Journal of Electron Spectroscopy and Related Phenomena 142 (2005) 193–205
Ultrafast dissociation processes in the NO dimer studied with
time-resolved photoelectron imaging
Masaaki Tsubouchia , Cornelis A. de Langeb , Toshinori Suzukia,∗
b
a Chemical Dynamics Laboratory, RIKEN, Wako 351-0198, Japan
Laser Centre, Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081,
1081 HV Amsterdam, The Netherlands
Available online 13 November 2004
Abstract
Ultraviolet photodissociation of the NO dimer is studied with femtosecond time-resolved photoelectron imaging (TR-PEI) spectroscopy.
Pump pulses in the range 200–235 nm are employed, while probe pulses are kept at 300 nm. The time dependencies of the observed photoelectron kinetic energies and photoelectron angular distributions support a picture in which valence state optically excited in the dimer evolves
on a time scale of <1 ps to the dimer 3s Rydberg state. This dimer Rydberg state then undergoes fragmentation on a time scale of a few ps.
In this study we focus on dissociation into an NO ground state fragment and an NO fragment in its 3s Rydberg A2 + state. Every stage of
this continuous process, viz. the dimer valence state, the dimer 3s Rydberg state, the separating NO(X) + NO(A) fragments, and the isolated
NO(A) fragment is interrogated with TR-PEI.
© 2004 Elsevier B.V. All rights reserved.
Keywords: Ultraviolet; TR-PEI spectroscopy; NO; NO dimer
1. Introduction
Nitric oxide (X2 ) has an unpaired electron in its ␲∗2p
highest occupied valence orbital. When two NO molecules
approach each other, these anti-bonding orbitals on each fragment overlap to form a weak chemical bond. This interaction
is largest when the two NO molecules are aligned parallel to
each other [1], and in fact the structure of the NO dimer in its
ground electronic state has been determined to be cis-planar
with C2v symmetry [2]. The strength of the bond is about
700 cm−1 [3], intermediate between a van der Waals bond
and a covalent bond.
Little is known about excited electronic states of the NO
dimer. The far ultraviolet (UV) absorption spectrum is quite
diffuse, with a maximum at ∼205 nm, and extends to 240 nm
[4,5]. Recent work employing fluorescence excitation spectroscopy with synchrotron radiation resolved some vibrational structure in the absorption spectrum, but the inherent
∗
Corresponding author. Fax: +81 48 467 1403.
E-mail address: toshisuzuki@riken.jp (T. Suzuki).
0368-2048/$ – see front matter © 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.elspec.2004.09.013
broadness still remained [6]. The multitude of excited electronic states of the dimer that are expected to contribute to
these absorption features have not been characterized. Moreover, no detailed electronic structure calculations have been
performed so far on the excited states present in this energy
region of the NO dimer.
From the heat of formation of the NO dimer, and the
electronic excitation energy in NO, it is anticipated that the
photoexcited NO dimer dissociates into NO(X) + NO(X),
NO(A) + NO(X), or NO(B) + NO(X) depending on the excitation wavelength. Since the 1980s Kajimoto et al. have
performed extensive studies on the energy partitioning and
vector correlation in 193 nm photodissociation of the NO
dimer [7–9]. This effort has been more recently extended by
Reisler and coworkers to dissociation at longer wavelengths
using velocity map imaging [10,11]. In 1986, Kimura and
coworkers have applied their one-color laser photoelectron
spectroscopy to the NO dimer. They observed clear signatures of photoionization from the NO monomer in its A state
[12], produced by photodissociation of the dimer within a
laser pulse duration (∼10 ns). The result indicated that dis-
194
M. Tsubouchi et al. / Journal of Electron Spectroscopy and Related Phenomena 142 (2005) 193–205
sociation occurs in a time much shorter than a nanosecond.
In fact, Naitoh et al. have observed strong angular anisotropy
of NO photofragments, from which the lifetime of the photoexcited NO dimer was speculated to be a fraction of its
rotational time period [9].
For the detailed study of dissociation in real time,
photoelectron spectroscopy combined with ultrafast laser
spectroscopy is a very powerful tool. The combination of
photoelectron spectroscopy with the pump–probe technique
has started in the 1980s with nanosecond time resolution
and has been extended to the picosecond and femtosecond
regime [13]. The first such experiment on the NO dimer was
by Blanchet and Stolow who employed femtosecond timeof-flight (TOF) ion and photoelectron detection, with a pump
wavelength of 210 nm and a probe of 287 nm [14]. More
recently, we performed time-resolved ion and photoelectron
imaging on 200.5 nm photodissociation of the NO dimer
[15]. These experiments were interpreted in terms of initial
excitation to one or more valence states of the NO dimer.
An almost isotropic distribution with a broad energy width
changed to a strongly anisotropic angular distribution with
a narrow energy width, which indicated formation of the 3s
Rydberg state of the dimer and, at later times, monomer fragments.
