Intense-field modulation of NO2 multiphoton dissociation dynamics

Article abstract of DOI:10.1063/1.1775768

The dissociation of NO₂ under strong-field conditions by femtosecond two-color fluorescence depletion spectroscopy was reported. The dissociation dynamics were interpreted in terms of nuclear motions over light-induced potentials formed by coup

Full text of DOI:10.1063/1.1775768

Intense-field modulation of NO 2 multiphoton dissociation dynamics
T. W. Schmidt, R. B. López-Martens, and G. Roberts
Citation: The Journal of Chemical Physics 121, 4133 (2004); doi: 10.1063/1.1775768
View online: http://dx.doi.org/10.1063/1.1775768
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/121/9?ver=pdfcov
Published by the AIP Publishing
Articles you may be interested in
Ion-pair dissociation of N 2 O in the 16.25 – 16.41 eV : Dynamics and electronic structure
J. Chem. Phys. 129, 064312 (2008); 10.1063/1.2965593
Femtosecond time-resolved photoelectron-photoion coincidence imaging of multiphoton multichannel
photodynamics in N O 2
J. Chem. Phys. 128, 204311 (2008); 10.1063/1.2924134
Dissociative excitation of acetyl cyanide by ultraviolet multiphoton absorption
J. Chem. Phys. 118, 6348 (2003); 10.1063/1.1555617
Nonlinear intensity dependence in the infrared multiphoton excitation and dissociation of methanol pre-excited to
different energies
J. Chem. Phys. 117, 9793 (2002); 10.1063/1.1501280
Femtosecond fluorescence depletion spectroscopy of NO 2 multiphoton dissociation dynamics
J. Chem. Phys. 111, 7183 (1999); 10.1063/1.480046
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.59.226.54 On: Mon, 08 Dec 2014 22:32:48

JOURNAL OF CHEMICAL PHYSICS
VOLUME 121, NUMBER 9
1 SEPTEMBER 2004
Intense-field modulation of NO multiphoton dissociation dynamics
2
T. W. Schmidt,a) R. B. L o´ pez-Martens,b) and G. Robertsc)
Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
͑
Received 23 March 2004; accepted 2 June 2004͒
We report on the dynamics of multiphoton excitation and dissociation of NO at wavelengths
2
Ϫ2
between 395 and 420 nm and intensities between 4 and 10 TW cm . The breakup of the molecule
2
ϩ
2
is monitored by NO A ⌺ nЈϭ1,0→X ⌸ nЉϭ0 fluorescence as a function of time delay between
r
the driving field and a probe field which depletes the emission. It is found that generation of
2
ϩ
nЈϭ0 and 1 NO A ⌺ results in different fluorescence modulation patterns due to the intense
probe field. The dissociation dynamics are interpreted in terms of nuclear motions over
light-induced potentials formed by coupling of NO valence and Rydberg states to the applied field.
2
2
ϩ
Based on this model, it is argued that the time and intensity dependences of A ⌺ nЈϭ0
2
2
ϩ
→
X ⌸ nЉϭ0 fluorescence are consistent with delayed generation of NO A ⌺ nЈϭ0 via a
r
2
˜
2
light-induced bond-hardening brought about by the transient coupling of the dressed A B and
Rydberg 3s␴ ⌺ states of the parent molecule. The increasingly prompt decay of A ⌺ nЈϭ1
2
2
ϩ
g
ϩ
2
→
X ⌸ nЉϭ0 fluorescence with increasing intensity, on the other hand, is consistent with a direct
r
2
2
ϩ
˜
surface crossing between the X A and 3s␴ ⌺ dressed states to generate vibrationally excited
1
g
products. © 2004 American Institute of Physics. ͓DOI: 10.1063/1.1775768͔
I. INTRODUCTION
hinder molecular dissociation by modulating the amplitude
of the field on the time scale of the locally relevant vibra-
The development of high-power laser amplifiers has
opened up new possibilities for the study of molecular be-
havior in intense electric fields. Whereas the electronic de-
grees of freedom of a molecule respond on the time scale of
the laser field oscillations, the nuclei respond over a slower
time scale determined by the cycle-averaged Stark shift of
the field-dressed eigenstates of the light-molecule interac-
tion. The dynamics of nuclear motion under such conditions
tional period.6
In this work we describe experimental observations on
the dissociation of NO2 under strong-field conditions by
femtosecond two-color fluorescence depletion spectroscopy.
Three-photon absorption from a driving ͑pump͒ field at ␭1
ϭ395–420 nm promotes the parent molecule to a state
2
ϩ
3
which dissociates to NO A ⌺ and O P. The observation
2
ϩ
2
of A ⌺ →X ⌸ NO fluorescence in the intense-field
r
is often explained in terms of light-induced potentials
1
photofragmentation of NO suggests that the nascent laser-
2
͑
LIPs͒, which afford an adiabatic representation of the
excited state has as its molecular contributor a Rydberg state
of 3s␴ nature, assuming an electronically adiabatic dissocia-
tive evolution. A time-delayed coupling ͑probe͒ field modu-
forces acting on the nuclei in different dressed electronic
eigenstates. An intense laser pulse typically creates a wave
packet of electronic and vibrational ͑and rotational͒ states
whose temporal evolution proceeds over two or more field-
dressed potential energy surfaces coupled by the E vector of
the laser light.
2
ϩ
2
lates the A ⌺ nЈϭ1,0→X ⌸ nЉϭ0 fluorescence emitted
r
by the molecular fragment over a time scale of up to 3 ps.
The presence of more than one open vibrational channel for
the NO fragment allows the effect of an intense, nonresonant
probe field on the final vibrational state-selectivity to be in-
vestigated. The experimental findings are interpreted in terms
of the effect of field strength on the LIPs prepared by the
pump pulse, which allows the form of the time- and
intensity-dependent appearance of nЈϭ0 and 1 A ⌺ NO to
be rationalized in terms of dissociative evolution through
different light-induced crossings.
LIPs have been invoked to explain bond softening and
2
bond hardening of diatomic molecules in an intense field. In
this way, Bucksbaum et al. were able to explain photofrag-
ϩ
ment kinetic energy distributions of H2 at intensities above
Ϫ2 3
ϩ
5
0 TW cm , while the photodissociation of HD has been
2
ϩ
manipulated by exploiting interferences between wave pack-
4
ets on different LIPs to favor different exit channels. Vari-
ous adiabatic LIP shaping schemes have been proposed to
bring about selective transfer of vibrational-state populations
In the weak-field limit, the absorption spectrum of NO
2
5
˜
2
˜
2
of molecules while strong, nonresonant laser fields have
is dominated by the A B2� X A1 transition, which in-
Ϫ1
been used to Stark-shift LIPs in such a way as to enable or
creases steadily in intensity from its origin near 10 000 cm
to the lowest-energy dissociation threshold ͑to give NO
2
3
Ϫ1 7
a͒Present address: University of Sydney, School of Chemistry, NSW 2006,
X ⌸ ϩO P) at 25 130.6 cm
r
.
The complexity of the
2
2
˜
˜
Australia.
A B � X A spectrum arises mainly from strong coupling
2
1
b͒
Present address: Lund Institute of Technology, P.O. Box 118, SE-
2
2
˜
˜
of the A B and X A states, which has been the subject of
2
1
2
2100 Lund, Sweden.
c͒
numerous experimental and theoretical investigations span-
ning many decades.7 The spectral signature is further com-
Present address: Department of Physics, University of Newcastle, New-
castle upon Tyne NE1 7RU, United Kingdom.
,8
0021-9606/2004/121(9)/4133/10/$22.00
4133
© 2004 American Institute of Physics
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
28.59.226.54 On: Mon, 08 Dec 2014 22:32:48
1

4134
J. Chem. Phys., Vol. 121, No. 9, 1 September 2004
Schmidt, L o´ pez-Martens, and Roberts
2
ϩ
2
2
˜
A ⌺ nЈϭ2–0� X ⌸ nЉϭ0 electron-vibration transitions
plicated by the presence of a linear B B state, weakly
r
1
1
8͑a͒
2
to within the two-photon bandwidth of the incident field.
Consequently, in this work the peak pump intensity was fixed
͑to within Ϯ17%) at I ϭ5.3 TW cm to avoid any contri-
bution to the fluorescence signal from nonresonantly excited
background NO. The fundamental beam from the regenera-
tive amplifier provided 140 fs probe ͑coupling͒ pulses at
wavelengths ␭2ϭ790, 800, 830, and 840 nm ͑pump and
probe wavelengths were not independently tunable in these
experiments͒, which were routed through a Mach-Zehnder
interferometer for temporal adjustment relative to the pump
˜
coupled to the X A ground state through Renner-Teller
coupling and a bent but spectrally inaccessible A state.
