J. Phys. Chem. 1994, 98, 3352-3360
3352
Femtosecond Real-Time Probing of Reactions. 16. Dissociation with Intense Pulses A. Matemy,' J. L. Herek, P. Cong,* and A. H. Zewail' Arthur Amos Noyes Laboratory of Chemical Physics,$ California Institute of Technology, Pasadena, California 91 I25 Received: December 27, 1993'
In this contribution, we consider the wave packet dynamics in the dissociation reaction of N a I at different laser powers for both the preparation and the probing. The probing is made for the asymptotic N a fragment as well as the transition-state complex [Na I]$*. A novel nonlinear behavior at higher intensities is reported and examined here with a new set of experiments. This behavior reflects the change in the absorption cross section along the reaction coordinate and can be quantified using a simple kinetic picture and a classical model of the dynamics.
.-.
I. Introduction Intense femtosecond pulses can induce a number of interesting phenomena.' Most often, nonlinearities arise from multiphoton processes,2 saturation of transitions? or the perturbation of the potential governing the dynamics.4 In the first paper of this ~ e r i e s , ~ the influence of possible saturation of transitions by the pump and/or the probe was discussed in terms of a kinetic model. It was found that although the intensity of the transients was not linear with respect to laser powers for high pulse intensities, the shape of the transients was not dramatically affected by pump or probe saturation (particularly the former). In the following contribution, we demonstrate that the variation in the absorption cross section along the reaction coordinate induces a nonlinearity for the asymptotic product absorption while maintaining the linearity for the transition-state species. The process examined here is the dissociation of NaI following femtosecond pulse excitation and femtosecond pulse probing, both at different levels of peak powers. The dissociation of NaI in real timebs has been studied extensively, both experimentally and theoretically. It involves the avoided crossing between the covalent and ionic potentials, as shown in Figure 1. The dynamics is described by the following steps:
The ground states of Na+ and I- ions both 'SO; consequently,they combine to give only one molecular state of 1Z+symmetry. Given the large spin-orbit splitting of iodine, Hund's case c coupling is used to describe the covalent surfaces. Using this coupling scheme, the ground-state 2Sl/2sodium and 2P3/2 iodine atoms will give rise to several covalent states, of which transitions to three-two with Q = 1 and one with Q = 0+-will be optically allowed from the ionic ground state. In the dmbatic representation, both Q = O+ and 1 covalent states correlate asymptotically with the neutral atoms. As a result of nonadiabatic coupling with the ground state, however, the O+ covalent state and the ionic ground state interact at their crossing point R , (6.93 A); it is this interaction which makes NaI a rich and versatile system for the study of elementary nuclear dynamics. Previous experiment~6.~*~~1 have explored the resonant wave packet motion of the [Na I]$* activated complex, both by direct detection of the species within the adiabatic well and by
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To whom correspondence should be addressed. Deutsche Forschungsgemeinschaft (DFG) postdoctoral fellow. t Present address: Department of Chemistry, University of California, San Diego, CA 92093. 8 Contribution No. 8909. Abstract published in Advance ACS Abstracrs, March 1, 1994.
m-
NC+I
h
3
7 .t
E! v
10
1 4
-
Na++I Na+I
0-
-lo
-
-20
-
a
'
-30 0
2
4
8
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I2
14
16
Intemuclear Separation (A) Figure 1. Relevant low-lying potential energy curves of the NaI reaction together with the scheme for pump and probing at different internuclear separations. Starting from the ionic ground state, the pump pulse (Ap) prepares a coherent wave packet on the covalent i7 = O+, 1 A states. A femtosecond pulse at wavelength A*, probes the dynamics of the wave packet evolution in the transition-state region, while a probe pulse at wavelength A", monitors the buildup of the fragment Na atoms. The laser-inducedfluorescence arim from theexcitedpotential [Na*(ZP,/L1/2) + I(2P3/2)1. observationof the free Na atoms which leak through the LandauZener'' coupled region. Typically, a femtosecond pump pulse prepares the system on the repulsive branch of the covalent potential energy surface(s), and the subsequent nuclear motion is probed via femtosecond excitationto the potential energy surface corresponding to Na*(2Pl/2,p/2) I(2P3/2).The final wave packet formed on this potential surface is monitored as a function of pumpprobe delay by emission of atomic resonance fluorescence via the Na D-line transitions. The wavelength of the second pulsedeterminesthe species probed.11 When the probe wavelength is tuned to the free Na absorption (-589 nm), the resulting transients, uon-resonancewtransients, correspond to the buildup of product. Transients taken with probe pulses which are not in resonance with theNa D-linetransitionsare called uoff-resonance" transients; such transients yield information on the dynamics of the [Na I] t* transition-state complexes. By varying the probe wavelength, the dynamics of the dissociative process could be effectively viewed at different positions along the reaction coordinate (R).13J4 For example, on-resonance probing (Ampr probing in Figure 1) yields the dynamics at very large (essentially infinite) values of R, whereas if the probe is tuned away from the Na resonance, the resulting transients correspond to dynamics
+
0022-365419412098-3352$04.50/0 Q 1994 American Chemical Society
Femtosecond Real-Time Probing of Reactions at finite values of R showing the oscillatory behavior of the wave packet trapped inside the adiabatic well (A*, probing). This paper provides a detailed study of the femtosecond transients which result from probing the system with pulses spanning thespectral region of the asymptoticNa or thecomplexes [Na I]$*. Special emphasis is given to the dependence of these transients on the power of the pump and/or probe laser(s). In the linear power regime, we recover the results of previous studies of the dynamics.9 At higher powers we observe a nonlinear behavior which we discuss theoretically using a classical picture, and also a kinetic model for the overall trends. The outline of the paper is as follows: In section 11, a brief description on the experimental setup and procedure is provided, followed by an account of its application to the NaI system in section 111. Section I11 also provides the background information relevant to our experiments. The theoretical model is outlined in section IV, and the results are presented in section V. Concluding remarks are given in section VI.
The Journal of Physical Chemistry, Vol. 98, No. 13, 1994 3333
*..
