Photoinitiated predissociation of the NO dimer in the region of the second and third NO stretch overtones

Article abstract of DOI:10.1021/jp046226w

Photofragment yield spectra and NO(X²a??_1/2,3/2; v = 1, 2, 3) product vibrational, rotational, and spin-orbit state distributions were measured following NO dimer excitation in the 4000-7400 cm^-1 region in a molecular beam. Photofragment yield spectra were obtained by monitoring NO(X²a??; v = 1, 2, 3) dissociation products via resonance-enhanced multiphoton ionization. New bands that include the symmetric v₁ and asymmetric v₅ NO stretch modes were observed and assigned as 3v₅, 2v₁ + v₅, v₁ + 3v₅, and 3v₁ + v₅. Dissociation occurs primarily via ??v = -1 processes with vibrational energy confined preferentially to one of the two NO fragments. The vibrationally excited fragments are born with less rotational energy than predicted statistically, and fragments formed via ??v = -2 processes have a higher rotational temperature than those produced via ??v = -1 processes. The rotational excitation likely derives from the transformation of low-lying bending and torsional vibrational levels in the dimer into product rotational states. The NO spin-orbit state distribution reveals a slight preference for the ground ²a??_1/2 state, and in analogy with previous results, it is suggested that the predominant channel is X²prod;_1/2 + X²a??_3/2. It is suggested that the long-range potential in the N-N coordinate is the locus of nonadiabatic transitions to electronic states correlating with excited product spin-orbit states. No evidence of direct excitation to electronic states whose vertical energies lie in the investigated energy region is obtained. ? 2005 American Chemical Society.

Full text of DOI:10.1021/jp046226w

J. Phys. Chem. B 2005, 109, 8407-8414
8407
Photoinitiated Predissociation of the NO Dimer in the Region of the Second and Third NO
Stretch Overtones†
A. B. Potter, J. Wei, and H. Reisler*
Department of Chemistry, UniVersity of Southern California, Los Angeles, California 90089-0482
ReceiVed: August 20, 2004; In Final Form: NoVember 1, 2004
Photofragment yield spectra and NO(X2Π1/2,3/2; V ) 1, 2, 3) product vibrational, rotational, and spin-orbit
state distributions were measured following NO dimer excitation in the 4000-7400 cm-1 region in a molecular
beam. Photofragment yield spectra were obtained by monitoring NO(X2Π; V ) 1, 2, 3) dissociation products
via resonance-enhanced multiphoton ionization. New bands that include the symmetric ν1 and asymmetric ν5
NO stretch modes were observed and assigned as 3ν5, 2ν1 + ν5, ν1 + 3ν5, and 3ν1 + ν5. Dissociation occurs
primarily via ∆V ) -1 processes with vibrational energy confined preferentially to one of the two NO
fragments. The vibrationally excited fragments are born with less rotational energy than predicted statistically,
and fragments formed via ∆V ) -2 processes have a higher rotational temperature than those produced via
∆V ) -1 processes. The rotational excitation likely derives from the transformation of low-lying bending
and torsional vibrational levels in the dimer into product rotational states. The NO spin-orbit state distribution
reveals a slight preference for the ground 2Π1/2 state, and in analogy with previous results, it is suggested that
the predominant channel is X2Π1/2 + X2Π3/2. It is suggested that the long-range potential in the N-N coordinate
is the locus of nonadiabatic transitions to electronic states correlating with excited product spin-orbit states.
No evidence of direct excitation to electronic states whose vertical energies lie in the investigated energy
region is obtained.
I. Introduction
deposited in fragment rotation. Dissociation fragments appear
in both spin-orbit states, mostly as NO(X2Π1/2) + NO(X2Π3/2
)
The nitric oxide dimer, a weakly covalently bound complex,
is an intriguing system for studies of photodissociation dynam-
ics. The ground state of (NO)2 is formed by the pairing of two
π* orbitals on NO, leading to a weak (710 ( 10 cm-1) but
covalent N-N bond. Evidence of the chemical nature of the
intermolecular bond is seen in ab initio calculations, as well as
in experimental examinations of the strong and broad UV
absorption that peaks at 205 nm.1-6 The equilibrium geometry
of gas-phase (NO)2 has been determined by microwave spec-
troscopy to be a trapezoidal cis-planar structure.7,8 The N-O
bond length is 1.161 Å, the N-N bond is 2.236 Å, and the
ONN angle is 99.6°. Because of the disparity between the
strengths of the N-O and N-N bonds, dissociation following
excitation of N-O stretch vibrations in the dimer displays
evidence of restricted intramolecular vibrational energy distribu-
tion (IVR), as often associated with predissociation of van der
Waals complexes.9-17
Vibrational predissociation following N-O stretch excitation
in the ground electronic state has been studied both experimen-
tally and theoretically.11-17 In a comprehensive series of studies,
Casassa et al. have found that the lifetimes of the ν1 symmetric
(1868 cm-1) and ν5 asymmetric (1789 cm-1) N-O stretch
modes are different: 880 ( 260 and 39 ( 8 ps, respectively.13
Dissociation fragments are produced with 70-80% of the
available energy deposited into translation, with up to 12% in
product rotation. In the first overtone region, the lifetimes of
the ν1 + ν5 and 2ν5 states are 34 ( 6 and 20 ( 3 ps,
respectively,17 and one of the NO(X2Π) products is preferen-
tially in V ) 1. Only 3% of the remaining available energy is
pairs, but with contributions also from the NO(X2Π1/2) +
NO(X2Π1/2) channel. Two mechanisms have been considered
in explaining the energy disposal: electronically nonadiabatic
vibrational predissociation and vibrational potential coupling that
occurs solely on the ground-state surface.13,17 Additionally, a
hybrid mechanism has been proposed in which the total
dissociation rate is determined predominantly by nonadiabatic
crossings, while partial rates to specific product channels are
affected by further vibrational potential coupling.16
The issue of the participation of excited electronic states in
the dissociation is intriguing, because seven excited electronic
states correlating with two NO(X2Π) fragments are calculated
to lie in the region below 8000 cm-1 (1 eV). The vertical
excitation energy of the lowest state was recently calculated by
Tobita et al. at 1498 cm-1; the highest is at 7425 cm-1.1 On
the basis of their microwave and radio frequency spectra,
Western et al. inferred the existence of low-lying singlet state-
(s) correlating with ground-state products from differences
between expected and observed spin-rotation coupling con-
stants.8 They estimated the average excitation energy of this
state(s) at ∼4500 cm-1, clearly within the range of the electronic
states calculated ab initio. In an absorption spectrum of liquid
NO, Mason observed a rising IR absorption beginning at 1160
nm (8620 cm-1), which was assigned to NO dimer electronic
transitions.18
The ground-state infrared spectroscopy of (NO)2 in the N-O
stretch region has been investigated as well.19-29 The 1600-
4000 cm-1 gas-phase spectrum was characterized by Dinerman
and Ewing at 77-150 K, allowing them to assign both N-O
fundamental stretches, the first asymmetric stretch overtone and
* Corresponding author. E-mail: reisler@usc.edu.