In this paper, experimental results from an extensive
femtosecond time-resolved pump–probe photoelectron
imaging (TR-PEI) spectroscopic study on the NO dimer
are summarized. Various aspects of photoionization of the
NO monomer relevant to the dimer experiments are also
discussed, to clarify the effects of multiphoton ionization
and rotationally coherent excitation that might obscure the
experimental observation of ultrafast reaction dynamics.
These experiments constitute an excellent example of the
detailed information that can be obtained with sophisticated
methods of photoelectron spectroscopy for excited states in
molecular species. The valence states excited in the dimer
evolve on a time scale of <1 ps into the dimer 3s Rydberg
state. This dimer Rydberg state then undergoes fragmentation on a ps time scale into an NO ground state fragment and
an NO fragment in its 3s Rydberg A2 + state. Every stage
of this dissociation process, that starts with optical excitation
of a valence state in the NO dimer and ends with NO(X)
and NO(A) fragments being fully separated, is tracked with
TR-PEI.
This special journal issue is devoted to Professor Kimura
who belongs to the pioneers of photoelectron spectroscopy.
It is therefore fitting to focus in this contribution on what
novel time-resolved experimental methods in photoelectron
imaging [13] can contribute to our understanding of intricate
competing excited state decay processes that occur on an
ultrafast time scale. The simultaneous time-resolved observation of photoelectron kinetic energy distributions (PKEDs)
and photoelectron angular distributions (PADs) in the same
experiment is a unique feature of the technique and generally
leads to novel information on molecular species of chemical
and physical interest such as the NO dimer.
2. Experimental
In this paper, we shall describe three experiments: (i)
one-color three-photon ionization of the NO monomer;
(ii) two-color (1 + 1 ) REMPI via the A state of the NO
monomer; and (iii) two-color (1 + 1 ) REMPI of the NO
dimer. The first two are relevant for the selection of
appropriate probe laser wavelengths in the third experiment.
The femtosecond laser system used is the same as in
our previous work [15–17]. A schematic diagram of our
experimental set up is presented in Fig. 1. The output of a
YVO4 -pumped Ti:Sapphire oscillator was amplified by a
Nd:YLF pumped regenerative amplifier to generate a 1 kHz
pulse train centered at 802 nm. This light was split into two
equal intensity beams that pumped two commercial optical
parametric amplifiers (OPAs) to generate tunable UV light.
In experiment (i), the output of one of the OPAs was used for
the ionization light. The UV light in the range 320–330 nm
was focused by a quartz lens with a focal length of 500 mm,
and directed into the molecular beam chamber. An iris
inserted into the optical path was used to control the laser
power entering the chamber. The typical pulse energy was
less than 10 ␮J/pulse. In experiments (ii) and (iii), the tunable
pump pulse (200–235 nm) used to excite the NO monomer or
dimer from their respective ground states was generated by
sum-frequency generation in a thin BBO I crystal (0.5 mm
thickness), using the fundamental light from the regenerative
amplifier and UV light in the range 265–335 nm from one
of the OPAs. The probe pulse was derived from another
OPA. The pump and probe pulses were focused by quartz
lenses with focal lengths of 450 mm (pump) and 300 mm
(probe), respectively. The pump and optically delayed probe
pulses were directed into the chamber with a small angle
(<1◦ ) between their k vectors and spatially overlapped with
the molecular beam. The laser power of the pump and
probe beams were adjusted so as to obtain the best contrast
ratio for the two-color photoion signal, as monitored by
the current from a microchannel plate (MCP) detector. The
typical pulse energies were less than 1 ␮J/pulse for the pump
pulse and ∼3 ␮J/pulse for the probe pulse. Polarization
directions of the pump and probe lasers were parallel to
each other and to the face of the charged particle imaging
detector.
Photoelectrons produced by the probe laser pulse were
accelerated up to a kinetic energy of ∼2 keV in an electric
field parallel to the molecular beam and projected onto a
position-sensitive imaging detector. The electric field formed
an immersion lens that focused the electrons spatially such
that the image only reflected the electron momentum parallel
to the detector face [18]. The field-free region (45 cm) was
shielded with a ␮-metal tube to avoid an external magnetic
field. The imaging detector consisted of a dual microchannel
plate backed by a phosphor screen (40 mm in effective
diameter), and a slow-scan charge-coupled device (CCD)
camera (512 × 512 pixels). The photoelectron images on
M. Tsubouchi et al. / Journal of Electron Spectroscopy and Related Phenomena 142 (2005) 193–205
195
Fig. 1. Schematic diagram of the experimental set up. In (1 + 1 ) REMPI experiments, the pump pulse was generated by sum-frequency generation
ωpump = ω0 + ω1 with a BBO I crystal.
the phosphor screen were captured by the camera and
integrated for 6 × 105 laser shots. The observed electron
images were transformed back to the 3D photoelectron
scattering distributions by an inverse Abel transformation.
