces phénomènes dans les différentes phases: fluides supercri tiques, liquides, clusters et matrices.
I. Introduction The dynamics of molecular iodine in solution have attracted considerable attention for more than 50 years [1]. The particular beauty of this system lies in its apparent simplicity, two atoms in a bulk solvent. An accurate characterization of the gas phase potential energy curves of several iodine electronic states together with numerous available literature on its behavior in different phases make the system appealing as a prototype for the study of a wi de variety of dynamical processes. With visible laser pulses in the wavelength range of 420 to 800 nm, three different electronic states can be excited, the repulsive B 1 u Π), and the bound B 0 (3П) and А1и(3П) states (Fig. 1). Relative absorption strengths as a func tion of excitation wavelength have been obtained by Tellinghuisen [2]. For solvent-free io dine, if excitation is above the В state dissociation limit [3], a direct photodissociation on either the П or the В state occurs within a few hundred femtoseconds [4]. In the presence of high pressure rare gases [4] or in I2/Ar van der Waals complexes [3,5,6], a recombination of the dissociating iodine atomic fragments and the formation of "new" iodine molecules on excited В state vibrational levels is observed. In compressed rare gases (up to 100 bar) this "caging" process occurs in less than one picosecond as demonstrated in time-resolved ex periments and confirmed by molecular dynamics simulations [4]. If excitation is to bound vibrational-rotational В state levels, the dynamics of the free iodine molecules are governed by the В state potential energy curve. With femtosecond resolution, the coherent vibrational and rotational wave packet motion was monitored in real time [7] and from experiments at several different excitation energies this potential was ex-
— 568 —
Fig. 1: Electronic potential energy surfaces of I2 relevant to the present study. Six of the ten states correlating with ground state atoms are shown. Solid lines designate gas phase potential (for references see A. Matemy, Ch. Lienau and A. H. Zewail, in preparation.). The dashed line shows the solvent shift of the D' ion-pair state in argon at 1600 bar and 293 K, as approximated from the solvent shift on the D' -> A fluorescence emission. Ver tical arrows indicate optical transitions (at 0 bar) used to excite (620 nm) the molecule and to probe (310 nm) the dissociation and recombination dynamics of iodine in supercritical rare gas solvents. The optical transitions that are involved in the excitation are X - >B, X -> A, X —>1пи. В —>E, В —>f A’ —>D', A—>ß, X —>D are the dominant probe transitions in the wavelength range from 270 to 400 nm. In most experiments the intense D —>A fluo rescence is detected.
— 569 — traded [8]. The decay rate of free molecules on the В state, which is the sum of the rates for radiative decay and spontaneous predissociation, is on the order of (1 µs)-1 [9]. In the presence of buffer gases, a predissociation of В state molecules is observed, resulting from a solvent-induced transition from the В to a repulsive electronic state that correlates with ground state iodine atoms. This predissociation most likely involves the re pulsive a'0g+(3Σ- ) or alg(3n) states [10,11] and its rate increases with buffer gas density. Predissociation cross sections at various excitation wavelengths have been determined for a variety of bath gases and are tabulated in Ref. 12. In parallel to the predissociative В state quenching, iodine-solvent collisions induce a vibrational relaxation within the В state. Ex periments in rare gases indicate that even in low vibrational levels, vibrational relaxation rates are comparable to those for predissociation [13]. In high pressure argon, femtosecond time-resolved studies [4] demonstrated not only the increase of the solvent-induced predis sociation rate with density but also the collision-induced dephasing of the coherent В state vibrational wave packet motion. While, at excitation energies close to the В state dissocia tion limit, dephasing occurs within one or two vibrational periods, a significantly longer persistence of the vibrational coherence was observed if low vibrational levels are excited. A geminate recombination of the atomic fragments formed in the В state predissociation could not be detected in these experiments at 100 bar argon pressure. In liquid solvents, В state predissociation occurs on a time scale of hundreds of fem toseconds (250 fs in liquid hexane for excitation with 580 nm pulses [10]). The separation of the atomic iodine fragments is hindered by the surrounding solvent atoms. A large frac tion of the dissociating atom pairs recombine and form new iodine molecules on one of the bound iodine valence states. This geminate atomic recombination has been the topic of a great number of experimental and theoretical studies over the last decades (for an excellent review see Ref. 14). It is generally thought to occur in the following sequence of steps: • the iodine molecule dissociates and the atomic fragments transfer their excess kinetic energy to the solvent, • the atomic iodine pair re-encounter and • collisions with surrounding solvent molecules stabilize this encounter pair in a bound electronic state that correlates with ground state iodine atoms. The new iodine molecules are formed in high vibrational levels and will transfer the excess vibrational energy, in a sequence of collisions, to the solvent. Molecules that are formed in excited electronic states -A'2W(3П) or Alu (3П) - undergo an electronic transi tion to the ground X-state which is again followed by vibrational energy transfer until finally a thermalized distribution of ground state molecules is reached. The groups of Troe and van den Bergh established the quantum yield for geminate recombination in a variety of gaseous and liquid solvents [15,16], and from these measurements proposed a model for steady-state
— 570 — caging. Much less is known about the actual dynamics of the recombination process. Pico second experiments from Harris’ group [17,18] indicated an ultrafast recombination that oc curs in less than 2 picoseconds. From ground state recovery experiments [14,17,19] in a variety of molecular solvents it was inferred that at least 50 % of the recombining atoms are trapped on the excited A/A’ states. Quantum yields for recombination into the different states and for non-geminate recombination could be determined for different solvents at sev eral excitation wavelengths. The detrapping rate out of the A/A' states is strongly solvent dependent [20] and ranges from (100 ps)-1 in cyclohexane to less than (5 ns)-1 in liquid xe non. The vibrational relaxation on the electronic ground state surface has been studied in considerable detail, both experimentally [14,18,21] and theoretically [22-26]. It was found that vibrational relaxation through the upper half of the ground state well is rapid and occurs typically on a time scale of 10 ps in molecular solvents. Relaxation is slower in the lower ground state vibrational levels and equilibration is complete within a few hundred picosec onds. Even in monatomic liquid solvents like xenon, 6000 cm-1 of energy are lost in less than 150 ps. Relaxation through the lower half of the ground state well is much slower and takes several nanoseconds [18]. In a number of picosecond experiments, iodine dissociation and recombination dynamics have been followed after excitation above the dissociation energy of the weakly bound Alu( Π) state. Here, dissociation is direct and in liquids, gemi nate recombination dynamics and yields are similar to those for excitation into the В state [17,19,23]. Direct femtosecond resolution of caging was made recently. It was demonstrated that in large argon clusters recombination of fragment iodine atoms to form the new iodine bond occurs after 600 fs as a coherent process inside the solvent cage [27]. In argon and krypton matrices, a similar time scale for the recombination was observed. Coherence was pre served throughout the recombination process and the recombinant molecules were shown to vibrate coherently on the A/A' surfaces even after an extensive amount of vibrational energy was transferred to the surrounding rare gas cage [28]. In large clusters and matrices, re combination is followed by vibrational energy relaxation which occurs on a time scale of tens of picoseconds. To examine the density and solvent effect on the dynamics we initiated, in a series of experiments with femtosecond time resolution, studies of the real time dynamics of iodine in compressed solvents in the gas-to-liquid transition region [29]. The dissociation and re combination dynamics of iodine were probed in supercritical solvents (helium, neon, argon, krypton and others) in the pressure range 0 to 2500 bar. This approach allowed us to study reaction dynamics in solvents whose state changed from an essentially "ideal" gas at low pressures through the gas-to-liquid transition region to a liquid-like fluid at the highest pres sures examined. Through variation of the pressure the number of iodine-solvent collisions is increased and the time between collisions is gradually brought to the time scale of the
— 571 — nuclear motion of the solute while a variation of the specific rare-gas solvent changes the nature of each iodine-solvent collision. These experiments were aimed at providing a de tailed microscopic picture for the dissociation and recombination of iodine in fluid solvents, with the hope of elucidating the elementary steps of the reaction mechanism in the con densed phase. We used 60 fs laser pulses, centered at 620 nm, to excite ground state iodine mole cules. A large fraction, 62%, of the excited molecules reached low vibrational levels ν' = 6 11 of the bound В0u+(3П) state [7,8] (centered around ν' = 8), while 34 % were placed on the weakly bound Alu(3П) state and the remainder on the dissociative B"1u(1Π) state [2]. The dynamics of the prepared wave packet were then interrogated by a second ul trashort laser pulse, whose wavelength could be varied from 270 to 400 nm. This probe pulse could excite molecules near the outer turning point of the В state into either the f 0g or E0g ion-pair states of iodine. We detected the laser-induced ion-pair state fluorescence as a function of the delay time between pump and probe pulses. The fluorescence intensity is a measure of the В state population at the probed internuclear distances. The probe laser could also monitor molecules from different vibrational levels [30] of the weakly bound A'2 u( П) and Alu(3П) states by excitation into the D'2g or ßlg ion-pair states. Fluo rescence induced from molecules in high vibrational levels on the ground state, however, will be shown to be negligible under our conditions. Thus, in our experiments, we are mainly sensitive to the coherent wave packet motion within the bound В state, the collisioninduced В state predissociation and the recombination of the dissociating atom pair, which is followed by vibrational relaxation on the A/A' states. In this paper, we will briefly discuss the solvent effect on the ion-pair state fluores cence. We present experiments on the solvent- and pressure-dependence of the coherent В state vibrational wave packet motion and the В state predissociation dynamics. We will then discuss experiments using various probe wavelengths to examine the geminate recom bination dynamics in compressed argon at 1600 bar. These experiments facilitate a conclu sive interpretation of the pump-probe transient and provide a detailed picture of the recom bination dynamics in compressed rare gases. Results on geminate recombination yields are compared to a diffusion-based theoretical model. Finally, the experiments in compressed rare gases are compared to related experiments in clusters, matrices and liquids.