† Part of the special issue “George W. Flynn Festschrift”.
10.1021/jp046226w CCC: $30.25 © 2005 American Chemical Society
Published on Web 02/01/2005

8408 J. Phys. Chem. B, Vol. 109, No. 17, 2005
Potter et al.
the first combination band.22 These assignments were further
refined by Menoux et al. in the 1800-3700 cm-1 region.27
Matrix spectroscopy up to 6000 cm-1 in argon and nitrogen
matrices revealed the presence of 2ν5, ν1 + ν5, and in the case
of argon matrix spectroscopy also 2ν1.30,31 Neither study reported
(NO)2 absorptions to higher N-O stretch overtones. Nour et
al. measured the Raman spectrum of solid (NO)2 and character-
ized ν1 as a nearly pure N-O stretching mode, while ν5
exhibited stronger coupling to the ν3 in-plane bend.32 More
recent force constant calculations by Krim and Lacome dem-
onstrated that ν1 possesses 99.7% N-O stretch character, while
the ν5 normal mode is composed of 82.4% N-O stretch and
17.6% bend.31 This result led the authors to conclude that ν5
provides a faster channel of predissociation than ν1, as it
facilitates coupling between the N-O asymmetric stretch and
the N-N stretch via the ONN bend. In addition to gas-phase
and matrix studies, spectral features at 3708 and 3515 cm-1 of
liquid NO were attributed to NO stretch vibrations of (NO)2.18
In that study, the presence of a second NO stretch overtone at
∼5200 cm-1 was also suggested.
state-selected NO(X2Π; V) fragments are ionized and accelerated
vertically toward a 1 in. diameter microchannel plate (MCP)
detector through a Wiley-McLaren TOF mass spectrometer.
The mass spectrometer separates m/e ) 30 and 60 (correspond-
ing to NO and (NO)2, respectively). The (NO)2 yield is
determined by monitoring the mass spectrum during one-color
nonresonant ionization at 280 nm. Under these experimental
conditions, no clusters higher than dimer are observed. An
estimate of the rotational temperature, Trot ) 4 K, in the
molecular beam is obtained by measuring the REMPI spectrum
of the NO A2Σ+(V ) 0) r X2Π(V ) 0) transition in mixtures
of 1% NO. This estimate is in agreement with the (NO)2
rotational temperatures determined from simulations of the
experimental NO photofragment yield spectra obtained by
vibrational excitation of the NO dimer (see section III).
The IR photolysis radiation is obtained from a Nd:YAG laser-
pumped OPO-OPA system (LaserVision, 0.4 cm-1 bandwidth).
The laser operates in the 4000-7400 cm-1 region with an output
of 7.5-22 mJ. The IR wavelength was calibrated using the
photoacoustic spectrum of methane.34 The beam is steered to
the chamber with CaF2 optics and focused using a f ) 20 cm
lens. The UV detection pulse is generated by frequency doubling
the output of a Nd:YAG pumped dye laser system (Coumarin
480 and LD498, 0.2 cm-1 bandwidth). The laser wavelength is
tuned to the NO A2Σ+(V ) 0) r X2Π(V ) 1, 2, 3) transitions
at 236.2, 247.0, and 258.7 nm, respectively. To avoid mul-
tiphoton dissociative ionization of (NO)2 with the UV pulse (and
saturation of the MCP detector signal),9 the detection laser
intensity is kept below 0.1 mJ and is only mildly focused (f )
40 cm). Both the pump and probe beams have parallel
polarization (i.e., in the plane of the molecular and laser beams).
The REMPI spectra are converted to rotational state populations
by using line strength appropriate for saturated transitions (see
section III).
The goal of the present study is to further investigate the
nonadiabatic transitions between electronic states following
overtone excitation in the NO dimer. Specifically, we wish to
distinguish between long-range interactions that happen in the
asymptotic region of the potential and lead to excited spin-
orbit states of NO, nonadiabatic interactions in the Franck-
Condon vertical region, and direct excitation to excited elec-
tronic states. We also wish to explore patterns in energy disposal
that shed light on the predissociation mechanism. To this end,
we carried out measurements in the molecular beam of the
spectroscopy and predissociation of (NO)2 at 4000-7400 cm-1
,
covering the region of the second and third NO stretch
overtones. The measured spectra reveal the presence of previ-
ously unobserved NO stretch overtones and combination bands.