Nitric oxide 16% in He (experiments (i) and (ii)) or 5% in
Ar (experiment (iii)) was expanded continuously into a source
chamber from a pinhole 50 ␮m in diameter at a stagnation
pressure of 1.5 or 2.5 atm, respectively. The jet was skimmed
and introduced into the ionization chamber as a supersonic
molecular beam 1 mm in diameter. The source and main
chamber pressures were 3.0 × 10−4 and <1.0 × 10−7 Torr,
respectively. The rotational temperature of NO in the beam
was determined to be 7–10 K in He and 3–5 K in Ar by
(1 + 1) REMPI spectroscopy of NO via the A state with a
nanosecond laser. In experiment (iii), consistent results were
obtained with the carrier gases of He and Ar, which ruled
out any contribution from NO-rare gas complexes. This is
illustrated in Fig. 2 where the time dependence of photoelectron kinetic energy distributions is shown for NO/He and
NO/Ar mixtures with a pump wavelength of 200 nm and a
probe wavelength of 300 nm. Since formation of the NO
dimer is not efficient in the NO/He mixture, the contribution of the non-resonant two-photon ionization of the NO
monomer appears around zero time delay. Except for this
contribution, both results are identical, indicating that the
role played by NO/Ar complexes in our results is negligible.
3. Results and discussion
3.1. Wavelength dependence of one-color multiphoton
ionization
In general, multiphoton ionization can occur efficiently
with short laser pulses. In order to perform reliable
pump–probe experiments, it is important to choose laser
wavelengths that do not induce strong one-color signals. To
demonstrate this, we present here the one-color photoionization of NO in the wavelength region of 320–330 nm. Fig. 3(a)
shows the ionization scheme used. The images shown in
Fig. 4(a) are inverse Abel transforms of the observed photoelectron images, corresponding to slices through the 3D
scattering distributions of photoelectrons. The polarization
vector of the laser beam is vertical in the plane of the figure.
Except for the image obtained with 325 nm light, all images
consist of progressions of anisotropic sharp rings. On the
other hand, the strong sharp ring that appears in the image
taken at 325 nm is quite isotropic, indicative of a coincidental resonance at the two-photon level. The candidate for this
resonant state is the ν = 4 level of the C(2 ) state which is
located at 7.65 eV above the X(2 1/2 ), ν = 0 state. This state
possesses a 1 + core and a Rydberg 3p␲ electron.
Fig. 4(b) represents the PKEDs extracted from the images
shown in Fig. 4(a). All peaks were easily assigned to the vibrational levels of the NO+ X(1 + ) final state. The vibrational
progressions were seen to peak at ν+ = 0 in all PKEDs. This
196
M. Tsubouchi et al. / Journal of Electron Spectroscopy and Related Phenomena 142 (2005) 193–205
Fig. 2. Time dependence of the photoelectron kinetic energy distributions obtained from samples of: (a) a NO/He 16% mixture at 3.2 atm; and (b) a NO/Ar 5%
mixture at 2.3 atm. The pump and probe laser wavelengths are 200 and 300 nm, respectively. Except for the contribution of non-resonant two-photon ionization
of the NO monomer around zero time delay in the NO/He mixture, both results are the same. This implies that the influence of NO/Ar complexes on our results
is negligible.
intensity distribution differs from the PKED obtained by the
single-photon ionization with a He(I) light source [19], where
the transition to ν+ = 1 dominates. It is noted that in a zero
kinetic energy pulsed field ionization (ZEKE-PFI) study with
two-photon non-resonant ionization [20], the ν+ = 0 band of
NO+ is also the most intense, in agreement with our PKED
obtained with non-resonant three-photon ionization. This result indicates that the PKED observed in non-resonant multiphoton ionization is not governed by the Franck–Condon
overlap between the ground neutral and ionic states, but is
strongly affected by the virtual states passed through in the
ionization process.
The coincidental one-color (2 + 1) REMPI process at
325 nm accesses C(2 ), ν = 4. One-photon ionization from
this excited Rydberg state is expected to obey ν = 0 propensity. Indeed, the vibrational excitation is predominantly conserved, leading to ionization to the NO+ (1 + ), ν+ = 4 final
state.
The PADs for the ν+ = 0 and 4 components of the images
taken with 320 and 325 nm light are shown in Fig. 4(c). The
dots represent our experimental results, and the solid lines
show the least-squares fits to
I(θk ) ∝ 1 + β2 P2 (cos θk ) + β4 P4 (cos θk ) + β6 P6 (cos θk ),
(1)
Fig. 3. Experimental scheme of the photoionization of the NO monomer for:
(a) one-color three-photon ionization; (b) (1 + 1 ) REMPI via the A state.
