16829
J. Phys. Chem. 1995,99, 16829- 16834
Femtosecond Study of Multiphoton Ionization Processes in
K2
at Moderate Laser Intensities
R. de Vivie42iedle,*vt B. Reischl: S. Rutz? and E. Schreiber* Institut f i r Physikalische und Theoretische Chemie, Freie Universtitat Berlin, Takustrasse 3, 0-14195 Berlin, Germany, and Institut fur Experimentalphysik, Freie Universitat Berlin, Amimallee 14, 0-14195 Berlin, Germany Received: June 28, 1995; In Final Form: September I , 1995@'
Femtosecond pump-probe experiments on the potassium dimer are simulated by quantum dynamical calculations and compared with the experimentally found results. At moderate laser intensities three neutral electronic states dominantly participate in the ionization process. The transition mechanism is a pure ( I 2)-photon pump-probe process. The two-photon ionization process is located at the outer turning point of the wave packet in the state of the K2 molecule. Both the favorable spectroscopic properties and the special molecular dynamics induced by the moderate laser intensities combine to open a Franck-Condon window for ionization via the 2Il-4 state which allows the selective detection of the vibrations in the A I L + state.
+
r-
1. Introduction
hI
Argon-Ion-Laser Femtosecond techniques have recently been advanced in wide 1 I 1 spectral regions (ultraviolet-near to directly probe molecular motions in real time. Various examples of bound /A Titanium:Sapphire-Laser state dynamics2-I2have been investigated by experimental and theoretical groups over the last few years. In a further step the main goal is to influence a molecular system to prefer either single transition pathways or distinctive reaction ~hannels.'~-I~ In particular, Gerber and EngeI4-* studied in their work femtosecond time-resolved multiphoton ionization of the Na2 molecule in great detail. Recently pump-probe experiments with femtosecond laser pulses have been performed on the related molecule K2.17 One aspect of these investigations is to compare the dynamics of K2 to those of its lighter homologue Na2 and to evaluate the characteristic differences. Complementary aspects in this series of homologues have also been studied for Cs2.I8 For K2 the experiments were performed at moderate laser intensities in the range of 0.5 GW/cm2. The calculations are carried out for moderate laser fields in the range 0.1-2.2 GW/cm2. The advantage of these intensities is that competing multiphoton processes become unlikely in K2. Therefore the ionization signal reflects a single dominant multiphoton process and thus allows a clear assignment of the experimental ion signal and the corresponding excitation process. The preliminary analysis Figure 1. Experimental setup: S, spectrometer; A, autocorrelator; At, of the observed signals indicates that they reflect exclusively delay time; SEM, secondary electron multiplier; QMS, quadrupole mass the dynamics of the AI&+ state.19 Quantum dynamical spectrometer; LTD, Langmuir-Taylor detector. calculations are performed to analyze and interpret the relevant The parameters of the laser output, the wavelength spectrum processes in the pump-probe experiment in detail. and the autocorrelation trace, were recorded by means of a spectrometer and a scanning autocorrelator (Spectra Physics 2. Experimental Section model 409). Figure 2 presents the so measured spectrum and The experimental setup consisting of an ultrafast laser, a the corresponding autocorrelation trace at Iz = 840 nm (central pump-probe setup, and a supersonic molecular beam source wavelength) with an autocorrelation width of 153 fs (fwhm). is illustrated in Figure 1. Assuming a sech2 pulse shape of the femtosecond laser, this An argon ion laser-pumped regenerative1y mode-locked correlation width corresponds to a pulse duration (fwhm) of titaniumsapphire laser (Spectra Physics models 2080 and 3960, less than 100 fs. The spectral width of the femtosecond pulse respectively) generates femtosecond pulses with a repetition rate spectrum covered 160 cm-' (fwhm), so the pulses reached I .5 of 80.5 MHz. The tuning range covered about 100 nm of the times the Fourier limit. infrared spectral region around 850 nm. To realize a pump-probe setup, a Michelson-like arrangement was used to split the laser beam and to realign it collinearly ' Institut fur Physikalische und Theoretische Chemie. by use of 50% beam splitters with the same polarization. The * Institut fur Experimentalphysik. Abstract published in Advance ACS Abstracts, October 15, 1995. length of one of the Michelson branches could be controlled
1 S I
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1
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k
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0022-3654/95/2099- 16829$09.00/0
0 1995 American Chemical Society
de Vivie-Riedle et al.