The vibrational and rotational state distributions of product
NO(X2Π1/2,3/2) are determined and compared with previously
observed (NO)2 predissociation dynamics from lower vibrational
levels of the ground and excited electronic states. The picture
that emerges is similar to that of vibrational predissociation of
van der Waals dimers, with nonadiabatic interactions in the exit
channel resulting in population of both NO spin-orbit states.
Following photodissociation, every energetically allowed NO
fragment vibrational level except NO(X2Π; V ) 0) can be
detected. The V ) 0 dissociation fragments cannot be monitored
because the UV wavelength necessary for their REMPI detection
is strongly absorbed by (NO)2 (which undergoes UV absorption
at wavelengths <242 nm), generating a large background ion
signal.
In the case of NO(X2Π; V ) 1) detection, the frequency of
the detection laser pulse is above the threshold for UV electronic
absorption in (NO)2. Even in the absence of the IR laser
radiation, our current experiments show some background of
NO(X2Π1/2; V ) 1), possibly from two-photon dissociative
ionization,9 which is much colder rotationally than the corre-
sponding fragment from IR photodissociation and cannot be
completely suppressed. Therefore, we optimize the IR + UV
product signal by monitoring the NO(X2Π3/2) fragment, which
is not observed in UV-only photodissociation. The contribution
of NO(X2Π1/2) from dissociative ionization is minimized by
maintaining low intensity of the UV pulse. Additionally, the
UV detection pulse is delayed by g10 ns relative to the IR
photolysis pulse to avoid depleting the (NO)2 ground-state
vibrational population with UV excitation. There is no back-
ground signal in the region of NO(X2Π1/2,3/2; V ) 2, 3) detection.
Two types of experiments are performed. First, NO photo-
fragment yield spectra are acquired by scanning the photolysis
laser with the detection laser fixed at specific bandhead
wavelengths to detect selectively NO(X2Π3/2; V ) 1, 2, 3) by
1 + 1 REMPI. Each point in the spectrum represents the sum
of signals from 30 laser firings. The IR laser intensity is kept
constant throughout the region of the observed spectral bands.
II. Experimental Methods
The experiments are performed using a seeded supersonic
molecular beam of (NO)2 and laser infrared photodissociation
of the dimer. Following dissociation, the vibrationally excited
NO fragments are ionized by resonance-enhanced multiphoton
ionization (REMPI) and detected by time-of-flight (TOF) mass
spectroscopy.
The vacuum chamber consists of two differentially pumped
chambers, the source chamber and the detection chamber, which
are joined by a skimmer-equipped flange.33 Both chambers are
evacuated by turbomolecular pumps. The piezoelectric pulse
nozzle is mounted ∼30 mm from the skimmer (Beam Dynamics,
1.51 mm diameter) in the source chamber. With the nozzle
operating at 10 Hz, the pressure in the detection region is ∼4
× 10-7 Torr.
Nitric oxide dimer is formed in a free-jet expansion of NO
in a 70%:30% Ne:He gas buffer. A pulsed molecular beam
containing up to 20% NO in 2 atm of the carrier gas propagates
through the skimmer into the detection chamber. The molecular
beam is crossed in the photodissociation region by coaxial pulsed
IR photolysis and UV detection laser beams, which intersect
the molecular beam at right angles. Following photodissociation,

Photoinitiated Predissociation of the NO Dimer
J. Phys. Chem. B, Vol. 109, No. 17, 2005 8409
Figure 2. Photofragment yield spectra obtained by monitoring (a) NO-
2
2
(X Π3/2; V ) 2) and (b) NO(X Π3/2; V ) 3).
energy Erot(J) (a Boltzmann plot). We find that similar slopes
are obtained when different branches are used, confirming that
the spectra are indeed obtained under saturation conditions and
alignment effects can be neglected. The final rotational distribu-
tion is generated by averaging the population of each J state
obtained by using branch lines that are not too severely
overlapped. The solid lines in Figure 1b show least-squares fits
to the Boltzmann plots from which the rotational temperature
is generated. The spin-orbit population ratios for each observed
NO(X2Π; V) dissociation product following excitation of each
(NO)2 vibrational level are obtained from integration of the
rotational state distributions for each product spin-orbit state.
Product vibrational distributions are calculated from the
measured yield spectra in two steps. First, the rovibrational
spectrum for each (NO)2 vibrational band, obtained under
unsaturated conditions, is integrated and normalized by the
Franck-Condon factors of the monitored NO A2Σ+(V ) 0) r
X2Π3/2(V ) 1, 2, 3) transition36 and the fraction of the
NO(X2Π3/2; V) product distribution that is ionized by the
detection laser at the bandhead frequency. In the second step,
the final NO product vibrational distribution is determined by
Figure 1. (a) NO A2Σ+(V ) 0) r X2Π(V ) 2) REMPI spectrum
following 3ν5 dissociation. The top plot is the experimental spectrum,
and the bottom is the fit to the data. (b) Boltzmann plots of the
NO(X2Π1/2,3/2; V ) 2) fragment rotational state distributions extracted
from the above spectrum. The closed and open symbols correspond to
the Π1/2 and Π3/2 spin-orbit states, respectively. The solid line
corresponds to the linear least-squares fit to the data, as described in
the text.
In typical measurements, the delay between the photolysis and
detection laser pulses is maintained at ∼10 ns. In experiments
aimed at detecting longer living excited states, the delay between
the laser pulses is increased to 50 ns. In the second type of
experiments, the REMPI spectra of the fragments are measured
by fixing the photolysis pulse at the maximum of the IR
absorption feature while scanning the detection laser frequency
through the selected A2Σ+(V ) 0) r X2Π(V ) 1, 2, 3) transition.