where I(θ k ) is the observed intensity, Pn (cos θ k ) are Legendre
polynomials of degree n, and βn are the anisotropy parameters. The scattering angle θ k is measured from the polarization
axis of the laser beam. The PAD for ν+ = 0 is anisotropic
in the direction of the polarization vector, while that for
ν+ = 4 is quite isotropic. The anisotropy parameters extracted from the fitting are β2 = 2.10 ± 0.06, β4 = 0.74 ± 0.09,
and β6 = −0.16 ± 0.10 for ν+ = 0, and β2 = −0.04 ± 0.05,
β4 = 0.17 ± 0.05, and β6 = 0.02 ± 0.06 for ν+ = 4. The method
used for our error analysis has been described in a previous paper [21]. The isotropic PAD for ν+ = 4 observed with
M. Tsubouchi et al. / Journal of Electron Spectroscopy and Related Phenomena 142 (2005) 193–205
197
Fig. 4. (a) Photoelectron images of the NO monomer measured in one-color three-photon ionization with 320, 322.5, 325, and 330 nm light. These images
are slices through the 3D photoelectron scattering distributions obtained by inverse Abel transformation of the original images. The polarization vector of the
laser beam is vertical in the plane of the figure; (b) PKEDs extracted from the images; (c) PADs for the ν+ = 0 and 4 components of the images taken with 320
and 325 nm light, respectively. The dots represent experimental results, and the solid lines are the least-squares fits of the experimental PADs to an expression
which includes Legendre polynomials up to sixth order.
325 nm light strongly supports the assignment of the intermediate state to C(2 ), since in an atomic-like picture the
interference between the s and d outgoing waves originating from one-photon ionization of the 3p␲ Rydberg electron
would tend to reduce the anisotropy in the PAD.
In order to suppress one-color multiphoton ionization
in our TR-PEI, the probe wavelength was chosen to be
off-resonant with the excited state and the laser power was
reduced as much as possible not to induce off-resonant
three-photon ionization processes.
3.2. Probe wavelength and the effect of rotationally
coherent transients
Photoexcitation using polarized broad-band laser light
creates an aligned ensemble of molecules through creation of
a non-stationary superposition of different J states accessed
via the P, Q, and R branch transitions when a single photon is
employed [22,23]. The alignment created rapidly diminishes
due to dephasing of these J components, known as anisotropy
decay. In the gas phase, rotational dynamics processes are
periodic, and the diminishing alignment revives at regular
intervals due to rephasing of the J components.
Any ultrafast pump–probe experiment is subject to such
rotational coherence dynamics. On the one hand, this is useful
because detection of such periodic modulations of the molecular alignment provides a way of determining rotational con-
stants of complex molecules. This technique is known as rotational coherence spectroscopy [22–24]. On the other hand,
this effect is problematic in that it potentially complicates the
experimental observation of transients from which information on ultrafast reaction dynamics must be extracted. In order
to avoid such complications, in one-photon pump and onephoton probe experiments a magic-angle alignment of the
pump and probe laser polarizations is sometimes employed.
This particular experimental arrangement cannot be utilized
in our pump–probe photoelectron imaging experiment. To
ensure the cylindrical distribution of photoelectrons around
the polarization vector of the light required for performing an
inverse Abel transform, pump and probe polarizations must
be chosen parallel to each other.
In the case of photoionization, the integral cross section
is not particularly sensitive to the molecular alignment: as
far as we know, only one example has been reported by
Riehn et al. for observation of alignment effect in the integral
cross section [25]. This is in contrast to the situation with
bound-bound transitions where the transition dipole moment
direction is well defined in the molecular frame, making the
transition sensitive to molecular alignment in the laboratory
frame. In photoionization, transition dipole moments with
different directions can coexist, since the final state of the
transition has continuum character where various outgoing
partial waves can fulfil the symmetry, energy, and angular
momentum requirements. Therefore, ionization almost al-
198
M. Tsubouchi et al. / Journal of Electron Spectroscopy and Related Phenomena 142 (2005) 193–205
ways occurs with similar magnitudes from differently aligned
molecules.
On the other hand, photoionization differential cross sections show at least some sensitivity to molecular alignment,
as these observables reflect the partial wave composition in
the outgoing photoelectron wavefunction [26]. Thus, if one
attempts to observe only the effect of ultrafast reaction on the
time-dependent photoelectron angular distribution, a probing
scheme that is insensitive to molecular axis alignment of the
product will be useful.
Time-dependent molecular axis alignment is generally expressed by an expansion into a series of spherical harmonics:
P(θ, t) =
AK0 (t)YK0 (θ, φ),
(2)
K
where YK0 (θ, φ) are the Kth order spherical harmonics, and
AK0 (t) the time-dependent alignment parameters. The angles
(θ, φ) are measured from the polarization axis of the pump
laser. When the alignment is created by an n-photon excitation, the expansion terms are limited to those with K = 0, 2,
. . ., 2n. In one-color excitation, the axis distribution is cylindrically symmetric and does not depend on the azimuthal
angle.
When the aligned state is ionized by one-photon of probe
light whose polarization is parallel to that of the pump light,
the PAD in the laboratory frame (LF-PAD) is described as
I(θk , t) ∝
βL (t)PL (cos θk )
L
= 1 + β2 (t)P2 (cos θk ) + · · · + βK+2 (t)PK+2 (cos θk ), (3)
where the anisotropy parameters βL are related to the alignment parameters AK0 as follows [27,28]:
√
2L + 1 βL (t) =
aKL0 AK0 (t).
