Wave packet dynamics on the repulsive potential surface of BaFCH3 excited at 745 nm

Article abstract of DOI:10.1016/S0009-2614(02)00266-X

We studied the time evolution of the wave packet formed by the excitation of the Ba?FCH₃ complex with a 120 fs laser pulse at 745 nm to its electronic ?' state which is repulsive at the ground state geometry and decays to Ba and CH₃F fragments. By applying probe pulses with different wavelengths of 400 and 267 nm, respectively, we observed strongly different time dependences of the pump-probe signals for the BaF⁺ and Ba⁺ ions determined by the Franck-Condon windows available in both cases. The experimental results are qualitatively confirmed by theoretical studies based on ab initio calculations of the corresponding potential energy surfaces.

Full text of DOI:10.1016/S0009-2614(02)00266-X

8
April 2002
Chemical Physics Letters 355 (2002) 449–456
www.elsevier.com/locate/cplett
Wave packet dynamics on the repulsive potential surface
of BaFCH excited at 745 nm
3
a
a
a,
b
b
*
V. Stert , H.-H. Ritze , W. Radloff , K. Gasmi , A. Gonzalez-Ure n~ a
a
Max-Born-Institut f €u r Nichtlineare Optik und Kurzzeitspektroskopie, Max-Born-Str. 2A, D-12489 Berlin, Germany
b
Instituto Pluridisciplinar, Universidad Complutense de Madrid, Juan XXIII-1°, E-28040 Madrid, Spain
Received 20 September 2001; in final form 7 February 2002
Abstract
We studied the time evolution of the wave packet formed by the excitation of the Ba ꢀ ꢀ ꢀ FCH
3
complex with a 120 fs
laser pulse at 745 nm to its electronic A state which is repulsive at the ground state geometry and decays to Ba and CH
fragments. By applying probe pulses with different wavelengths of 400 and 267 nm, respectively, we observed strongly
0
~
3
F
þ
þ
different time dependences of the pump–probe signals for the BaF and Ba ions determined by the Franck–Condon
windows available in both cases. The experimental results are qualitatively confirmed by theoretical studies based on ab
initio calculations of the corresponding potential energy surfaces. Ó 2002 Elsevier Science B.V. All rights reserved.
1
. Introduction
tions have shown that at the equilibrium geometry
0
~
of the ground state the A state potential curve is
strongly repulsive along the Ba–C coordinate. The
calculated frequency of the vertical transition from
The study of the intracluster harpooning reac-
tion in Ba ꢀ ꢀ ꢀ FCH initiated by excitation to its
3
0
~
À1
~
electronic A state with femtosecond laser pulses at
the ground to the excited A state is 13500 cm
6
conversion from the initially excited state to the
18 nm has led to the conclusion that the internal
(corresponding to a wavelength of 745 nm). This
value was confirmed in femtosecond two-color
two-photon resonance ionization experiments in
which the resonant wavelength was tuned across
the resonance [2]. The large width of the measured
0
~
next lower electronic A state is the rate-deter-
mining process of the reaction [1,2]. By the internal
conversion the vibrational energy is gained which
is necessary to overcome the barrier of the har-
pooning reaction leading to the stable BaF prod-
uct. This has been confirmed in our studies based
on the corresponding ab initio calculated potential
energy surfaces [2]. Furthermore, these calcula-
À1
resonance of about 400 cm agrees very well with
the theoretically estimated value for the two-color
ion signals. This large width mainly represents the
0
~
~
broad Franck–Condon region of the X ! A
transition.
In the present Letter we study the dynamics of
complex after excitation to its
the Ba ꢀ ꢀ ꢀ FCH
3
0
~
*
electronic A state. Because no vibrational energy
is deposited in the complex we do not expect a
Corresponding author. Fax: +49-30-6392-1259.
E-mail address: radloff@mbi-berlin.de (W. Radloff).
0
009-2614/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved.
PII: S0009-2614(02)00266-X

450
V. Stert et al. / Chemical Physics Letters 355 (2002) 449–456
chemical reaction leading to BaF product forma-
tion. Instead we are interested in the wave packet
~
dynamics starting from the directly excited A
retical investigations are compared and
discussed.
