Two-photon dissociation of the NO dimer in the region 7.1-8.2 eV: Excited states and photodissociation pathways

Article abstract of DOI:10.1063/1.1825381

A study of excited states of the NO dimer is carried out at 7.1-8.2 eV excitation energies. Photoexcitation is achieved by two-photon absorption at 300-345 nm followed by (NO)₂ dissociation and detection of electronically excited products, mostly in n=3 Rydberg states of NO. Photoelectron imaging is used as a tool to identify product electronic states by using non-state-selective ionization. Photofragment ion imaging is used to characterize product translational energy and angular distributions. Evidence for production of NO(A²Σ⁺), NO(C²Π), and NO(D²Σ⁺) Rydberg states of NO, as well as the valence NO(B²Π) state, is obtained. On the basis of product translational energy and angular distributions, it is possible to characterize the excited state(s) accessed in this region, which must possess a significant Rydberg character.

Full text of DOI:10.1063/1.1825381

Two-photon dissociation of the NO dimer in the region 7.1–8.2 eV: Excited states and
photodissociation pathways
V. Dribinski, A. B. Potter, I. Fedorov, and H. Reisler
Citation: The Journal of Chemical Physics 121, 12353 (2004); doi: 10.1063/1.1825381
View online: http://dx.doi.org/10.1063/1.1825381
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 121, NUMBER 24
22 DECEMBER 2004
Two-photon dissociation of the NO dimer in the region 7.1–8.2 eV: Excited
states and photodissociation pathways
V. Dribinski, A. B. Potter, I. Fedorov, and H. Reisler
Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
͑Received 8 September 2004; accepted 6 October 2004͒
A study of excited states of the NO dimer is carried out at 7.1–8.2 eV excitation energies.
Photoexcitation is achieved by two-photon absorption at 300–345 nm followed by (NO)2
dissociation and detection of electronically excited products, mostly in nϭ3 Rydberg states of NO.
Photoelectron imaging is used as a tool to identify product electronic states by using
non-state-selective ionization. Photofragment ion imaging is used to characterize product
translational energy and angular distributions. Evidence for production of NO(A 2⌺ϩ), NO(C 2⌸),
and NO(D 2⌺ϩ) Rydberg states of NO, as well as the valence NO(B 2⌸) state, is obtained. On the
basis of product translational energy and angular distributions, it is possible to characterize the
excited state͑s͒ accessed in this region, which must possess a significant Rydberg character.
© 2004 American Institute of Physics. ͓DOI: 10.1063/1.1825381͔
NO͒ →NO A 2⌺ϩ͒ϩNO X 2⌸͒,
I. INTRODUCTION
͑
͑
͑
2
͑II͒
Studies of highly excited electronic states of molecules
present significant experimental and theoretical challenges.
The increased density of electronic states leads to a high
probability of intramolecular interactions and multiple decay
channels—radiative, nonradiative, and dissociative. Experi-
mental studies of highly excited states are hampered by tech-
nical difficulties as well as complexity of data interpretation,
and are mostly limited to studies of resonance enhanced mul-
tiphoton ionization ͑REMPI͒. At the same time, the charac-
terization of such states and their couplings to bound states
and/or dissociative continua is essential for complete under-
standing of many atmospherically important photochemical
processes, as well as the development of accurate quantum-
mechanical models.
The nitric oxide dimer (NO)2 has attracted considerable
attention recently because of its unique bonding character
that involves the singly-occupied antibonding orbitals of the
NO monomers.1–3 The resulting N–N bond is weak
͑710Ϯ10 cmϪ1͒ ͑Refs. 4–6͒ and its behavior is intermediate
between van der Waals and covalent binding.6,7 Its electronic
structure and photodissociaton dynamics have intrigued both
experimentalists and theorists. The low-lying electronic
states of the dimer, which are located below 1 eV, correlate
with two NO(X 2⌸) fragments,
⌬Hϭ44 910 cmϪ1 5.57 eV͒
͑
NO͒ →NO B 2⌸͒ϩNO X 2⌸͒,
͑
͑
͑
2
͑III͒
⌬Hϭ46 190 cmϪ1 5.73 eV͒.