(4)
σ(t)
K
In this expression, σ(t) = K aK00 AK0 (t) is the integral
cross section, and aKL0 includes all information on the ionization dynamics.
Fig. 5(a) shows the calculated alignment parameters in
the A(2 + ) state of NO, created by one-photon excitation
from the X(2 1/2 ) state. In this calculation a rotational
temperature of 5 K was assumed. The absolute values of the
alignment
parameters are such
√ that A20 /A00 reaches its largest
√
(2/ 5) or smallest (−1/ 5) magnitude, when molecules
are aligned parallel or perpendicular to the polarization axis
of the pump laser, respectively [23,27]. Since the ← transition is perpendicular in character, the molecular axes
are aligned perpendicular to the polarization direction
immediately following one-photon excitation. Subsequently,
the molecular axis alignment evolves periodically with a half
revival time of 4.2 ps and a full revival time of 8.4 ps in the A
state. The revival time in ns is given by τ revival = 1/2B, with B
the rotational constant in GHz. The rotational constant of the
NO(A) state is 59.85 GHz [29]. Fig. 5(b) and (c) shows the
Fig. 5. (a) The calculated alignment parameter, A20 /A00 , in the A state of the
NO monomer created by one-photon excitation from the X(2 1/2 ) state at
a rotational temperature of 5 K; (b) time-dependent anisotropy parameters
β2 ; (c) β4 , observed in (1 + 1 ) REMPI with 226 nm pump and 323, 305,
285, and 255 nm probe laser wavelengths, are shown. The dots represent
experimental results, and the solid lines are the least-squares fits to Eq. (4).
time-dependent anisotropy parameters observed in (1 + 1 )
REMPI obtained with different probe laser wavelengths.
The features arising from the rotational wave packet motion
are clearly identified in the figure at ∼4.2 and 8.4 ps. Note
that the sign and depth of the modulation changed gradually
as the probe wavelength was changed. This implies that the
ionization dynamics of the NO+ (X) ← NO(A) transition
depend intricately on the probe laser wavelength, i.e. on the
photoelectron kinetic energy. A detailed analysis of the corresponding ionization dynamics is discussed elsewhere [17].
As shown in Fig. 5, the anisotropy parameters exhibit
periodic variations reflecting the rotational recurrences of
the molecular axis alignment. However, the depth of the
observed modulation becomes almost negligible at a pump
laser wavelength of 305 nm. As far as the NO(A) fragment
is concerned, the use of 305 nm as a probe wavelength
minimizes the effect of molecular axis alignment on the
anisotropy of the observed PADs. It should be noted that
this does not ensure that ionization of the NO dimer at
305 nm is neither sensitive to molecular axis alignment:
although the rotational constants of the excited state(s) of
the NO dimer are not known, the ground state values of B
∼ 5 GHz lead to a rotational dephasing time of ∼1 ps at a
rotational temperature of 30 K. This time scale is comparable
to the reaction time. The rotational dephasing of the NO
dimer prior to dissociation would reduce the anisotropies of
photofragment angular distributions [9,10,15]. On the other
hand, the photoelectron angular anisotropy may increase on
femtosecond or picosecond time scales despite the rotational
dephasing, if electronic dephasing occurs in the dimer.
M. Tsubouchi et al. / Journal of Electron Spectroscopy and Related Phenomena 142 (2005) 193–205
Fig. 6. Experimental scheme of the (NO)2 photodissociation.
3.3. Ultraviolet photodissociation of the NO dimer
3.3.1. Time dependence of the integral ionization cross
section
A schematic diagram of our pump–probe experiments
on the NO dimer is depicted in Fig. 6. Experiments are
performed with a variable pump wavelength in the range
200–235 nm and a fixed probe wavelength of 300 nm. The
far ultraviolet (UV) absorption spectra were observed and
found to be diffuse, with a maximum at ∼205 nm [4,5].
To obtain insight into the nature of the excited states, we
performed SAC-CI calculations [30] by employing the
Gaussian’03 package [31] with a 6–31 + G* basis set. The
molecular structure of the NO dimer is fixed to cis-planar
with C2v symmetry (located in the yz plane). The N-N axis is
defined as the y-axis following the convention. Calculations
predict an electronic state with B2 symmetry at a vertical
excitation energy of 5.97 eV (208 nm) from the ground state.
The calculated transition dipole moment lies along the N N
bond, in agreement with what was concluded experimentally
[9,10,15]. The character of this excited state is predominantly
one-electron promotion from the bonding orbital ␲∗2p + ␲∗2p
with a1 symmetry to the repulsive valence orbital ␲∗2p − ␲∗2p
with b2 symmetry (note that 2p is the notation of the p orbital
of the NO moiety, with this orbital located in the yz plane).