0
state. The steep slope of the repulsive potential
curve at the equilibrium distance of this com-
plex should cause a fast removal of the initially
prepared wave packet out of the detectable
Franck–Condon region. Thus, a one-dimensional
treatment with respect to the corresponding frag-
mentation coordinate is sufficient for the descrip-
tion of the main reaction channel.
In a pump–probe experiment the observable
Franck–Condon region depends not only on the
Franck–Condon factors for the pump-photon
initiated transition from the ground to the excited
state but is also determined by the access to the
vibrationally excited levels of the ionic state after
the absorption of the probe photon. Thus, holding
constant the pump photon energy we expect sig-
nificant changes for the observed time-evolution of
the pump–probe signals after variation of the
probe photon energy.
2. Experimental
The experimental setup used has been described
in detail in our earlier papers [3,4] and will be
summarized here only briefly. The weakly bound
Ba ꢀ ꢀ ꢀ FCH
3
complexes were prepared in a mo-
lecular beam by the adiabatic expansion of a gas
mixture containing laser desorbed Ba vapor and
3
molecular CH F gas (10%) in He (1 bar) carrier
gas. The interaction channel of the vaporization
source was cooled down to about )130 °C in order
to enlarge the cluster concentration. The energy of
the focused radiation (diameter: 0:2 ꢀ ꢀ ꢀ 0:3 mm) of
the vaporization laser (SHG of a Nd:YAG laser)
was restricted to low values (0.7 mJ) in order to
reduce chemical reactions in the gas mixture near
the laser heated Ba rod. The molecular beam was
crossed by two weakly focused copropagating la-
ser beams in the interaction region of a time-of-
flight (TOF) mass spectrometer. The laser system
used was a commercial Ti:sapphire laser and am-
plifier system (Clark MXR) tuned to 800 nm (1.55
eV) which is combined with a commercial OPA
system (Clark I-GOR-SHG). The second har-
monic of the OPA signal wave tuned to 745 nm
Hence, the present study is concerned to femto-
second pump–probe experiments, where the
0
~
Ba ꢀ ꢀ ꢀ FCH
the pump wavelength of k
whereas the wavelength of the probe pulse is
3
complex is excited to the A state at
1
¼ 745 nm (1.65 eV)
ð1Þ
ð2Þ
chosen as k2 ¼ 400 nm (3.1 eV) or k2 ¼ 267 nm
(
4.65 eV). In the former case the sum energy of the
absorbed pump and probe photons exceeds only
slightly the ionization potential (4.5 eV) of the van
der Waals complex. This means, a relatively small
increase of the vertical difference of the potential
was used for the excitation of the Ba ꢀ ꢀ ꢀ FCH
3
0
~
complex to its electronic A state. The second or
third harmonic of the Ti:sapphire laser at 400 nm
(3.1 eV) or 267 nm (4.65 eV) was applied to probe
the excited clusters and the products by ionization.
The width (FWHM) of the laser pulses was about
120 fs. Typical values of the laser fluences were
0
~
energies between the A and the cationic ground
0
~
state just after the initial excitation of the A state
will immediately lead to the disappearance of the
ion signal because the Franck–Condon window is
very narrow. In the latter case, however, large
excess energy is available in the ion state of the
complex which should allow to follow the evolu-
tion of the wave packet on the repulsive potential
2
about 0:2 mJ=cm for the pump pulse at 745 nm
and about 1:5 mJ=cm for the probe pulse at 400
nm, respectively.
2
The ion signals were detected by a micro-
channel plate detector in the TOF mass spec-
trometer, digitized by a fast digital oscilloscope
(Tektronix TDS520A) and stored and processed
by a PC.
A standard delay line was used to scan the delay
time between the pump and the probe pulses. At a
repetition frequency of 33 Hz the mass spectra
were accumulated typically for 50 laser pulses at
0
~
surface of the excited A state for a rather long
delay time.