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Time Delay (ps) Figure 2. Dependence of the FTS transients of [Na4]:* complexes on the pump and probe pulse powers (A, CJ 301 nm, A, CJ 620 nm). The transients were taken with the following relative pump and probe powers: P, = 1.0, P p = 1.0 ( 0 ) ;P, = 1.0, P p = 0.21 (X); PpIJ= 1.0, P, = 22 ( 0 ) ;Pp = 3.5, Pp = 3.3 (A);P p = 3.5, Pp = 0.12 (+). Each data set has been normalized (see ref 9).
II. Experimental Section The experimental methodologyof femtosecondtransition-state spectroscopy (FTS) is presented in ref 5. The specific details pertinent to FTS experiments of the NaI system are provided in ref 9. In this section, only a brief description of the experimental setup shall be given. The laser pulses were generated in a colliding pulse mode-locked ring dye laser (CPM) and amplified in a Nd: YAG-pumped four-stagedyeamplifier (PDA). Theoutput pulses had 20-Hz repetition rate and were centered at approximately 620 nm. The temporal pulse width was measured to be 60-80 fs. The experiments required two different wavelengths for pump and probe pulses. To produce pump pulses at about 310 nm (fwhm = 5 nm), part of the PDA output was doubled by second harmonic generation in a thin, phase-matched KD*P crystal. Each pulse had an energy of up to 10FJ. For probe pulses around 589 nm, we generated a white-light continuum by focusing the remaining PDA light into a HzO cell. Interference filters of different spectral widths (10 and 1 nm) were used to select the required spectral region from this continuum. The pump and the probe beams were delayed in time relative to one another in a Michelson interferometer arrangement. The beams were collinearly reeombined and focused into the reaction cell. Excess water in the samplewas removed by heating the cell under vacuum for several hours before sealing it. During the experiments, the cell was heated to approximately 650 OC. The vapor pressure of the sample was estimated to be about 100 mTorr, corresponding to a number density of 5 X 101' molecules/cm3 (ref 15). Laser-induced fluorescence (LIF) was collected orthogonal to the coincident laser beams. After suppressingstray light by means of a monochromator, the signal was detected with a Hamamatsu R1527 photomultiplier and integrated by a digital boxcar. A microcomputeracquired the boxcar data and controlled the optical delay line. For experiments where exact timing was required, the zero of time (the delay at which the pump and probe pulses were temporally coincident) was determined by taking the crosscorrelation of the two pulses. For this purpose, the collinear laser beams were focused into a thin, phase-matched KD*P crystal, and their difference frequency was detected by a photomultiplier. Both the pump and the probe pulses could be attenuated by variable neutral density filters. The relative intensities of the pump and the probe lasers were measured by means of a photodiode set up behind the sample cell. Care was taken to keep the pulse intensities in a range where the photodiode showed a linear response to power changes. During every experiment, the intensity was continuously monitored.
0
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Time Delay (ps) Figure3. Dependenceof the FTS transients (probepulse centered at 589 nm, spectral width about 10 nm) on the pump pulse powers (A, CJ 310 nm). The transients were taken with the following relative pump powers: X, 0.1; 0,0.24; +, 0.91; B, 1.6; 0,3.7; A,5.7. The low-power transients resemble the integral of the off-rceonance FTS transients and shows the buildup of the Na atoms. In contrast to this, the high-power transients are falling after the initial sharp rise. Note that A, used here is slightly different from that used to obtain the transients shown in Figure 2 (see ref 9).
In. Preliminaries Previous studies of NaI dissociation reported on some power dependen~ies.~J~ In general, the intensity of the FTS transients was found to be essentially linear with respect to the pump and probe pulse intensities, with one exception: on-resonance transients (A, = 589 nm) showed a marked pump-intensity dependence. While theoverall shape of the transients taken with probe pulses not resonant with the Na D-lines was observed to be independent of the pump power (see Figure 2), those taken with probe pulses centered at 589 nm showed dramatic changes as the pump power was increased. Figure 3 illustrates the pump-intensity dependenceof transients obtained with probe pulses spanning the spectral region of the Na D-line transitions. When the pump is at low intensities, the transient has a fast initial rise followed by a slowly rising signal which shows an asymptotic behavior at long delay times. The ascending series of plateaus reflects the oscillatory dynamics of the [Na I]'* transition-statecomplexes. For high pump powers, however, the transient looks quite different. After the fast rise, the signal intensity is not rising, but falling. Again, it shows an asymptotic behavior at long times. The transient is modulated by oscillations which show descending amplitudes and finally can no longer be resolved. While this power dependence was first reported in 1989: its
3354 The Journal of Physical Chemistry, Vol. 98, No. 13, 1994 origin was not well understood. Experimentally, a femtosecond laser pulse centered at 589 nm probes the dissociation product Na by resonant excitation corresponding to the Na D-line transitions. The two Na D-line absorptions are at approximately 589 nm; their combined transition line width is less than 1 A. The probe laser pulse used in most of the studies reported here has a spectral width of =10 nm and in some experiments = 1 nm. Therefore, only relatively few of the total probe photons can be absorbed by the Na atoms, as most of the photons have energies which are red- or blue-shifted from the Na Ddine energies. Earlier workghas shown that both red- and blue-shifted (from the D-lines) photons excite the [Na I]** transition-state complexes. For moderate pump and probe powers, the intensity of the overall signal increases stepwise (see Figure 3) at early times, corresponding to "bursts" of Na produced with each passage of the transition-state complexes through the Landau-Zener coupled region. The transient does not show any obvious off-resonance contribution. The fact that the on-resonance signal dominates indicates that the absorption cross section of the Na atoms is greater than the time-averaged absorption cross section of the [Na I]** transition-state complexes (vide infra). The overall transient obtained with higher pump powers shows features which clearly point to a large off-resonancecontribution (see Figure 3). The transient has the oscillatory structure characteristic of an off-resonance transient; even the period matches that of the off-resonance signal, which is a signature of the A O+ state. Additionally, the overall decay time is on the same order as that of the off-resonance signal. To understand why the off-resonance component becomes a significant contribution for high pump pulse intensities, one must first understand the role of the pump laser in FTS experiments. The pump photons are absorbed by the ground-state NaI molecules to produce [Na I] t* transition-state complexes,after the initial covalent complexes [NaI]*, as discussed below. Over a wide range of pump powers, the number of [Na I] t* complexes is directly proportional to the number of pump photons.gJ6 Clearly, a larger number of transition-state complexes result in a larger number of Na atoms. Hence, if the number of probe photons remains constant, both contributions to the overall signal will increase, provided that not all probe photons (on- or offresonant) are absorbed. As the absorption cross section of the Na atoms is large ( U N ~is 1 X 10-12 cm2),17we might expect that the relatively few resonant probe photons will be strongly absorbed if the concentration of the Na atoms is high enough. Later, we will call this condition "depletion". Such depletion can be considered as a "hole burning" in the spectral distribution of the probe photon flux (see Figure 4). When all of the resonant probe photons are absorbed by Na atoms, the on-resonance signal contribution will no longer rise, even when the pump power is increased. As stated above, the absorption crosssectionofthe [Na I]*transition-statecomplexes is expected to be smaller than that of the Na atoms. Hence, there should be no depletion of the off-resonance photons. This expectation is supported by the observation that off-resonance absorption by the transition-state species shows no nonlinear behavior when the pump power is varied over a wide range (see Figure 2). Consequently, the off-resonance signal wit1 continue to increase with increasing pump power, while the on-resonance contribution will reach a constant plateau. The net result is that the overall transient is dominated by the on-resonancecontribution at low pump powers (Le., the expected linear regime behavior) and by the off-resonance component at high pump powers. The shape reflects the large absorption cross section and narrow absorption line width of free sodium and the relatively smaller absorption cross section of the [Na I]** transient species.