Although the experimentally observed maximum of UV photoabsorption of the NO dimer lies around 205 nm, we do not
expect that ab initio calculations at this level are sufficiently
accurate to compare with experimental results. However,
judging from the oscillator strength that is much greater
than those to neighboring electronic states, it is likely that
UV excitation of the dimer prepares this valence state. More
accurate preliminary ab initio EOM-CCSD calculations were
carried out by Levchenko and Krylov with 6-311(2+, 2+)G**
and 6–311(2+, 2+)G(2df, 2pd) basis sets which take the interactions between valence and Rydberg states into account (see
discussion in [11]). They found two adiabatic states with B2
symmetry with large oscillator strengths of ∼0.45 and ∼0.2
at vertical excitation energies of 6.1 and 6.4 eV above the
ground electronic state. These two states result from config-
199
uration interactions between a 3py Rydberg state and valence
states, in which the oscillator strengths are carried by valence
characters.
In the case of the NO dimer the geometry is such that
there exist symmetry operations under which the monomers
are exchanged. Excitation of the dimer can then be viewed as
excitation of either monomer fragment, leading to two excited
states of the dimer that are degenerate in first order. However,
in such a picture these initially degenerate vibronic states are
coupled through the so-called exciton coupling. For the purpose of our discussion two effects are expected. First, excited
vibronic energy levels may shift. Secondly, the selection rules
associated with transitions from the ground state to these vibronically coupled excited states are relaxed, and intensities
are affected. In order to make reliable predictions the strength
of the exciton coupling is important [32]. In many ways the
situation is reminiscent of the well-known Jahn–Teller effect.
The dissociation channel (NO)2 * → NO(X2 ) +
NO(A2 + ) is energetically open for pump wavelengths
shorter than ∼223 nm. For λpump > 223 nm, the only available ionization channel is from the NO dimer to (NO)2 + .
The (NO)2 + photoions, however, can partly dissociate
into NO(X2 ) + NO+ (X1 + ) as the combination of pump
and probe photons employed provides sufficient internal
energy for (NO)2 + . For example, λpump = 223 nm and
λprobe = 300 nm provide a maximum (NO)2 + internal energy of 0.95 eV, when the photoelectron kinetic energy is
assumed zero. This exceeds the binding energy of (NO)2 +
by 0.62 eV. This dissociative ionization channel is open
for λpump < 237 nm in combination with λprobe = 300 nm.
For λpump < 223 nm, dissociation into NO(X) + NO(A)
can take place. The probe photon (300 nm) is sufficiently
energetic to ionize the NO(A), but not the NO(X) fragment.
The pump–probe experiment via this process leads to
the final fragments NO(X) + NO+ (X). Although the NO+
photoion signal produced in this process is identical in ion
mass detection to that arising from dissociative ionization,
these processes can be disentangled from measurements
of the dependence on the pump–probe time delay and
photoelectron distributions. It should be noted that in
addition to the threshold at 223 nm described above, there
is a second threshold (not shown in the figure). For pump
photons with wavelengths shorter than 215 nm the accessed
excited state of the NO dimer can also dissociate into
NO(X2 ) + NO(B2 ). Again, the probe photons used are
always energetic enough to photoionize the NO(B) fragment
to the ground cation state NO+ (X). However, in view of the
valence electronic structure of the NO(B) state one-photon
ionization to NO+ (X) would require a two-electron process,
making this channel less probable [33].
In Fig. 7 the temporal profiles of the NO+ , (NO)2 + , and
photoelectron intensities are shown as a function of the delay
time between a pump pulse of 207 nm and a probe pulse of
300 nm. In addition, the cross-correlation signal between the
pump and the probe pulses is shown. It is apparent that the
decay time of the (NO)2 + ion signal is only slightly longer
200
M. Tsubouchi et al. / Journal of Electron Spectroscopy and Related Phenomena 142 (2005) 193–205
Fig. 7. Temporal profiles of NO+ , (NO)2 + , and photoelectron intensities.
The pump and probe laser wavelengths are 207 and 300 nm. Diamonds (♦)
show the cross-correlation profile between these laser pulses obtained by the
(1 + 1 ) non-resonant two-photon ionization of the NO monomer.
than the cross correlation time (∼228 ± 29 fs). This ultrafast
process is ascribed to the non-radiative decay of the optically
prepared valence state to other electronic state(s).
As described in a previous paper [16], the time profile of
the (NO)2 + ion signal intensity consists of three components:
(i) a sharp spike found at time t = 0; (ii) an exponential decay
originating from a real population decay of the photoexcited
NO dimer; and (iii) a long-lived component described as a
step function. The ratio of the first and second components
strongly depends on the laser intensity. Therefore, the first
component can be assigned as a non-linear response from the
sample that reflects the cross correlation between the pump
and probe pulses. The fact that this ratio increases for longer
pump wavelengths is presumably due to smaller photoabsorption cross sections of the dimer at these wavelengths [5].
However, the existence of ultrafast decay components within
100 fs, a time scale much shorter than our time resolution,
cannot be ruled out. The intensity of the third component
was very small. This component may originate from a small
amount of long-lived NO dimer or the fragmentation of higher
clusters.