П. Experimental The experimental setup used is similar to the one described elsewhere [31] and will only be briefly discussed here. The fs laser pulses were generated from a colliding-pulse mode-locked ring dye laser (CPM) and amplified in a four-stage, Nd:YAG-pumped dye
—572 — amplifier (PDA). The amplified pulses were temporally recompressed in a double-pass, two-prism arrangement before being separated into pump and probe lasers by a 50/50 beam splitter. Half of the light was focused into a KD*P crystal to generate the 310 nm probe pulse, and the fundamental was removed with a UG 11 filter. The relative timing between the two pulses was varied with a high-precision, computer-controlled actuator. The pump arm contained two polarizers and a half-wave plate to allow variation of the angle between the polarizations of the two lasers. This angle was kept constant at 54.7° (rotational anisotropy effects in the transients will be detailed later). The pump and probe lasers were recombined with a dichroic beam splitter and then focused slightly beyond the center of the high-pressure cell. Care was taken to prevent continuum generation within the cell. Laser-induced fluorescence was collected perpendicular to the laser propagation di rection, collimated into a monochromator, and detected with a photomultiplier tube (PMT). The spectral resolution of the monochromator was set at 6 nm FWHM. The pulses were 60 fs in duration. The high-pressure cell was constructed from stainless steel and designed to withstand pressures of up to 4000 bar [32]. Four windows, 6 mm in diameter, were centered in each of the four walls, and the cell had a total volume of 0.2 cm3. The input window was 4.0 mm thick quartz, while the output and fluorescence-collection windows were 2.8 mm thick sapphire. Pressure in the cell was monitored with a precision strain-gauge pressure trans ducer. After introducing the iodine carefully, the cell was filled with the solvent gas, which was compressed to the desired pressure in an iterative process. To reach the highest pres sures, the solvent was precompressed by cooling the gas in a pressure-resistant cryotrap. The high-pressure cell showed no decrease in pressure during the course of an experiment. Fluorescence signal from the PMT was averaged in a boxcar integrator and recorded as a function of actuator position in a computer. The transients were fitted to a sum of expo nential rise and decay functions using standard software that takes into account the 60 fs pulse widths. As mentioned before, excitation from the В state is to either the E3П(0+ g jor f^Ogj ion-pair states. In argon and krypton, a very efficient collision-induced electronic conver sion [33] from the E or f to the energetically lowest ion-pair state, D', is induced. The de tected fluorescence comes entirely from the D'—>A' transition and only one fluorescence band is detected in the spectrum. The center wavelength of this transition is strongly pres sure dependent and is found to shift from 342 nm at 0 bar to 374 nm at 2000 bar argon and to 370 nm at 300 bar krypton. Even more pronounced solvent shifts have been observed in large argon clusters [34] and rare gas matrices [35]. The gas-phase potentials of the iodine valence states are expected to be only weakly perturbed by inert solvents [36], and this redshift therefore reflects a solvent-induced lowering of the ion-pair state surfaces (see Fig. 1). These fluorescence shifts are evidently due to a solvation of the molecular dipole in the D’
— 573 — ion-pair state by the dielectric of the rare gas solvent. The pressure dependence of the sol vent-shift can be understood in terms of classical cavity cell models of solvent shift theories [36,37]. In the lighter rare gases this pressure-induced shift is far less pronounced (from 342 nm at 0 bar to 345 nm at 2000 bar helium and to 347.5 nm at 2080 bar neon), see Fig. 2. Moreover two additional fluorescence bands are observed at 270 and 290 nm in both helium and neon, even at the highest pressures. These bands most likely arise from transitions from the originally excited f ion-pair state to valence states and this indicates that electronic quenching of the initially excited ion-pair-state is less effective in these solvents than in ar gon or krypton. A very strong perturbation of the ion-pair states is observed in krypton. Besides the strong solvent-induced red- shift of the D'—>A' transition maximum, an increase in pressure significantly broadens this transition [36]. At pressures above 200 bar, an additional broad band fluorescence is induced by absorption of 310 nm probe pulses. This fluorescence ex tends from 310 nm to more than 450 nm in the red. Its intensity increases with pressure such that at p = 600 bar the entire fluorescence spectrum is dominated by this band and de-
Pressure (bar) Fig. 2: Solvent-induced red shift on the D -> A transition in compressed rare gases. The solid lines are linear interpolations between the experimentally observed red shift and ε -1 . . . ~ —- as suggested by classical cavity models (Ch. Lienau and A. H. Zewail, in prepara tion). ε is the static dielectric constant of the solvent.
— 574 — tection of D'—>A' two-photon fluorescence becomes difficult. This absorption is likely to arise from a charge-transfer transition of iodine-solvent complexes, as are known to be pres ent in polar liquids (for a review see e.g. Ref. 38).
III. Results and Discussion In the following, we present a series.of femtosecond pump-probe experiments on io dine in supercritical rare gases at pressures between 0 and 2500 bar. The experimental transients (Fig. 3) reflect different aspects of the iodine dynamics. The oscillatory modula tion of the fluorescence intensity at early times is indicative of coherent dynamics of the excited В state wave packet and the loss of coherence induced by iodine-solvent interac tions. At early times, we note a decay of the fluorescence intensity and this reflects the de population of the В state due to solvent-induced predissociation. At sufficiently high pres sures, the initial decay of the LIF intensity is followed by a slower rise. The rise at long times reflects the geminate recombination of iodine atoms onto the A/A' state and the vibra tional relaxation of the nascent iodine molecules. These different aspects of the dynamics of iodine in rare gas solvents, i.e. coherent wave packet dynamics on the В state, В state predissociation, geminate recombination and vibrational relaxation, will be addressed sepa rately in the following sections.