To determine the rotational state distributions of V * 0 NO
products, the REMPI spectra are fit by using a set of Gaussian
basis functions which reproduces the resolved peaks well. Each
basis function has the experimentally measured 0.4 cm-1 line
width and is centered at the calculated rotational line position
for the A2Σ+(V ) 0) r X2Π(V ) 1, 2, 3) transition. The spectral
line intensities are determined by a least-squares fit using
Tikhonov regularization,35 a procedure that stabilizes the line
intensities in the overlapped region of the spectrum. The line
intensities, each corresponding to a specific NO(ArX) rovi-
bronic transition, are determined for each spectral branch.
Rotational populations are calculated from the intensities by
using linestrengths for fully saturated conditions in the REMPI
detection. The observed linewidth of 0.4 cm-1, which is greater
than the laser bandwidth (0.2 cm-1), supports the saturation
assumption.
2
including the population of the Π1/2 state, obtained from the
2Π1/2/2Π3/2 ratios. The errors in the vibrational distributions
represent primarily the precision in the laser alignment, which
is optimized for each measurement, and variations in laser
intensity at the multiple detection frequencies needed to detect
the different NO(X2Π; V) states.
III. Results and Analysis
Assignment of Vibrational Transitions of the NO Dimer.
Photofragment yield spectra were obtained for each product NO-
(X2Π; V ) 1, 2, 3) state that could be detected. Although the
full 4000-7400 cm-1 range was scanned and the delay increased
to 50 ns, only the vibrational transitions shown in Figure 2 were
observed. cis-(NO)2 has C2V symmetry with the molecule in the
a-b plane and the C2 rotation axis along the b-axis. Therefore,
rovibrational a-type transitions are expected to upper levels of
b2 symmetry, and b-type bands are expected for upper levels
of a1 symmetry.
An example of the experimental REMPI spectrum for NO-
(X2Π; V ) 2), obtained following 5299.1 cm-1 excitation and
its fit, is shown in Figure 1a. Figure 1b shows NO(X2Π; V )
2) rotational state populations obtained by analysis of each
spectral branch and plotted as ln[P(J)/(2J + 1)] vs NO rotational

8410 J. Phys. Chem. B, Vol. 109, No. 17, 2005
Potter et al.
Figure 3. Simulated a-type rotational spectra for the (a) 3ν5, (b) 2ν1 + ν5, (c) ν1 + 3ν5, and (d) 3ν1 + ν5 vibrational transitions. The solid and
dashed plots correspond to the experimental and simulated spectra, respectively. The rotational stick spectra are also shown for comparison. See the
text for details of the simulations.
TABLE 1: Transition Assignments and Comparisons with
Calculationsa
reproduced best both the overall widths of the vibrational bands
and the shapes (peaks and valleys) of the structural features
within each band. Although both increased temperature and
Lorentzian width cause broadening of the spectral features, only
combinations within the ranges specified above give acceptable
simulations of the data.
In summary, all the observed bands could be simulated by
a-type transitions without a significant change in rotational
constants or Lorentzian linewidth. Only the weak band around
7200 cm-1 could not be characterized exclusively as an a- or
b-type band, because of its poor signal-to-noise ratio.
observed origin
calculated origin
(cm-1
exp - calc
(cm-1
assignment
(cm-1
)
)
)
ν5
1789.10b
1868.25c
3559.32d
3626.45d
1790.34
1868.49
3559.32
3626.47
5303.9
5443.3
7075.3
7240.7
-1.24
-0.24
1.01
-0.02
-3.5
6.0
ν1
2ν5
ν1 + ν5
3ν5
2ν1 + ν5
ν1 + 3ν5
3ν1 + ν5
5300.4 ( 0.4e
5449.3 ( 0.4e
7073.4 ( 0.4e
7238.7 ( 0.4e
-1.9
-2.0
To assign the new transitions, we performed a normal-mode
analysis including the known fundamental and first overtone
band origins of the asymmetric N-O stretch (ν5), the N-O
symmetric stretch (ν1), and the ν1 + ν5 combination band as
well as the observed transitions from this work.17,24,28 The
assignments and comparisons of experimental with calculated
values are listed in Table 1. The new bands are tentatively
assigned as 3ν5, 2ν1 + ν5, ν1 + 3ν5, and 3ν1 + ν5. The harmonic
frequencies and anharmonicity constants determined from this
a The harmonic frequencies and anharmonicity constants determined
from this analysis are ω1 ) 1878.2, ω5 ) 1801.5, ø11 ) -9.67, ø55
)
-11.19, and ø15 ) -32.36 cm-1 b Reference 28. c Reference 29.
.
d Reference 17. e This work.
The band origins were determined from spectral simulations.
The new transitions observed in this work were simulated as
a-type transitions (see Figure 3) by using the simulation program
ASYROT.37 In the simulations, published ground-state rotational
constants were used,8 whereas the upper state rotational
constants were approximated using the average of the previously
determined values derived for 2ν5 and ν1 + ν5.17 The spectral
resolution of the measured bands is insufficient for accurate
determination of upper state rotational constants and their
variation with excitation energy. However, values of the band
origins are not affected significantly by small changes in
rotational constants. The derived band origins are listed in Table
1.