Materny et al.
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Wavelength (A) Figure 4. Schematicrepresentationof the "depletion"effect. The strong absorption of the free sodium atoms results in a dip in the spectral distribution of the probe photon flux (a Gaussian pulse shape is shown). The depth of this dip depends on the concentration of Na atoms in the laser interaction volume.
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IV. Theoretical Section A. Population Kinetics. In this section, we shall relate the ebserved power dependencies detailed above to a simple kinetic
Figure 5. Schematicrepresentation of the kinetic model used to describe the FTS rcsults. The statcs are labeled by numbers: 11) is the ionic I&+ ground state of NaI. The covalent A O+ state is labeled by 12). The dashed line symbolizes part of the oscillatorydynamicsof the wave packet trapped in the adiabatic potential well which are not considered in the kinetic model. 14) is the ground state of the Na atoms, 13) is the final state of the A*v, and 15) is that of the A", excitation. The corresponding absorption cross sections are labeled at each transition.
model. The quantum effects, such as the steps reflecting the resonance motion of the [Na I]** complexes, are suppressed by this model. The model, however, gives the trends with power changes, especiallyfocusing on thedecay and buildup rates. Figure 5 shows a five-level schematic of the pumpprobe process that includes both on-resonance and off-resonance probing (A+pr and Ampr, respectively). The reaction begins at the time the pump pulse reaches the sample in the interaction region, Le., the overlap volume of pump and probe focus. This volume is defined by the interaction length 1 and the laser CFOSS section S in the focus. The pump photons excite the NaI molecules (initial concentration n,), thereby producing n2 [Na I] ** transition-state complexes after the covalent [NaI]* species. For short times after the excitation, the n2 concentration is determined solely by the pump photon flux 4pu.(t) and by the cross sections of absorption and stimulated emission, u12= u21,which describe both processes taking place during the pulseduration. In the rateequations below, we assume that the absorption cross section 4 1 2 is independent of frequency over the spectral range of the pump pulse. This means that each pump photon sees the same ul2. As the absorption cross section of NaI is only varying slowly in the considered range1*(=310 f 5 nm), this is a good approximation. Equation 1 gives thechange -.a
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Femtosecond Real-Time Probing of Reactions in the concentration of
n2
The Journal of Physical Chemistry, Vol. 98, No. 13, 1994 3355
due to the pump laser pulse:
immediately after the probe laser pulse is given by
dn,(t)/dt = 4Jpu(0q2b1(0- n2(t)l (1) If we assume that for the short time of the pulse duration the total concentration of NaI in thegroundandexcited states is a conserved quantity, we can substitute nl(0)- n2(r) for nl(t). Integrating eq 1 over the entire pulse width then gives
n,(t,) = 1/2n,(--)(1 - e-*‘12*p)
(24
+ t,)
= 1 / 4 n , ( ~ ) (1 e-2u12*p)(1 - e-2ua*p)e-kfd ( 5 ) Finally, the detected laser-inducedfluorescence (LIF) arises from the excited Na* atoms (concentration n5, see Figure 5). The off-resonance contribution to n5 occurs via the dissociation of the excited transition-state complexes; the resulting concentration of Na* atoms is n,(td
n,O*(t>td+t,) = n,(td+tp)(l -
where
apu= J-:@,”(t)
dt
(2b)
The total number of pump photons per unit area is apu, and t, is the time after which the pulse is practically over. After the pump pulse interaction ends, the dynamic part of the process begins. The wave packet propagates on the repulsive limb of the A O+ state toward the lower potential energy regions of larger internuclear separation. When the crossing region is encountered, the wave packet bifurcates into two components; one is trapped inside the adiabatic well, while the other escapes diabatically to the outside and gives the final products of the reaction, free Na and I atoms. The relative weight of these two components is determined by the Landau-Zener curve-crossing probability. The trapped part of the wave packet executes a periodic motion inside the adiabatic well. Whenever the crossing region is met, a fraction is lost due to nonadiabatic crossing. As mentioned above, by omitting the fine details of the wave packet oscillations,the dissociation process can then be described by the following equations
n,(t) = n,(t,~e-~‘
(3a)
n4(t) = n2(t,)(1 - e-k‘)
(3b) where k is the Landau-Zener leaking rate constant, n2(t,) is the concentration of transition-state complexes arising from the excited NaI* molecules prepared by the pump pulse, and n d ( f ) is the concentration of Na atoms at time t . Here, we consider the case when t >> t,. The wavelength of the probe photon determines the spatial region in which the wave packet motion is followed in real time. We first consider the off-resonance contribution. The probe photons with A,, # 589 nm promote the [Na I]t* transitionstate complexes to the upper excited-state potential where they proceed to Na*(2P1p,3p)+ I(2P3/2)with a time constant k’and finally give rise to fluorescence. The concentration of excited transition-state complexes n3 changes due to the probe photon flux ,@,, analogous to eq 1. The resulting concentration is described by n,(td
+ t,) = ‘/znz(td)( 1 - e-2s23”)
-
f--
ns(td+tp) ( 6 ) Here, we take into account that the time constant k’ is small compared to the 16-11s lifetime of the fluorescence. If we assume that no nonlinear effects are present, the off-resonance contribution of the overall transient will steadily increase with increasing pump and probe power. Now we consider the on-resonance contribution to the overall transient. Recall that only few of the total number of probe photons are resonant and hence can be absorbed. The photon flux is given by 4lPr XqjPr,where X can be determined by comparing the line width of the Na D-lines to the spectral width ofthe probe pulse. Theansatz for thechangeoftheconcentration of excited Na* atoms due to the probe pulse is found (in analogy to dq 1) to be
- ns”(r)) = @*pr(t)a4s(n4(td)- 2n,””(t))
dn,””(t)/dt= $*pr(t)a4,(n4(t)
(7)