͑
The origin of the lowest of these states was determined
by photoelectron and photoion imaging studies to be at 5.12
eV. These studies, carried out at excitation energies below
the dissociation threshold for channels ͑II͒ and ͑III͒, together
with preliminary ab initio calculations, provide evidence for
assigning the optically excited state as a mixed Rydberg
(3p)/valence state.14 It was suggested that strong absorption
to this state is important up to at least 6.3 eV. The excited
state, which is bound by at least 3500 cmϪ1, is predissocia-
tive and products appear on a time scale of a few
picoseconds.6–13
In the present paper we extend our studies of the photo-
dissociation of the NO dimer to the region 7.1–8.2 eV, ac-
cessed by two-photon excitation at 300–345 nm. This exci-
tation region contains a manifold of Rydberg and valence
states but is below the energy where ion-pair states are pre-
dicted to lie.1 By using photoelectron imaging, we identify
channel ͑II͒ as a major pathway, and observe for the first
time the two channels,
NO͒ →NO X 2⌸͒ϩNO X 2⌸͒,
͑
͑
͑
2
NO͒ →NO C 2⌸͒ϩNO X 2⌸͒,
͑
͑
͑
͑I͒
2
͑IV͒
͑V͒
⌬Hϭ710 cmϪ1 0.088 eV͒.
͑
⌬Hϭ53 081 cmϪ1 6.58 eV͒
͑
NO͒ →NO D 2⌺ϩ͒ϩNO X 2⌸͒,
Seven such excited states were predicted and investigated by
ab initio methods,1–3 but have yet to be observed experimen-
tally. Experimental studies of electronically excited states
have thus far focused on the near UV region ͑5.0–6.2 eV͒
where two additional dissociation channels have been ob-
served and investigated6–13
͑
͑
͑
2
⌬Hϭ54 002 cmϪ1 6.70 eV͒.
͑
We also find evidence for the participation of channel ͑III͒.
From analyses of photoelectron spectra of products, as well
0021-9606/2004/121(24)/12353/8/$22.00
12353
© 2004 American Institute of Physics
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12354
J. Chem. Phys., Vol. 121, No. 24, 22 December 2004
Dribinski et al.
sion Abel ͑BASEX͒ transform method,20 is used to obtain
angular and translational energy distributions of either pho-
toelectrons or NOϩ ions.
In order to confirm that the measured signals originate
from two-photon dissociation of the NO dimer followed by
one-photon ionization of the products, the dependencies of
these signals on NO concentration and laser energy are mea-
sured. Both photoelectron and NOϩ ion signals exhibit iden-
tical dependencies on concentration and laser power with
exponents of 1.6Ϯ0.3 and 2.6Ϯ0.4, respectively. The nearly
quadratic NO concentration dependence confirms that the
observed NO products derive from (NO)2 . The laser power
dependence justifies the assumption that two-photon disso-
ciation followed by partially saturated one-photon ionization
of NO photofragments in Rydberg states leads to the ob-
served photoelectrons and NOϩ ions.
The only background signal observed in our experiments
results from nonresonant three-photon ionization of cold NO
in the molecular beam. However, this background constitutes
less than 1% of the total signal in our experiments and can be
ignored.
FIG. 1. Schematic diagram of two-photon excitation of (NO)2 with subse-
quent detection of NO(A), NO(C), and NO(D) fragments by one-photon
III. RESULTS AND DISCUSSION
nonresonant ionization at the same photon energy via ⌬ ϭ0 transitions.
v
A. Photoelectron kinetic energy distributions:
Identification of dissociation channels
As stated above, several dissociation channels are ener-
getically accessible in the region of study. At first glance it
may seem impossible to distinguish among these channels in
a one-color experiment. However, owing to the Rydberg na-
ture of the A 2⌺ϩ, C 2⌸, and D 2⌺ϩ product states of NO,
generated via channels ͑II͒, ͑IV͒, and ͑V͒, respectively, they
can be unambiguously identified in the product photoelectron
spectra. There are two major factors that make the assign-
ments possible.
as their translational and angular distributions ͑obtained by
velocity map imaging͒, we are able to characterize the ex-
cited electronic state of the dimer accessed optically in this
energy region. Most likely it has a significant Rydberg char-
acter, is weakly bound, and it predissociates via nonadiabatic
couplings to lower Rydberg and valence states.
II. EXPERIMENTAL METHODS
The experimental arrangement has been described
elsewhere,14,15 and only relevant experimental details are
presented here. Vibrationally and rotationally cold (NO)2
molecules (Trotϭ3–5 K) are obtained in a molecular beam
by supersonic expansion of gas mixtures containing 10%–
20% NO in He at a backing pressure of 2 atm.7 The NO
dimer is promoted to 7.1–8.2 eV by two-photon transitions
at 300–345 nm. The radiation is generated by frequency
doubling the linearly polarized output of a Nd:YAG ͑YAG—
yttrium aluminum garnet͒ laser pumped dye laser system
͑Spectra-Physics GCR230 with Continuum ND6000,
Rhodamine 640, and DCM; 0.2–0.5 mJ; 40–50 cm focal-
length lens, ␶pulseϭ5–10 ns). Following two-photon absorp-
tion, the NO dimer dissociates producing NO fragments in
3s and 3p Rydberg states ͓channels ͑II͒, ͑IV͒, and ͑V͔͒.