Simulations such as those shown in Figure 3 were obtained
for T ) 4 ( 1 K and convoluted with a Voigt profile. The
Gaussian component of the linewidth was set at the 0.4 cm-1
IR laser bandwidth, and it dominated the spectrum. The
Lorentzian component that best fits the data has a width of 0.2
( 0.1 cm-1, corresponding to a lifetime of 36 ( 17 ps. This
value is similar to those measured previously for 2ν5 and ν1 +
ν5.17 Simulations in the ranges given by the error bars
analysis are ω1 ) 1878.2, ω5 ) 1801.5, ø11 ) -9.67, ø55
)
-11.19, and ø15 ) -32.36 cm-1. It should be noted that the
normal-mode analysis used in this assignment, while valid at
low vibrational excitation, is increasingly inadequate for higher
overtones. However, the observed band origins agree rather well
with the normal-mode calculations; moreover, all the upper
vibrational states have b2 symmetry, consistent with observation
of only a-type bands.
Because the vibrational spectra are obtained by measuring
yields of NO(X2Π; V ) 1, 2, 3) products rather than by direct
absorption measurements, we cannot preclude the possibility
that other overtone or combination bands of (NO)2 are excited,
but either their lifetimes are longer than the maximum time
delays achieved in our experiments (50 ns) or dissociation from
these bands generates only NO(X2Π; V ) 0) + NO(X2Π; V )
0). Additionally, we searched but did not find evidence for broad
resonances that could be attributed to direct absorption to

Photoinitiated Predissociation of the NO Dimer
J. Phys. Chem. B, Vol. 109, No. 17, 2005 8411
repulsive electronic states, which according to theory should
lie in this region (the calculated oscillator strength is 2 × 10-6).2
NO(X2Π; W ) 1, 2, 3) Photofragment Yields. Following
dissociation from the N-O stretch second overtone region of
(NO)2 [3ν5 and 2ν1 + ν5, henceforth referred to as (NO)2(m )
3) to denote three quanta of NO stretch], NO(X2Π) fragment
vibrational levels V ) 0, 1, 2 are energetically accessible and V
) 1, 2 are monitored [i.e., NO(V ) m - 2) and NO(V ) m -
1), respectively]. Representative photofragment yield spectra are
shown in Figure 2. Integration and normalization of the spectra
obtained by monitoring V ) 1 and 2 (as described in section II)
give relative populations P(V ) 2)/P(V ) 1) ) 0.97 ( 0.30 and
7.3 ( 0.7 for dissociation from 3ν5 and 2ν1 + ν5, respectively.
The errors in these measurements represent the spread in results
of multiple measurements and the accuracy of the spin-orbit
state distributions. Taking into account the ground-state dis-
sociation energy of (NO)2,38 four channels are energetically
accessible following (NO)2(m ) 3) dissociation:
NO(V ) m - 2), respectively] give relative populations P(V )
3)/P(V ) 2) ) 5.7 ( 0.7 for ν1 + 3ν5, indicating that the major
channel is 5 (∆V ) -1), followed by 7 (∆V ) -2). Again, we
cannot detect NO(X2Π; V ) 0), but considering that NO(X2Π;
V ) 1) is not produced in detectable amounts, channel 10 seems
unlikely. Following 3ν1 + ν5 dissociation, only NO(X2Π; V )
3) can be detected [P(V ) 3)/P(V ) 2) > 10], eliminating every
channel except channel 5. This suggests that ∆V ) -1 is the
dominant pathway.
Product Spin-Orbit State Ratios. Spin-orbit state ratios,
[2Π1/2]/[2Π3/2], for each observed NO(X2Π; V) fragment fol-
lowing dissociation from the (NO)2 vibrational level are listed
in Table 2. The ratio in most cases is near unity, with a slight
preference for the ground 2Π1/2 state. The exception is dissocia-
2
tion via 3ν1 + ν5, which shows a strong preference for Π1/2
.
Previous studies of (NO)2(m ) 1, 2) predissociation13,17 showed
that the main spin-orbit channels were NO(Π1/2) + NO(Π3/2
)
and NO(Π1/2) + NO(Π1/2). Because in almost all cases [Π1/2]/
[Π3/2] > 1, we assume, in analogy with previous findings, that
the excess [Π1/2] derives only from the Π1/2 + Π1/2 channel
(i.e., the Π3/2 + Π3/2 channel is neglected).
(NO)2(m ) 3) f NO(X2Π; V ) 2) + NO(X2Π; V ) 0) (1)
f NO(X2Π; V ) 1) + NO(X2Π; V ) 1) (2)
f NO(X2Π; V ) 1) + NO(X2Π; V ) 0) (3)
f NO(X2Π; V ) 0) + NO(X2Π; V ) 0) (4)
Product NO(X2Π1/2,3/2; W ) 1, 2, 3) Rotational Distribu-
tions. Boltzmann plots [ln[P(J)/(2J + 1)] vs Erot(J)] of product
rotational state distributions are shown in Figure 4. All give
fairly good straight lines, and rotational temperatures are derived
from the slopes of the least-squares linear fits as a measure of
the rotational excitation. Rotational temperatures for both the
NO(V ) m - 1) and NO(V ) m - 2) fragments are listed in
Table 2 for m ) 3 and 4. The percent of energy deposited in
rotation for each dissociation channel is summarized in Table
3. To obtain this estimate, two assumptions are made. First, as
described above, we assume that only the Π1/2 + Π3/2 and Π1/2
+ Π1/2 channels are populated. Second, it is assumed that the
unobserved NO(X2Π; V ) 0) cofragment in each channel is
produced with the same amount of rotational energy as the
observed NO(X2Π; V ) 1, 2, 3) fragment. This assumption is
reasonable when the rotational excitation is low and derives
mainly from transformation of low-lying bending and torsional
levels into rotational wave functions (see section IV). The
average rotational energy per fragment is determined from the
rotational temperature as <Erot> ) kTrot.
where channels 1 and 2 represent ∆V ) -1 dissociation and
channels 3 and 4 represent ∆V ) -2 and ∆V ) -3 processes,
respectively. For each channel, both spin-orbit states for each
NO fragment are energetically allowed.