where 8.45 is the absorption cross section of the Na atoms. For the last substitution we assume that I l k >> t,. One important point here is the consideration of the possible depletion of the probe photons by the Na atoms. The total absorption of all onresonant probe photons in the interaction volume is described by the following equation
a’*,$ = Ns”
(8) where a*,$ is the total number of on-resonant probe photons flowing through the laser cross section S and Nson n p V i s the number of excited Na* atoms in the interaction volume V. We now perform several substitutions to eq 7. Assuming a Gaussian laser pulse, we can characterize the flux of probe photons in the interaction region by
4*pr(t) = (l/S)(a*p$)g(t
- td)
(9) where g(t - td) is a Gaussian distribution centered at td. Substituting the number of Na* atoms Nson(t) = nson(t)Y,and replacing a*,$ by B*pcS - N50n(t),we arrive at the following ansatz:
(4)
where td is the delay time between pump and probe pulse, a,, is the total number of probe photons per unit area (analogous to 9 , in eq 2b), and 8 2 3 is the absorption cross section of the transition-state complex. In contrast to the absorption of the NaI ground-state molecules and the free Na atoms, theabsorption of the transition-state complex is a dynamical process. Therefore, we must consider the dynamics of the dissociation in order to understand the physical meaning of the value 623. The kinetic model assumes that all probe photons (at all times) see the same absorption cross section corresponding to the transition 12) 13). In the following subsection, we will discuss the physical interpretation of 8 2 3 using results for transition-state absorption obtained from classical dynamics. Introducing the results of eq 3a and eq 2a into eq 4, the concentration of the excited transition-state complexes, n3,
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Integrating eq 10 over the duration of the probe pulse and introducing the interaction length 1 = VIS, we finally obtain the following expression:
The concentration of Na atoms (n4) is directly related to the initial concentration of [Na I] $* transition-state complexes (n2), which in the model is given by eq 3b describing the leaking process due to the curve crossing. The concentration of transitionstate complexes depends on the pump power. This relation was already given in eq 2a. Thus, the pump power can be introduced
Materny et al.
3356 The Journal of Physical Chemistry, Vol. 98, No. 13, 1994
in eq 11 by making use of the following relation:
The overall transient arises from LIF of the excited Na* atoms whose concentration is the sum of off- and on-resonance components: n50fl (eq 6) and nso” (eq 11). B. D y ~ m i c aAbsorption l of Transition-StateComplexes. The classical9 and quantum8 dynamics for this reaction have been detailed in a number of publications (see ref 19 and references therein). For our purpose here, we shall consider the classicalmechanical model developed by Bersohn and Zewail.14 In this model, the absorption of transition-state complexes is explicitly given from consideration of the equation of motion:
off-resonance (C)
The total energy is E , and V(R)is the potential energy. R is the internuclear separation of the fragments (here Na and I), and p is the reduced mass. By the use of the known potential data (see e.g. ref 9), a solution of eq 13 is possible which relates the internuclear distance R with time 1. In an experiment with a 310-nm pump pulse, the classical velocity is about 0.03 A/fs.I9 Assuming a half-width of 50 fs for the laser pulse, the classically calculated maximum width (hwhm) AR is about 1.5 A a t long R’s. Experimental determination gives a value of -0.5 A.11J9 The probe pulse opens a window for observation of the moving fragments. The absorption is maximum when the fragments are at a distance R* defined by the center of this window. The distribution of energy can be Lorentzian with a half-width y (or Gaussian, for example). The half-width y could exceed the natural line width by orders of magnitude.14 In the BZ model,14 the absorption is expressed as a function of R by the following relation:
A(R) =
Cy
[AV(R)- AV(R*)I2+ y2
(14)
where AV(R) is the potential difference and Cgives the strength of the absorption. In the classical and quantum calculations, the magnitude of the transition dipole is taken to be constant. However, the transition moment changes abruptly at R,; if the system is on the covalent part of the adiabatic potential, it has a large absorption cross section, but if it is on the ionic part, the cross section is relatively much less. Introducing the solution R ( t ) from eq 13 in eq 14 transforms the space-dependent absorption A ( R ) into a time-dependent absorption A ( ? ) . The shape of A(?) is reflected in the experimentally-detected LIF obtained as a function of time delay when consideration of the temporal pulses is taken into a ~ c o u n t . ~ J ~ The dynamical absorption cross section can be related to the absorption cross section extracted from the simulations (i.e., fits) of the experimental transients to the kinetic model. The timedependent absorption (or cross section) shows resonance peaks, as evidenced experimentally (see Figures 2 and 3) and shown theoretically (classical and quantum). The kinetic model’s rate equations average these resonances, and hence the value of the dynamical absorption crqss section at a given R is also averaged over time, Le.,
where Tis the period of the motion inside the adiabatic well. For a Lorentzian u ~ ( twith ) maximum u ~and hwhm , ~6, eq~15 gives ~ 823 ( ? T S / T ) U R , ~ ~where , 6 includes both the transient time of the wave packet and the pulse duration. In the present experiment, d / T i s about 0.5; the time-averaged absorption cross section 8 2 3 has about the same order of magnitude as the dynamical cross section UR. There are several contributions which we have not addressed so far. In particular, the dispersion of the wave packets within
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A
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total
20 30 Time Delay (ps) 10
40
Figured Results of model calculationsof the overall transient performed for a fixed probe power and varying pump powers. The time-averaged absorption cross section 4 2 3 is cm2;all other parameters are listed in the text. (a) Change of the overall transients. The relative pump powers are labeled for each transient. Transients for low (b) and for high (c) pump powers. The on- and off-resonance contribution to the overall transients are labeled in panels b and c.