In the following at first we present the ex-
perimental results for the two wavelength com-
binations. In the next part we simulate the
pump–probe signals in a theoretical study. Fi-
nally the results of the experimental and theo-

V. Stert et al. / Chemical Physics Letters 355 (2002) 449–456
451
each delay time s and averaged over 50 up- and
down scans of the delay line.
to the delay time zero (see Section 4.3). This fit
curve is only slightly broader than the cross cor-
relation function (dashed line) which is symmetri-
cal to the delay time zero but was shifted here to
the position of the measured signal curve for direct
comparison.
3
. Experimental results
þ
3
.1. Probe pulse wavelength of 400 nm
The BaF mass channel shows no two-color
signal (Fig. 1b). Only the background signal is
observed caused by two-probe photon ionization
of the BaF molecules already formed in the laser
vaporization zone near the Ba metal rod. Re-
membering that probe photons with an energy of
3.1 eV are sufficient to detect excited BaF products
In Fig. 1 the measured time-dependent ion sig-
þ
þ
nals of Ba ꢀ ꢀ ꢀ FCH and BaF are displayed as a
3
function of the delay time between the pump pulse
at
k
1
¼ 745 nm and the probe pulse at
¼ 400 nm. The observed parent ion signals are
fit very well by the calculated curve (full line in Fig.
ð1Þ
k
2
~
of the intracluster reaction initiated via A state
excitation of the parent complex [1,4] we conclude
that no such products will be formed after exci-
1
a) the maximum of which has a distance of 45 fs
0
~
3
to its A state.
tation of Ba ꢀ ꢀ ꢀ FCH
þ
No Ba ions have been detected as well (not
shown in Fig. 1) because the probe photon energy
of 3.1 eV is too small to ionize the Ba atoms
1
(
(
IP ¼ 5.21 eV) which are formed in the D state
1.41 eV) after the nonreactive fragmentation of
~
0
the parent cluster on the A potential surface (cf.
1]). A nonresonant absorption of a pump and a
[
probe photon does not exceed the Ba ionization
potential as well. Due to this reason experiments
with a larger probe photon energy of 4.65 eV are
of particular interest.
3.2. Probe pulse wavelength of 267 nm
In Fig. 2 the time-dependent ion signals of
Ba ꢀ ꢀ ꢀ FCH
3
, BaF and Ba are displayed for the
pump wavelength k
1
¼ 745 nm and the probe
ð2Þ
wavelength k2 ¼ 267 nm. At the corresponding
probe photon energy of 4.65 eV the parent
complex (IP ¼ 4.5 eV) is ionized by only one
probe photon. Hence, the simultaneous absorp-
tion of the pump and probe photons near s ¼ 0
þ
will lead to a depletion of the Ba ꢀ ꢀ ꢀ FCH signal
3
due to any reaction initiated by the pump photon
(see the step in Fig. 2a). Compared to corre-
sponding results previously obtained for the ex-
þ
Fig. 1. Time-dependent ion signals of Ba ꢀ ꢀ ꢀ FCH (a) and
3
þ
BaF (b) as a function of the delay time s between the pump
~
citation of the A state by the pump wavelength of
pulse at 745 and the probe pulse at 400 nm. (a) The solid line
represents the calculated curve according to the theory (see
text), whereas the dashed line denotes the cross correlation
function of the laser pulses which is shifted onto the maximum
of the measured signal curve for comparison.
6
18 nm [3] here a much weaker depletion occurs
reflecting the significantly smaller absorption and/
or reaction cross sections for the excitation of the
~
A state.
0

452
V. Stert et al. / Chemical Physics Letters 355 (2002) 449–456
þ
Ba signal (cf. Fig. 2b,c) one can conclude that
þ
the time-dependence of the BaF signal for
s > 400 fs is determined by the nonreactive frag-
0
~
mentation of A state excited Ba ꢀ ꢀ ꢀ FCH
3
clusters
into Ba þ CH
3
F. The solid lines in Fig. 2b,c are
theoretical curves which are calculated in the
following section.