Dissociation via 2ν1 + ν5 clearly favors channel 1, indicating
that ∆V ) -1 is the predominant pathway. Due to the nature
of the experiments, we cannot distinguish between NO(X2Π; V
) 1) fragments formed via channels 2 and 3. We are also unable
to detect NO(X2Π; V ) 0); however, considering that P(V ) 1)
is much smaller than P(V ) 2), a significant contribution from
channel 4 is unlikely. On the other hand, with 3ν5 dissociation,
P(V ) 2) and P(V ) 1) are nearly identical, suggesting that
dissociation from 3ν5 proceeds via a somewhat different pathway
than ν1 + 2ν5, and that both ∆V ) -1 and ∆V ) -2 NO(X2Π;
V ) 1) producing processes (i.e., channels 2 and 3) may be
important (see section IV).
IV. Discussion
Dissociation from states in the N-O stretch third overtone
region of (NO)2 [ν1 + 3ν5 and 3ν1 + ν5, henceforth referred to
as (NO)2(m ) 4)] can produce NO(X2Π; V ) 0, 1, 2, 3)
fragments. Six channels are energetically possible:
Spectroscopy and Photophysics. The rovibrational bands
assigned in this study were obtained by detecting NO(V > 0)
photofragments. Vibrational levels correlating with two NO(V
) 0) fragments could not be observed, and therefore, the
assignments given in Table 1 are based only on partial
observations and are considered tentative. For example, it is
not clear why the 4ν5 band is not observed. It should also be
borne in mind that a normal-mode basis was used in the analysis.
Although this treatment is valid at low excitation energies, it
should start to fail for high overtones, especially considering
the long N-N bond in the NO dimer (2.236 Å), which may
hinder coupling between the two NO bonds. A more complete
treatment of the spectroscopy should await measurement of the
full absorption spectrum in this region. For the purpose of the
present discussion, however, we consider the agreement between
the experimental and calculated band origins satisfactory, and
in the discussion we use the assignments given in Table 1.
We also note that no significant broadening of the bands with
increasing vibrational excitation is observed, and a similar
Lorentzian width, corresponding to a lifetime of 20-50 ps,
satisfactorily simulates all the bands in the (NO)2(m ) 2-4)
(NO)2(m ) 4) f NO(X2Π; V ) 3) + NO(X2Π; V ) 0) (5)
f NO(X2Π; V ) 2) + NO(X2Π; V ) 1) (6)
f NO(X2Π; V ) 2) + NO(X2Π; V ) 0) (7)
f NO(X2Π; V ) 1) + NO(X2Π; V ) 1) (8)
f NO(X2Π; V ) 1) + NO(X2Π; V ) 0) (9)
f NO(X2Π; V ) 0) + NO(X2Π; V ) 0)
(10)
Unlike (NO)2(m ) 3) dissociation, some of these channels can
be eliminated on the basis of the experimental observations. In
both ν1 + 3ν5 and 3ν1 + ν5 dissociation, no signal from NO-
(X2Π; V ) 1) can be detected; therefore, channels 6, 8, and 9
are eliminated. Integration and normalization of the NO(X2Π;
V ) 3) and NO(X2Π; V ) 2) signals [i.e., NO(V ) m - 1) and

8412 J. Phys. Chem. B, Vol. 109, No. 17, 2005
Potter et al.
TABLE 2: Energy Disposal following (NO)2(m ) 3, 4) Dissociationa
m ) 3
m ) 4
normal mode
3ν5
2ν1 + ν5
ν1 + 3ν5
3ν1 + ν5
b
well depth (cm-1
)
953.3 ( 0.4
0.97 ( 0.3
860.6 ( 0.4
7.3 ( 0.7
971.8 ( 0.4
5.7 ( 0.7
891.0 ( 0.4
>10
184.6 ( 21.4
170.3 ( 27.0
7.62 ( 0.76
P(V ) m - 1)/P(V ) m - 2)
T
T
rot (Π1/2, V ) m - 1) (K)
rot (Π3/2, V ) m - 1) (K)
88.1 ( 5.8
118.1 ( 7.2
83.0 ( 2.9
1.39 ( 0.13
70.2 ( 5.2
126.0 ( 13.8
0.89 ( 0.12
92.7 ( 8.9
62.6 ( 5.9
1.64 ( 0.17
401.7 ( 47.6
540.8 ( 94.0
1.57 ( 0.42
56.5 ( 2.2
[Π1/2]/[Π3/2] (V ) m - 1)
1.21 ( 0.12
141.7 ( 24.3
199.7 ( 27.3
1.13 ( 0.11
T
rot (Π1/2, V ) m - 2) (K)
Trot (Π3/2, V ) m - 2) (K)
[Π1/2]/[Π3/2] (V ) m - 2)
a m denotes the total number of NO stretch quanta in the vibrational state of the dimer. b The well depth is the energy difference between the
separated NO fragments and the observed vibrational transition in (NO)2. See text for details.
Figure 5. Schematic diagram showing the correlation between the
Figure 4. Boltzmann plots for the (a) NO(X2Π1/2; V) and (b)
separated NO(Va) + NO(Vb) fragment channels and the observed (NO)2
NO(X2Π3/2; V) fragments following dissociation from different vibra-
N-O stretch vibrations. Both normal- and local-mode vibrational
tional transitions. The solid line corresponds to a linear least-squares
assignments are marked. The corresponding well depths are given in
fit to the data, and the slope is proportional to the rotational temperature
Table 2.
of the fragment. The NO dimer and NO vibrational levels that
correspond to each plot are given next to each symbol.