The time profile of the (NO)2 + ion can be expressed as the
sum of the following functions:
I(t) = C1 f1 (t) + C2 f2 (t) + C3 f3 (t),
2 1
2
t
f1 (t) =
exp −2
,
100∆ π
∆
4
f2 (t) =
π∆
+∞
−∞
dt1
+∞
t1
t2 − t1
× exp −
τ
f3 (t) =
4
π∆2
+∞
−∞
dt1
4{t 2 + (t2 − t)2 }
dt2 exp − 1
∆2
,
+∞
t1
(5)
(5a)
(5b)
4{t12 + (t2 − t)2 }
,
dt2 exp −
∆2
(5c)
where t is the pump–probe delay time, τ the time constant
associated with a single exponential decay, ∆ the crosscorrelation time, and C1 , C2 , and C3 are fitting constants.
f1 (t) is the cross correlation between the pump and probe
pulses, and f2 (t) and f3 (t) represent an exponential decay and
a step function that are both convoluted with the pump and
probe pulse shapes. These equations were derived by assuming equal pulse widths for the pump and probe lasers. These
variables and functions were also used in our previous paper [16], although the explicit definitions were not provided.
Note that, because of the finite pulse widths of the pump and
probe lasers, signal is obtained even for negative time delays,
i.e. when the maximum of the probe pulse occurs earlier than
the maximum of the pump pulse. Fig. 8(a) and (b) shows the
temporal profiles of (NO)2 + observed by pump pulses of 200
and 220 nm, respectively, and a probe pulse of 300 nm. The
fitted curves are also shown in the same figures as solid lines.
The experimental profiles are well fitted to Eq. (5), and we obtained decay times of 190 ± 60 and 820 ± 120 fs for the pump
pulses of 200 and 220 nm, respectively. The dotted, dashed,
and dot-dash lines correspond to the first, second and third
components mentioned above, respectively. Note that very
weak oscillatory structure observed around 0.6 and 1 ps is
ignored in the fitting process. To confirm the validity of our
analysis, we fitted the observed decay to different functional
forms. In Fig. 8(c) and (d), we show a fitting curve obtained
under the conditions of C1 = 0 and C3 = 0, respectively. For
the decay measured at the 200 nm pump wavelength, even
if the first (spike) component was neglected in the analysis
(Fig. 8(c)), the fitted curve agreed well with the observed
profile, and a decay time of 150 ± 50 fs was obtained. On the
other hand, if we neglected the third (step function) component (Fig. 8(d)), the fitting quality became worse than that in
Fig. 8(a) and (c).
In Fig. 9, which is taken from our previous work [16], this
(NO)2 + signal decay time is plotted with an open circle as
a function of pump wavelength. The decay time constants
are seen to increase for longer pump wavelengths. Also in
Fig. 9, independent results of ultrafast photoelectron imaging spectroscopy are presented. These photoelectron results
show, as a function of pump wavelength, the time constants
associated with the formation of the dimer 3s Rydberg state
that evolves from the excited dimer valence state(s). In the
range of pump wavelengths where both (NO)2 + and photoelectron results are available, the dephasing time constant of
the valence state(s) and the formation time constant of the
3s Rydberg state of the dimer are seen to agree quite well. It
is noted that the dephasing time varies smoothly below and
above the energetic threshold of λpump ∼ 223 nm for dissociation into NO(A) + NO(X).
3.3.2. Time-dependence of the differential ionization
cross section
In Fig. 10 typical results of our photoelectron imaging
spectroscopic experiments are presented for a pump wavelength of 203 nm and a probe wavelength of 300 nm. On the
M. Tsubouchi et al. / Journal of Electron Spectroscopy and Related Phenomena 142 (2005) 193–205
201
Fig. 8. Temporal profiles of (NO)2 + observed by pump pulses of (a, c, and d) 200 and (b) 220 nm and a probe pulse of 300 nm. The open circles are experimental
values. The solid lines are least-squares fits to Eq. (5), and the dotted, dashed, and dot-dashed lines represent different components of the convoluted function:
component 1 (dotted) is the non-linear response of the molecule, components 2 (dashed) and 3 (dot-dashed) correspond to the exponential decay and the step
function convoluted with the laser cross correlation, respectively. In figures (a) and (b), the complete form of Eq. (5) was used in the fitting process. In figures
(c) and (d), the first and the last components were neglected in the analysis, respectively; see the text.
left-hand side the raw experimental images projected onto
the detector surface are given for pump–probe delay times
of 0, 0.3 and 3 ps. On the right-hand side the corresponding
slice images of the 3D photoelectron scattering distributions
calculated by inverse Abel transformation are shown. The
polarization directions of pump and probe lasers are vertical in the plane of the figure. At a first glance, it is obvious
that at short delay times a rather isotropic and structureless
distribution is obtained which for longer times evolves to a
strictly anisotropic and sharp pattern. Clearly, the time dependencies of both the photoelectron kinetic energy (radius)
Fig. 9. Excitation wavelength dependence of the decay () and rise (䊉)
time constants determined by least-squares fits to the observed time profiles
of (NO)2 + photoion signals and the photoelectron peak area of the Rydberg
component, respectively.
distributions and the angular distributions contain a plethora
of information about ultrafast processes in the NO dimer.