4. Theoretical treatment
Up to now only preliminary theoretical results
exist regarding the potential energy surfaces of
Ba ꢀ ꢀ ꢀ FCH [1]. Therefore we will recapitulate the
ab initio calculations of its X and A electronic
3
0
~
~
À1
~
states and the ground electronic state X of the
cation. After that, in a one-dimensional treatment
the Ba ꢀ ꢀ ꢀ FCH
3
stretching is quantized (vibra-
tional quantum number v) and the Franck–Con-
0
~
~
don factors for the optical Xðv ¼ 0Þ ! A !
À1
~
X ðvÞ transition are determined. This allows us to
simulate the pump–probe ion signal in dependence
0
~
on the dynamics on the A potential surface.
4.1. Ab initio calculations
þ
þ
Fig. 2. Time-dependent ion signals of Ba ꢀ ꢀ ꢀ FCH (a), BaF
3
The quantum-chemical computations were
carried out in a similar way as already represented
2]: Using the MOLPRO program package [5] the
inner 46 Ba electrons were described by the effec-
tive core potential MBS-ECP2 [6]. By means of the
basis set (6s7p6d3f)/[3s3p6d3f] the remaining 10
electrons were considered. Here the s and p func-
tions given [6] were used. Then we added the
functions s(0.008), p(0.008), d(0.96632, 0.89383,
þ
(
b) and Ba (c) versus delay time s between pump pulse at 745
nm and probe pulse at 267 nm. The different notation of the
measured points (circles, squares) correspond to different runs
of the experiment. The thick solid lines are the theoretical
curves the deviations of which from the experimental results –
in particular for delay times s P 600 fs – are discussed in the
text. The thin solid line (c) symmetrical to the delay time zero
represents the cross correlation curve due to the nonresonant
absorption of the pump and probe pulses by the Ba atoms.
[
0
.27320, 0.10389, 0.010) and f(0.70, 0.35, 0.12).
þ
The BaF ion signal (Fig. 2b) is characterized
by a fast decay followed by a small tail which
decreases down to the background level after a
The s, p and d basis functions of the aug-cc-pVTZ
basis set were taken for fluorine. For a suitable
description of the F electron affinity we added the
diffuse functions s(0.03, 0.0078, 0.003, 0.001),
p(0.070, 0.020) and d(0.14) [7] revealing a
(15s8p4d)/[9s6p4d] fluorine basis set. For carbon
we used a (13s7p4d)/[7s5p4d] basis set, where the s,
p and d functions of the aug-cc-pVTZ basis set
were augmented by s(0.010, 0.0025), p(0.0086) and
d(0.057) [7]. The hydrogen atoms were described
by the s and p functions of aug-cc-pVTZ leading to
the (6s3p)/[4s2p] basis set.
þ
few ps. The missing of a long time stable BaF
product signal means that we did not find any
indication for an intracluster reaction proceeding
~
after A state excitation of the parent complex in
~
contrast to the excitation of the A state at 618 nm
0
þ
[
3]. The measured BaF signal is only due to
fragmentation of the parent cluster ions after the
reaction in the ionic state. Because its time-de-
pendent decay is complementary to the rise of the

V. Stert et al. / Chemical Physics Letters 355 (2002) 449–456
453
The state-averaged complete active space self-
consistent field (CASSCF) method was applied
The wave function of the neutral vibronic
ground state was determined in the interval be-
ꢀ
assuming C3v symmetry of the Ba ꢀ ꢀ ꢀ FCH
3
com-
tween 3.8 and 5.0 A using N ¼ 20 (number of grid
0
~
points). The A state was treated in the interval
plex. The two Ba valence electrons were distrib-
uted among 10 active orbitals. The carbon and
fluorine 1s electrons were frozen in the subse-
quent multi-reference configuration interaction
procedure using the Davidson correction
ꢀ
between 3.6 and 18.0 A, here we have taken
N ¼ 2000. The same N-value was chosen for the
cationic ground state, but the interval was slightly
ꢀ
extended to 3:3 ꢀ ꢀ ꢀ 18:0 A.
0
~
(
MRCI+Q).