ONN bend, as is typical in van der Waals clusters. The overall
TABLE 3: Estimated Average Rotational Energy in NO(Wa)
and NO(Wb)a
tendency to favor processes in which one vibrational quantum
is lost is also typical of predissociation of van der Waals
complexes.
Eavl([Π1/2] + [Π3/2])
(cm-1
<Erot>/Eavl
(NO)2 (V)
3ν5
Va
Vb
)
(%)
In the predissociation of van der Waals complexes, the
spectral shift of a vibrational transition is often proportional to
the strength of the potential coupling between the intramolecular
and van der Waals modes.39 By analogy, the coupling strength
between the NO stretch modes and the dissociative N-N
coordinate in (NO)2 may be related to the frequency shift, and
hence to the well depths of the (NO)2(m ) 3, 4) complexes.
The well depth is defined here as the difference between the
energy of the separated NO(Va) + NO(Vb) product pairs and
the energy of the observed vibrational transition in (NO)2. Figure
5 depicts schematically several such plots, where the spin-
orbit splitting in NO(X2Π) is suppressed. In the plots, the NO-
(Va) + NO(Vb) pairs that correlate with the lowest levels in a
local mode description of the NO stretch vibrations, [Va, Vb],
are also shown. Although the observed transitions were assigned
using a normal-mode basis where the N-O motions are coupled,
1
1
2
1
1
2
2
3
3
0
1
0
0
1
0
0
0
0
2588.2
712.4
740.3
2739.6
863.8
891.7
2513.7
693.9
859.9
9
32
14
5
17
16
24
16
26
2ν1 + ν5
ν1 + 3ν5
3ν1 + ν5
a The estimates were obtained assuming that only the Π1/2 + Π1/2
and Π1/2 + Π3/2 channels are significant and that the rotational
temperatures of NO(Va) and NO(Vb) are similar.
region. Thus, no evidence of state-specific strong couplings to
excited electronic states is obtained. Rather, the predissociation
rates appear to be determined mostly by the coupling between
the NO and N-N stretch coordinates, either directly or via the

Photoinitiated Predissociation of the NO Dimer
J. Phys. Chem. B, Vol. 109, No. 17, 2005 8413
when the NO monomers are at large distance, the coupling
between the two NO motions is weakened, and a local-mode
model becomes more appropriate. The NO(Va) + NO(Vb)
fragments correlated with the observed (NO)2 vibrational levels
were determined from the normal-local mode correlation
diagram given elsewhere40 and are listed in Figure 5. The well
depths are given in Table 2 and, as expected, are greater for
vibrational levels with multiple quanta of ν5.
+ NO(X2Π) threshold, which takes place on an electronically
excited state that is bound by at least 3600 cm-1 9,10
The product
.
rotational energies from this more strongly bound potential are
apportioned rather statistically, as is typical of barrierless
vibrational predissociation mechanisms, except that the low-
frequency torsional mode couples less effectively to the other
modes.9,10 In contrast, the rotational distributions in ground-
state dissociation of the NO dimer, which is bound by 710 cm-1
,
cannot be interpreted by invoking either statistical or impulsive
Predissociation. One of the goals of the present work was
to find direct or indirect signatures of the participation of the
seven electronically excited states, which are calculated at <1
eV in the vertical Franck-Condon region and correlate with
ground-state NO(X2Π) products. The vibrational levels of b2
models.17
The low level of product rotational excitation is characteristic
of expansion of low-level wave functions of “disappearing
vibrational modes” (e.g., bending and torsion) into rotational
degrees of freedom.43 This is also the explanation given for
lower parent excitations (m ) 1, 2), where between 3 and 12%
of the available energy is deposited in rotation.13,17 Referring
to excitation channels that derive from ∆V ) -1 processes, such
as channels 1 and 5 (see below), and assuming that the energy
available to rotation is partitioned equally between NO(V ) 0)
and NO(V ) Vi) products, which is reasonable for this mecha-
nism, we find that between 14 and 26% of the available energy
is deposited in product rotation (Table 3). This suggests that a
similar mechanism is responsible for rotational excitation
throughout the entire energy range. The rotational energy is
higher for the ∆V ) -2 process (channel 7), probably because
more energy is available for distribution in rotation and
translation.
3
symmetry excited in this study may couple to the A2 excited
electronic state by spin-orbit coupling (vertical excitation
energy is 4402 cm-1) or to either the 1B1 or 1A1 excited
electronic states by Coriolis coupling (vertical excitation energies
of 2433 and 3624 cm-1, respectively).1,2 The similarity of the
energy disposal patterns for predissociation via vibrational levels
excited at 1800-7300 cm-1 argues against state-specific nona-
diabatic transitions in the Franck-Condon region. More likely,
the couplings between surfaces correlating with Π1/2 + Π3/2
and Π1/2 + Π1/2 products, which are separated asymptotically
by 123 cm-1, take place in the flat, long-range part of the
potential near the asymptotic region, where coupling matrix
elements have magnitudes similar to the energy separations of
surfaces.