Wave packet calculations have shown that an initial, vibra-
1
2
2
0
1
Ϫ2
9
2
˜
tionally ‘‘pure’’ adiabatic state prepared on the A B poten-
tial breaks down within 100–200 fs to form an incoherent
mixture of states responsible for vibrationally chaotic
2
1
0
2
motions. The statistical nature of the NO →NO X ⌸
2
r
3
ϩO P dissociation at perturbative field strengths has been
probed in the time domain by Wittig and co-workers, who
performed extensive measurements of the rate of formation
of X ⌸ NO as a function of energy above threshold as a
test of theories of unimolecular decomposition.
Higher-lying Rydberg states of NO have also been char-
acterized by spectroscopy, principally by Grant and
co-workers. Much of this work has centered on the bright
p␴ ⌺ lines, though the resonance-enhanced multiphoton
2
ϩ
2
pulses. Formation of NO A ⌺ nЈϭ0, 1, and 2 final vibra-
r
2
ϩ
2
11
tional states was probed by depleting A ⌺ nЈ→X ⌸rnЉ
ϭ0 fluorescence as a function of pump-probe time delay,
probe intensity, and pump wavelength. The maximum inten-
sity of the probe beam could be varied between I2ϭ0.5 and
4.0 TW cm depending on wavelength. That NO resulted
from the dissociation of NO was confirmed by the absence
of detectable fluorescence when NO alone was irradiated by
the pump and probe fields together and separately at intensi-
2
0
1
2
Ϫ2
2
ϩ
u
3
2
ionization spectrum in the energy range (70–75)
ϫ10 cm is heavily congested as many states with differ-
3
Ϫ1
ent principal quantum numbers are accessible. These experi-
0
Ϫ2
0
Ϫ2
mental studies and the theoretical work of Lee13 indicate that
ties of I1ϭ5.3 TW cm and I2Ͻ2.0 TW cm . ͑At higher
0
2
2
ϩ
2
values of I it is possible to detect A ⌺ nЈϭ2→X ⌸ nЉ
r
the potential surfaces of the NO Rydberg states are similar
in shape, and that the outermost electron has little effect on
bonding. The involvement of high-lying states in multipho-
2
ϭ0 emission due to nonresonant Stark shifting of two-
1
8͑b͒
photon absorption at ␭ ϭ400 nm.
͒
1
Pump and probe laser beams were directed collinearly
into a quartz cell containing a slow flow of NO2 gas at a
steady-state pressure of Ϸ1 Torr. The pump beam was
brought to a tight focus in the center of the cell with a f/8
lens. The probe beam, in contrast, was brought to a looser
ton dissociative ionization of NO at intensities of
2
1
2
Ϫ2
10
W cm has been probed by femtosecond spectroscopy
coupled with coincidence imaging of photoelectron and pho-
toion products in work by Davies et al.14 This work estab-
lished that at an excitation wavelength of 375.3 nm, the pre-
dominant dissociative process traced out a pathway over a
focus with a f/16 lens such that NO molecules irradiated by
2
2
3
the driving field experienced an almost constant transverse
distribution of coupling intensity. The temporal resolution of
the experiment was limited by the cross-correlation width of
the pump and probe pulses, which was measured to be 180
Ϯ15 fs by sum-frequency generation in a 100 ␮m thick
␤-barium borate crystal. Spatial characterization of the indi-
vidual beam foci and their mutual overlap in the interaction
region was performed by diverting the beams onto the ele-
ment of a charge-coupled device camera located in a position
repulsive potential correlating with NO C ⌸ ϩO P, while
r
angular photoelectron distributions gave information on the
molecular orientation during fragment separation. The struc-
tural deformation of NO by fields with intensities above
has been investigated by mass-resolved mo-
mentum imaging. The present paper describes in more de-
tail the results advertized in our earlier communication on
2
1
5
Ϫ2
10
W cm
1
5
2
ϩ
3
the NO →NO A ⌺ and O P dissociation at applied inten-
2
1
2
13
Ϫ2
16
sities in the 10 –10 W cm range.
equivalent to the flow cell containing NO gas. The fluores-
2
The balance of the paper is organized as follows: The
experimental approach adopted to make measurements of
intense-field NO dissociation is described in Sec. II. Results
are presented in Sec. III while Sec. IV gives the forms of the
potential energy surfaces used in Sec. V to interpret the ex-
perimental findings in terms of nuclear motions over LIPs.
Concluding remarks are given in Sec. VI.
cence emitted in a direction perpendicular to the direction of
propagation of the laser beams was collimated, focussed into
a 1/8 m monochromator, and detected photoelectrically.
Whereas the 1 nm bandpass of the monochromator allowed
2
2
ϩ
2
selective detection of A ⌺ nЈϭ0,1,2→X ⌸ nЉϭ0 transi-
r
tions at 226, 215, and 205 nm respectively, transitions to the
2
individual spin-orbit components of the X ⌸ doublet could
r
not be resolved. The temporal evolution of the dissociation
was recorded by averaging 100 individual measurements of
the depleted fluorescence at pump-probe time delays across
II. EXPERIMENT
To form the driving field, intense 100 fs pump pulses
were generated at wavelengths ␭ ϭ395, 400, 415, and 420
the range from ␶ ϭϪ1.5 to 3.0 ps.
D
1
nm by frequency doubling the output of a 10 Hz regenera-
tively amplified Ti:sapphire laser. The pump wavelengths
III. RESULTS
1
7
used here are all removed from known two-photon
2
ϩ
2
A ⌺ nЈ� X ⌸ nЉϭ0 resonances of NO in the weak-field
Figure 1 displays fluorescence depletion transients per-
taining to formation of the nЈϭ0 and 1 A ⌺ NO final
states at a pump wavelength of ␭ ϭ400 nm and different
coupling intensities. At substantial negative time delays, e.g.,
r
2
ϩ
2
2
ϩ
limit. A previous study of A ⌺ →X ⌸ fluorescence exci-
r
tation of NO revealed, however, a congestion in the emission
1
Ϫ2
spectrum at applied intensities above 10 TW cm when ␭1
ϭ395–415 nm due to the cycle-averaged Stark shift of
␶DϽϪ500 fs, when the coupling field precedes the pump
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.59.226.54 On: Mon, 08 Dec 2014 22:32:48

4135
J. Chem. Phys., Vol. 121, No. 9, 1 September 2004
NO2 multiphoton dynamics
field, the observed fluorescence signal is simply determined
by three-photon absorption by NO at 400 nm and dissocia-
2
2
ϩ
tion to the NO A ⌺ nЈϭ0 and 1 levels, which subsequently
fluoresce over a time scale of between 190 and 240 ns. At
1
9
2
ϩ
large positive delay times, e.g., ␶ у500 fs, the A ⌺ nЈ
D
2
→
X ⌸ nЉϭ0 fluorescence is suppressed by the coupling
r
light. The extent to which the fluorescence is depleted at
␶Dу500 fs increases with increasing coupling intensity for
both nЈϭ0 and 1, although the contrast between depleted
and undepleted fluorescence becomes less pronounced due to
the contribution of the intense coupling field to direct re-
moval of ground-state NO at large negative time delays, for
2
2
3
example, via the lowest-threshold NO →NO X ⌸ ϩO P
2
r
dissociation channel or multiphoton ionization. Across the
range of time delays Ϫ300Ͻ␶ Ͻ500 fs, the fluorescence
D
depletion is modulated by the most intense portions of the
two field components as they are swept across each other in
time.
Figure 1 shows that the pump-probe time delay needed
2
ϩ
2
to reach a constant A ⌺ nЈϭ0→X ⌸ nЉϭ0 fluorescence
r
depletion level is approximately ␶ у400 fs irrespective of
D
2
ϩ
2
probe intensity. In the case of A ⌺ nЈϭ1→X ⌸ nЉϭ0
r
fluorescence, the delay time for full depletion decreases from
0
2
Ϫ2
Ӎ300 fs at a probe intensity of I ϭ0.5 TW cm
͑e͒ to within the pump-probe correlation width at I2
ϭ4.0 TW cm in Fig. 1͑h͒. The different dependences of
an effective ‘‘dissociation time’’ for generation of nЈϭ0 and
A ⌺ NO on probe intensity suggest that the final vibra-
in Fig.