16830 J. Phys. Chem., Vol. 99, No. 46, 1995 ca. 500 fs
Ii
E/103cm-' dfS Figure 2. Spectrum (a) and autocorrelation trace (b) of pump and probe laser pulses. AT and AE are the values at fwhm.
by a computer-driven translation stage with a mechanical resolution better than 0.1 pm. A laser pulse (probe pulse) passing through this arm of the Michelson arrangement is optically delayed in time with respect to a pulse (pump pulse) running via the other Michelson branch. The mechanical resolution of the translation stage limited the possible minimum temporal step of the pump-probe experiment to an amount of less than 1 fs. Each of the laser pulses had an average power of about 200 mW in the zone of interaction with the molecular beam. Being focused with a 400 mm lens, the peak power of one laser therefore reached about 0.5 GW/cm2. The molecular beam was produced in an oven consisting of a high-temperature corrosion resistant alloy (TZM, titaniumzirconium-molybdenum) oven tube. In this oven tube pure potassium was evaporated at a temperature of 850 K and coexpanded with argon as a carrier gas through a 70 pm nozzle. The oven was radiatively heated by two groups of tungsten filaments, where one of the filament groups was used to install a temperature gradient of about 100 K between the nozzle region and the rest of the oven. This setup was necessary to avoid clogging of the nozzle by condensing potassium. With an argon pressure of 4.2 bar, this source provided a continuous beam of cold potassium molecules with rotational and vibrational temperatures of about 10 and 50 K, respectively. Photoionized potassium dimers were mass filtered by means of a quadrupole mass spectrometer with a resolution of mlhm > 240 in the mass region of K2. The through-passing K2 ions were detected by a secondary electron multiplier. The pump-probe spectrum is given by the amount of ions produced by interaction of the laser pulses with the molecular beam being continuously recorded as a function of the delay time between the pump and the probe pulse.
3. Theory Various theoretical treatments for multiphoton ionization processes in diatomics have been discussed in detail in previous ~ o r k . ~ Here - ' ~ we summarize our approach, which has some special features for pump-probe experiment at moderate intensities. The time dependent Schrodinger equation is written in matrix representation:
The q ; = +;(R,t) represent the nuclear wave functions in electronic states i =1, 2, 3, ..., n. Equation 1 is solved without
0
ca5OOlS
2
Experiment
"
Theory
4 6 delay 1 ps
8
1
10
Figure 3. Comparison between measured pump-probe and calculated ionization signal as a function of delay time between the laser pulses. The upper theoretical curve is obtained by discretizing the continuum of the ejected electron. The lower theoretical curve is obtained for the more efficient evaluation which includes only one optimally selected kinetic energy Ek of the photoelectron.
further approximations, and within the model all multiphoton processes are included. The diagonal elements Hii of the Hamiltonian are given by Hii = TR Vii, where TR= P2/2mis the kinetic energy operator of the nuclei and Vii are the potential energy surfaces of the molecule in the absence of any laser fields. The off-diagonal elements describe the interaction with the laser field in the dipole approximation and are given by Hij = -pyc(t) with transition dipole moments pij. The electromagnetic field c(r) is a superposition of pump and probe fields of the type EO cos wr s(r), where €0 is the amplitude of the electromagnetic field, w the laser frequency, and s(r) a shape function. Gaussian functions are chosen as shape functions for both the pump and the probe pulse. The pump and probe pulses have the same wavelength and intensity and their shape is well described by a Gaussian. The basic technique used to propagate the wave packet in the spatial domain is the FFT meth~d.~O-*~ As we want to compare our results with a molecular beam experiment at low temperature, we neglect rotational degrees of freedom and suppose that the system is prepared in the lowest vibrational state u = 0 of the electronic ground state, thus:
+
Due to the wavelength of 840 nm employed in the experiment and the selection rules for optical transitions, five electronic states could in principle contribute to the ionization process, Le. X'Z,', A'Z:,+, 4IZg+, 2Il-4, and the K2+ ion ground state. The relevant potential energy surfaces are shown in Figure 5, and the transition dipole moments are obtained from ab initio data.24 Two of the electronic states, namely the 4'&+ and the 2'l-Ig states are very close in energy. The excitation mechanism connected with them is separated into two independent processes, neglecting possible interference during the multiphoton process. It was checked that this approximation is valid in the case of moderate laser field intensities. Thus for any specific process, only three neutral states X'Z,+, A'Z,+, and 4IZg+ or X'Zgf, A'&+, and 2Il-4 have to be considered simultaneously in the quantum dynamical description. Due to the ejection of the electron with energy E, a continuum is superimposed on the K2+ ion state I. Energy conservation in the whole system, molecule plus laser field, restricts the total region of the continuum to an interval [O,c]. In the present case