These fragments are ionized nonselectively by one-photon
absorption at the same wavelength, provided the photon en-
ergy exceeds the ionization energy of the Rydberg state via
The geometries and electronic core structures of the
A 2⌺ϩ, C 2⌸, and D 2⌺ϩ Rydberg states of NO are similar
to those of the NOϩ(X 1⌺ϩ) ion, which results in similar
rovibrational energy levels and a strong propensity for ion-
ization via diagonal (⌬ ϭ0) transitions ͑the Franck–
v
Condon factors for such transitions exceed 0.99͒.21 As a con-
sequence, ionization of different vibrational levels within the
same Rydberg state produces photoelectrons with almost
equal kinetic energies, and the photoelectron spectra consist
of sets of well-resolved narrow peaks, each corresponding to
ionization of a specific NO Rydberg state. In addition, ion-
ization corresponding to the peak in the photoelectron kinetic
energy ͑eKE͒ spectrum of each Rydberg state captures most
of the Franck–Condon-active vibrational states of the ion
and, therefore, the ionization probability is large. In contrast,
ionization from the X 2⌸ and B 2⌸ valence states gives rise
to a broad vibrational state distribution in the ion, and ion-
ization at a specific wavelength may capture energetically
only a subset of these states. Moreover, since the electronic
configuration of B 2⌸ requires excitation of an inner elec-
tron, two-electron excitation is needed to produce the ground
X 1⌺ϩ state of NOϩ, leading to substantially lower prob-
abilities for one-photon ionization.22 Thus, the observed
ϩ
Ry
⌬ ϭ ϩϪ Ryϭ0 transitions, where
and
v
are the vi-
v
v
v
v
brational levels of the ion and Rydberg states, respectively.
The excitation scheme is shown in Fig. 1.
The velocity map imaging technique,16,17 combined with
event counting and centroiding18,19 and the basis set expan-
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J. Chem. Phys., Vol. 121, No. 24, 22 December 2004
Dissociation of the NO dimer
12355
at half maximum of this feature is 55 cmϪ1. Such a narrow
peak can only be a result of ionization of one or two vibra-
tional levels in NO(A). However, levels NO(A, ϭ0–7) are
v
accessible at 7.75 eV via channel ͑II͒. Due to the slight dif-
ferences in spectroscopic constants for NO(A) and
NOϩ(X),23 photoelectrons resulting from ionization of
NO(A, ϭ7) would have a kinetic energy of 1060 cmϪ1, i.e.,
v
330 cmϪ1 higher than that of photoelectrons generated by
ionization of NO(A, ϭ0). The observed eKE peak position
v
͑maximum at 720 cmϪ1͒ and the narrow width provide
strong evidence for low vibrational excitation in the NO(A)
fragment. No definitive conclusion about vibrational excita-
tion of NO(C) and NO(D) fragments can be drawn from the
photoelectron spectrum, because the measured relative
widths of the peaks (⌬E/Eϭ4.7% and 5.1% for C and D
states, respectively͒ are close to the resolution limit of our
imaging setup.
Photoelectron spectra exhibiting similar peaks corre-
sponding to NO(A,C,D) products are obtained at other ex-
citation energies up to 8.18 eV, and their ratios do not vary
significantly with energy. Production of higher Rydberg
states is not observed, even though the thresholds for
NO(E 2⌺ϩ)ϩNO(X 2⌸), NO(F 2⌬)ϩNO(X 2⌸), and
NO(H 2⌺ϩ,H 2⌸)ϩNO(X 2⌸) ͑7.63, 7.78, and 7.86 eV,
Ј
respectively͒ are lower than the excitation energy. Minor
traces of these states are detected in the photoelectron spectra
at higher laser intensities, but these weak features exhibit
much stronger laser power dependencies and are attributed to
accidental 2ϩ1 REMPI signals of either cold NO in the mo-
lecular beam or vibrationally/rotationally excited NO(X)
fragments.