0
1
Ϫ2
2
ϩ
1
tional levels are reached via different intensity-dependent
mechanisms. Further evidence for this hypothesis can be gar-
nered from the transient signals at Ϫ300р␶ р300 fs,
D
where the modulation of fluorescence from different NO lev-
els is qualitatively different as a function of probe intensity.
0
Ϫ2
At I ϭ0.5 and 1.0 TW cm , Figs. 1͑a͒ and 1͑b͒ show
2
2
ϩ
2
that there is a sudden peak in A ⌺ nЈϭ0→X ⌸ nЉϭ0
r
fluorescence with a full width at half maximum of Ϸ150 fs
located at ␶ Ӎ200 fs. Because the cross correlation width of
D
pump and probe pulses was measured to be 180 fs and the
fluorescence reaches a maximum 200 fs after ␶ ϭ0, the
D
peak cannot be attributed to the kind of coherent effects
sometimes observed in pump-probe spectroscopies of multi-
photon excitation at zero time delay ͑see, for example, Ref.
2
ϩ
2
0͒. That A ⌺ nЈϭ0 NO formation is sensitive to a tran-
sient field effect can be seen from Figs. 1͑a͒ and 1͑b͒, which
show that as the probe intensity is increased by a factor of 2
0
Ϫ2
2
ϩ
at I р1.0 TW cm , the 200 fs enhancement in A ⌺ nЈ
2
2
ϭ0→X ⌸ nЉϭ0 fluorescence remains essentially constant
r
͑
as measured by the area under the peak͒, whereas Figs. 1͑c͒
0
2
Ϫ2
and 1͑d͒ indicate that for I Ͼ1.0 TW cm , the fluorescence
transients exhibit a minimum localized around ␶ ϭ0 whose
D
0
full width at half maximum depth doubles when I2 is in-
Ϫ2
creased from 2.0 to 4.0 TW cm . The appearance of tran-
2
ϩ
2
sient maxima and minima in the A ⌺ nЈϭ0→X ⌸ nЉ
r
2
ϩ
2
FIG. 1. NO A ⌺ nЈϭ0,1→X ⌸ nЉϭ0 fluorescence depletion transients
ϭ0 fluorescence trace in the region of ␶ ϭ0 can be ratio-
D
r
Ϫ2
for ␭ ϭ400 nm and ␭ ϭ800 nm at different probe intensities (TW cm ):
nalized in terms of the time evolution of the dressed states of
the light-molecule coupling, as discussed in in Sec. V.
Figures 1͑e͒–1͑h͒ reveal that fluorescence from
A ⌺ nЈϭ1 NO is not as highly modulated at short delay
times compared to that from the zero-point level, and that the
1
2
0
.5 ͑a͒ and ͑e͒; 1.0 ͑b͒ and ͑f͒; 2.0 ͑c͒ and ͑g͒; and 4.0 ͑d͒ and ͑h͒. The
0
Ϫ2
intensity of the pump field is I ϭ5.3 TW cm in each case. Traces ͑a͒
1
2
ϩ
through ͑d͒ pertain to nЈϭ0 in the A ⌺ state, traces ͑e͒ through ͑h͒ are for
nЈϭ1. The cross correlation of the pump and probe pulses is shown as a
dashed line. The vertical line at 200 fs serves to guide the eye ͑see Sec. V͒.
2
ϩ
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
28.59.226.54 On: Mon, 08 Dec 2014 22:32:48
1

4136
J. Chem. Phys., Vol. 121, No. 9, 1 September 2004
Schmidt, L o´ pez-Martens, and Roberts
Ӎ200 fs, in contrast to the result for the same intensity ob-
tained at shorter wavelengths ͓Fig. 1͑a͔͒. Qualitatively simi-
2
ϩ
lar fluorescence depletion behavior for the A ⌺ nЈϭ0
2
→
X ⌸ nЉϭ0 transition was recorded at ␭ ϭ420 nm,
r
1
where again it was found that the opening of a transient
2
ϩ
dissociation channel leading to NO A ⌺ nЈϭ0 at small de-
lay times was restricted to increasingly higher intensities.
The observed signal-to-noise ratios and logarithmic
variation in gain of the photomultiplier tube as a function of
2
ϩ
2
wavelength of the A ⌺ nЈϭ0 and 1→X ⌸ nЉϭ0 band
r
origins precluded a quantitative determination of the relative
final state distributions. To obtain the data displayed in Figs.
1
and 2, the detector gain was maintained at a constant value
when monitoring fluorescence from a given nЈ level of NO
2
ϩ
A ⌺ at different probe intensities, but had to be altered to
record transients at different pump and detection wave-
2
ϩ
lengths. Despite the fact that the NO A ⌺ nЈϭ2 state is
2
ϩ
energetically accessible at ␭ ϭ395 nm, no A ⌺ nЈϭ2
1
2
0
1
→
X ⌸ nЉϭ0 fluorescence could be monitored at I
r
Ϫ2
ϭ5.3 TW cm . This nonobservation was confirmed by ex-
amination of the spectrally dispersed fluorescence spectrum
recorded in the absence of the coupling field, which showed
2
ϩ
0
1
Ϫ2
emission from NO A ⌺ nЈϭ2 only at I у25 TW cm
,
where nonresonant excitation of accumulated NO dominates
the fluorescence spectrum.1
8͑a͒
2
ϩ
2
FIG. 2. NO A ⌺ nЈϭ0→X ⌸ nЉϭ0 fluorescence depletion transients
r
for ␭ ϭ415 nm and ␭ ϭ830 nm at different peak probe intensities
TW cm ): 0.5 ͑a͒; 1.0 ͑b͒; 1.9 ͑c͒; and 3.2 ͑d͒. The maximum intensity of
the pump field is I ϭ5.3 TW cm in each case. The cross correlation of
1
2
Ϫ2
(
IV. POTENTIAL ENERGY SURFACES
0
1
Ϫ2
the pump and probe pulses is shown as a dashed line. The vertical line at
To visualize the nuclear motions of NO2 during the
intense-field dissociation in terms of the relevant LIPs, di-
2
00 fs serves to guide the eye ͑see Sec. V͒.
2
ϩ
2
˜
abatic PESs pertaining to the 3s␴ ⌺g Rydberg and A B
2
states were calculated and shifted downwards in energy rela-
onset of the full depletion regime becomes more sharply de-
2
˜
0
tive to the PES of the X A state by three and one photon
1
fined with increasing probe intensity. At I ϭ1.0 and
2
Ϫ2
energies, respectively. In this way, the location of the light-
induced curve crossings relative to the dissociation coordi-
nate could be examined. Analytical expressions for the PESs
were calculated as described briefly in the following sec-
tions.
2
.0 TW cm ͓Figs. 1͑f͒ and 1͑g͔͒ there is a hint of a tran-
sient maximum between 0 and 200 fs, but the maxima are
similar in amplitude to the fluctuations in fluorescence at
0
large negative and positive delay times. When I is increased
2
Ϫ2
to 4.0 TW cm ͓Fig. 1͑h͔͒, any transient maximum at ␶D
Ӎ200 fs is completely masked by full fluorescence depletion
˜ 2
˜ 2
A. X A and A B diabatic states
1
2
at ␶ Ͼ0.
D
2
2
˜
˜
Recent calculations of the diabatic X A and A B
For ␭ ϭ415 nm and different coupling intensities, Fig.