the well was not considered. Such dispersion is evident in the experimental results by the increase in width of the second and subsequent peaks relative to that of the first peak.I0JI Also, as discussed below, the influence of the purely repulsive Q = 1 neutral states20is not explicitly included. Contributions from these states lead to changes in the first peak (see pertinent discussion in ref 9) of the off-resonance and in the sharply rising edge of the overall transient. Finally, we did not include the effect of the initial vibrational and rotational excitations at the temperature used. These considerations have been discussed in refs 8 and 9. V. Results and Discussion
To examine the model results of section IV, we made comparison with experimental results. For the system under consideration, various parameters are defined. The density of NaI molecules nl is 1.5 X 1015 cm-3, the diameter of the laser spot is 50 pm, and the interaction length 1 is 2.5 mm. The spectral width of the probe pulse was taken to be 10 nm for the model calculation. (The 1-nm-width case is discussed later.) The width of the combined sodium D-lines is about 0.5% of this spectral range. The absorption cross section for NaI at 310 nm, ul2,is 2 X 10-1’ cm2 (ref 18), and that for the N a D-lines u4s is 1 X 10-l* cmz (ref 17). The time-averaged absorption cross section for the [Na I]$* transition-state complexes ~ 2 was 3 varied to give the best similarity to the experimental results reported in section 111. The first simulation, using eqs 6 and 11, demonstrates the influence of pump power on the overall transient; the probe power is held constant. In panel a of Figure 6, the drastic change in transient shape from a rising signal seen at low pump powers to a falling signal at high pump intensities is clearly seen. The oscillatory fine structure is missing in the simulated transients due to the insensitivity of the model to the resonance motion as mentioned above. In addition, the rise in the calculated transients is instantaneous because we did not perform a convolution with the shape of the laser pulses. These points do not diminish the utility of the model in explaining the changes in the shape of the
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The Journal of Physical Chemistry, Vol. 98, No. 13, 1994 3357
Femtosecond Real-Time Probing of Reactions
7 / -
o.20 0.10
Y,
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on-resonance
-5 on-resonance
off-resonance
0
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Time Delay (ps) Figure7. Results of model calculationsof the overalltransient performed for a fixed pump power and varying probe powers. The parameters used for the simulations are listed in the text. (a) Change of the overall transients. The relative probe powers are labeled for each transient. Transients for low (b) and for high (c) probe powers. The on- and offresonance contribution to the overall transients are labeled in panels b and c.
ove:all transient due to different laser powers. Panels b and c of Figure 6show the different contributionsto the overall transient for low and high pump power, respectively. In the low-power transient, the on-resonance contribution dominates, while at high power, the signal is primarily due to off-resonance absorption. The on-resonance component shows a slowly rising signal, reflecting the buildup of free Na atoms. The off-resonance transient is the LIF signal of the transition-state complexeswhich decreases according to the lifetime of the [Na-I] t* transitionstate complexes. The decay is characterized by the rate constant k. In the high-power transient (panel c), the on-resonance component is in the depletion region where the increase of its contribution is considerably slowed down. The onset of depletion can also be observed in panel a. For longer delay times, only the on-resonance contribution to the overall transient remains, as all molecules have dissociated. For lower pump powers, the number of probed Na atoms rises with rising pump intensity, while for higher pump powers, this number is determined by the number of probe photons and therefore reaches an asymptotic value. As mentioned in section 111, the experiments indicate that the shape of the overall transient is affected only by variations in pump power; it does not change with probe power in the range studied. However, our model makes an additional prediction. Figure 7 shows the results of model calculations in which the pump laser intensity is held constant and the probe power is varied. In panel a, the overall changes in the transient shape are shown to be much less drastic than those seen for pump power changes (Figure 6). The low-power transient is only slightly falling, while at higher (sufficient) probe intensities,the transient is rising overall and becomes flat for longer delay times. Panels band c show the on- and off-resonance contributions to the overall transients for both low and high probe power. The change in the ratio between these components is clear. The changes are most apparent when the pump power is relatively high, as demonstrated in Figure 7. For lower pump powers, the changes are less significant. The model calculations suggest several possible experiments to test the assumptions. As such, two different types of
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15
20
25
30
35
Time Delay (ps) Figure 8. Experimental transients as a function of pump power (probe pulse centered at 589 nm, spectral width about 10 nm). The points are
the experimentaldata while the curves are the fits from simulationsusing the theoretical model derived in section IV. The relative pump powers are labeled for each transient.