FIG. 2. Photoelectron image and the corresponding eKE obtained following
two-photon excitation of (NO)2 at 320 nm. The three peaks correspond to
2
2
ionization of NO(A
ciation of the NO dimer. The inset shows the position and width of the
⌺ ⌺
ϩ), NO(C 2⌸), and NO(D ϩ) produced in disso-
2
NO(A
⌺
ϩ) peak in more detail ͑see text͒.
At wavelengths longer than 330.4 nm, none of the ener-
getically allowed vibrational states of NO(A) can be ionized
product photoelectron spectrum reflects predominantly ion-
ization of Rydberg states of NO.
by one-photon absorption via ⌬ ϭ0 transitions, and the ion-
v
ization probability of NO(A) becomes negligible compared
to those of NO(C) and NO(D). Hence, channels ͑IV͒ and
͑V͒ can be studied selectively, which proves especially help-
ful in interpreting the NOϩ photofragment translational en-
ergy distributions ͑see below͒. A typical photoelectron im-
age, obtained at ␭ϭ345 nm (2h␯ϭ7.19 eV), and the
corresponding eKE distribution are depicted in Fig. 3. As
expected, only two major features remain and they corre-
spond to the ionization of NO(C) and NO(D) products with
relative integrated peaks, NO(C):NO(D)ϭ1.00:0.39
Ϯ0.01. Again, the product ratios do not vary significantly in
the 331–345 nm range.
The low-intensity features observed at lower kinetic en-
ergies are assigned as ionization of NO(B) products gener-
ated via channel ͑III͒. The assignment is based on the corre-
spondence between spectral features and calculated
photoelectron energies and Franck–Condon factors for one-
photon ionization of the NO(B) state at 345 nm ͑see Fig. 3
and Appendix͒. The probability for direct one-photon ioniza-
tion of NO(B) to NOϩ(X), though low, is non-negligible.22
In some cases, such ionization can be facilitated by partici-
pation of highly excited neutral Rydberg states lying above
the first ionization asymptote, followed by autoionization.24
The integrated intensity of the NO(B) photoelectron signal
at 345 nm is comparable to that of the NO(C) state. Taking
Figure 2 shows a photoelectron image obtained from the
ionization of NO fragments arising from two-photon disso-
ciation of (NO)2 at 320 nm (2h␯ϭ7.75 eV) and the corre-
sponding photoelectron translational energy distribution ob-
tained by integrating the total intensity at each radius over all
angles. Several conclusions can be drawn from this figure.
First, three distinct narrow rings are observed in the image,
corresponding to three narrow peaks in the eKE distribution.
The positions of these peaks agree with those calculated for
one-photon ionization of the A 2⌺ϩ, C 2⌸, and D 2⌺ϩ
Rydberg states of NO ͑730, 8899, and 9820 cmϪ1, respec-
tively͒. Therefore, we conclude that reactions ͑2͒, ͑4͒, and
͑5͒ participate in 7.75 eV photodissociation.
Second, by integrating the area of each photoelectron
peak, we obtain the relative yields of the three Rydberg states
NO(A):NO(C):NO(D)ϭ1.00:0.48Ϯ0.01:0.27Ϯ0.02. This
estimate is based on the assumption that the ionization prob-
abilities for these states are comparable, as justified by the
identical laser power dependencies for all three peaks. Note
that production of NO(A) remains the dominant dissociation
channel even though the excitation energy is 2.18 eV higher
than the threshold of channel ͑II͒. Channels ͑IV͒ and ͑V͒,
whose thresholds are higher, are also observed.
Third, analysis of the width of the low eKE peak ͓corre-
sponding to ionization of NO(A)] shows that the full width
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12356
J. Chem. Phys., Vol. 121, No. 24, 22 December 2004
Dribinski et al.
FIG. 3. Photoelectron image and the corresponding eKE obtained following
two-photon excitation of (NO)2 at 345 nm. The two large peaks correspond
FIG. 4. Ion image and the corresponding translational energy distribution of
NOϩ ions resulting from the ionization of products of two-photon dissocia-
tion of (NO)2 at 320 nm. The short vertical bars in the upper part of the plot
show the thresholds for the production of different vibrational states of
ground and three Rydberg states of NO.
2
to ionization of NO(C 2⌸) and NO(D
⌺
ϩ). The short vertical bars show
the positions of possible ionization peaks of NO(B 2⌸). The length of the
line is proportional to the FC factor ͑right scale͒.
into account the low detection probability of the NO(B) state
and the limited number of the vibrational levels that can be
detected, we conclude that channel ͑III͒ is more populated
than channels ͑IV͒ and ͑V͒. At 320 nm the contribution of
NO(B) product to the photoelectron signal, though still de-
tectable, is considerably smaller relative to products in A, C,
and D states.
highly vibrationally and rotationally excited. Such conclu-
sion is especially obvious for the NO(A)ϩNO(X) channel.