1
2
1
2
ϩ
2
PESs have employed a direct interpolation between ab initio
points21 and analytical expressions fit to ab initio data to
map out the region around the conical intersection. We used
an expansion in Morse coordinates for the two N-O bond
lengths R and R ͑with R уR ) and a cubic function for
the angular degree of freedom ␪ with optimized coeffi-
cients from Ref. 22͑b͒ to construct two-dimensional PESs in
2
displays the A ⌺ nЈϭ0→X ⌸ nЉϭ0 fluorescence
r
22
monitored in real time. The dissociation energetics are such
2
ϩ
that nЈϭ0 is the only A ⌺ level expected at this wave-
length in the weak-field limit; a search for emission from
2
ϩ
nЈу1A ⌺ levels did not result in unambiguously record-
1
2
1
2
2
3
able signals. At the lower photon energy, a constant level of
2
ϩ
2
A ⌺ nЈϭ0→X ⌸ nЉϭ0 fluorescence depletion is not
r
the neighborhood of the conical intersection where R1,2
achieved until ␶ Ӎ700 fs. The similarity between the results
obtained at ␭ ϭ415 and 400 nm is clearest for the highest
probe intensities of I ϭ1.9 and 3.2 TW cm . As I is in-
creased above 1.0 TW cm , there is a minimum in the fluo-
D
(
ϭR or R ) Ͻ2.0 Å. In this region both lower and upper
1 2
diabatic surfaces, V and V , are bound along R . The
˜
lower X A state becomes dissociative at R у2.0 Å. To
1 1
1
0
2
Ϫ2
0
2
X
A
1
Ϫ2
2
rescence near ␶ Ӎ0 fs and transient maximum at ␶D
simulate the correct asymptotic behavior of V , the switch-
D
X
ing function of Leonardi et al.2 was employed to link the
bound and dissociative regions, while the potential along the
intact N-O dimension was described by a Morse curve con-
structed from spectroscopic parameters17 with no angular de-
pendence in the asymptoic region. Details of this repesenta-
2͑b͒
Ӎ200 fs. These effects are not so pronounced at ␭1
ϭ415 nm compared to ␭ ϭ400 and 395 nm due to a poorer
1
signal-to-noise ratio at lower incident pulse energies. For the
same reason, the fluorescence trace shown in Fig. 2͑a͒ for
0
2
Ϫ2
I ϭ0.5 TW cm displays no maximum fluorescence at ␶D
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.59.226.54 On: Mon, 08 Dec 2014 22:32:48

4137
J. Chem. Phys., Vol. 121, No. 9, 1 September 2004
NO2 multiphoton dynamics
2
2
˜
˜
between the X A and A B states has been the focus of a
1
2
number of earlier studies ͑see, for example, Ref. 26͒, which
have been extended to describe the shape of the dissociative
regions.27
2
¿
B. 3s␴ ⌺ Rydberg state
g
2
ϩ
To the best of our knowledge, a PES for the 3s␴ ⌺g
Rydberg state of NO has never been reported. Experimental
2
work has shown, though, that the vibrational frequencies of
ϩ
1
ϩ
g
NO2 X ⌺ are within a few wave numbers of those of the
3
2
8
p␴ Rydberg state of the neutral molecule. It is assumed
here that this is also the case for the 3s␴ Rydberg state.
1
ϩ
ϩ
While a global PES for X ⌺g NO2 also seems never to
have been reported, there have been experimental studies of
the vibrational and rotational parameters2
8,29
of the linear
structure at the potential minimum, as well as notable theo-
retical explorations.1
3,30
Force constants were calculated by
Lee at a CCSD͑T͒ level of theory with an extensive basis set
including g-type functions for quadratic terms and f-type
functions for cubic and quartic terms in the expansion of the
1
3
potential as a function of R and R . A recent report by
1
2
F u¨ z e´ ry et al.31 confirms the linear configuration of NO at
ϩ
2
1
ϩ
the global minimum of the X ⌺g PES.(
b)
To construct the bound portion V (R ,R ,␪) of the
R
1
2
Rydberg 3s␴ potential, the harmonic force constants calcu-
lated by Lee13 were rescaled to reflect the experimental re-
sults in Ref. 28͑a͒. To represent the unbound potential
(
u)
V
(R ,R ,␪) of the 3s␴ state we adopted a switching
R
1 2
function in a manner similar to that used by Leonardi et al.
for VX .2
2͑b͒
The global PES V (R ,R ,␪) of the Rydberg
R 1 2
state was thus expressed as a weighted sum of bound and
unbound potentials,
(
b)
V ͑R ,R ,␪͒ϭT0,3s␴ϩ͑1Ϫ␹͒V ͑R ,R ,␪͒
R
1
2
R
1
2
(
u)
ϩ␹V ͑R ,R ,␪͒,
R
1
2
where the switching function
1
ϭ 2
␹
͕
1ϩtanh͓␣͑R ϪR1,eϪ␦͔͒
͖
1
(
b)
transforms V (R ,R ,␪) into an unbound potential
R
1
2
˜
2
˜
2
FIG. 3. Field-free potential surfaces of the X A ͑a͒, A B ͑b͒, and Ryd-
1
2
2
ϩ
(u)
R
2
berg 3s␴
⌺
͑c͒ diabatic states of NO2 as a function of N-O bondlength
V
͑R ,R ,␪͒ϭDe,3s␴͕1Ϫexp͓Ϫ␤3s␴͑R ϪRe,3s␴͔͒
͖
1
2
1
and ONO angle. The 3s␴ 2⌺ϩ potential is shifted downwards in energy by
ˆ
2
Ϫ1
ϩDe,A
͕
1Ϫexp͓Ϫ␤ ͑R ϪRe,A͔͒
͖
7
5 000 cm
.
A
2
2
ϩF ␪ exp͓Ϫ␤ ͑R ϪRe,3s␴͔͒
␪
␪
␪
1
represented by a sum of Morse curves and an exponentially
tion may be found in Refs. 23 and 22͑b͒. The PESs of the
decaying angular dependence; it is assumed that dissociation
2
2
(u)
˜
˜
2
ϩ
X A and A B states are plotted separately for perspicuity
1
2
to A ⌺ NO over VR (R ,R ,␪) proceeds with no signifi-
1 2
in Figs. 3͑a͒ and 3͑b͒.
cant energy barrier. The well depth of V (R ,R ,␪) of 2.79
R
1
2
Calculations of the adiabatic states generated by the
eV and energy T0,3s␴ϭ5.81 eV of the zero-point level were
2
2
˜
˜
strongly coupled X A and A B states have been reported
fixed by the dissociation energy of NO , the relative ioniza-
1
2
2
previously by several groups of investigators. An accurate
two-dimensional PES computed at the multireference singles
and doubles configuration interaction level of theory was
employed by Klippenstein and Radivoyevitch to investigate
transient molecular configurations at dissociative N-O dis-
tances of 2–3 Å, while Katagiri and Kato used complete-
active-space self-consistent-field calculations to describe the
dissociative region at RON-Oу3 Å.25 The conical intersection
tion potentials of NO and NO , and their zero-point
2
energies7
,17,28,32
while the rate of exponential decay of the
angular amplitude F␪␪ with R1 was chosen in accordance
with the PES calculated by Theodorakopoulos et al. for the
ionic state.30 Numerical values of the various parameters
2
4
(u)
on which ␹ and VR (R ,R ,␪) depend are listed in Table I
1
2
and the field-free potential V (R ,R ,␪) is displayed in
R
1
2
Fig. 3͑c͒.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.59.226.54 On: Mon, 08 Dec 2014 22:32:48

4138
J. Chem. Phys., Vol. 121, No. 9, 1 September 2004
Schmidt, L o´ pez-Martens, and Roberts
TABLE I. Parameters used to construct the unbound potential
(
u)
2
ϩ
V
(R ,R ,␪) of the 3s␴
⌺
state: D
and De,A are the dissociation
e,3s␴
R
1
2
2
ϩ
energies of the 3s␴ NO2 and A ⌺ NO states, Re,3s␴ and Re,A are the
equilibrium N-O separations of the states along the bond length coordinates
R1 and R , and ␤
and ␤A are the usual Morse ␤ functions; F␪␪ and ␤␪
3s␴
2
characterize the magnitude and decay of the angular potential along R ; and
1
␣
and ␦ characterize the switching function ␹.