III. 1. Coherent wave packet dynamics In isolated iodine molecules, the coherent vibrational motion of the electronically ex cited molecules on the В state can be monitored over tens of picoseconds (Fig. 3). The ex perimental magic angle transient directly shows the average vibrational frequency while the interference pattern in the signal modulation, which has a period of about 9 ps, originates from the superposition of excited vibrational eigenstates and their difference in oscillation period arising from the anharmonicity of the excited state potential. The fluorescence intensity as a function of time delay τ contains frequency compo nents which correspond to energy differences wiy =ω(i) - ω ( j ) between different vibra tional eigenstates i and j in the В state, and the amplitude Aij of the component with fre quency wij depends on the frequency spectrum of the light pulses and the electronic sur faces which are involved in the light-matter interaction [36,8]. In the presence of a rare gas solvent, the free propagation of the vibrational wave packet on the В state is disturbed by iodine-rare gas collisions. This results in a loss of co herence or a dephasing of the vibrational iodine motion. The oscillatory modulation of the fluorescence signal is consequently damped. This damping was first observed in argon at pressures up to 100 bar [4] and later at pressures of up to 800 bar [29]. Under these condi-
— 575 —
Fig. 3: Femtosecond transients of iodine in compressed supercritical argon at 293 К at pressures of 0, 201, 594 and 1628 on two time scales. Experiments have been recorded us ing LIF detection at "magic" angle polarization between pump (620 nm) and probe (310 nm) wavelengths. Detection wavelength was varied with pressure to optimize LIF signal. Note the persistence of coherent vibrational motion of the В state wave packet for two ps at a pressure of 594 bar. The initial peak on the first oscillation reflects the direct dissociation of the fraction of molecules that is excited onto the repulsive A state. The 15 ps transients in dicate the increase in В state predissociation rate with increasing pressure. At 1600 bar, the rise in signal intensity at delay times longer than 4 ps reflects the geminate recombination of iodine atoms and the subsequent vibrational relaxation within the A/A' states. Except for the 0 bar data, the step size used in these transients (up to 16 ps) was too large to resolve the coherent wave packet motion.
— 576 — tions the loss of vibrational coherence occurs on a picosecond time scale and becomes more rapid at higher pressures. At a pressure of 600 bar, e. g., vibrational coherence persists for about 2 ps or seven vibrational periods (Fig. 3). Dephasing is induced by a variety of differ ent mechanisms [4,39-42]. Both elastic and inelastic collisions contribute to the total rate of dephasing. In simple cases, the various processes may be divided into two categories, those which cause population relaxation (T1type), e.g. through vibrational relaxation within the В state or collision-induced predissociation, and those which merely induce phase shifts in the В state wavefunction without causing population (or energy) relaxation ("pure" or T2 type dephasing). In our experiments at high argon pressures it was observed that the loss of vi brational coherence occurs on approximately the same time scale as the exponential decay of the transient intensity. The exponential decay is due to collision-induced predissociation of the В state as will be discussed in Section III.2. A consistent finding was made in a study on the reaction dynamics of iodine in liquid hexane solution by Scherer et al [10]. Here the В state coherence dephasing time, T2, was found to equal the 230 ps population lifetime, Ti, within experimental error. It was concluded that both vibrational dephasing and В state depopulation occur from a solvent-induced predissociation. In order to test this conclusion we set out to perform new experiments in the lighter rare gases helium and neon, where collision-induced predissociation is significantly slower than in argon. In neon, at a pressure of 794 bar (Fig. 4), a strong modulation of the fluores cence signal is observed at early times and vibrational coherence persists for about 13 vi brational periods or 4 ps. This modulation within the first 4 ps strongly resembles the modulation on the 0 bar transient. The interference pattern observed at 0 bar for time delays of about 9 ps, however, is entirely damped. If we gradually lower the pressure from 794 to 403 bar and then to 100 bar, we find, to our surprise, that the transient modulation pattern on the fluorescence transient changes only slightly. At both pressures a similar modulation pattern is observed during the first four picoseconds, the interference pattern at later times, however, does not recur. At the lowest pressure, 100 bar, collision-induced predissociation occurs with a rate of (33.4 ps)-1, evidently about an order of magnitude slower than the dephasing of the coherent vibrational motion. We therefore have to conclude that in neon, unlike in liquid hexane or high pressure argon, collision-induced predissociation is not the dominant mechanism which causes the vibrational dephasing. Experiments in high pressure helium (Fig. 5) confirm this conclusion. A persistence of vibrational coherence for more than two picoseconds (9 vibrational periods) is observed at the highest pressure, 1960 bar, of our study. After 3 picoseconds, the modulation is entirely damped and, at this high pressure, the dephasing time is again similar to the В state lifetime, which is 2.8 ps. As the pressure is reduced to 400 bar, corresponding to a predissociation rate of (14 ps)-1, the vibrational coherence persists for 5 ps. The oscillatory modulation re sembles the one observed in neon at the same pressure. The interference pattern that is ob-
— 577
Fig. 4: Vibrational dephasing and solvent-induced predissociation. Femtosecond transients (up to 13 ps) for iodine in supercritical neon at a temperature of 293 К and pres sures of 0, 100, 403 and 794 bar. The damping of the oscillatory modulation on the tran sients reflects the dephasing of the coherent vibrational wave packet motion within the В state. Note that at a pressure of 100 bar, predissociation is significantly slower than vibra tional dephasing. "Magic" angle polarization between pump (620 nm) and probe (310 nm) wavelengths was used. Detection wavelength: 270 nm, except for the 0 bar transient (342 nm). served after 9 picoseconds in the absence of a buffer gas is again damped. At a helium pres sure of 100 bar, slight indications for coherence persist at delay times of more than six pico seconds: the dephasing, however, is almost complete after 5 ps. This has to be compared to the much slower predissociation rate of (39 ps)-1. As in the case of neon solvent it therefore has to be concluded that predissociation is not the dominant dephasing process. The Fourier transformations (square roots of the power spectrum) of the oscillatory transient (Fig. 5) indicate that vibrational relaxation plays a major role in the dephasing. The Fast Fourier Transform of the 0 bar transients indicates the distribution of vibrational levels which is excited by the pump and reveals the energy differences between adjacent vi-
—578 —
Fig. 5: Vibrational dephasing in helium: Left side: Oscillatory modulation on the femtosecond transients after subtraction of the underlying decay due to solvent-induced predissociation. Note the rapid dephasing at a helium pressure of 100 bar. "Magic" angle polarization between pump (620 nm) and probe (310 nm) wavelengths was used. Detection wavelength: 270 nm at 0 and 1960 bar and 342 nm at 100 and 400 bar. Right side: Fast Fourier transform of the oscillatory modulation. At 0 bar, the Fourier spectrum reveals the energy differences between adjacent vibrational В state levels wij =w(i)-w(j). The dis tribution of vibrational levels, which is excited by the pump laser, reaches from ν' = 6 to ν' = 11 and is centered around ν' = 8. As the helium pressure increases, the Fourier spectrum broadens and shifts to lower vibrational levels. This indicates an efficient relaxation of the vibrational В state distribution on the time scale of the coherent wave packet motion.