experiments were performed. One way to check the theoretical model is to obtain transients for different pump and/or probe powers. The change in the overall shape of the transients can then be directly observed and compared to the results from simulations. The ratio of on- and off-resonance contributions is easily determined by changing the spectral width of the probe pulses. By tuning the central wavelength of the probe pulses away from the Na D-line resonance, we will obtain information on the contributions from red- or blue-shifted absorption to the time-averaged cross section 423. To monitor the overall shape of the transients requires a relatively long time, especially since for low laser intensities many accumulations must be summed to achieve a reasonable signal-to-noise level. As such, it is difficult to keep the experimental conditions constant. Therefore, in order to obtain accurate information over a wide range of pump and probe powers, we additionally determined the intensity of the LIF for a few fixed delay times. These times were chosen such that theon- and off-resonancecontributionsto theoverall transient were weighteddifferently. The resulting changes in LIF intensity can again be compared to the simulations obtained using the theoretical model. In the simulations, only one parameter is unknown-the absorption cross section of the [Na-.I]t* transition-state complexes, 423. As it is always difficult to experimentally determine the absolute powers of the pump and probe laser pulses in the interaction region, evaluating 423 via off-resonance transients is nontrivial and the possibleerror is large. By obtaining a transient with Xprok = 589 f 5 nm, the off-resonancecontribution is always related to the on-resonance contribution as described by the theoretical model. As the absorption cross sections of both the Na atoms (445) and the NaI molecules ( 6 1 2 ) are well kn0wn,17Js exact knowledge of the laser intensitiesand the interaction volume is not required. The absorption cross section of the Na atoms serves as a referencefor the determination of that of the transitionstate complexes. In the following subsections, theoretical fits of the experimental data are presented. For each intensity dependence study, the resulting transients were fitted simultaneously, i.e., using the same set of parameters (fixed or floating). This procedure allows the parameter determination to be based on as many experimental results as possible. The method used for such optimization calculations is described elsewherea21 A. The Transient Shape. The most significant change in the shape of the overall transient occurs when the pump power is varied. Figure 8 shows transients obtained for four different pump powers; the labels indicate the relative values of the pump
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10 15 20 25 30 35 Time Delay (ps) Figure 9. Experimentaltransients as a function of probe power (probe pulse centered at 589 nm, spectral width about 10 nm). The points are the experimentaldata while the curves are the fits from simulationsusing the theoretical model derived in section IV. The relative probe powers are labeled for each transient. -5
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intensity. The points are the experimental data while the solid curves are the fits obtained with the theoretical model derived in section IV. The power variation over 2 orders of magnitude changes the shape of the overall transient considerably. The transient taken for relative pump power 0.01 is dominated by LIF resulting from on-resonance absorption. After an initial sharp rise, the signal level rises slowly to a constant level at long delay times. At higher pump powers, the transient is no longer rising but begins to fall until it reaches a final level. The oscillations at high powers resemble those seen for transients obtained with probe pulses which are totally off-resonant with the Na D-line transitions, indicating that the dominant contribution here is the off-resonance component. Ignoring the oscillations,the theoretical model is able to simulate the changing shape of the overall transients very well. The only discrepancy occurs at early times, when the measured transient shows a steeper leading edge than the simulated one. This difference is most likelydue to contributions from the purely repulsive fl = 1 neutral states20 which were not included in the calculations. The fits were performed on all transient data a t once, floating only one parameter, ~ 3 The . optimum value for the time-averaged absorption cross section ~ 2 of 3 the [N-I] t* transition-state complexes was found to be 1.5 X cm2 with a standard deviation of 0.3 X lt15cm2. Note that this standard deviation only shows that the value is reproducible within a small range in all our simulations. Therefore, it is a measure of the quality of the experimental data used; it is not the deviation from the “real” absorption cross section. The latter deviation is rather determined by all approximations inherent in the model. Therefore, thevalue found for 6 2 3 may only be considered as an estimation. According to the model calculations given in section IV, variation of the probe power should only modestly affect the shape of the overall transients. In Figure 9, we show the change of the overall transients observed when varying the probe power over a range of about 2 orders of magnitude. Again, the measured data are indicated by points while the results from the simulations are the full curves. The relative probe powers are labeled for each transient. The transient obtained with relative power 0.02 was already very weak in intensity and could only be sufficiently resolved after nearly 1 h of accumulation. After the initial sharp rise, this transient shows a slightly decreasing fluorescence intensity. Going to higher probe powers, the shape changes slowly to a nearly flat transient. The pump power for this series was chosen to be high enough to obtain falling transients and low enough to achieve flat transients using the full range of probe power. The observed changes of the shapeof theoverall transients
10 15 20 25 30 35 Time Delay (ps) Figure 10. Same as Figure 8 except for probe pulses centered at 589 nm having spectral width of about 1 nm.
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are only slight, as predicted by the theoretical model calculations (see Figure 7). The simulation of the experimental data is able to reproduce the changes of the transients quite well. Note that the same set of parameters used in the simulation of the pump power dependence (Figure 8) are employed again here. In the experiments described above, a 10-nm-band-pass interference filter centered a t about 589 nm was used to produce the probe pulse. To change the ratio of on- and off-resonance contributions, we used a narrower band-pass filter with a width of about 1 nm. Still we were able to change the shape of the overall transients considerably by varying the pump power. In Figure 10, we show transients obtained with spectrally narrow probe pulses centered at about 589 nm. The relative values of the pump powers are labeled at the different transients. The high-power transient (relative power 1.O) again shows decreasing LIFintensity after the initial sharp rise. The pump power required to achieve falling transients is higher for the spectrally narrow probe pulse than it was for the broad pulses, as the off-resonance contribution is now much smaller. As the number of Na atoms is directly related to the number of transition-state complexes, the on-resonance contribution also increases, but only to the point where photon depletion becomes effective. From there on, the overall transient changes slowly in shape (Figures 7 and 9). Again in Figure 10, the discrepancy a t the rising edge can be observed. The measured transients are steeper than the simulations, especially when the on-resonance contribution dominates (lower pump powers). This again can be understood by assuming that dissociation via the fl = 1 states instantaneously increases the number of free Na atoms. As shown here and elsewhere? off-resonance absorption occurs not only on the low-energy side of the Na D-lines but also when the probe laser is tuned to the blue. In ref 9, experiments investigated the effective tuning range of the probe for which LIF signal could be obtained. It was found that the off-resonance tuning extended much further to the red than to the blue. As this behavior in tuning range is a function of the differences between the excited-state potentials involved in the transition, it can be used to deduce the potential difference change with time.l3 To gain more information concerning the transitions to the excitedstate potentials, we estimated the red and blue off-resonance absorption cross sections near the Na D-line energies. This was done by tuning the spectral range of the probe laser either to the low- or the high-energy side of the Na D-lines. As the ratio of red to blue off-resonance photon numbers was known, the fits of the transients yielded time-averaged absorption cross sections for the complexes which could be used to determine their lowand high-frequency parts, respectively. The result of these experiments is that, within the standard deviation, no difference between the two contributions to the time-averaged absorption