At the same time, it was shown above that the NO(A) pho-
toelectron spectrum at this wavelength is characteristic of a
product that is rather cold vibrationally. Thus, we argue that
most of the vibrational excitation is contained in the NO(X)
cofragment.
Better resolved structures are seen in the 345 nm image
͑Fig. 5͒, where the NO(A) channel is not detected. The prod-
uct translational energy distribution shown in Fig. 5 corre-
sponds to very little vibrationally unexcited NO, and the
B. Photofragment translational energy distributions
While photoelectron spectra of dissociation products are
used to identify product channels, ion translational energy
distributions provide information on product internal excita-
tions, and therefore on dissociation dynamics.
most prominent feature can be assigned to NO(C, ϭ0)
v
The image of NOϩ ions resulting from nonselective ion-
ization of NO(A), NO(C), and NO(D) fragments generated
in (NO)2 dissociation at 320 nm is shown in Fig. 4, along
with the corresponding ion translational energy distribution.
No narrow features are resolved with this non-state-selective
detection scheme. A large number of rotationally and vibra-
tionally excited products are energetically allowed in the dis-
sociation and, by energy conservation, this leads to a broad
distribution of product kinetic energies ͑see marks in Fig. 4͒.
However, one important conclusion can be drawn from the
figure: the observed product translational energy distribution
starts far below the maximum allowed energetically and
peaks at low values. This indicates that the products are
ϩNO(X, ϭ2) ͑see marks in the figure͒. Note that ϭ2 is
v
v
the highest vibrationally excited level of NO(X) allowed by
the energy available to channel ͑IV͒ at this excitation energy.
In this regard, the dissociation dynamics is similar to that of
the NO(A)ϩNO(X) channel.
Referring to Fig. 5, the observed distribution must also
contain contributions from NO(B) produced via channel
͑III͒, as follows from the analysis of the corresponding pho-
toelectron spectrum ͑Fig. 3͒. However, the photofragment
translational energy distribution for this channel must be
broad, because NO(B) in a range of vibrational states can be
ionized. Consequently, this channel is expected to contribute
little to the fragment signal at any given translational energy.
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J. Chem. Phys., Vol. 121, No. 24, 22 December 2004
Dissociation of the NO dimer
12357
FIG. 5. Ion image and the corresponding translational energy distribution of
NOϩ ions resulting from the ionization of the products of two-photon dis-
sociation of the NO dimer at 345 nm. The thresholds for production of all
2
ϩ
the allowed vibrational states of NO(X 2⌸), NO(C 2⌸), and NO(D
⌺ )
are shown with vertical bars.
FIG. 6. Angular anisotropy parameters ␤i obtained by fitting the experimen-
tal product angular distributions to Eq. ͑4͒. The corresponding translational
energy distributions are shown for reference.
C. Photofragment recoil anisotropy
Due to the two-photon nature of the excitation step lead-
ing to dimer dissociation, the analysis of product angular
distributions is more involved than in one-photon absorption
of linearly polarized light followed by fast dissociation. In
the latter case, the fragment angular distribution can be ex-
pressed by the well-known equation,25
where P4(x) is the fourth Legendre polynomial.
The meaning of the anisotropy parameters ␤2 and ␤4
can be understood by considering a few limiting cases. If the
first photon absorption is dominated by only one intermedi-
ate state, then
I ␪͒ϭC 1ϩ␤P cos ␪͒ ,
͑1͒
͑
͓
͑
͔
2
where ␪ is the ejection angle with respect to the laser polar-
ization axis, P2(x) is the second Legendre polynomial, C is
the normalization constant, and ␤ is the anisotropy parameter
whose value is defined by the relative orientation of the frag-
ment recoil direction with respect to the dipole moment of
the initial transition. ␤ is also sensitive to the dissociation
lifetime and dynamics.7,26,27
The angular distributions of dissociation products in
two-photon absorption can be obtained by multiplying distri-
butions of the form of Eq. ͑1͒ for each of the two absorption
steps and integrating over all possible intermediate steps ͑in-
volving virtual and/or actual states of the parent molecule
located at the energy of the first photon͒.28 The equation
becomes,
I ␪͒ϭI ␪͒I ␪͒,
͑3͒
͑
͑
͑
1
2
where I1(␪) and I2(␪) are angular distributions of the form
of Eq. ͑1͒ for the first and second photon absorptions, respec-
tively. If both transitions are of parallel nature ͑i.e., the tran-
sition dipole moments lie parallel to the laser polarization
axis͒ then I1(␪)ϭI2(␪)Хcos2 ␪ and I(␪)ϭC cos4 ␪, which
corresponds to ␤2ϭ20/7Ϸ2.86 and ␤4ϭ8/7Ϸ1.14. In the
case of one parallel and one perpendicular transitions, I(␪)
ϭC cos2 ␪ sin2 ␪, ␤2ϭ5/7Ϸ0.71 and ␤4ϭϪ12/7ϷϪ1.71;
and for two perpendicular transitions ␤2ϭϪ10/7ϷϪ1.43
and ␤4ϭ3/7Ϸ0.43.