— 579 — levels which is excited by the pump and reveals the energy differences between adjacent vi brational levels: ωi,i-1= ω(i) —ω(i —1). То a first approximation, the amplitude at the fre quency ωi,i-1 in the Fourier spectrum reflects the population in the vibrational eigenstates i and i-1 [8]. The maximum in the Fourier spectrum at 0 bar corresponds to the frequency ω8,7 =113.0 cm-1 and the width of the Fourier spectrum reflects the number of vibrational eigenstates which are populated by the pump laser pulse [43]. At a helium pressure of 100 bar, the Fourier spectrum broadens, because of the solvent induced damping of the modula tion and the fluctuations in vibrational frequencies. Several distinct frequency components can be resolved and we note that the intensity of components with a frequency of more than 114 cm-1 increases significantly compared to the 0 bar transient. The same trend is contin ued as the pressure is increased to 400 bar. The spectrum is almost entirely smeared out, only a weak shoulder at low frequencies can be resolved. The entire spectrum shifts to higher frequencies, the amplitude maximum is now centered at 115 cm-1. At the highest pressure of 1960 bar, the spectrum is entirely structureless, significantly broader than at the lower pressures and strongly blue-shifted to a center wavelength of 118 cm-1. This shift of the Fourier spectrum to higher frequencies indicates a relaxation of the vibrational population in the excited В state on the time scale of coherent vibrational wave packet motion. This vibrational relaxation becomes more rapid with increasing pressure, consequently the probed vibrational distribution relaxes to lower quantum-numbers and the mean oscillation period shifts to higher frequencies. We note that this conclusion relies on the assumption that the gas-phase vibrational frequencies remain unchanged in high pressure helium. In light of the weak electrostatic interaction between iodine and helium atoms [44] and the negligible solvent-induced red-shift on the ion-pair state fluorescence emission, this assumption appears to be realistic. Moreover, a (weak) red shift of the vibrational frequen cies is found in nonpolar liquid solvents [45]. (The solvent effect on the В state potential will be tested in molecular dynamics simulations which are currently underway). We there fore conclude that vibrational relaxation occurs on the time scale of coherent vibrational motion and that vibrational coherence is at least partly preserved during these inelastic col lisions. This conclusion is consistent with recent femtosecond experiments on the dissocia tion and recombination of iodine in rare gas matrices [28], where coherence of the vibra tional motion was found to persist after dissociation, geminate recombination and substan tial loss of vibrational energy. A similar observation was made in the photodissociation of I3 ■ Here the fragment ion I2' vibrates coherently on a time scale which is comparable to that of vibrational cooling [46]. We note, that the fast dephasing at 100 bar relative to that at 2000 bar in helium is sur prising if it is assumed that isolated binary collisions are the key to the dephasing. It might, possibly, indicate the important role of iodine-solvent clusters for the dephasing dynamics in compressed supercritical fluids. The role of solute-solvent complexes for reaction dynamics
— 580 — in solution will be examined in further experimental and theoretical studies which are in progress.
ΙΠ. 2. В state predissociation In all solvents, we observe a decay of the В state fluorescence signal that is underlying the oscillatory modulation from the coherent vibrational wave packet motion. This decay reflects the depopulation of the В state resulting from solvent-induced predissociation. A collision between iodine and a solvent atom can induce a transition from the В state onto a nearby repulsive potential. In nonpolar solvents, the repulsive potentials which are involved in the predissociation are assigned to the alg( П) and a'0g(3 Σ ) states [10,12]. Both states cross the В state near the outer turning point at low vibrational energies(alg near ν' = 1 and a'0g+ near ν' = 5).
Fig. 6: Collision-induced В state predissociation rates kpred in supercritical rare gases (helium, neon, argon and krypton) at pressures between 0 and 2500 bar and at a tem perature of 293 K. Excitation is at 620 nm. In low pressure gases (< 10' bar), the collision-induced predissociation has been studied in considerable detail [12,13,47]. In this pressure regime, the predissociation is in-
— 581 — duced by isolated binary collisions between iodine and the gas atom or molecule. The pre dissociation rate has been related to the quenching probability ppred per iodine-solvent collision and the binary collision frequency Z/2-Rg · a quenching cross section, σ pred, is defined as the product of ppred and the cross-section of the collision pair [13]. Assuming a simple hard-sphere collision frequency, predissociation rate constants are then given by, кpred = &pred
^ ^ A P>
[1]
where ϋ is the mean thermal velocity (m/s) of the collision pair, NA is Avogadro's number and p is the solvent density (mol / m ). (In the limit of low-pressure gases, p = pRTand kpred becomes proportional to pressure as given by the Stern-Volmer relationship). At a pressure of 4-10-5 bar and at room temperature the quenching cross sections have been measured by Capelle and Broida [47] to be: He: 1.4 Â2, Ne: 4.4 Â2, Ar: 17.6 Â2, Kr: 35.8 Â2, for excitation at 623.4 nm, and He: 1.1 Â2, Ne: 2.6 Â2, Ar: 16.0 Â2, Kr: 30.5 Â2. for excitation at 607.1 nm.
Fig. 7: Collision induced В state predissociation rates kpred in supercritical rare gases (heli-um, neon, argon and krypton) as a function of solvent density. The solid lines show linear interpolations between predissociation rate and density at pressures of up to 1200 bar.
— 582 — If this concept of isolated binary collisions can be transferred to high pressure super critical rare gases, we expect a strong variation of the predissociation rate with increase in pressure. This is observed in all four rare gases, helium, neon, argon and krypton (Fig. 6). In each solvent the predissociation rate increases monotonically with pressure, e.g. in he lium from (150 ps)-1 at 25 bar to (2.8 ps)-1 at 1960 bar. While predissociation rates at con stant density are of similar magnitude in helium and neon, a significant increase in the rates occurs as the solvent is changed to argon and krypton. In argon, a predissociation rate of (0.95 ps)-1 is reached at the highest pressure of our study and this value approaches the В state predissociation rate of (0.3 ps)-1 in liquid hexane [10]. If the predissociation rate is correlated with density, a linear relationship is obtained in all solvents (Fig. 7). We note that the correlation is excellent for pressures below 1200 bar, while slight deviations occur at higher pressures. Experimental predissociation rates are slightly faster than expected from linear correlation at p < 1200 bar and the deviations increase with increasing pressure. This (approximately) linear dependence between predissociation rates and density suggests that the quenching cross sections σ рred can be extracted from Eq. (1). From a lin ear correlation at pressures below 1200 bar we obtain the following values for о pred for excitation at 620 nm: He: 0.98 Â2, Ne: 2.20 À2, Ar: 11.1 À2, Kr: 21.4 Â2. Within experimental error, these values are in excellent agreement with those which have been obtained at a foreign gas pressure of 4-10-5 bar by Capelle and Broida. Evidently, the physical mechanism which causes the solvent-induced predissociation remains the same, even though the pressure varies by seven orders of magnitude and the density and the pre dissociation rate at high pressures are similar to that of liquid solvents. Isolated binary col lisions are seemingly the dominant cause of predissociation and the long range order of the solvent at high pressures is of less importance. This indicates that a short range interaction induces the coupling between the bound and the repulsive state. The actual "dissociation" of the molecule occurs only when iodine and the solvent atom are at very short intemuclear distances. Changing the solvent atom changes the nature of each particular iodine-solvent colli sion, i.e. the strength of the induced dipole - induced dipole interaction (which depends on the polarizability of the solvent) and the time scale of the collision (which depends on the relative velocity, and thus on the reduced mass of the collision pair). If the predissociation mechanism is the same at low and at very high pressures, gas phase models should be appli cable in order to explain the variation in quenching cross section with solvent atom. Selwyn