Femtosecond Real-Time Probing of Reactions cross section could be found. In order to learn more about the nature of the excited-state potentials which are responsible for the different off-resonance transitions, it would be necessary to also study polarization effects. In previous FTS studies from this laboratory, the influence of changing the relative polarizations of the pump and probe beams on the transient shapes has already been investigated.9.22.23 However, no quantitative comparisons to the theory of reaction alignment22.23 have been done so far for the NaI system. An in-depth study of the excited-state potentials will be the subject of one of our future publications. B. The Intensity of the Laser-Induced Fluorescence. In order to test the model over a wide range of pump and probe powers, we investigated the dependence of the Na LIF intensity on the pump or probe power for a few fixed time delays. Some results from similar experiments were already published elsewhere9(see also section 111). Such measurements allowed for a more detailed investigation of the power dependence of the overall transient. To monitor the on- and off-resonance contributions to the overall transient, we selected three different time delays. The behavior of the off-resonance contribution was followed by choosing the first time delay such that the wave packet produced by the pump laser pulse did not yet pass the crossing region. Therefore, the signal arising for this delay time contained essentially no onresonance contribution. As the oscillation period for the wave packet trapped in the adiabatic well is about 1.28 ps for a pump laser wavelength of -310 nm, we chose t l 320 fs, a time delay which corresponds to approximately half the time necessary for the wave packet to reach the outer turning point. The second delay time, t2,was -1.2 ps; a t approximately this time, the overall transients taken with high pump power reach their maximum. At time t2, we expect contributions of both the on- and the offresonance fluorescence. Finally, the third time delay t 3 is at a relatively long time delay of about 42.3 ps where essentially all of the [ N a 4 ] * * transition-state complexes have dissociated to Na and I atoms. Therefore, the signal at t3 should be mainly determined by the on-resonance contribution to the total LIF signal. The correct timing was checked by taking cross-correlations of the pump and probe laser pulses. To obtain reliable signal intensities, we took care in monitoring the background signal levels. The pump and the probe each contributed a background level to the observed LIF signal which was independent of the time delay between the pump and probe pulses. For high pump powers, considerable two-photon excitation could be observed. Scattered light from the probe laser also caused a small background which changed with varying probe power. These and all other contributing constant signalswere carefully measured and later subtracted from the signal intensities. Panel a of Figure 11 shows results of experiments in which the pump power was varied. The different points represent the measured LIF intensities for t l , 22, and t3. The full curves are the fitted power dependencies of the total LIF signals a t the corresponding time delays. As mentioned above, the fits were simultaneously performed on all available experimental data at once. Therefore, all simulations were performed with the same parameters. The power dependence of the signals at tl and t2 is similar, suggesting that at both of these times off-resonance fluorescence dominates. The model calculations shown in Figure 6 already pointed to such a result. The model enables us to separate the two contributions to the total LIF signal. Panels b and c of Figure 11 show the calculated on- and off-resonance power dependence, respectively, corresponding to the simulations shown in panel a. Here, it becomes clear that the signal at early times is mainly due to the off-resonance contribution (not only for high pump powers). This observation is also verified by a comparison of the experimental and theoretical results obtained for time delays tl and t z with those for time delay t3. The experimental data show the onset of depletion of the probe photons
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Pump Intensity (relative measure) Figure 11. Intensity changes of the transient signal for varying pump powers (probe pulse centered at 589 nm, spectral width about 10 nm) taken at fixed time delays between pump and probe pulses. (a) Experimental data for the three time delays which are represented by different points. The solid curves show the results of a simulation using the theoretical model derived in section IV for each time delay. Panels band c show the calculated on- and off-resonancecontribution to the LIF signals shown in panel a, respectively. The time delays are labeled for each curve. for high pump powers, corresponding to a high concentration of Na atoms. On the contrary, the influence of the depletion on the signal at t 2 is very small. The simulation resembles the experimental result, and as thesplitting intoon- and off-resonance contributions shows, at this long time delay ( t 3 ) , on-resonance fluorescence dominates the signal. The fact that at early times the overall transient is dominated by the off-resonance contribution in an interesting result. As was found earlier: the large initial rising edge of the overall (on-resonance) transient does not correlate with the decrease in height between the first and second peak of a transient obtained from off-resonant probing. A proposed explanation for this observation included a second channel by which the NaI molecules may dissociate. This second pathway corresponds to the Q = 1 potential surfaces24 which are also accessible from the ground state. However, by now considering the effect of the off-resonant part of the probe spectrum, it is straightforward to explain the shape of the overall transient which reproduces the complementary dynamics on which the on- and the off-resonant LIF is based. The Q = 1 states seem to play only a minor part in the shape of the overall transient. As the probe power dependence was also of interest, we again recorded the changes of the LIF intensities for the fixed time delays t l , t z , and t3. Figure 12 shows the measured changes of the LIF intensity for the three time delays. The experimental data are presented by points while the simulations are given as full curves. Panel a shows the results obtained for relatively low pump power, while in panel b the pump power was approximately 3 times greater. Again, comparing the intensity changes for tl and t2, we note only small differences, suggesting that at early times the off-resonance contribution dominates. The influence of the depletion of the probe photons can be seen by comparing the ratio of the signal changes for t z and t 3 of panel a and panel b. For low pump power, the rise of the t3 intensities is steeper than that found for 22, resulting in higher LIF intensities for t3
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Materny et al. cross section of the [Na-.I]t* transition-state complexes at frequencies used in the experiments. This time-averaged absorption cross section was found to be on the order of 10-'bm2. The dynamical model used here invokes the classical equation of motion and a kinetic description for the average population change. It would be interesting to consider the full quantum aspect of the dynamics, as done before? but now in the nonlinear regime.25 Another interesting problem for future study is the effect of the femtosecond laser power on the optical and radiative collisions in the high-power regime.26
Ackaowledgment. This work was supportedby Air Force Office of Scientific Research. A.M. gratefully acknowledges a postdoctoral fellowship by the Deutsche Forschungsgemeinschaft. 0.0 0.2
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Probe Intensity. (relative measure) . Fiflre 12* Intensity changes Of the transient for varying probe powers (probe pulse centered a t 589 nm, spectral width about 10 nm) taken at fixed time delays between pump and probe pulses. Results for moderate (a) and high 0) pump powers. Experimental data for the three time delays are represented by different points. The solid lines show the results of a simulation using the theoretical model derived in section IV for each time delay. The time delays are labeled for each curve.
than for tz. In panel b, the t3 intensities are smaller than the t2 signals. This difference is due to the photon depletion which prevents the on-resonance contribution which dominates at t3 from further increasing, while at t l and t2 the considerable offresonance component still rises with increasing pump powers.