The dependencies of the anisotropy parameters on prod-
uct translational energies in two-photon dissociation of
(NO)2 at 320 and 345 nm are presented in Fig. 6. In order to
confirm the two-photon nature of the dimer’s excitation and
I ␪͒ϭC 1ϩ␤ P cos ␪͒ϩ␤ P cos ␪͒ ,
͑2͒
͑
͓
͑
͑
͔
2
2
4
4
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12358
J. Chem. Phys., Vol. 121, No. 24, 22 December 2004
Dribinski et al.
exclude the possibility of participation of higher-order exci-
tations, the experimental angular distributions at each trans-
lational energy were fit with the extended equation,
velocity, and ␶ is a characteristic lifetime of the molecule
before dissociation. Using Eqs. ͑5͒ and ͑6͒ with the experi-
mental ␤2 and ␤4 values and a rotational temperature T
ϭ3–5 K for parent (NO)2 in the beam, we obtain dissocia-
tion lifetimes of Ϸ0.7 ps and Ϸ1.2 ps at 7.75 eV ͑320 nm͒,
and 7.19 eV ͑345 nm͒, respectively; i.e., the dissociation
lifetime decreases at higher excitation energies. These life-
times are longer than a vibrational period, implying a predis-
sociative mechanism rather than direct dissociation from a
repulsive excited state. Another indication of the predissocia-
tive nature of the excited state is the detection of a weak
dimer-ion signal (m/eϭ60) in excitation wavelengths in the
region 7.1–8.2 eV. In other words, even with a nanosecond
laser, ionization of the excited dimer state competes with
dissociation. A predissociation mechanism can also explain
the observed high internal ͑vibrational and rotational͒ exci-
tation of the dissociation products.
I ␪͒ϭC 1ϩ␤ P cos ␪͒ϩ␤ P cos ␪͒
͑
͓
͑
͑
2
2
4
4
ϩ␤6P6 cos ␪͒ ,
͑4͒
͑
͔
which contains also a sixth Legendre polynomial responsible
for three-photon processes. Figure 6 shows that at both
wavelengths, ␤2 and ␤4 have nonzero values at all product
translational energies, while ␤6Ϸ0 within the accuracy of
our experiments. It is also evident that at higher fragment
translational energies both ␤2 and ␤4 have large positive
values, producing a nearly cos4 ␪ angular distribution. This
indicates that a parallel transition with one dominating vir-
tual intermediate state is accessed ͑no real dimer states are
expected at the one-photon energy͒, and the transition dipole
moments for both absorption steps are aligned along the
N–N bond ͑i.e., B2 symmetry in C2v point group͒. Since the
ground state of the NO dimer has A1 symmetry, we conclude
that the state ͑or states͒ initially accessed at 7.1–8.2 eV must
also be of A1 symmetry.
D. The nature of the excited state
The experimental results described above allow us to
characterize the optically excited state. The large signals
from NO products in Rydberg states point to a correlation
between the product channels and parent dimer excited
state͑s͒ with significant Rydberg character. The bound nature
of the state is supported by the observation of a (NO)ϩ2 par-
ent ion signal in ionization via the neutral dimer’s excited
state. The (NO)ϩ2 ion is bound by ϳ5000 cmϪ1, and the 5.12
eV excited state is bound by at least 3500 cmϪ1. The obser-
vation of a dimer ion mass at m/eϭ60 confirms that the
excited state of the neutral dimer has a lifetime long enough
to allow ionization by a nanosecond laser beam. An absorp-
tion spectrum in this wavelength region is unavailable, but
the 2ϩ1 REMPI spectrum of the NO dimer at 300–345 nm
appears to have diffuse structures.