Parameter
Value
Parameter
Value
De,3s␴ ͑eV͒
Re,3s␴ ͑Å͒
2.91
De,A ͑eV͒
12.04
1.064
2.929
Ϫ2.469
0.1
1.122
4.130
2.568
5.0
Re,A ͑Å͒
␤3s␴
F␪␪ ͑eV͒
(ÅϪ1
(ÅϪ1)
␤A (Å
␤␪ (rad
␦ ͑Å͒
Ϫ1
)
Ϫ1
)
␣
)
V. INTERPRETATION OF RESULTS
˜
2
FIG. 4. ͑a͒ Contour plot of the X A ground-state potential as a function of
1
The multiphoton dissociation energetics of NO are such
2
ˆ
the ONO angle and equivalent N-O bond lengths (R1 and R ). Superim-
posed in gray shading upon the contours up to an energy of 4500 cm are
2
that three photons at ␭Ӎ400 nm are required to generate
Ϫ1
2
ϩ
A ⌺ NO in low-lying vibrational levels in the weak-field
the crossing seams with the A B and 3s␴ 2
2
ϩ
˜
⌺
potentials shifted down-
2
limit. Over the range of wavelengths used in this work, for-
wards by energies corresponding to one and three photons, respectively. ͑b͒
2
ϩ
˜
2
mation of nЈϭ2 A ⌺ NO is feasible at ␭ ϭ395 nm and is
1
Contour plot of the A B2 potential shifted downwards by one photon en-
2
ϩ
isoenergetic at ␭ ϭ400 nm; the nЈϭ1 and 0 A ⌺ levels
ergy, showing its intersections with potentials representing the
X,NϪ1 , and R,NϪ3 states. In ͑a͒ and ͑b͒ the contour interval is
500 cm : in ͑a͒ the lowest contour is 1500 cm above the electronic
minimum; in ͑b͒ the contours decrease from 4500 cmϪ1 above the X A1
state minimum. The white arrows show the direction in which the crossing
seams shift relative to the contoured potential when the photon wavelength
is changed from 420 to 395 nm. ͑c͒ Cross section of diagram ͑a͒ at O Nˆ O
ϭ134° for a photon energy of 25 000 cm (␭1ϭ400 nm). The horizontal
lines indicate the energies ͓Ref. 22͑b͔͒ of the ͑0,0,0͒ and ͑1,0,0͒ vibrational
͘
levels relative to the ͉X,N state minimum.
͘
͉X,N ,
1
͉
1
͘
͉
͘
are energetically accessible at longer wavelengths, except
that only nЈϭ0 can be reached at ␭ ϭ415 and 420 nm.
Ϫ1
Ϫ1
1
˜
2
2
ϩ
Owing to the 3s␴ Rydberg nature of the NO A ⌺ state, it
is asumed here that it derives adiabatically during NO dis-
2
2
ϩ
sociation from the 3s␴ ⌺ Rydberg state of the parent. ͑In
2
ϩ
3
Ϫ1
the weak-field limit, NO A ⌺ ϩO P correlate with six
g
potential surfaces in C symmetry.͒ At the shortest wave-
s
length used in the experiments, ␭ ϭ395 nm, three-photon
1
absorption promotes NO to a superposition of levels that lie
2
2
below the thresholds for formation of 3p␲ C ⌸ and 3p␴
D ⌺ NO. The Rydberg NO levels which correlate with
these NO states could be mixed with the 3s␴ ⌺ Rydberg
state by the polarization induced by the applied field, how-
ever, and in this way populated by three-photon absorption.
r
2
ϩ
the dressed-state dynamics leading to fragmentation pre-
sented here. Within the remit of this model, the contribution
of the probe field is to enhance the probability of adiabatic
passage over the potentials dressed by the driving field when
the two pulses act at the same time, and to suppress
2
2
ϩ
2
2
2
ϩ
2
As no C ⌸ →X ⌸ and D ⌺ →X ⌸ fluorescence was
r
r
r
2
ϩ
2
A ⌺ nЈ→X ⌸ nЉϭ0 fluorescence through the provision
r
observed, we do not discuss this possibility here. Dissocia-
2
ϩ
2
1
of light-induced crossings between the A ⌺ state and
higher-lying NO Rydberg levels at later times when it acts
alone.
tion of NO to form NO X ⌸ ϩO D final states is also
2
r
g
energetically feasible at the photon energies required to gen-
2
ϩ
erate A ⌺ NO nЈϾ0 levels. If either one or both fields
were to stimulate this channel and subsequent A ⌺ nЈ
2
ϩ
In an intense field environment, two routes afford a
2
minimum number of curve crossings by which NO can ar-
2
�
X ⌸ nЉ multiphoton absorption, then an increase in
r
2
ϩ
2
rive at the dissociative portion of the 3s␴ Rydberg state.
A ⌺ nЈ→X ⌸ nЉϭ0 fluorescence would be expected
r
These are the interactions between the
͉
͉
X,N
X,N
͘
͘
and
and
over a time scale determined by the rate of dissociation fol-
lowed by decay over 190–240 ns ͑Ref. 19͒ determined by
the Einstein coefficient. Because this expectation is contrary
͉
͉
R,NϪ3
A,NϪ1
͘
͘
dressed states, and between the
and
͉
A,NϪ1
͘
and
͉R,NϪ3
2
͘
states. Figure 4͑a͒
2
1
˜
displays a contour plot of the X A potential as a function of
to the observed findings, the NO →NO X ⌸ ϩO D path-
1
2
r
g
the two bond lengths and angle, superimposed upon which
way is also not considered in the interpretation of the data.
2
˜
As discussed below, absorption of three photons at ␭1
Ӎ400 nm leaves the molecule in a position where it can
are the crossing seams with the downwards shifted A B
2
2
ϩ
and 3s␴ ⌺ Rydberg potentials, while Fig. 4͑b͒ shows the
2
˜
same intersections superimposed upon the contours of the
access crossing seams between the dressed X A and 3s␴
1
2
2⌺ϩ
states. The dressed states derived from the bare electronic
states are labeled X,NϪn A,NϪn , and R,NϪn
where NϪn represents the driving ͑pump͒ laser field with
Rydberg states and between the A B and 3s␴ ⌺
2
2
ϩ
˜
˜
A B potential. ͓Although a ridge of the
͉
X,NϪ1
surface, we do not discuss dis-
state simply on the basis of mul-
tiplication of probabilities for three surface crossings to gen-
͘
potential
2
2
intersects with the
͉A,NϪ1
͘
sociation via the X,NϪ1
͉
͘
͉
͘
,
͉
͘
͉
͘
,
͉
͘
2
ϩ
erate A ⌺ NO.͔ Figure 4͑c͒ shows a cross-sectional slice
n photons removed by absorption. The additional crossings
which arise when molecular levels are dressed with probe
photons are not considered in the simplified description of
through all three potentials at the ground-state equilibrium
2
˜
angle. Plotted within the well of the X A potential in
1
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.59.226.54 On: Mon, 08 Dec 2014 22:32:48

4139
J. Chem. Phys., Vol. 121, No. 9, 1 September 2004
NO2 multiphoton dynamics
Fig. 4͑c͒ are the energies of the (␯ ,␯ ,␯ )ϭ(0,0,0) and
1
2
3
͑1,0,0͒ vibrational levels.
Inspection of Fig. 4 reveals that the intersection between
2
Ϫ1
˜
the X A and Rydberg potentials occurs Ϸ2700 cm
in
1
2
˜
energy above the X A minimum at an elongated bond
1
2
˜
Ϫ1
length of R1,2Ӎ1.28 Å. In contrast, when the A B potential
is shifted downwards by 23 810–25 315 cm , correspond-
2
ing to absorption of a single photon from the pump field, its
repulsive limb intersects the ground-state potential near the
weak-field Franck-Condon region, where the resulting
͉
A,NϪ1
͘
and
͉
X,N
͘
dressed states exhibit an avoided inter-
FIG. 5. Contour plot of the 3s␴ 2
by three quanta of the photon energy ͑with ␭ ϭ395–420 nm) as a function
ϩ
⌺
Rydberg potential shifted downwards
section. Owing to the location of the light-induced intersec-
1
2
2
ˆ
˜
˜
of the ONO angle and a single N-O bond length (R ) when the other is fixed
tion between the X A and A B potentials, it is proposed
that transfer to the
step by which NO population in the vibrationally unexcited
mode is transferred out of the ground state. Figure 4͑b͒ sug-
1
1
2
ϩ
1
ϩ
at the equilibrium separation R ϭ1.1223 Å of NO2 X ⌺g ͓Refs. 13 and
͉
A,NϪ1
͘
state is the predominant initial
2
2
˜
8͑b͔͒. The contour labeled ‘‘0’’ traces out the zero of energy ͑relative to the
2
2
1
˜
2
ing shows the crossing seam with the A B potential shifted downwards by
one quantum of photon energy and the dark arrow repesents a notional
trajectory leading to nЈϭ0 NO A ⌺ .
2
gests that, once promoted to the
ecule bends and elongates as it evolves towards the equilib-
rium position of the A,NϪ1 state, which at low intensities
would be close to the field-free location at R1,2Ӎ1.28 Å and
͘
͉A,NϪ1 potential, the mol-
2
ϩ
͉
͘
by the
͘
͉A,NϪ1 potential. We make the hypothesis that the
␪
Ӎ100°. Wave packet calculations reveal that, at least in the
fragmentation proceeds in a vibrationally adiabatic way, i.e.,
perturbative limit, the vibrational superposition state created
2
ϩ
2
the zero-point level of NO2 leads to NO A ⌺ nЈϭ0, while
parent molecules excited with a single quantum of symmet-
ric stretch motion lead to the A ⌺ nЈϭ1 final NO state.