— 583 — and Steinfeld [48] have introduced such a model in order to describe the parametric depend ence of the predissociation probability per collision on the macroscopic solvent properties. The quenching efficiency σ pred is expressed as:
[2]
where a is the polarizability and I the ionization energy of the solvent. The reduced mass is μ and Rc is the (hard-sphere) radius of the collision pair. From Eq. (2) we obtain the fol lowing predissociation cross sections, normalized to o(He)= 1.0 À,
in good agreement with experiment in compressed rare gases. This indicates that the mechanism which governs the collision-induced predissociation is the electric-field induced coupling between the bound В and the repulsive state. We note however, that care must be taken in extrapolating the Selwyn-Steinfeld model to liquid molecular solvents. In hexane at room temperature a predissociation rate of (0.3 ps)-1 was observed experimentally, while an extrapolation of Eq. (2) from argon at 1600 bar to liquid n-hexane at ambient pressure pre dicts a decay constant of 2.0 ps [49]. This indicates the importance of extending our studies from atomic to molecular solvents. Experiments in molecular solvents which bridge the gap between the gas and the liquid phase could be of great help for a detailed understanding of the dynamics in solution. Such experiments are currently in progress. III. 3. Geminate recombination The fate of the pair of atomic fragments which are formed after photoexcitation of io dine will be the topic of this section. Atom formation occurs either through solvent-induced В state predissociation as discussed above or through direct dissociation from excitation onto the A or B" states. The atomic fragments will initially separate from each other and transfer their excess kinetic energy to the solvent. Free iodine atoms can undergo solventmediated atomic recombination [3] where M denotes a solvent atom. In this recombination process, vibrationally excited iodine molecules are formed on either the electronic ground state or on those bound electronic states that correlate with ground state iodine atoms, e.g. A or A'. In each of these bound
— 584 States the newly formed iodine molecules transfer vibrational energy to the surrounding sol vent atoms. Those molecules which are born in excited electronic states will eventually un dergo an electronic transition to the ground state. In general, recombination processes can be divided into two classes: • geminate recombination acts of two fragments from the same parent molecules, and • non-geminate recombination acts of atomic fragments belonging to two different par ent molecules. At rare gas pressures of less than 100 bar, non-geminate recombination is the only signifi cant recombination process. Non-geminate recombination requires the diffusive approach of fragments from different molecules and this occurs, under our experimental conditions, on a micro- to millisecond time scale. The concentration of molecules that recombine within the time scale of our experiments (one nanosecond) is therefore too small to be detec-
Fig. 8: Predissociation and geminate recombination in argon: Experimentally ob served LIF transients (up to 200 ps) for iodine in argon at a temperature of 293 К and pres sures between 200 and 1965 bar. Excitation is at 620 nm, probe wavelength 310 nm. Note the pronounced biexponentiality on the recombination signal at a pressure of 1628 bar. Fluorescence detection is at 354 nm - 200 bar, 360 nm - 400 bar, 364 nm - 800 bar, 370 nm - 1628 bar.
— 585 — ted. Consequently, the transients at these low pressures reflect only the dynamics of iodine molecules on the originally excited electronic state. In a series of experiments in argon sol vent (Fig. 8) [29], we observe that at pressures above 200 bar, the fast decay of the predis sociation signal is followed by a slower rise in fluorescence intensity. This rising transient, whose intensity increases strongly with solvent pressure, reflects the geminate atomic re combination and the subsequent vibrational relaxation of the newly bom iodine molecules. We tentatively assigned this "recombination" transient to molecules formed on the excited A/A' state. ΙII.3.1. State of caging: Probe wavelength dependence In order to test the assignment of the state of caging (X vs. A/A') and to investigate geminate recombination and vibrational relaxation dynamics in more detail, we performed a series of experiments in argon at 1600 bar varying the probe laser wavelength from 275 nm to 400 nm (Fig. 9). The fluorescence signal at early times arises from molecules within the originally excited В state as discussed above. The initial В state signal is observed at all probe wavelengths, and its intensity decays exponentially with a rate of (1.2 ps)-1, the solvent-induced predissociation rate, see Sec. III.2. LIF signal at later times can arise from re combined iodine molecules on three different electronic states, X, A and A'. Each electronic state has an allowed optical transition to low-lying ion-pair states: X —>D, A—>ß, A' D'. Due to the strong coupling between these ion-pair states in argon, all three transi tions lead to the same fluorescence emission from the vibrationally relaxed lowest ion-pair state: D' —>A'. This fluorescence is detected in our experiments. In order to interpret the experimental transients, we need to consider which electronic states can be involved in the absorption of a probe photon at a given probe wavelength. We will give a qualitative discussion of the absorption of each of these transition based on the classical Franck-Condon principle [50]. It states that both nuclear positions and momenta of a molecule remain unchanged during the absorption of a photon, and this implies that the kinetic energy of a particle is conserved during the transition. In this classical picture, all diatomic molecules at a given intemuclear distance absorb light at the same wavelength. This absorption wavelength is then given by the energy difference between the potential en ergy surfaces of the two electronic states involved in the transition (Mulliken's difference potentials [51,52]). The difference potentials for isolated gas-phase I2 molecules are shown in Fig. 10. It can be seen that at a pressure of 1600 bar argon a laser pulse centered at 310 nm can be absorbed by molecules in all three electronic states. The diagram also shows that a 310 nm photon can be absorbed by ground state molecules only at intemuclear distances much larger than the equilibrium X-state distance of 2.67 Â, corresponding to high vibra tional levels with Evib > 7000 cm'1. Molecules in the A or A' state, however, can absorb at large intemuclear distances as well as at distances close to the equilibrium distance of 3.06A
— 586 —
Fig. 9a: Transients of iodine in compressed supercritical argon at a pressure of 1600 bar on a time scale of 200 ps (0.67 ps/data point). The maximum intensity of the В state signal around t=0 has been normalized to unity. The В state LIF decay is independent of the probe wavelength and occurs at a rate of (1.2 ps)-1. The В state fluorescence is followed by a slower rise, which reflects the geminate recombination onto the A/A'-state and the vibra tional relaxation dynamics within these states. The inserts for Хрrobe = 287.0 and 298.5 run show experiments performed under identical conditions on a time scale of 800 ps (2.67 ps/data point). The insert for Xprobe = 346.2 nm shows a transient taken under identical conditions with a time delay of 0.133 ps/data point. The overlay shows the same transient after subtraction of the single-exponential В state decay with a rate of the (1.2 ps)-1 . This transient reflects only the geminate recombination and vibrational relaxation dynamics. For this transient, the vertical scale has been enlarged by a factor of three relative to the tran sient that includes the В state dynamics.
—587 —
Fig. 9b: Transients of iodine in compressed supercritical argon at a pressure of 1600 bar on a time scale of 200 ps (0.67 ps/data point) using probe wavelengths between 355.0 and 377.3 nm. Experiments have been recorded at a temperature of 293 К using LIF detec tion at "magic" angle polarization between pump (620 nm, 60 fs) and probe (variable wave length) laser. The detection wavelength was adjusted at each probe wavelength in order to optimize D' —>A' fluorescence and minimize overlap with scattered probe laser light. No dependence of the transients on the detection wavelength could be observed. The transient at 7probe = 377.3 nm shows only the predissociative В state decay with a rate of (1.2 ps) . Recombination onto iodine valence states is not probed at this wavelength. The inserts show experiments performed under identical conditions on a time scale of 25 ps (0.133 ps/data point). On these transients the initial single-exponential В state decay has been subtracted. The LIF intensity on these transients is relative to the maximum В state inten sity.