Previous studies have shown that m ) 1, 2 excitations lead
Extending the studies of vibrational predissociation to higher
overtones allows us also to examine the relative importance of
∆V ) -1 and -2 processes and the disposition of vibrational
energy in the two NO moieties. We find that, except for the
case of excitation of 3ν5 discussed below, ∆V ) -1 processes
are dominant and most of the excitation resides in one NO
product. A comparison with the self-relaxation of NO(V), in
which transient (NO)2 formation is invoked, is instructive.44-51
to probabilities of producing the excited NO(Π1/2) + NO(Π3/2
)
channel that range from 0.58 to 0.95.13,17 Almost no fragments
are produced via the Π3/2 + Π3/2 channel. With the exception
of 3ν1 + ν5, which shows a large preference for the lower spin-
orbit states, the spin-orbit ratios obtained in the present study
following dissociation in the second and third overtone regions
(m ) 3 and 4) are rather similar to those in the m ) 1 and 2
regions. Thus, the spin-orbit ratios do not show clear trends
with increasing NO dimer vibrational excitation, though the Π1/2
+ Π3/2 channel appears favored in many of the levels, indicating
that nonadiabatic interactions can be quite efficient.
The slightly endothermic vibration-to-vibration (V-V) energy
transfer in 300 K NO collisions has long been attributed to long-
range multipole interactions between NO collision partners.44-46
The unusually rapid vibrational-to-translational (V-T) relaxation
rate has been explained by strong attractive forces between the
NO radicals.46 Below 80 K, where endothermicity prohibits
V-V transfer, V-T energy transfer plays the dominant
role.44,45,50 Specifically, Smith and co-workers studied the
vibrational relaxation rates in NO(X2Π; V ) 3) + NO(X2Π; V
) 0) collisions down to 7 K and found that the relaxation rate
increases strongly with decreasing temperature. They proposed
that transient formation of the NO dimer takes place with
lifetimes with respect to predissociation that are sufficiently long
for energy transfer to occur.50 Smith and co-workers concluded
that the high relaxation rates were dominated by V-T energy
transfer, rather than V-V energy exchange.50 This explains the
dominance of processes in which vibrational excitation is not
apportioned statistically among the two NO moieties, such as
we observe in m ) 4 excitation, and suggests that a significant
source of NO(V ) 1) from (NO)2(m ) 3) dissociation would
be channel 3.
This behavior is typical of spin-orbit couplings that take
place in the asymptotic region, where several electronic states
coalescence toward product channels that are close in energy.
For example, in the barrierless unimolecular reaction of several
NO-containing molecules (e.g., NO2, NCNO, tert-butyl NO),41,42
where the rotational and vibrational degrees of freedom are
apportioned statistically, the product spin-orbit states are
generated with nonstatistical distributions that vary from
molecule to molecule with no particular trend. This has been
interpreted as an indication that the requisite nonadiabatic
transitions take place near the asymptotic region of the potential,
after the rovibrational distributions have been established, with
the size of the coupling matrix elements and the extent of the
crossing seam determining the final outcome.42
The mechanism that determines the vibrational and rotational
energy disposal in the overtone excitation of the NO dimer is
similar to that in vibrational predissociation of van der Waals
clusters, despite the covalent nature of the N-N bond. ∆V )
-1 processes dominate, and the time scale for dissociation is
determined by the coupling between the NO stretch excitation
and the N-N reaction coordinate, either directly or via the ONN
bend.
For m ) 3 excitation, we first discuss 2ν1 + ν5 dissociation.
In this case the V ) 2/V ) 1 population ratio is quite high (7.3),
and the rotational temperatures of V ) 2 and V ) 1 are similar
(Table 2). Referring to results obtained in ν1 + 3ν5 excitation,
in which ∆V ) -1 and ∆V ) -2 processes are clearly
distinguished, we note that the rotational temperature of
fragments generated by the ∆V ) -1 process is significantly
lower than that generated via ∆V ) -2. This suggests that the
The “cold” rotational distributions following overtone stretch
excitation can be compared and contrasted with our recent work
on the photodissociation of the NO dimer near the NO(A2Σ+)

8414 J. Phys. Chem. B, Vol. 109, No. 17, 2005
Potter et al.
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rather small fraction of V ) 1 that is generated in 2ν1 + ν5
dissociation derives from channel 2 (∆V ) -1) rather than
channel 3.
The situation following excitation of 3ν5 is different. Here,
the vibrational population is divided equally between V ) 2
and V ) 1, and the rotational temperature of V ) 1 is higher
than that of V ) 2, as is more typical of ∆V ) -2 processes.
We therefore suggest that the contribution of channel 3 to 3ν5
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dissociation involving multiple quanta of ν5, a mode that is
coupled more strongly to the bending mode and the N-N
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V. Summary
The IR predissociation of the NO dimer was studied in the
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3ν5, and 3ν1 + ν5. The observed levels involve only excitation
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Vibrational, rotational, and spin-orbit distributions were
determined for all of the observed product NO states. The major
dissociation pathway involves ∆V ) -1, as is typical of systems
where the coupling between the high- and low-frequency modes
is weak. ∆V ) -2 processes are more prevalent in predisso-
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and ∆V ) -2 processes, while the former is the main source
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The products’ spin-orbit ratios show a slight preference for
the ground X2Π1/2 level, and in analogy with previous results,
it is suggested that the dominant channel is X2Π1/2 + X2Π3/2
.
The similarity of the spin-orbit ratios in excitation of most of
the NO dimer vibrational states points to the long-range part of
the potential in the N-N coordinate as the locus of nonadiabatic
transitions to electronic states correlating with excited product
spin-orbit states. Thus, it appears that vibrational nonadiabatic
coupling following V-T transfer takes place at shorter N-N
separations, while the spin-orbit ratios are determined at long
range, where several potential curves coalesce. No evidence of
direct excitation to electronic states whose vertical energies lie
in this energy region is obtained.
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Acknowledgment. We thank Lin Feng and Vladimir Drib-
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Science Foundation and the donors of the Petroleum Research
Fund, administered by the American Chemical Society, is
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