Within this framework, the shifted potentials shown in Figs.
˜
on the A B potential becomes statistically distributed over
2
ˆ
the phase space associated with the ONO bending and ON-O
stretching degrees of freedom over a time scale of 100–200
fs, so that the opportunity exists for population to reach the
region of the avoided intersection between the
2
ϩ
9
4
and 5 enable the effect of applied intensity on the disso-
͉
A,NϪ1
͘
and
␪
ciation probability to be rationalized qualitatively, as dis-
cussed in the following sections.
͉
R,NϪ3 states found at R1,2Ӎ1.15–1.25 Å and
͘
Ϫ1
Ӎ120°–130° for energies below 4500 cm . Clearly, the
fate of the population restrained by the A,NϪ1 state de-
pends on the local laser intensity. At perturbative intensities,
2
¿
A. Generation of NO A ⌺ nЈÄ0
͉
͘
On the basis of the above hypothesis, it is postulated that
2
2
˜
˜
the molecule can fragment via A B –X A state mixing to
give NO X ⌸ ϩO P. At higher intensities, the popula-
tion can make a diabatic crossing to the ͉R,NϪ3 state,
͘
while at higher intensities again it may remain trapped within
the adiabatic well formed from the coupled potentials of the
2
1
NO molecules residing in the ͑0,0,0͒ zero-point level lead
2
2
3
11
2
ϩ
r
ultimately to NO A ⌺ nЈϭ0 via two light-induced surface
crossings, the first from the X,N state to the A,NϪ1 state
and then, after a period of wave packet evolution during the
driving pulse, from the A,NϪ1 state to the R,NϪ3 state.
Figure 5 shows that the intersection between the A,NϪ1
and R,NϪ3 state potentials can place the molecule on the
Rydberg surface, at energies above the dissociation thresh-
͉
͘
͉
͘
9
͉
͘
͉
͘
͉
A,NϪ1
͘ ͘
and ͉R,NϪ3 states.
͉
͘
For vibrationally excited NO populations in which one
2
͉
͘
quantum of symmetric stretch motion is excited, an alterna-
tive possibility exists for population transfer out of the initial
state. This relies upon the energetic proximity of the ͑1,0,0͒
2
ϩ
old, at the equilibrium bond length of NO A ⌺ nЈϭ0. Once
on the Rydberg potential, molecules transferring from the
level to the surface intersection between the
͘
͉X,N and
͉
͘
A,NϪ1 state can undergo impulsive dissociation from a
bent configuration during and after the driving pulse. In-
͉
R,NϪ3 states at R1,2Ӎ1.22–1.32 Å and ␪Ӎ120°–140°.
͘
In this case, the effect of an applied field is, in addition to
creasing the intensity of the driving field enhances the sepa-
generating the surface intersection, to suppress the possibil-
ration between the
͉
A,NϪ1
͘
and
͘
͉X,N states and between
2
˜
ity of population retransferring back to the X A state from
the R,NϪ3 and
͉
͘
͉
A,NϪ1
͘
states at their respective
1
the adiabatic potential formed from the
R,NϪ3 states at longer bond lengths ͓see Figs. 4͑a͒ and
͑c͔͒.
When deposited on the
͉
X,N
͘
and
avoided crossings, the effect of which is augmented further
by the probe field. The consequence of the increasing adia-
baticity is that population becomes ensnared within the tem-
porary bound state formed as the field strength increases,
thereby suppressing temporarily the yield of final NO
͉
4
͘
͉
1
͘
R,NϪ3 potential, the molecule
Ϫ1
Ϫ1
has between 2340 cm (␭ ϭ420 nm) and 6860 cm (␭1
ϭ395 nm) energy available above the Rydberg dissociation
asymptote to channel into translation and rotation-vibration
levels of the NO A ⌺ state. Figure 5 shows a contour
representation of the Rydberg potential surface in which one
bond length is maintained at the equilibrium separation of
the X ⌺ ground state of NO2 (R ϭ1.1223 Å).
this configuration, the
2
ϩ
A ⌺ nЈϭ0. The effect is analogous to the bond hardening
ϩ
2
observed in the dissociation of H and its isotopic variants at
2
ϩ
13
Ϫ2 2–4
intensities up to 5ϫ10 W cm
.
Evidence in support of
this conjecture is supplied in Figs. 1 and 2. In Figs. 1͑c͒ and
1͑d͒ and Figs. 2͑c͒ and 2͑d͒, a minimum in the fluorescence
signal is observed at the maximum intensity when the pump
and coupling fields are maximally overlapped in time at ␶D
1
ϩ
g
ϩ
13,28͑b͒
At
2
͉
R,NϪ3
͘
potential is intersected only
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.59.226.54 On: Mon, 08 Dec 2014 22:32:48

4140
J. Chem. Phys., Vol. 121, No. 9, 1 September 2004
Schmidt, L o´ pez-Martens, and Roberts
2
ϩ
ϭ0. As the driving field decays, a burst of A ⌺ nЈϭ0 NO
is released at short positive delay times and the fluorescence
it subsequently emits is suppressed by multiphoton excitation
to ͑Stark-shifted͒ higher-lying Rydberg levels18 and likely
ionization induced by the probe field. ͑Depletion of NO
We postulate that it is due to dissociation via different
LIPs formed in the temporal region extended by the driving
2
ϩ
field that the transient behavior recorded by NO A ⌺ nЈ
2
ϭ1→X ⌸ nЈϭ0 fluorescence is qualitatively different to
r
2
ϩ
that relating to formation of NO A ⌺ nЈϭ0. Inspection of
Figs. 1͑e͒–1͑h͒ shows that there is a hint of a fluorescence
2
ϩ
2
A ⌺ nЈϭ2→X ⌸ nЉϭ0 fluorescence at total intensities
r
Ϫ2
greater than about 11 TW cm has been observed in experi-
peak located at 0р␶ р200 fs preceded by a minimum at
D
ments in which NO alone was irradiated by a bichromatic
␶ Ӎ0, but this feature is not as pronounced as that for NO
D
1
8͑b͒
2
ϩ
field with components centered at ␭ϭ400 and 800 nm.
͒
A ⌺ nЈϭ0. Instead, the overwhelming characteristic of
2
ϩ
2
2
ϩ
2
That the peak in A ⌺ nЈϭ0→X ⌸ nЈϭ0 fluorescence is
Figs. 1͑e͒–1͑h͒ is the depletion of A ⌺ nЈϭ1→X ⌸ nЈ
r
r
centered at the same delay time (Ӎ200 fs) in each transient
shown in Figs. 1 and 2 ͓except Figs. 1͑d͒ and 2͑a͒ where
fluorescence depletion and a low signal-to-noise ratio, re-
spectively, conspire to prevent its observation͔ suggests a
ϭ0 fluorescence which sets in as the probe field sweeps past
the pump: this is consistent with a direct LIP crossing during
the driving field ͑enhanced by the probe field͒ followed by
an adiabatic dissociative evolution into the asymptotic region
2
ϩ
common mechanism for production of A ⌺ nЈϭ0 NO at
these intensities. Consistent with bond hardening, Figs. 1͑c͒
and 1͑d͒ and 2͑c͒ and 2͑d͒ also indicate that the dip in
͘
of ͉R,NϪ3 and probe-induced multiphoton excitation of
2
ϩ
incipient NO A ⌺ nЈϭ1 molecules as discussed before
͑Sec. V A͒.
2
ϩ
2
A ⌺ nЈϭ0→X ⌸ nЈϭ0 fluorescence which occurs when
r
the pump and coupling fields overlap in time and space in-
creases in prominence as the applied intensity is increased.