The 190 lowest eigenfunctions of the A state
potential were taken into account and their over-
lap integrals with the ground vibronic wave func-
tion were calculated. This allows the calculation of
3
Varying the distance between Ba and FCH the
geometry of fluoromethane was optimized by
minimizing the energy for a given distance.
0
~
~
Although the equilibrium geometry of the X
the wave packet on the potential curve of the A
electronic state is bent [1] the barrier to linearity is
À1
electronic state after excitation with an optical
pulse of given length and carrier frequency. Due to
only a few cm . Thus, the complex can be char-
acterized as a quasi-symmetric top with a Ba ꢀ ꢀ ꢀ C
the finiteness of the considered r
interval our
description is only valid until the wave packet has
BaꢀꢀꢀC
ðeÞ
equilibrium distance (in C3v symmetry) of r
¼
BaꢀꢀꢀC
:239 A [1]. For the correct determination of the
ꢀ
ꢀ
reached the right boundary (18.0 A) – but this is
4
ground state wave function we have calculated the
sufficient for our purposes. Inside the rBaꢀꢀꢀC inter-
val of the ground cationic state we have found 169
bound vibrational states. The overlap integrals of
these wave functions with the 190 eigenfunctions
ꢀ
potential energy between 3.8 and 5.0 A with an
ꢀ
increment of 0.1 A.
0
~
À1
The A state is only weakly bound (D
e
¼
0
~
1
25 cm ), its equilibrium geometry is C -sym-
ꢀ
of the A state were calculated. Now the ionization
probability (in dependence on the vibrational
quantum number of the ion) due to the action of
an optical probe pulse can be determined. Here for
simplicity we made the assumption that the tran-
sition dipole moment of the ionization step does
not depend on rBaꢀꢀꢀC. Furthermore, we assume
Gaussian-shaped pump and probe pulses with a
length of 120 fs (FWHM) and neglect saturation
effects by these pulses.
3
v
ðeÞ
metric with r
¼ 6:2 A [1]. Thus, the vertical
BaꢀꢀꢀC
0
~
~
X ! A optical absorption leads to the excitation
0
~
of the repulsive part of the A potential followed
0
~
3
F. The A
by fragmentation into Bað6s5dÞ þ CH
state potential was calculated for distances rBaꢀꢀꢀC
between 3.6 and 5.0 A with an increment of 0.1 A ,
ꢀ
ꢀ
ꢀ
between 5.0 and 10.0 A with an increment of 0.5 A
ꢀ
ꢀ
and between 10.0 and 18.0 A with an increment of
ꢀ
.0 A.
2
The ground electronic state of the cation is
À1
strongly bound ðD
e
¼ 6710 cm Þ with the poten-
4.3. Results of simulations
ðeÞ
ꢀ
tial minimum at r
metric configuration [1]. This potential was
¼ 4:090 A in a C3v-sym-
BaꢀꢀꢀC
At first we will discuss the pump–probe signals
ð2Þ
0
~
calculated at the same points as the A state po-
for the probe photon wavelength k2 ¼ 400 nm.
tential, additionally the points between rBaꢀꢀꢀC
¼
The pump pulse wavelength was fixed at 745 nm
0
~
ꢀ
ꢀ
3
considered.
:3 ꢀ ꢀ ꢀ 3:6 A with an increment of 0.1 A were
corresponding to the resonant excitation of the A
electronic state [2]. For these photon energies the
maximal vibrational energy of the cation is about
4
.2. Pump–probe signal simulation
0.2 eV (assuming 4.5 eV for the adiabatic BaFCH
3
ionization potential). Thus, we have considered
þ
The wave functions of the vibrational eigen-
stretching
the excitation of the (Ba ꢀ ꢀ ꢀ FCH
3
Þ
stretching
vibration from v ¼ 0 to v ¼ 10 (fundamental mstretch
states belonging to the Ba ꢀ ꢀ ꢀ FCH
3
À1
motion were obtained using the method of discrete
variable representation (DVR) in the special form
of the Gauss–Lanczos–Morse DVR [8].