Both ␤2 and ␤4 decrease significantly in the region of
low product translational energies ͑below 500 cmϪ1͒. This
trend has been observed previously for the anisotropy param-
eter ␤ in one-photon dissociation of several molecules, in-
cluding (NO)2 ,7,27,29 and successfully explained by a semi-
classical model based on angular momentum conservation,
which takes into account nonaxial recoil due to rotation of
the molecular frame during dissociation of low-temperature
species terminating in products with high rotational excita-
tion. Likewise, the observed decrease in anisotropy param-
eters in our experiments indicates the formation of highly
rotationally excited fragments.
The measured values of the anisotropy parameters at
higher product translational energies are ␤2ϭ2.5Ϯ0.1, ␤4
ϭ0.9Ϯ0.1 at 320 nm and ␤2ϭ2.15Ϯ0.05, ␤4ϭ0.75Ϯ0.05
at 345 nm. These values are close to the limiting values of
␤2ϭ2.86 and ␤4ϭ1.14 for a parallel transition with a paral-
lel intermediate step. The slight reduction in the anisotropy
parameters cannot be accounted for by the presence of a
perpendicular component, because in this case one of the
anisotropy parameters would have undergone a much larger
reduction than the other ͑as demonstrated above, in perpen-
dicular transitions ␤2 and ␤4 have opposite signs͒. The de-
viations from the maximum values of the anisotropy param-
eters at high product translational energies can be explained
by rotation of the parent dimer prior to dissociation. Follow-
ing the simple classical derivation of Jonah for one-photon
transition,30 we obtain for the case of two-photon dissocia-
tion,
Based on the A1 symmetry of the excited state of the
dimer and the energies of the dimer Rydberg states estimated
by using the Rydberg formula,31 four possible candidates
emerge: 3dx2, 3dx Ϫy2, 4s ͑estimated energies ϳ7.2 eV͒,
2
and 4pz ͑ϳ7.5 eV͒, where z is perpendicular to the N–N
bond in the plane of the molecule (C2 axis͒. The observed
NO Rydberg products are all in nϭ3 states, and therefore
correlate with nϭ3 Rydberg states of the dimer, providing
some preference for the 3d states. However, experiments and
calculations at lower energies show that a state with a spe-
cific Rydberg character in the dimer does not necessarily
evolve adiabatically to product NO monomer in the corre-
sponding Rydberg state.14 The electronic state reached at 5.6
eV has a mixed B2 valence/Rydberg (3px) character, but the
major product is NO in the 3s Rydberg state. In the present
experiments the simultaneous production of several elec-
tronically excited states of NO indicates that more than one
excited state of the NO dimer participates in the dissociation.
This underscores the importance of nonadiabatic interactions
between excited states in the region of study. Valence dimer
states leading to NO products in excited valence states ͓e.g.,
NO(B)] probably participate as well, and states with a mixed
valence/Rydberg nature are likely.
␶ ␻2ϩ1
2
␤e2ffϭ
␤e4ffϭ
␤2 ,
͑5͒
͑6͒
2
4␶ ␻2ϩ1
2
2
␶ ␻2ϩ1͒ 9␶ ␻2ϩ1͒
͑
͑
␤4 ,
2
2
4␶ ␻2ϩ1͒ 16␶ ␻2ϩ1͒
͑
͑
where ␤i (iϭ2,4) is the anisotropy parameter for the nonro-
tating parent molecule, ␻ is its classical rotational angular
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J. Chem. Phys., Vol. 121, No. 24, 22 December 2004
TABLE I. Calculated Franck–Condon factors for the ionization of NO(B 2⌸, ϭ1–12).