— 588 —
Fig. 10: Difference potentials for isolated gas-phase iodine molecules (solid line) and iodine in argon at 1600 bar and 293 К (dashed line). In high-pressure argon, all iodine ionpair states have been assumed to be lowered in energy by an amount ΔΕ. This decrease in energy has been obtained from the experimentally observed red shift in the D' —>A' fluo rescence emission spectrum (see Fig. 2) and was assumed to be independent on intemuclear distance. Iodine gas-phase potentials have been taken from the literature, for references see A. Matemy, Ch. Lienau and A. H. Zewail, in preparation. and 3.08 Â, respectively. If the probe laser is tuned to the red of 340 nm, absorption cannot occur from X-state molecules: the photon energy is not sufficient to reach the ion-pair states. At probe wavelengths longer than 340 nm the "recombination" LIF signal arises ex clusively from molecules on the A or A' states. The difference potentials indicate that, to the red of 370 nm, none of the three optical transitions should be probed in absorption. This prediction is confirmed experimentally in argon at 1600 bar. At a probe wave length of 377.3 nm (Fig. 9) only the predissociative В state decay is observed. The decay is single-exponential and its decay rate of (1.2 ps)-1 is the same as extracted previously from experiments at a probe wavelength of 310 nm. At 371.8 nm a residual LIF signal is ob served at delay times up to 30 ps. Based on the difference potentials this signal arises from highly vibrationally excited molecules on the A or A' state. Intemuclear distances larger than the equilibrium distance are probed and therefore molecules in vibrationally relaxed levels are not seen. The known exponential В state decay can be subtracted from the total
— 589 — LIF signal and the remaining "recombination" signal shows a fast rise followed by a slower decay. We note that the fluorescence signal does not decay all the way to zero. A very weak, slowly decaying fluorescence remains for about 200 ps. From a simple biexponential analysis of the signal we obtain a rise time of about 1 ps and a decay time of 13 ps (for a detailed analysis of the probe-wavelength dependent transients at 1600 bar and at other pressures see Ref. 30). We conclude that this fast rise time indicates an extremely fast geminate recombination process, as observed in liquid solvents. This ultrafast recombination which occurs on a similar time scale as in matrices and large rare gas clusters indicates a "direct" recombination mechanism that takes place inside a solvent "cage". After dissipation of excess kinetic energy to the surrounding solvent atoms, the atomic iodine fragments re main at close internuclear distances, imprisoned inside the first solvent shell, before recom bination occurs. Highly vibrationally excited iodine molecules are thus bom on the A or A' state surface within less than 2 ps. The decay of the LIF signal reflects the relaxation into lower vibrational levels and therefore out of the probe "window". This vibrational relaxa tion within the A/A' state occurs with a rate of (13 ps)-1. Analogous results are obtained if the probe laser is tuned further to the blue (369.5 to 362.6 nm). The intensity of the "recombination" signal increases and the rise and decay time remain similar, in agreement with the above assignment. As the laser frequency is switched to "blue" probe wavelengths (287 to 310 nm), the difference potentials indicate that vibrationally relaxed levels or internuclear distance close to the equilibrium distances of 3.06 Â and 3.08 À of A or A' state are probed. We expect a much slower rise of the "recombination" signal limited by vibrational relaxation through A/A' state. Indeed, the LIF signal following the В state decay shows a rise with a rise time of, again, 13 ps. This fast rise, however, is followed by a slower rise, with a rate of about (200 ps)-1. The fluorescence intensity increases slightly up to delay times of 800 ps, the maximum time range of our experiment. This long persistence of the "recombination" signal is consistent with the expected slow electronic transition from the excited A/A' to the ground state. The difference potentials (Fig. 10) show that molecules in high vibrational ground state levels (Evib > 6000 cm-1) are probed at these "blue" wavelengths. For example, a wavelength of 310 nm corresponds to probing of ground-state molecules with a vibrational energy of more than 7000 cm-1. It is known from picosecond pump-probe experiments in liquid xenon [18] that vibrational relaxation through the upper half of the ground state po tential is rapid and occurs on a time scale of 100 ps in liquid xenon. In these experiments, the density of the monatomic solvent is similar to that of argon at 1600 bar. In our expe riments, vibrational relaxation through high vibrational ground state levels is thus expected to occur on a similar time scale as in xenon. Ground state molecules should therefore give rise to a LIF transient that displays a fast rise reflecting the ultrafast geminate recombination and a much slower decay within at most a few hundred picoseconds as the ground state vi-
— 590 — brational distribution relaxes through the probed window. Such a transient rise and decay is not resolved in the present experiments. In fact, in the wavelength range from 277 to 310 nm the LIF signal following the В state decay increases monotonically for at least 800 ps. Conclusively, fluorescence that is induced by ground state molecules is too weak to signifi cantly affect the shape of the transients. This indicates that the extinction coefficient in high vibrational X-state levels is much weaker than that for molecules in relaxed A/A'-state. It does not, however, mean that the quantum yield for recombination onto the ground state is low. We recall that experiments by Kelley et al. [19] indicate that in nonpolar liquid solu tion quantum yields for recombination onto the X and A/A' states are of similar magnitude. The strong fluorescence from A/A' state molecules at wavelengths around 300 nm is ex pected, as it is known that the extinction coefficient for the D' 0 to the A/A'-state dynamics on LIF transients recorded with a pump wavelength of 620 nm and a fixed probe wavelength of 310 nm for "magic" angle polarization between both lasers. These rise times reflect the recombination dynamics of iodine atoms and the subsequent vibrational relaxation dynamics within the A/A'-states. (b) Amplitude of the LIF intensity at long times (t = 170 ps), relative to the initial В state signal (recombination amplitude arec) in helium, neon, argon and krypton for pressures be tween 0 and 2500 bar. The amplitudes reflect the probability for geminate recombination onto the A/A'-state.
— 594 — counter radius ( Rc < r0 ), this "encounter pair" can either recombine or continue the random motion through the solvent. The total yield for geminate recombination is then given as [56]: [5] The first factor Rc / r0 is dependent on the initial separation of the dissociating iodine at oms and increases to unity in the limit of high pressures. The second factor in eq. (5) de scribes the relative importance of the probability for collisional stabilization versus diffusional separation of the encounter pair. The constant kfec is taken as the product of the limiting third order rate coefficient for the non-geminate re combination of iodine at low pressures [57] and the solvent concentration: 2 о 2 d[l2 ] / dt = k[I] [M] = k°ec[I] . The pressure diffusion coefficient for iodine atoms is de noted by D (a discussion of how pressure dependent diffusion coefficients were extrapolated will be given elsewhere [36]). The probability
increases towards
unity with increasing pressure since the solvent concentration increases and kgec follows; the diffusion coefficient is inversely proportional to the density. In contrast in the low pres sure limit kgrec —>0 and prec goes to zero. As an example we consider the case of argon at 1600 bar: Rc = 5.5 Â, r0 = 7 À and prec = 0.6; thus Φrec = 0.5. Fig. 13 shows the dependence of the yield on pressure and solvent atom, together with the theoretical results. The predictions of the model are in reasonable agreement with the experimental results. This supports the importance of the probability for "in-cage" colli sional stabilization of the newly formed iodine molecule (or "cage capture") in competition with penetration of the first solvent shell ("cage break-out"). The probability is a measure of the "rigidity" or "hardness" of the cage, and in a microscopic picture, reflects the interac tions of iodine with the surrounding solvent atoms. At very high pressures (or in the limit ing case of iodine imprisoned in large argon clusters or matrices) this probability is close to unity, and the dynamics are entirely dominated by the ultrafast recombination within the (rigid) solvent cage. As we lower the pressure of the solvent, this probability gradually de creases and a finite fraction of the atoms can leave the solvent cage and start a diffusive motion throughout the solvent. At high pressures in argon (1600 and 2000 bar), a pronounced bi-exponentiality of the recombination signal is observed: a large fraction of atoms recombine within a few picosec onds, while others undergo ("secondary") recombination processes, which occur on a sig nificantly longer time scale. A further decrease in prec (as the pressure is lowered), in-
— 595 — creases the fraction of atoms which leave the solvent cage and increases the importance of diffusive recombination. At the lowest pressures in our study, this probability tends towards zero, so that the motion of the iodine atoms is dictated by random diffusion through the sol vent.