C. Dissociation times
It is difficult to give a secure interpretation of the tran-
sients recorded under intense-field conditions in terms of a
direct dissociation time, as can be performed for perturbative
excitation,11 because the observed real-time behavior de-
pends not only on the dynamics of the molecular fragmenta-
tion per se but also on how the field distorts the electron
potential surfaces over which the nuclei evolve as well as on
2
¿
B. Generation of NO A ⌺ nЈÄ1
Owing to the favorable proximity of the ͑1,0,0͒ vibra-
tional level of NO with a light-induced surface intersection
͉X,N and ͉R,NϪ3 potentials for extended
͘ ͘
N-O bonds over the range of wavelengths used here, it is
2
between the
2
ϩ
postulated that NO A ⌺ nЈϭ1 is generated by direct cross-
ing from the X,N to the R,NϪ3 state. Motion along the
symmetric stretch coordinate permits NO to proceed over
how it enacts detection of the asymptotic states. For the NO
2
2
ϩ
2
ϩ
3
͉
͘
͉
͘
3s␴ ⌺ →NO A ⌺ nЈϭ0ϩO P channel, the pump and
probe intensities control the times at which access to the
Rydberg dissociation continuum is available. For the channel
2
͘ ͘
the diabatic barrier between the ͉R,NϪ3 and ͉X,N states;
the surface crossing then enables escape of vibrationally ex-
cited population during the contemporaneous laser pulses
followed by adiabatic dissociation to form nЈϭ1 A ⌺ NO.
That Fig. 5 exhibits no intersection between the shifted 3s␴
2
ϩ
leading to nЈϭ1 A ⌺ product, the probe pulse is more
2
ϩ
2
readily able to deplete the incipient A ⌺ nЈϭ1→X ⌸ nЈ
r
2
ϩ
ϭ0 fluorescence at higher intensities, under which condi-
tions it also brings about greater barrier suppression and
thereby faster dissociation for a given pump photon energy.
The span of delay times required for complete fluorescence
depletion may therefore be considered as only an approxi-
mate measure of the time required for rupture of the ON-O
bond following three-photon absorption at ␭ϭ395–420 nm
2⌺ϩ
Rydberg potential and that of the X A state when one
N-O bond is fixed at the ionic equlibrium separation ͑close to
that of A ⌺ NO͒ further suggests that the route to disso-
ciation via the intersection between the dressed Rydberg and
2
˜
1
2
ϩ
͉
X,N
tionally excited NO A ⌺ levels, while the crossing of
R,NϪ3 with the A,NϪ1 state leads predominantly to
A ⌺ nЈϭ0. Whereas, at room temperature, only about
.2% of NO molecules occupy the ͑1,0,0͒ level, population
͘
states is primarily responsible for generation of vibra-
Ϫ2
2
ϩ
when the intensity is greater than about 6 TW cm . The
2
ϩ
2
ϩ
results of Ӎ600 fs for NO 3s␴ ⌺ →NO A ⌺ nЈϭ0
͉
͘
͉
͘
2
3
2
ϩ
ϩO P at ␭ ϭ415 nm ͓deduced from Fig. 2͑b͔͒ and
1
Ӎ500 fs for NO2 3s␴ 2⌺ →NO A ⌺ nЈϭ1ϩO P at
ϩ
2
ϩ
3
0
2
can be driven to excited vibrational states by Rabi cycling
during the intense pump pulse. To estimate the magnitude of
this effect, we integrated the Liouville equation for the time
evolution of a density containing the ͑0,0,0͒ and ͑1,0,0͒ lev-
␭1
ϭ400 nm ͓deduced from Fig. 1͑e͔͒ nevertheless stand in
broad agreement with the sub-500-fs fragmentation time re-
ported by Davies et al. for three-photon photodissociation of
2
14
NO to yield NO C ⌸ at ␭ϭ375 nm.
2
r
2
2
˜
˜
els of the X A state and a single level of the A B state
during a 100 fs driving field with I ϭ5.3 TW cm . The
1
2
Ϫ2
0
1
2
VI. CONCLUSIONS
˜
parametrized quadratic polynomial form of the A B
2
33
2
˜
�
The observations reported in this paper provide an ex-
ample of how an intense laser field can alter the fragmenta-
tion of a molecule in real time. We have examined the mul-
was used to calculate Rabi frequencies for transitions from
2
2
˜
˜
different locations on the A B and X A potential
2
1
2
2͑b͒
2
ϩ
3
surfaces.
This three-level model predicts that 82% of the
tiphoton dissociation of NO to generate NO A ⌺ ϩO P
2
Ϫ2
population initially in the ͑0,0,0͒ level can be cycled into the
level excited with a single quantum of symmetric stretch
vibration at times near the center of the laser pulse.
at intensities between 5.8 and 9.3 TW cm promoted by a
driving field with wavelengths between 395 and 420 nm.
2
ϩ
Formation of the nЈϭ1 and 0 vibrational levels of the A ⌺
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
128.59.226.54 On: Mon, 08 Dec 2014 22:32:48

4141
J. Chem. Phys., Vol. 121, No. 9, 1 September 2004
NO2 multiphoton dynamics
2
ϩ
2
3
4
5
NO state was monitored by depletion of A ⌺ nЈ
A. Giusti-Suzor, F. H. Mies, L. F. DiMauro, E. Charron, and B. Yang, J.
Phys. B 28, 309 ͑1995͒.
P. H. Bucksbaum, A. Zavriyev, H. G. Muller, and D. W. Schumacher,
Phys. Rev. Lett. 64, 1883 ͑1990͒.
E. Charron, A. Giusti-Suzor, and F. H. Mies, J. Chem. Phys. 130, 7359
͑1995͒.
B. M. Garraway and K.-A. Suominen, Phys. Rev. Lett. 80, 932 ͑1998͒; M.
Rodriguez, K.-A. Suominen, and B. M. Garraway, Phys. Rev. A 62,
2
→
X ⌸ nЈϭ0 fluorescence by an off-resonant coupling
field.
The experimental observation of the time dependence of
the fluorescence at different intensities has been interpreted
in terms of dissociation via light-induced avoided crossings
r
2
2
˜
˜
between dressed states formed from the X A , A B , and
1
2
0
53413 ͑2000͒; I. R. Sol a´ , B. Y. Chang, J. Santamar ´ı a, V. S. Malinovsky,
Rydberg 3s␴ states of the parent molecule during the driving
field followed by suppression of the light-emitting NO
A ⌺ state by the probe field. In this scenario, absorption of
three 395–420 nm photons by NO results in population of
the Rydberg state: because NO A ⌺ is the observed final
state, it is suggested that the NO Rydberg state has 3s␴
character and that formation of the nЈϭ1 and 0 levels
proceeds vibrationally adiabatically during the dissociation.
Given the energetics and the intensity dependence of NO
and J. L. Krause, Phys. Rev. Lett. 85, 4241 ͑2000͒.
H. Niikura, P. B. Corkum, and D. M. Villeneuve, Phys. Rev. Lett. 90,
6
7
2
ϩ
2
03601 ͑2003͒.
See, for example, A. Delon and R. Jost, J. Chem. Phys. 95, 5686 ͑1991͒;
10, 4300 ͑1999͒ and references therein; A. Delon, R. Jost and M. Jacon,
2
1
2
ϩ
ibid. 114, 331 ͑2001͒, and references therein.
8
2
D. K. Hsu, D. L. Monts, and R. N. Zare, Spectral Atlas of Nitrogen
Dioxide ͑Academic, New York, 1978͒, and references therein.
F. Santoro and C. Petrongolo, J. Chem. Phys. 110, 4419 ͑1999͒.
A. Delon, R. Jost, and M. Lombardi, J. Chem. Phys. 95, 5701 ͑1991͒; R.
Brandi, F. Santoro, and C. Petrongolo, Chem. Phys. 225, 55 ͑1997͒.
G. A. Brucker, S. I. Ionov, Y. Chen, and C. Wittig, Chem. Phys. Lett. 194,
301 ͑1992͒; S. I. Ionov, G. A. Brucker, C. Jaques, Y. Chen, and C. Wittig,
J. Chem. Phys. 99, 3420 ͑1993͒; C. Wittig and S. I. Ionov, ibid. 100, 4714
2
ϩ
⌺
9
0
1
2
ϩ
A ⌺ nЈϭ0 and 1 formation, two routes which permit ac-
11
2
ϩ
cess to the dissociation continuum of the 3s␴ ⌺ Rydberg
state via a minimum number of light-induced crossings have
been invoked to explain the temporal characteristics of the
fragmentation. In the first case, generation of
͑
1994͒; S. I. Ionov, H. F. Davis, K. Mikhaylichenko, L. Valachovic, R. A.
Beadet, and C. Wittig, ibid. 101, 4809 ͑1994͒; P. I. Ionov, I. Bezel, S. I.
Ionov, and C. Wittig, Chem. Phys. Lett. 272, 257 ͑1997͒; I. Bezel, P.