Dissociation of the NO dimer
12359
v
vB vϩ
0
1
2
3
4
1
2
3
4
5
6
7
8
9
Ͻ4 ϫ 10Ϫ6
Ͻ4 ϫ 10Ϫ6
Ͻ4 ϫ 10Ϫ6
Ͻ4 ϫ 10Ϫ6
4.51 ϫ 10Ϫ6
1.35 ϫ 10Ϫ5
3.15 ϫ 10Ϫ5
7.22 ϫ 10Ϫ5
1.49 ϫ 10Ϫ4
2.75 ϫ 10Ϫ4
4.83 ϫ 10Ϫ4
8.07 ϫ 10Ϫ4
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
9.02 ϫ 10Ϫ6
3.16 ϫ 10Ϫ5
8.57 ϫ 10Ϫ5
2.16 ϫ 10Ϫ4
4.83 ϫ 10Ϫ4
9.65 ϫ 10Ϫ4
1.77 ϫ 10Ϫ3
2.98 ϫ 10Ϫ3
4.70 ϫ 10Ϫ3
7.00 ϫ 10Ϫ3
¯
¯
¯
¯
7.26 ϫ 10Ϫ4
1.63 ϫ 10Ϫ3
3.22 ϫ 10Ϫ3
5.72 ϫ 10Ϫ3
9.23 ϫ 10Ϫ3
1.37 ϫ 10Ϫ2
1.89 ϫ 10Ϫ2
2.45 ϫ 10Ϫ2
¯
¯
¯
1.93 ϫ 10Ϫ2
2.68 ϫ 10Ϫ2
3.38 ϫ 10Ϫ2
3.91 ϫ 10Ϫ2
4.18 ϫ 10Ϫ2
¯
¯
10
11
12
4.51 ϫ 10Ϫ2
3.99 ϫ 10Ϫ2
3.09 ϫ 10Ϫ2
IV. SUMMARY
Photofragment fluorescence spectra obtained by Ka-
jimoto et al. following one-photon dissociation of (NO)2 at
193 nm revealed the presence of this channel with a broad
vibrational distribution of the NO(B 2⌸) product that en-
compassed all the energetically allowed levels.8 Therefore,
we calculated Franck-Condon factors for transitions originat-
Excited states of the (NO)2 dimer in the 7.1–8.2 eV
region were studied by two-photon dissociation and detec-
tion of NOϩ ions and photoelectrons produced by nonreso-
nant ionization of excited NO products. Three Rydberg states
of NO were identified as dissociation products: NO(A 2⌺ϩ),
NO(C 2⌸), and NO(D 2⌺ϩ), all belonging to the nϭ3 Ry-
dberg series. Evidence for production of NO(B 2⌸) is ob-
tained as well. The NO(X 2⌸) fragments possess significant
vibrational excitation, whereas the Rydberg NO cofragments
are vibrationally colder. The products have large amounts of
rotational excitation.
The time scale for dissociation is ϳ1 ps, typical of pre-
dissociation rather than direct dissociation from a repulsive
state. The appearance of (NO)ϩ2 parent ions in the REMPI
spectrum confirms the bound nature of the optically acces-
sible state. Based on the observed A1 symmetry of the upper
state and the Rydberg nature of the products, the initially
ing in ϭ1–12. Because the geometries of NO(B) and
v
ground-state NOϩ are different,23 all five accessible vibra-
tional levels of the NOϩ ion are included.
In order to compute the Franck–Condon factors, vibra-
tional eigenfunctions of both NO(B 2⌸, ϭ0–12) and
v
NOϩ(X 1⌸ϩ, ϭ0–4), as well as their overlaps, are calcu-
v
lated by using the Morse function32 to model diatomic inter-
nuclear potentials. This is done with a computer program
given in Ref. 33. Spectroscopic constants of NO(B) and
NOϩ(X) are used to estimate the parameters of the Morse
potential.23 This approach results in a somewhat increased
depth of the potential well in the NO(B) state ͑by Ϸ20%͒,
but generates the correct positions of the vibrational energy
levels. Therefore, this is a valid model for levels far below
the dissociation asymptote of NO(B). However, we have
also confirmed that the use of the experimental dissociation
energy in the NO(B) Morse potential produces qualitatively
similar Franck–Condon factors and, therefore, does not af-
fect our conclusions.
excited dimer state may possess a significant 3dx2, 3dx Ϫy2,
2
4s, or 4pz Rydberg character. Nonadiabatic transitions to
other Rydberg and valence states lead to the final product
channels.
This study demonstrates that photoelectron spectroscopy
of products can serve as a useful tool in identifying product
electronic states even in non-state-selective ionization.
The values of the Franck–Condon factors are summa-
rized in Table I and also shown in Fig. 3 in the text.
As seen from the table, only higher ( ϭ8–12) vibra-
v
ACKNOWLEDGMENTS
tional levels of the B state possess non-negligible Franck–
Condon factors with the allowed ion states, and the positions
of those transitions in the photoelectron spectrum are in good
agreement with the observed low-intensity features ͑Fig. 3͒.
Support by the National Science Foundation and the Do-
nors of the Petroleum Research Fund administered by the
American Chemical Society is gratefully acknowledged. The
authors thank Albert Stolow, Carl Hayden, Anna Krylov, and
Sergei Levchenko for helpful discussions and sharing with
them unpublished experimental and theoretical results.
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