¼ 177 cm ). We obtained time-dependent pump–
probe ion signals very similar to the cross corre-
lation function (CCF) of the laser pulses. Our

454
V. Stert et al. / Chemical Physics Letters 355 (2002) 449–456
calculated signal curve was only about 5% broader
than the CCF curve but was shifted 45 fs towards
larger delay times relative to the CCF (see Fig. 3a).
Such a behavior is typical for a pumped state
lifetime much shorter than the laser pulse length.
However, in our case this effect is not caused by
leaves the Franck–Condon region for the ioniza-
tion.
Another situation occurs if the probe wave-
length is considerably shorter. This leads to an
0
~
increase of the ‘effective lifetime’ of the A state.
The results are illustrated in Fig. 3a for the pump
wavelength of 745 nm and variable wavelengths of
the probe pulse. The maximum of the pump–probe
signal of the parent cation is monotonically shifted
to larger delay times starting with the excitation of
0
~
the A state lifetime but is due to the fact that the
wave packet created by the pump pulse rapidly
À1
~
only the ground vibrational level of the X state,
proceeding with cationic vibrational levels with
vibrational energies up to 0.1, 0.3, 0.5 eV and fi-
nally considering all bound levels.
We are especially interested in the probe
ð2Þ
wavelength of k2 ¼ 267 nm. Here the probe
photon energy is sufficient to ionize high-lying
vibrational cationic levels up to the fragmentation
continuum. This situation corresponds to the
curve on the top in Fig. 3a. In principle, also a
þ
BaF signal may be expected considering that the
þ
þ
reaction ðBaFCH
3
Þ ! BaF þ CH
3
can take
place if after ionization enough vibrational energy
is stored in the parent ion. In Fig. 3b the calculated
þ
BaF signal is shown assuming that the barrier for
the reaction in the ion lies at 0.1, 0.3 and 0.5 eV
internal energy. Why the BaF as well as the
curve drop down for delay
times larger than 500 fs? This effect arises from the
delayed fragmentation of the parent complex in
~
the excited A state leading to the steep increase of
the Ba signal shown in Fig. 3c. For delay times
larger than 800 fs this is practically the only ion
signal.
The reason for this stepwise rise of the Ba
signal is illustrated in Fig. 4. After the action of the
pump pulse the created wave packet freely evolves
þ
þ
highest ðBaFCH
3
Þ
0
þ
þ
Fig. 3. Calculated ion signals of Ba ꢀ ꢀ ꢀ FCH
3
(a), BaF (b) and
0
~
Ba (c) as a function of the delay time s between the pump pulse
at 745 nm and the probe pulse at 267 nm. The quantities Evib in
on the A potential curve. Due to the Franck–
Condon principle the ionization is vertical, in
(
a) denote the vibrational energies of the parent ion reaching up
þ
addition, the kinetic energy of the Ba $ FCH
3
À1
to the dissociation threshold E
0
. The curves for BaF (b) are
þ
0
~
motion is transferred from the A state to the X
~
obtained by subtracting the Ba ꢀ ꢀ ꢀ FCH curves for different
3
þ
state. The Ba formation by the parent ion dis-
vibrational energies ðEvib ¼ 0:1; 0:3; 0:5 eVÞ from the curve for
þ
~
0
E
vib 6 E
0
; the BaF formation by parent ion fragmentation
sociation starts if the A state wave packet reaches
a position where the kinetic energy equals the
binding energy in the cation. For a pump wave-
starts above the activation barrier Eact ¼ Evib. Both signals (a)
and (b) are restricted towards longer delay times by the disso-
þ
þ
ciation to Ba þ CH
3
F (cf. Fig. 4) leading to the Ba signal rise
þ
ꢀ
þ
length of 745 nm this is fulfilled at rBaꢀꢀꢀC ꢁ 8:5 A.
(c) complementary to the decay of the BaFCH3 and BaF
The corresponding kinetic energy (i.e., the binding
energy of the cation at this geometry) is about
signals near s ¼ 600 fs. For d-shaped pump and probe pulses
þ
the Ba signal rise is smeared out.