VI. Conclusions In this study, we have employed femtosecond transition-state spectroscopy to explore the dependence of the transition-state complexes [Na...I]t* and the fragment Na transients on the relative power of both the pump and the probe lasers. In the linear regime of powers, we recover the temporal behavior known for this r e a ~ t i o n .Beyond ~ the linear regime, we observe novel changes as the power increases, especially when detecting the final fragment. A theoretical model is introduced to describe the dynamics according to the correspondence between the decrease of the number of the [Na-I]t* transition-state complexes and the increase of the number of Na atoms. Due to the large absorption cross section of the sodium atoms, depletion of the probe photons that are resonant with the Na D-lines occurs when the concentration of Na atoms becomes high. This depletion is selective to the final fragment because of the change of the cross section of absorption along the reaction coordinate. The theoretical model was applied to simulate both the qualitative change of the shape of the overall transients and the quantitative change of the intensity of the LIF. The combination of the on-and off-resonancecomponents of the overall transients also related different physical parameters which are contained in a set of experimental d a t a taken under uniform conditions. As the absorption cross section of the Na atoms is well-known, it was used as a reference in order to determine the effective absorption
References and Notes (1) See articles in* Atomic and Molecular Processes with Short Intense Loser pulses; A, D,, Ed,;plenum press: New York, 1988 and references therein, (2) Laubereau, A. In Ultrashort Laser Pulses; Kaiser, W., Ed.; Springer: Berlin, 1992; Val. 60, p 35 and references therein. (3) Demtrocder, W. h e r Spectroscopy: Basic Concepts and Insrrumentation; Springer-Verlag: Berlin, 1981. (4) George,T. F.;Zimmerman,I. H.;Yuan, J.-M.;Laing,J.R.;DeVries, P. L. Acc. Chem. Res. 1977, 10, 449. 15) Rosker, M. J.: Dantus. M.: Zewail. A. H. J . Chem. Phvs. 1988.89. 6113. ' (6) Rose, T.S.;Rosker, M. J.; Zewail, A. H. J . Chem. Phys. 1988,88, 6672. (7) Rosker, M. J.; Rose, T. S.;Zewail, A. H. Chem. Phys. Lett. 1988, 146, 175. (8) Engel, V.; Metiu, H.; Ameida, R.; Marcus, R. A.; Zewail, A. H. Chem. Phys. Lett. 1988,152, 1. Engel, V.; Metiu, H. J. Chem. Phys. 1989, 90, 61 16. (9) Rose, T. S.;Rosker, M. J.; Zewail, A. H. J . Chem. Phys. 1989, 91, 7415. (10) Cong, P.; Mokhtari, A.; Zewail, A. H. Chem. Phys. Lett. 1990,172. 109. (11) Mokhtari, A.; Cong, P.; Herek, J. L.; Zewail, A. H. Nature 1990. 348, 225. (12) Landau, L. Phys. Z . Sowjetunion 1932,2,46. Zener, C. Proc. R . SOC.London 1933, A137, 696; 1933, A140, 660. Levine, R. D.; Bernstein. R. B. Molecular Reaction Dynamics and Chemical Reactivity; Oxford University Press: New York, 1987. (13) Bernstein, R. B.; Zewail, A. H. J . Chem. Phys. 1989, 90,829. (14) Bersohn, R.; Zewail, A. H. Ber. Bunsen-Ges. Phys. Chem. 1988,92, 373. (15) White, J. C. Appl. Phys. Lett. 1979, 33, 335. (16) Cong, P. Ph.D. Thesis, California Institute of Technology,Pasadena, CA, 1992. (17) Kibble, B. P.; Copley, G.; Krause, L. Phys. Rev. 1967, 153, 9. (18) Davidovits, P.; Brodhead, D. C. J. Chem. Phys. 1967, 46, 2968. (19) Zewail, A. H. Faraday Discuss. Chem. SOC.1991, 91, 207. (20) van Veen,N. J. A.; de Vries, M. S.;Sokol, J. D.; Baller, T.; de Vries, A. E. Chem. Phys. 1981,56, 81. (21) Materny, A.; Kiefer, W. J . Chem. Phys. 1992, 97, 841. Materny, A. Doctoral Thesis, Univ. of Wiirzburg, Wiirzburg, 1991. (22) Dantus, M.;Rosker, M. J.; Zewail, A. H. J . Chem. Phys. 1988,89, 6128. (23) Zewail, A. H. J . Chem. Soc., Faraday Trans. 2 1989, 85, 1221. Dantus, M.; Bowman, R.; Baskin, S.;Zewail, A. H. Chem. Phys. Lett. 1989, 159,406. Bowman, R.; Dantus. M.; Zewail, A. H. Chem. Phys. Lett. 1989, 161, 297. (24) Berry, R. S.In Alkali Halide Vapors;Davidovits, P., McFadden, D. L., Eds.; Academic: New York, 1979. (25) Fried, L. E.; Mukamel, S. Adu. Chem. Phys. 1993, 84, 435. Hammerich, A. D.; Kosloff, R.; Ratner, M. A. J . Chem. Phys. 1992,97,6410. (26) Lisitsa, V. S.;Yakovlenko, S . I. Sou. Phys. JETP 1974, 39, 759.