Multiphoton Ionization Processes in
3941 K,
J. Phys. Chem., Vol. 99,No. 46, 1995 16831
K2
Different methods of discretizing the electronic continua have been successfully employed in theoretical studies of ultrafast ionization proces~es.6.~~ Here, the continuum is simulated by discretizing the corresponding energy range by a sufficient number N of electronic states.26 Consequently, the integrals in the wave function and in the Hamiltonian are replaced by appropriate sums. Due to the orthogonality of the electronic basis functions Iqi) and IEk), the description of the discretized continuum also transforms into N sets of coupled differential equations and eq 1 becomes a system of four coupled equations:
'f
A
h = 840 nm
X 'E;
20
0
40
100 1
60 80 o/cm-'
IHXX
HXA
0
Figure 4. Fourier transform of experimental data from a 220 ps scan (4400data). 5 [
\
'="Of'",;
O L 4 5 L 3
5
7
kkk 3
5
7
3
bond length r /
5
7
3
5
7
A
Figure 5. Snapshots of the wave packets in their respective electronic states for a delay time of 300 fs between pump and probe lasers for the (1 2) ionization process in the K2 molecule. The wave packets are represented by their absolute value. The two-photon step is indicated by the arrows. The 2In, state is included in the dynamical calculation; the 4'&+ state is inactive.
+
of the K2 molecule E has the value of 0.0139 hartree. Thus in the case of K2 the nuclear wave function t+bn in eq 1 must represent a continuum. Thus the total wave function Y(t)is expanded in the basis of the neutral states' wave functions Yn-l(t) and the wave functions of the ion continumm YW). The continuous part Yc&)can be written as
(3) The subscript I indicates the ion ground state, and /E> are the electronic basis functions of the continuum associated with the kinetic electron energy E. The continuous part of the Hamiltonian can be written as
The second process is described when the 2'H, is replaced by the 4'Xg+ state in eq 6. The calculation is repeated for different values of the kinetic energy Ek of the ejected electron, and all contributions to the ion signal are added. This method converges reasonably fast for the simulation of the K2 pumpprobe experiment. Significant contributions to the ion signal are found only in the restricted range of 0.008-0.011 hartree (0.217-0.299 eV) for the kinetic energy Ek (the whole range is 0.0-0.0139 hartree). It was found that the contribution of a single optimally selected kinetic energy Ek already defines the dominant features of the total transient ionic signal. The reason is the comparably small energy range in the ion state defined by the second photon of the probe laser. In K2 the second photon of the probe laser does not reach the dissociation limit, in contrast with the case for Na2. Thus, in the present case only a small range of energies is important so that a representatitve energy Ek can be used to simulate the ion signal. The actual sum of the continuum states converges very fast. In addition, this method allows a careful and fast analysis with one optimally selected Ek to locate the region of possible transition paths.: The input for the quantum dynamical calculation was the ab initio data for dipole transition moments and potential curves24 and the parameters of the laser pulse, which are adjusted to the experimental values (fwhm of the laser intensity, 60 fs; Fourier transform limited band width 245 cm-I; wavelength, 840 nm). The available maximum values of the dipole transition moments p x and ~ PA4 (4 = 4'Xg+) are about 4.8 au (e.@) with the maxima located at a bond length of 10 and 8 Q, respectively. The value of P A 2 was set equal to the value of , 4 4 . To test its influence, this magnitude was varied as a constant value in the range between 2 and 4 au without any effect on the resulting ion signal. The dipole transition distribution is assumed to be independent of Ek and to have a constant value of ' 1 3 ~ ~ 2 . 4. Results The experimental result of the one-color three-photon pumpprobe experiment is presented in Figure 3 in comparison to the calculated temporal evolution of the K2 ion signal. The Fourier analysis, shown in Figure 4 of the experimental data, exhibits a strong dominant band in the region of -66 cm-' belonging to the A'&+ state and a very weak single line at -90 cm-' being attributed to the ground state.