Fig. 13: Comparison of experimentally determined quantum yields for geminate re combination with theoretical values from the diffusion-based model by Otto, Schroeder and Troe (see text). Quantum yields have been obtained by normalization of the recombination amplitude arec to the known experimental value for the caging yield in krypton at 400 bar of Φrec = 0.4. The validity of this normalization procedure relies on solvent and pressure in dependent extinction coefficients of I2 in the В and A/A' state at a wavelength of 310 nm (as discussed in the text). At a given pressure, a change of the solvent molecule thus corresponds to a change in the probability for cage capture versus cage break-out which relates to the rigidity of the first solvent shell. The change in this probability can be modeled by the decrease in diffu sion coefficient and the increase in efficiency for collisional stabilization of the iodine atom pair with increasing rare gas atom size. It is interesting to consider the time scale that the
—596 — OST model will predict for the caging in the diffusion model. At an argon pressure of 1600 bar, e.g., a biphasic recombination dynamic results from the model. A large fraction of at oms (about 50%) recombine within 10 picoseconds, while the remainder recombines on a longer time scale of about 200 ps; these values were obtained from the solution of the dif fusion equation for the change of the yield in time which is given in Ref. 56. This is at least in qualitative agreement with our experimental results at longer times and confirms the sig nificance of secondary or diffusive recombination. Our experimentally observed ultrafast geminate recombination on the time scale of 1 ps is, however, not part of the model, as it reflects the direct coherent caging in the solvent structure. This is not surprising, as a model which treats the solvent as a continuum neglects its microscopic structure and the iodinesolvent interactions. Molecular dynamics simulations may help in formulating a general model that accounts for both time regimes of solvation (work in progress).
III. 4. Comparison to studies in different solvent media We wish to end this paper with a brief comparison of the study in high pressure rare gases to related work in various solvent media. Of particular interest are here recent studies in rare gas matrices and jet-cooled van der Waals complexes of iodine. Liu. et al. [27] re ported on the coherent recombination dynamics of iodine in large argon clusters excited above the A state dissociation limit. In such cold van der Waals clusters iodine molecules are surrounded by a very rigid solvent structure, which prevents dissociating iodine atoms from breaking through the solvent wall. Such a structure presents the limiting case of the present study in which the quantum yield for geminate recombination is close to unity and where the recombination is entirely dominated by direct in-cage dynamics. This has been observed experimentally. The cage-induced recombination of iodine atoms proceeds coher ently and new iodine molecules are formed on the A or A' state within approximately 700 femtoseconds. At the probe wavelength of 310 nm, the recombination dynamics is followed by a slower (~ 30 ps) signal build-up, which resembles the dynamics observed in highpressure argon, even though the build-up time is slightly longer. Based on the spectral analysis given above, the signal at long delay times should reflect the accumulation of io dine molecules in low vibrational A/A' state levels. A recent probe-wavelength dependent study by Liu et al. supports this interpretation [58]. If excitation is to the bound В state re combination dynamics are preceded by a solvent-induced predissociation as in high-pressure rare gases. In cold argon and krypton rare gas matrices iodine molecules are surrounded by an even more rigid cage structure. Consequently the recombination proceeds coherently within about 1 picosecond. This coherent recombination and a coherent motion of the nascent io dine population has been observed experimentally by Apkarian et al [28]. Similar to our study, a variety of UV probe wavelengths ranging from 319 nm to 364 nm have been used to
— 597 — interrogate the dynamics of molecules in different vibrational levels on the A and A' states. No evidence for a contribution from ground state iodine molecules was reported. Variation of the probe wavelength allowed to probe the vibrational relaxation dynamics within the A/А' state that occur on a somewhat longer time scale than in room-temperature argon at high pressures (p = 1600 bar). The interpretation of the picosecond transients by Apkarian et al. is fully consistent with the results of the present work. It is of particular interest to note that for transients at wavelengths which probe a vibrationally "hot” A/A' state distribu tion, the LIF signal decays to zero within less than 50 ps (λprobe = 364 nm in argon matri ces). A residual fluorescence at longer times, which we observed in high pressure argon at 1600 bar and attributed to diffusive or secondary recombination, could not be detected in the matrix study. This is consistent with the interpretation of the high pressure argon ex periments as the probability for cage breakout in argon matrices is zero. Experiments on the dynamics of iodine in liquids, interrogated by UV laser pulses, have also been made [4,17]. In an early communication, Harris et al. reported on the UV transient absorption of iodine in CCl4 and hexane after excitation with 590 nm pulses. The probe wavelength dependence of the reported transients strongly resembles the transients that were reported above in argon at a pressure of 1600 bar. It is thus likely that the UV absorption in these experiments not only reflects the В state predissociation, that was too fast to be resolved, but also the fast geminate recombination and the subsequent vibrational relaxation within the A/A' state. If analyzed in terms of the model presented above, these experiments would suggest an A/A’ state vibrational relaxation rate of (5 to 10 ps)-l, which is comparable to the rate observed in argon at the highest pressures. In conclusion, femtosecond spectroscopy could be shown to be an invaluable tool to gain direct insight into elementary reaction steps in solution. A consistent picture emerges that describes the dissociation and recombination of iodine in gases, liquids, clusters and matrices. More studies are in progress and are aimed at understanding the nature of the coupling and the solute-solvent collision.
Acknowledgment This work was supported by the National Science Foundation. Ch. L. gratefully ac knowledges a postdoctoral fellowship by the Deutsche Forschungsgemeinschaft. We would like to thank Arnulf Matemy for his help in the experiments with variable probe wave lengths and for many stimulating discussions. We particularly wish to thank Chris Hyland for his suggestions and help.
— 598 —
References [1] J. Frank and E. Rabinowitch, Trans. Faraday Soc. 30, 120, (1934). E. Rabinowitch and W. C. Wood, Trans. Faraday Soc. 32, 547, 1381, (1936). [2] J.Tellinghuisen, J. Chem. Phys. 58, 2821 (1971). [3] K. L. Saenger, G. M. McClelland and D. R. Herschbach, J. Phys. Chem. 85, 3333, (1981). [4] A. H. Zewail, M. Dantus, R. M. Bowman and A. Mokthari, J. Photochem. Photobiol A 62,301,(1992). Y. Yan, R. M. Bowman, K. R. Whitnell and A. H. Zewail, Chem. Phys. Lett. 193.402, (1992). [5] J. J. Valentini and J. B. Cross, J. Chem. Phys. 77, 572, (1982). [6 ] J. M. Philippoz, H. van den Bergh and R. Monot, J. Phys. Chem. 91, 2545, (1987). [7] R. M. Bowman, M. Dantus and A. H. Zewail, Chem. Phys. Lett. 161.297, (1989). M. Dantus, R. M. Bowman and A. H. Zewail, Nature 343. 737, (1990). [8] M. Grubele, G. Roberts, M. Dantus, R. M. Bowman and A. H. Zewail, Chem. Phys. Lett. 166. 321. (1990). M. Grubele and A. H. Zewail, J. Chem. Phys. 98, 894, (1993). [9] G. A. Capelle and H. P. Broida, J. Chem. Phys. 58, 4213, (1973). [10] N. F. Scherer, L. D. Ziegler and G. R. Fleming, J. Chem. Phys. 96, 5544, (1992). N. F. Scherer, D. M. Jonas and G. R. Fleming, J. Chem. Phys. 99, 153, (1993); and references therein. [11] We note that a recent Resonance Raman study by Xu et al.(J. Xu, N. Schwentner, M. Chergui, submitted for publication) indicates that, in liquid xenon, for excitation into low vibrational В-state levels, very fast predissociation into the repulsive В"1и(^П) state might occur. The Raman spectra in liquid CCl4 , however, support predissociation into the a'0g+(^I') or alg(3FI) states. [12] J. I. Steinfeld, J. Phys. Chem. Ref. Data 13, 445, (1984). [13] R. B. Kurzel, E. G. Degenkolb and J. I. Steinfeld, J. Chem. Phys. 56, 1784, (1972). J. I. Steinfeld and A. N. Schweid, J. Chem. Phys. 53, 3304, (1970). R. B. Kurzel and J. I. Steinfeld, J. Chem. Phys. 53, 3293, (1970). J. I. Steinfeld and W. Klemperer, J. Chem. Phys. 42, 3475, (1965). R. Brown and W. Klemperer, J. Chem. Phys. 41, (1964), 3072. [14] A. L. Harris, J. K. Brown and С. B. Harris, Ann. Rev. Phys. Chem. 39, 341, (1988). [15] J. Schroeder and J. Troe, Ann. Rev. Phys. Chem. 38, 163, (1987). J. Troe, J. Phys Chem. 90, 357, (1986); and references therein. [16] J. C. Dutoit, J. M. Zellweger and H. van den Bergh, J. Chem. Phys. 78, 1825, (1983). J. C. Dutoit, J. M. Zellweger and H. van den Bergh, J. Chem. Phys. 72, 5405, (1980). [17] M. Berg, A. L. Harris and С. B. Harris, J. Chem. Phys. 84, 788, (1986). D. E. Smith and С. B. Harris, J. Chem. Phys. 87, 2709, (1987). [18] M. E. Paige and С. B. Harris, Chem. Phys. 149. 37, (1990). [19] D. F. Kelly, N. A. Abul-Haj and D. J. Jang, J. Chem. Phys. 80, 4105, (1984).