V. Stert et al. / Chemical Physics Letters 355 (2002) 449–456
455
laser pulse duration is much larger than the ‘life-
time’ of the excited state. In particular, the shift of
the curve maximum with respect to the delay time
zero is practically identical in both cases. Ac-
cording to our theoretical discussion, in the pre-
sent case this shift does not reflect a lifetime of the
0
~
excited A state (which is repulsive in the vertically
excited configuration) but is due to the residence
time of the excited wave packet within the Franck–
Condon window observable for the corresponding
pump–probe transitions.
5.2. Probe pulse wavelength of 267 nm
Fig. 4. Ab initio calculated potential energy curves of the ex-
0
~
cited electronic A state of Ba ꢀ ꢀ ꢀ FCH
3
and its ionic ground
In Fig. 2b,c the theoretical curves calculated in
Section 4 (cf. Fig. 3b,c) are displayed as full lines.
~
À1
state X as a function of the intermolecular distance r ¼ rBaꢀꢀꢀC
.
ð2Þ
The excess energy hm À IPðrÞ is available for the kinetic en-
2
For the ionic cluster reaction followed by dissoci-
þ
ergy EelðrÞ of the ejected photoelectron and the kinetic energy
E
kinðrÞ of the fragments according to the Franck–Condon rule.
ation to BaF and CH
E
3
an activation energy
act ¼ 0:3 eV has been assumed (Figs. 2b and 3b).
þ
The small contribution to the Ba signal sym-
metrical to the delay time zero (see Fig. 2c) is due
to the nonresonant absorption of the pump and
probe photons by free Ba atoms in the molecular
beam. In this way the zero delay time between the
pump and the probe pulses has been exactly de-
termined.
À1
800 cm , the time interval from the start of the
wave packet until this position is roughly 550 fs.
þ
The steepness of the Ba signal decreases if the
wave packet becomes broader near this position.
This is shown in Fig. 3c (dashed line). Assuming
an infinitely short pump pulse, the whole
0
~
~
Xðv ¼ 0Þ ! A Franck–Condon region is excited –
as a consequence the wave packet considerably
broadens during its propagation. The resulting
As it is seen in Fig. 2b,c the calculated signal
near s ꢁ 600 fs is much steeper than the measured
one. The main reason for this discrepancy should
be the crude assumption that the evolution of the
þ
Ba signal curve shows a step that is stronger
smeared out.
0
~
A state wave packet can be considered in an one-
dimensional way. Because the potential course
with respect to the intermolecular Ba ꢀ ꢀ ꢀ FCH
3
~
bending coordinate is very different for the X and
5
. Discussion of the results
0
~
A state we can expect that this bending vibration
may be excited with a remarkable probability in a
5
.1. Probe pulse wavelength of 400 nm
In Fig. 1a it was demonstrated the excellent
0
~
~
vertical X ! A transition. Consequently, there
exist portions of the wave packet with a smaller
agreement between the measured time-dependent
parent ion signals and the theoretical curve (solid
line) calculated in Section 4 (cf. Fig. 3a). If we
would assume an exponential decay for the excited
kinetic energy of the relative Ba ꢀ ꢀ ꢀ FCH stretch-
3
ing motion, arriving the position where the kinetic
energy equals that of the cation at a later time.
Thus, the whole wave packet will be considerably
spread during its propagation leading to a smear-
ing out of the ‘steps’ in Fig. 2b,c.
0
~
A state an optimized fit with the optical Bloch
equations would lead to a nearly identical curve
for the pulse width of 120 fs and an exponential
decay time of 40 fs. As can be shown, the differ-
ences between the ‘true’ fit curve and the fit curve
for an exponential decay are negligibly small if the
Another reason for this behavior is the follow-
ing: after the probe pulse action besides the ground
À1
~
cationic state ðX Þ also an excited cationic state
À1
~
(e.g., A ) may be populated. If its binding energy

456
V. Stert et al. / Chemical Physics Letters 355 (2002) 449–456
À1
þ
þ
remarkable Ba signal is detected. Although the
~
is considerably larger than that for X , the Ba
production starts at larger distances rBaꢀꢀꢀC (larger
0
~
3
interaction between Ba and FCH on the A sur-
0
À1
~
~
pump–probe delays) to a vertical A ! A tran-
face may be negligibly small, after the photoion-
ization the dissociation of the cationic complex
does not occur in accordance to the Franck–
Condon principle. This extreme behavior arises
from the relatively small asymptotic kinetic energy
0
À1
~
~
sition compared with A ! X .