16832 J. Phys. Chem., Vol. 99, No. 46, 1995
de Vivie-Riedle et al.
t = 510 fs
bond length r /
A
Figure 6. Snapshots of the wave packets in their electronic states for a delay time of 550 fs between pump and probe lasers shown for the ionization process in K2 for moderate laser field intensities.
For the theoretical calculations we had to introduce an arbitrary factor for the assumed dipole transition moment into the ion state with the value of P A 2 as the upper limit. Hence, we have to introduce a scaling factor to adjust the difference between the experimentally and theoretically applied intensities. The experimental laser field intensity was estimated to be 0.5 GW/cm2. The calculations were carried out for different low laser field intensities from 0.1 to 2.2 GW/cm2. At any intensity up to 0.8 GW/cm2 we found that only the A1Zuf state (the first state in the excitation ladder) is populated by the pump laser and no two-photon excitation takes place. At an intensity of 2.2 GW/cm* we also find small populations in the higher excited states 2Il3, and 4'&+, but the resulting ion signal as a function of delay time is the same as for the lower laser field intensities. We just find higher signal intensities in the case of the slightly higher laser field intensities. The results obtained for pulse intensities of 2.2 GW/cm2 are chosen as an example, because their pathway can be more easily visualized in terms of snapshots during the excitation process. In addition, we can study the role of the 2'lI, and the 4IZg+ state in this excitation process. First, we discuss the ionization process when the 2'lI, state is included in the dynamical calculations. Representative snapshots of the wave packets during the pump-probe excitation are shown in Figures 5 and 6 for two different delay times between pump and probe laser. The wave packets are represented in the figures by their absolute values to indicate their location, movement, and spreading. The sequence in Figure 5 shows the multiphoton excitation for a delay of 300 fs, and Figure 6 shows the ionization process for a 550 fs delay. These two figures represent the situations after excitation by the pump laser where the wave packets in the A'&+ state are close to the classical, either inner (Figure 6) or outer (Figure 5 ) , turning points. Both situations are, in principle, favored possible transitions, as the wave packets are most localized at these points and the overlap function between the wave packets in the different electronic states can be maximal. The situation after the pump pulse and just before the probe pulse is given in the first snapshot of Figure 5 . The pump laser with the selected intensity predominantly populates the A'&,+ state to an amount of 69%. The 2]lIgstate is populated only to an insignificant amount of 0.05%. Thus the dominant step is a one-photon transition due to the pump laser, and a twophoton transition has to be induced by the probe laser to reach the ionization limit. Due to its broad spectrum the pump laser induces a coherent superposition of the vibrational states in an energy region of about 245 cm-' (in the experiment 160 cm-' were reached, see Figure 2a). According to the Franck-Condon (FC) principle the transition from the ground state into the excited states takes place close to the inner turning points of the respective potential curve. The maximum of the wave
5 7 bond length r / A
3
Figure 7. Snapshot of the wave packet dynamics 240 fs after the pump pulse excitation, indicating the situation for a transition from the outer turning point of the AIX,+ state.