N. A. Abul-Haj and D. F. Kelly, Chem. Phys. Lett. 119, 182, (1985). N. A. Abul-Haj and D. F. Kelly, J. Chem. Phys. 84, 1335, (1986). [20] M. E. Paige and С. B. Harris, J. Chem. Phys. 93, 1481, (1990).
— 599 —
[21] X. Xu, S.-C. Yu, R. Lingle, H. Zhu and J. B. Hopkins, J. Chem. Phys. 95, 2445, (1991). [22]D. Nesbitt and J. T. Hynes, J. Chem. Phys. 77, 2130, (1982). [23] P. Bado, C. Dupuy, D. Madge, K. R. Wilson and M. Malloy, J. Chem. Phys. 80, 5531, (1984). P. Bado, P. H. Berens and K. R. Wilson, Proc. Soc. Photo-Opt. Instrum. Eng. 332. 230, (1982). [24] A. H. Lipkus, F. P. Buff and M. G. Sceats, J. Chem. Phys. 79, 4830, (1983). [25] C. L. Brooks and S. A. Adelman, J. Chem. Phys. 80, 5598, (1984). R. H. Stote and S. A. Adelman, J. Chem. Phys. 88 , 4415, (1988). [26] D. J. Russell and C. B. Harris, Chem. Phys. 183. 325, (1994). J. K . Brown, C. B. Harris and J. C. Tully, J. Chem. Phys. 89, 6687, (1988). J. K. Brown, D. J. Russell, D. E. Smith and C. B. Harris, Revue Phys. Appl. 22, 1787, (1987). [27] E. D. Potter, Q. Liu and A. H. Zewail, Chem. Phys. Lett. 200. 605, (1992). [28] Q. Liu, J. -K. Wang and A. H. Zewail, Nature, 364. 427, (1993). [29] R. Zadoyan, Z. Li, P. Ashjian, C. C. Martens and V. A. Apkarian, Chem. Phys. Lett. 218. 504,(1994). R. Zadoyan, Z. Li, C. C. Martens and V. A. Apkarian, to be published. [29] Ch. Lienau, J. C. Williamson and A. H. Zewail, Chem. Phys. Lett. 213. 289, (1993). Ch. Lienau and A. H. Zewail, Chem. Phys. Lett. 218. 224, (1994). [30] A Materny, Ch. Lienau and A. H. Zewail, in preparation [31] M. J. Rosker, M. Dantus and A. H. Zewail, J. Chem. Phys. 89, 6113, (1988). [32] We are grateful for the kind help given us by Dr. Dirk Schwarzer from the Max-PlanckInstitut für Biophysikalische Chemie in Göttingen in the design of the cell. For it to reach these high pressures is possible only because of the careful design. [33] A. L. Guy, K. S. Viswanathan, A. Sur and J. Tellinghuisen, Chem. Phys. Lett. 73, 582, (1980). [34] S. Fei, X. Zheng, M. C. Heaven and J Tellinghuisen, J. Chem. Phys. 97, 6057, (1992). [35] M. Macler and M. C. Heaven, Chem. Phys. 151.219, (1991). [36] C. Lienau and A. H. Zewail, in preparation [37] L. Onsager, J Am. Chem. Soc. 58, 1486, (1936). C. J. F. Böttcher, Theory of electric polarization, Elsevier, Amsterdam, 1973. [38] M. Tamres and J. Yarwood, in:"Spectroscopy and structure of molecular complexes", ed. by J. Yarwood, Plenum Press, New York, 1973. [39] R. M. Shelby, C. B. Harris and P. A. Cornelius, J. Chem. Phys. 70, 34, (1979). [40] K. S. Schweizer and D. Chandler, J. Chem. Phys. 76, 2296, (1982). [41] D. W. Oxtoby, Ann. Rev. Phys. Chem. 32, 79, (1981). D. W. Oxtoby, Adv. Phys. Chem. 40,1, (1979); 47,487, (1981). [42] S. F. Fischer and A. Laubereau, Chem. Phys. Lett. 35, 6 , (1975). [43] The fact that not all the frequency components ω i-1are resolved in the Fourier spectrum is due to the finite time delay τmax=16 ps up to which the 0 bar transient has been recorded. [44] D. H. Levy, Adv. Chem. Phys. 47 part I, 323, (1981). [45] W. Kiefer and H. J. Bernstein, J. Raman Spec. 1, 417, (1973). [46] U. Banin and S. Ruhman, J. Chem. Phys. 98, 4391, (1993). U. Banin, R. Kosloff and S. Ruhman, Chem. Phys. 183. 289, (1994).
—
600 —
[47] G. A. Capelle and H. P. Broida, J. Chem. Phys. 58, 4212, (1973). [48] J. E. Selwyn and J. I. Steinfeld, Chem. Phys. Lett. 4, 217, (1969). [49] The following parameters have been used: Lennard-Jones diameters: He - 2.576 Â, Ne2.789 Â, Ar - 3.418 Â, Kr - 3.6 Â, 12 - 4.982 Â, n-hexane - 5.909 Å. Polarizabilities (10-30 m3): He-0.2050, Ne - 0.3956, Ar -1.6411, Кr - 2.4844, hexane- 11.78. Ionization potentials (eV): He - 24.587, Ne - 21.564, Ar - 15.795, Kr- 13.999, hexane 10.18. [50] J. Frank, Trans. Faraday Soc. 21, 536, (1925). [51] R. S. Mulliken, Chem. Phys. 55, 309, (1971). [52] J. Tellinghuisen, J. Mol. Spectrosc. 103.455, (1984). [53] J. Tellinghuisen and L. F. Phillips, J. Phys. Chem. 90, 5108, (1986). [54] J. Zimmerman and R. M, Noyes, J. Chem. Phys. 18, 658, (1950). D. Booth and R. M. Noyes, J. Am. Chem. Soc. 82, 1868, (1960). L. F. Meadows and R. M. Noyes, J. Am. Chem. Soc. 82, 1872, (1960). [55] K. Luther and J. Troe, Chem. Phys. Lett. 24, 85, (1974). [56] B. Otto, J. Schroeder and J. Troe, J. Chem. Phys. 81, 202, (1984). [57] H. Hippier, K. Luther and J. Troe, Ber. Bunsenges. Phys. Chem. 77,1104, (1973). [58] Q. Liu, J. K. Wang and A. H. Zewail, to be published.