Ionov, and C. Wittig, J. Chem. Phys. 111, 9267 ͑1999͒; I. Bezel, D.
Stolyarov, and C. Wittig, J. Phys. Chem. A 103, 10268 ͑1999͒; D.
Stolyarov, E. Polyakova, and C. Wittig, Chem. Phys. Lett. 358, 71 ͑2002͒.
See, for example, F. X. Campos, Y. Jiang, and E. R. Grant, J. Chem. Phys.
2
ϩ
nЈϭ0 A ⌺ NO proceeds via a pair of avoided crossings
between the
͉
A,NϪ1
͘
and
͘
͘
͉X,N states and later between
dressed states. This mechanism is
characterized by a transient bond hardening which results in
ejection of a delayed burst of NO A ⌺ nЈϭ0 relative to the
͉
R,NϪ3 and
͘
͉
A,NϪ1
12
93, 2308 ͑1990͒; 93, 7731 ͑1990͒; 94, 5897 ͑1991͒; H. Matsui, E. E.
2
ϩ
Mayer, and E. R. Grant, J. Mol. Spectrosc. 175, 203 ͑1996͒; P. Bell, F.
Aguirre, E. R. Grant, and S. T. Pratt, J. Chem. Phys. 119, 10146 ͑2003͒.
T. J. Lee, Chem. Phys. Lett. 188, 154 ͑1992͒.
J. A. Davies, J. E. LeClaire, R. E. Continetti, and C. C. Hayden, J. Chem.
Phys. 111, 1 ͑1999͒; J. A. Davies, R. E. Continetti, D. W. Chandler, and C.
C. Hayden, Phys. Rev. Lett. 84, 5983 ͑2000͒.
time of maximum field strength. In the second case, resulting
1
1
3
4
2
ϩ
in formation of NO A ⌺ nЈϭ1, it is postulated that the
majority of trajectories leading to the final state proceeds
directly over the barrier formed by the avoided crossing be-
states, which gives rise to a
sharper fluorescence decay as a function of pump-probe time
delay. The experimental results suggest, in addition, that for-
mation of nЈϭ1 NO A ⌺ also occurs to some extent by
the same mechanism as that responsible for NO A ⌺
nЈϭ0 molecules. For both routes, population transfer to the
1
1
5
6
tween the
͉
R,NϪ3
͘
and
͉
X,N
͘
A. Hishikawa, A. Iwamae, and K. Yamanouchi, J. Chem. Phys. 111, 8871
͑
1999͒.
R. B. L o´ pez-Martens, T. W. Schmidt, and G. Roberts, J. Chem. Phys. 111,
183 ͑1999͒.
7
2
ϩ
17
K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure
IV: Constants of Diatomic Molecules ͑Van Nostrand Reinhold, New York,
2
ϩ
1979͒, pp. 466–480.
18
2
ϩ
͑a͒ R. B. L o´ pez-Martens, T. W. Schmidt, and G. Roberts, Phys. Rev. A 62,
13414 ͑2000͒; ͑b͒ T. W. Schmidt, R. B. L o´ pez-Martens, and G. Roberts,
3
s␴ ⌺ Rydberg state occurs across LIPs generated during
0
the period spanned by the driving field, whose dressing effect
is augmented during temporal overlap with the probe field;
after the two pulses have separated in time, the probe acts to
J. Phys. B 37, 1125 ͑2004͒.
1
2
9
0
L. G. Piper and L. M. Cowles, J. Chem. Phys. 85, 2419 ͑1986͒; J. Luque
and D. R. Crosley, ibid. 111, 7405 ͑1999͒ and references therein.
S. Pedersen, T. Baumert, and A. H. Zewail, J. Phys. Chem. 97, 12460
2
ϩ
2
suppress A ⌺ →X ⌸ fluorescence from the nascent NO.
r
͑
1993͒; A. Materny, J. L. Herek, P. Cong, and A. H. Zewail, ibid. 98, 3352
The time required for three-photon dissociation of NO to
2
͑1994͒; M. Blackwell, P. Ludowise, and Y. Chen, J. Chem. Phys. 107, 283
2
ϩ
3
give NO A ⌺ and O P at Terawatt intensities is found to
͑1997͒.
21
S. Mahapatra, H. Koppel, L. S. Cederbaum, P. Stampfuss, and W. Wenzel,
¨
be of the same order of magnitude as that for NO →NO
2
2
3
14
Chem. Phys. 259, 211 ͑2000͒.
C ⌸ ϩO P probed at perturbative intensities.
r
22
͑
͑
a͒ E. Haller, H. K o¨ ppel and L. S. Cederbaum, J. Mol. Spectrosc. 111, 377
1985͒; ͑b͒ E. Leonardi, C. Petrongolo, G. Hirsch, and R. J. Buenker, J.
Chem. Phys. 105, 9051 ͑1996͒; ͑c͒ S. Y. Grebenschikov, C. Beck, H.
Fl o¨ thmann, R. Schinke, and S. Kato, ibid. 111, 619 ͑1999͒; ͑d͒ V. Kurkal,
ACKNOWLEDGMENTS
P. Fleurat-Lessard, and R. Schinke, ibid. 119, 1489 ͑2003͒.
T.W.S. acknowledges Churchill College Cambridge for a
research studentship and the University of Sydney for an
Eleanora Sophia Wood Travelling Scholarship, and
R.B.L.-M. acknowledges EPSRC for the award of a research
studentship. This work was supported by EPSRC, the Isaac
Newton Trust, and the Royal Society of London through
generous equipment grants.
2
3
G. Hirsch, R. J. Buenker, and C. Petrongolo, Mol. Phys. 73, 1085 ͑1991͒.
S. J. Klippenstein and T. Radivoyevitch, J. Chem. Phys. 99, 3644 ͑1993͒.
H. Katagiri and S. Kato, J. Chem. Phys. 99, 8805 ͑1993͒.
24
2
2
5
6
G. Hirsch, R. J. Buenker, and C. Petrongolo, Mol. Phys. 70, 835 ͑1990͒;
76, 1261 ͑1992͒.
27
E. Leonardi, C. Petrongolo, V. Keshari, G. Hirsch, and R. J. Buenker, Mol.
Phys. 82, 553 ͑1994͒; R. F. Salzgeber, V. Mandelshtam, Ch. Schlier, and
H. S. Taylor, J. Chem. Phys. 109, 937 ͑1998͒; L. B. Harding, H. Stark, J.
Troe, and V. G. Ushakov, Phys. Chem. Chem. Phys. 1, 63 ͑1999͒.
2
2
8
9
͑
a͒ G. Bryant, Y. Jiang, and E. R. Grant, Chem. Phys. Lett. 200, 495
1
See, for example: B. M. Garraway and K.-A. Suominen, Rep. Prog. Phys.
͑1992͒; ͑b͒ G. K. Jarvis, Y. Song, C. Y. Ng, and E. R. Grant, J. Chem.
Phys. 111, 9568 ͑1999͒.
See, for example, G. P. Bryant, Y. Jiang, M. Martin, and E. R. Grant, J.
5
8, 365 ͑1995͒; C. Wunderlich, E. Kobler, H. Figger, and T. W. H a¨ nsch,
Phys. Rev. Lett. 78, 2333 ͑1997͒.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
28.59.226.54 On: Mon, 08 Dec 2014 22:32:48
1

4142
J. Chem. Phys., Vol. 121, No. 9, 1 September 2004
Schmidt, L o´ pez-Martens, and Roberts
3
3
3
1
2
3
Chem. Phys. 101, 7199 ͑1994͒; H. Matsui and E. R. Grant, ibid. 104, 42
1996͒; H. Matsui, J. M. Behm, and E. R. Grant, J. Phys. Chem. A 101,
717 ͑1997͒.
G. Theodorakopoulos, I. D. Petsakalis, and M. S. Child, J. Mol. Struct.:
THEOCHEM 434, 177 ͑1998͒.
A. K. F u¨ z e´ ry, R. Burcl, L. L. Torday et al. Chem. Phys. Lett. 334, 381
͑2001͒.
K. S. Haber, J. W. Zwanziger, F. X. Campos, R. T. Wiedmann, and E. R.
Grant, Chem. Phys. Lett. 144, 58 ͑1988͒.
J. Li e´ vin, A. Delon, and R. Jost, J. Chem. Phys. 108, 8931 ͑1998͒.
͑
6
30
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
28.59.226.54 On: Mon, 08 Dec 2014 22:32:48
1