packet in the A'&+ state has moved, due to its own time dependent dynamics, for the first time close to the outer turning point region when the probe pulse is turned on with a delay of 300 fs. The second and third snapshots in Figure 5 illustrate the situation around the maximum of the probe pulse for one selected energy Ek. The ionization takes place at the outer turning point of the AI&+ state as is indicated by the arrows in the second snapshot of Figure 5, and detailed investigations verify that this is the only efficient ionization pathway. It is a direct (vertical) two-photon transition, and a significant amount of population (1.87%) is transferred into the ion state (third snapshot). The last snapshot in Figure1 reproduces the situation after the probe laser pulse. The sequence of snapshots in Figure 6 shows the equivalent situations now for a delay time of 550 fs. The probe pulse is fired when the wave packet in the A'&,+ state has returned to its inner turning point region (first snapshot in Figure 6). Again, in the second and third snapshots of Figure 6 the situations close to the maximum of the probe laser are represented. The transition occurs at the inner turning point region, as indicated by the arrows in the first and second pictures of Figure 6. The amount of population (0.17%) transferred into the ion state is significantly smaller for this pathway, as can be seen from the last snapshot of Figure 6. The calculations were also performed with the 2IlI, state replaced by the 4'Z,+ state in eq 6. The resulting snapshots, corresponding to the pathway at the inner turning point of the AI&+ state, indicate a similar dynamical behavior to the case of the 2Il3, state and are not shown here. One snapshot (Figure 7) of the pathway at the outer turning point is selected to point out the different conditions for possible ionization pathways. Figure 7 reflects the situation with all five states included at the very beginning of the probe laser pulse. The relative positions of the wave packet in the AI&+, 4IXg+, and 2 ' n , states represent simultaneously the location of the corresponding turning points. Only the turning points of the wave packets in the 2'H, and A'C,+ states are located vertically one upon another. Therefore the transition pathway via the 4l2,+ state is also off resonant. The transition mechanisms described here define the total ion signal as a function of delay time between pump and probe laser. Comparison of the total ionic population is performed, including altematively the 2'lI, (Figure 8a) or the 4IZg+ state (Figure 8b) and for both pathways. The energy EAof the ejected
Multiphoton Ionization Processes in KZ outer-TP inner-TP
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J. Phys. Chem., Vol. 99,No. 46, 1995 16833
I
8 3c P
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a a a
.
5 2-
5
'inner-TP
-outer-TP
C
P
l
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4
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Figure 8. Compmson of the contributions to the total transient ion signal as a function of delay time at the inner (dotted line) and outer (solid line) transition pathways. Panel a shows the resulting ion population when the 2'n,state is included in the calculahon, and panel b shows the resulting ion signal when the 4l&+ state is included.
electron is optimized to the maximal transition possibility at the inner or the outer turning point region, respectively. It is evident that the pathway at the outer turning point region is the dominant process when the 2IJlg state is included in eq 6 (Figure 8a). The contributions from all other pathways are negligible. When the 2Il7, state is incorporated, the ion signal due to the inner tuming point process has hardly any characteristic features and very small transition amplitudes. The ion signal due to the outer tuming point process shows characteristic oscillations with a period of 500 fs; this corresponds exactly to the average vibrational splitting (-66 cm-I) of the eigenstates (v = 9-13) in the AIL+ state coherently excited by the pump laser pulse. The ion signal shows the same pattem, only lower intensities in the amplitudes, for a laser field intensity of 0.8 GW/cm2, when the 2'n, is not populated by the pump laser. Thus the 2II-4 state only serves as a resonant, but essentially necessary, state in the ionization process which need not be populated. The total ionic population as a function of delay time, calculated including the 4l$+ state as the active state, is shown in Figure 8b. The signals due to both pathways have very small amplitudes, and it is obvious that they add no significant contribution to the total process. The process connected with the outer tuming point shows pure oscillations with a period of 630 fs, corresponding to the average vibrational splitting (52 cm-I) of eigenstates (v = 33-38) in