Finally, a possible internal conversion due to
0
~
nonadiabatic interaction of the A state with the
00
000
~
~
lower bound A and A electronic states also
1
À1
correlating to the Bað DÞ þ CH F channel can
(about 800 cm ) of the relative motion between
0
3
~
the constituents at the A state and from the strong
lead to a delay of the fragmentation process. This
may be the reason for the trailing edges of
þ
interaction between Ba and FCH
À2
3
(asymptoti-
). In many other systems during the
þ
þ
the BaF and Ba signals around s ¼ 1 ps (see
cally ꢂ r
BaꢀꢀꢀC
Fig. 2b,c).
wave packet motion on a repulsive potential curve
the gained kinetic energy increases so rapidly that
after a short delay of the probe pulse only con-
tinuum states of the cation are accessed.
6
. Conclusion
Exciting the Ba ꢀ ꢀ ꢀ FCH
3
complex at 745 nm to
0
~
the electronic A state which is repulsive at the
vertically excited geometry we studied the evolu-
tion of the wave packet on the potential curve
Acknowledgements
This work was partially supported by the EU
TMR Programme within the ‘Access to Large
Scale Facilities’ activity (contract MPRI-CT-
3
followed by fragmentation to Ba and CH F. By
applying different probe–photon energies of 3.1
and 4.65 eV, respectively, we obtained results
which are interesting in a quite general sense.
The answer to the question: ‘When a fragmen-
tation process has been finished?’ cannot be given
in an unambiguous way, because it depends on the
special detection conditions which determine
whether the parent complex or separated frag-
ments are observed after the ionization process.
Using the probe wavelength 400 nm for the
199900084). Financial support by the Deutsche
Forschungsgemeinschaft through Sonderfors-
chungsbereich 450 is gratefully acknowledged. The
current support of the Madrid group research by
DGESof Sp ain grant PB97-0272 is gratefully ac-
knowledged as well.
References
ionization of the Ba ꢀ ꢀ ꢀ FCH complex pumped to
3
0
~
the repulsive part of the A state a small increase of
[
[
[
1] V. Stert, P. Farmanara, H.-H. Ritze, W. Radloff, K. Gasmi,
A. Gonzalez-Ure n~ a, Chem. Phys. Lett. 337 (2001) 299.
2] V. Stert, H.-H. Ritze, P. Farmanara, W. Radloff, Phys.
Chem. Chem. Phys. 3 (2001) 3939.
3
the separation between Ba and FCH is sufficient
to break the ionization process because the
Franck–Condon window for ionization is very
narrow due to the relatively small probe–photon
energy.
3] V. Stert, P. Farmanara, W. Radloff, F. Noack, S. Skow-
ronek, J. Jiminez, A. Gonzalez-Ure n~ a, Phys. Rev. A 59
(
[4] P. Farmanara, V. Stert, W. Radloff, S. Skowronek, A.
1999) R1727.
At the probe wavelength of 267 nm the wave
packet evolution can be followed on the potential
surface without time limitation. After the action of
the pump pulse the created wave packet freely
Gonzalez-Ure n~ a, Chem. Phys. Lett. 304 (1999) 299.
5] P.J. Knowles, H.-J. Werner, Theor. Chim. Acta 84 (1992)
[
9
5.
[
[
6] P.J. Hay, W.R. Wadt, J. Chem. Phys. 82 (1985) 299.
7] P. Piecuch, J. Mol. Struct. 436-437 (1997) 503.
0
~
evolves on the A surface. If the probe pulse is fired
ꢀ
before the distance rBaꢀꢀꢀC ꢁ 8:5 A is reached no
[8] V. Szalay, J. Chem. Phys. 99 (1993) 1978.