the 4IZg+ state. The ion signal due to the 4I&+ states vanishes completely, already for a laser field of 0.8 GW/cm2, when no population is induced in the 4'2,+ state by the pump laser. Thus, for moderate laser field intensities the 2'H, state is the only important state in the two-photon ionization step. The (1 2)-photon ionization process with the transition pathway located at the outer tuming point of the A'Z,+ state is confirmed by comparison of the experimental (upper curve) and theoretical ionization signals (two lower curves) as a function of delay time, presented in Figure 3. The position of the maxima and the envelope intensity modulation are reproduced by the calculations. All curves show strong oscillations with a period of 500 fs. This corresponds to the oscillation period of the wave packet prepared in the A'C,+ state (centered around v = 11) by the pump laser. The Fourier transform (Figure 4) of the
+
time resolved experimental pump-probe spectrum shows nearly exclusively the frequency contributions from the excited vibrational levels of the A'%+ state. This is confirmed by the calculated results which detect only the oscillations of the wave packet in the A'Z,+ state. The first maximum occurs after 250 fs, which is half the oscillation period. Due to the vertical transition, and following the Franck-Condon principle, the wave packet in the A'Z,+ state is prepared close to the inner turning point. In a time period of 250 fs it reaches the outer turning point, where the transition to the ion state takes place. The spreading of the wave function begins in the theoretical and experimental curves around 7 ps. It is interesting to compare the two theoretical curves. The upper curve represents the ion signal including the discretized continuum of states in the ion state region while the lower curve is obtained by including only one selected kinetic energy Ek of 0.0097 hartree (0.263 eV) in the calculation. Both curves are nearly identical and support the idea that a selected energy can represent the ionization process when the excitation limits the photoelectron range to be quite small. The continuum for one pathway can be represented by one optimally selected energy Ek where the classical difference potential analysis27defines the selection. This approximation significantly reduces the computation time required without appreciable loss of accuracy. The significance of this method increases with increasing number of degrees of freedom. Already a multiphoton pump probe spectrum of a three-dimensional problem can hardly be handled otherwise. The method is already successfully applied in the three-dimensional quantum dynamical calculation of the Na3 pump-probe spectrum.28 5. Discussion
As expected, the pump-probe ionization process in KZunder the influence of moderate laser field intensities investigated here shows some similarities to the transition mechanisms reported for Na2.436 For example, the spreading of the wave function, which occurs due to the anharmonicity of the potential energy surface of the A'&+ state, can also be detected in the K2 ion signal. Because of the higher laser intensities and choice of excitation w a ~ e l e n g t h in ~ ?the ~ Na;? experiments, in this case always a combination of multiphoton processes contributes to the transient ion signal. One of these processes in Naz, the (1 2)-photon transition process also takes place in KZunder the given conditions. However, in the case of K2 the laser intensity was reduced so far that a pure (1 2)-photon process takes place. Significant contributions from (2 1)-photon processes as reported for Naz4 at intensities of 50 GW/cm2 cannot be found. In the case of Kz,laser intensities up to 0.8 GW/cmZ solely cause the (1 2) process and even at intensities of 2.2 GW/cm2this process is still dominant. Additionally, the details of the (1 2) transition mechanism are different. The main difference is the location of the transition pathway. For moderate laser fields the ionization pathway is located at the outer tuming point of the AIL+ state, whereas Engel et alS6 showed that the (1 2) transition pathway in Na2 is close to the inner turning point. This transition pathway in K2 is the key difference in the dynamics of the Na2 and KZmolecules. The observed process is a (1 2)-photon transition via the 211-Ig state. The characteristics of pump and probe pulses, namely wavelength, intensity, and pulse width, prepare special 'femtosecond-induced' dynamics in the molecules. They define the potential curves involved, the energetic location of the wave packets on the potentials, and consequently also the location of the tuming points with respect to the nuclear coordinate. In K, the position of the turning points defines the possible regions for optimal resonant transitions.
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de Vivie-Riedle et al.
16834 J. Phys. Chem., Vol. 99, No. 46, 1995 The 2'n, state is of central importance in this process although it need not be populated. Under the prevailing dynamical conditions the 2In, state opens an optimal transition path, a so-called FC window, at the outer tuming point of the wave packet in the A'%+ state. The tuming points of both wave packets are located exactly at the same position (Figure 5, second snapshot, and Figure 7) and thus allow an optimal resonant transition which makes a significant two-photon ionization step possible. The A'&+-2111g transition is stronger than the X'Cg+-AICu+ transition. Only this situation renders the pure (1 2)-photon process possible without contributions of (2 1)-photon transitions. The other important feature of the FC window at the outer tuming point between the 2'n, and Ai%+ states is that it singles out selectively the oscillations in the A'%+ state. Although we find wave packets in the X'C,' and A ' Z + states, exclusively the motion of the A'&+ state wave packet is observed in the ion signal, which is different from the results for the Na2 molecule. In K2 at moderate laser intensities the motion of the wave packet in the X'C,+ state stays dark. Its outer tuming point lies outside the range of vertical FC overlap, and no transition into the 2 ' n , state can occur here. Contrary to the case for Na2: the ionization pathway in K2 located at the outer tuming point has its origin already in the A'&+ state and not only in the 2'n, state. In principle, a FC window at the inner tuming point of the AIC:,+ state as was found in Na2416would make it possible, due to the relative position of the potential curves, to probe in addition, depending on the laser intensities, the oscillations of the wave packet in the X'Z,+, 4'Cg+, and 2Il-4 states. Therefore this FC window would not be selective for the A'&+ state. This is indicated in the splitting of the corresponding ion signal, which reflects the interference of the contributions from either the AIC,+ and 2'n, states (Figure 8a) or the A'C:,+ and 4'Cg+ states (Figure 8b). The signal may also contain a small contribution from the three-photon ionization from the ground state, which may explain the corresponding weak peak in the experimental FT spectrum (Figure 4). However, neither in the 2]IIgstate nor in the 4'C,+ state does the location of the inner turning point of the prepared wave packet coincide well with the one of the wave packet in the A'%+ state. Consequently, the vertical transition step is not optimally resonant, and only a small transition amplitude is observed. The process via the 4'Cg+ state makes no significant contributions to the ion signal. Nevertheless, it is interesting that the pathway at the outer turning point reflects only the motion in the 4ICg+ state, while the motion in the A'&+ state stays dark. This can now easily be understood by the location of the corresponding outer tuming points. Its turning point relative to the A'&+ state tuming point is shifted significantly to greater bond length (Figure 5). No direct (vertical) twophoton transition is possible. The ionization step is a delayed (1 1) process which needs enhanced population in the 4l2,+ state. If it were possible to exclude the contributions from the 2'ngstate in the experiment, the motion in the 4'$+ state could be observed selectively. In principle this can be realized if one starts in a specific vibrational level of the A'&+ state, prepared, for instance, by excitation with a CW laser. The wavelength of both the pump and the probe laser must then be greater than 840 nm, so that the 2'nI, state cannot be reached anymore. Since the transition probability at the inner and outer tuming points is of small but similar intensity, the resulting ion signal would then show dominant oscillations with a period of 310 fs, corresponding to half of the period of the wave packet motion in the 4IC,+ state. The analysis shows that for the chosen pulse power and wavelength a selective FC window in the 2'ngstate exists in
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K2. In this case the pump and probe pulses have to be delayed to achieve ionization, which is then very efficient. The analysis of the excitation pathway is important with regard to controlling physical and chemical processes. The preparation of an optimal ionization path becomes most important in the case of large molecules which can hardly be ionized by stationary spectroscopy.29 The probing of selected modes in excited electronic states is an interesting aspect for large molecules whose excited states cannot be investigated on a nanosecond time scale because of their short lifetimes. Optimization of the processes can be obtained by fine tuning of the wavelength. Additional possibilities may also be achieved in combination with CW laser techniques.
Acknowledgment. We thank Prof. L. Woste and Prof. J. Manz for helpful and motivating discussions and Prof. W. Meyer for the ab initio data. Generous financial support by the Deutsche Forschungsgemeinschaft DFG through project SFB 337 and a Habilitationsstipendium (for R.dV.-R.) is gratefully acknowledged. References and Notes (1) Kaiser, W., Ed. Ultrashort Laser Pulses and Applications: Topics in Applied Physics Springer: Berlin, 1988; Voi. 60. (2) Khundkar, L. R.; Zewail, A. H. Annu. Rev. Phys. Chem. 1990,41, 15. Gruebele, M.; Roberts, G.; Dantus, M.; Bowman, R. M.; Zewail, A. H. Chem. Phys. Lett. 1990, 166, 459. (3) Janssen, M. H. M.; Bowman, R. M.; Zewail, A. H. Chem. Phys. Lett. 1990, 172, 99. (4) Baumert. T.; Grosser, M.; Thalweiser, R.; Gerber, G. Phys. Rev. Lett. 1991, 67, 3753. ( 5 ) Mmz, J., Woste, L., Eds. Femtosecond Chemistry Verlag Chemie: Weinheim, 1995, and references therein. In particular, see Chapters 2, 11, and 12 by A. H. Zewail, by V. Engel and Ch. Meier, and by T. Baumert, R. Thalweiser, V. Weiss, and G. Gerber.
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