Fig. 11 presents the time dependencies of the PKEDs obtained with pump wavelengths of 200, 203, 207, 210, and
213 nm and a probe wavelength of 300 nm. First, we note
that at all these wavelengths the excited state(s) accessed in
the NO dimer possess enough energy for dissociation into
NO(X) + NO(A) fragments. The ‘ridge’ that develops in the
three-dimensional ‘landscape’ at a kinetic energy between
0.3 and 0.4 eV for time delays > 200 fs is dominant. This
ridge corresponds for short time delays, <∼0.2 ps, to electrons resulting from one-photon ionization of the 3s Rydberg
state of the dimer, evolves for longer delay times (0.2–1 ps) to
the electron signal resulting from ionization of the separating
NO(X) and NO(A) fragment pairs, and corresponds for long
delay times (>2 ps) to ionization of the isolated NO(A) fragment. At short time delays, <200 fs, ionization signal from the
dimer valence state(s) to the dimer lowest ionic state is much
stronger than that from the dimer 3s state. At all pump wavelengths employed this process results in a rather continuous
distribution of electron kinetic energies with an intensity that
increases towards lower kinetic energy. Under careful examination of the time dependence of the photoelectron signal
that forms the ‘ridge’ it appears that at short delay times the
ridge occurs at slightly higher kinetic energies than at longer
delay times. This difference of up to 10–20 meV signifies the
evolution from dimer to monomer 3s Rydberg state.
For pump wavelengths longer than 223 nm dissociation
to NO(X) and NO(A) fragment pairs is no longer possible,
202
M. Tsubouchi et al. / Journal of Electron Spectroscopy and Related Phenomena 142 (2005) 193–205
Fig. 10. Raw (two-dimensional projection, left side) and inverse Abel transformed (slice, right side) photoelectron images obtained at delay times of 0, 0.3,
and 3 ps between 203 nm pump and 300 nm probe lasers. Raw images were integrated for 6 × 105 laser shots. The polarization directions of pump and probe
lasers are vertical in the plane of the figures.
but also formation of the dimer 3s Rydberg state is no longer
observed (not shown). However, as seen in Fig. 9, there is
no abrupt change of the electronic dephasing rate around
the energetic threshold for dissociation. This may imply that
the major deactivation pathway from the optically excited
valence state is not to the 3s Rydberg state of the NO dimer.
The optically excited valence state is repulsive along the
N N stretching coordinate, while the vibrational structure
observed in the UV absorption spectrum of the dimer implies
that there is vibrational motion sustained by a quasibound
electronic state. What is the origin of this metastability? The
EOM-CCSD calculations suggest that the optically bright valence state is strongly mixed with the 3py Rydberg state (see
in [11]). Interestingly, this situation is analogous to that in
the NO monomer, where strong Rydberg–valence interactions occur (with a coupling strength of 1382.6 cm−1 [34])
between the C(2 ) and B(2 ) states. It is noted, however,
that if we assume that the quantum defects of the Rydberg
states of (NO)2 are the same as those of the NO monomer
(δ = 0.7840 for the C(2 , 3p␲) state, and δ = 1.1038 for the
A(2 + , 3s␴) state [35]), the electronic origins of the 3p and
3s Rydberg states of the NO dimer are estimated to be T
∼ 48,180 and T ∼ 40,010 cm−1 from the ionization energy
(IE = 70,530 ± 5 cm−1 ) of the (NO)2 dimer [36]. This implies
that formation of the 3p Rydberg state of the NO dimer is
energetically possible at excitation wavelengths shorter than
∼208 nm. For longer wavelengths, it seems uncertain to what
extent the 3py Rydberg state plays a role in the photophysics
and photochemistry of the NO dimer.
In the C2v point group the valence state possesses B2 symmetry and the 3s Rydberg state A1 symmetry. These two potential energy surfaces can cross in C2v symmetry, but avoid
each other in a distorted configuration with lower symmetry,
i.e. a conical intersection of the potential energy surfaces. Formation of the 3s Rydberg state of the dimer is speculated to be
the result of molecular distortion in the valence state, for example along the anti-symmetric N O vibration, the N N O
bending, or the torsional motion that lower the symmetry.
This seems in accordance with our previous finding that the
NO fragments are vibrationally and rotationally excited [15],
suggesting that molecular deformation takes place during the
dissociation process. As for the torsional motion, it may not
M. Tsubouchi et al. / Journal of Electron Spectroscopy and Related Phenomena 142 (2005) 193–205
203
Fig. 11. Time dependence of the PKEDs obtained by: (a) 200 nm; (b) 203 nm; (c) 207 nm; (d) 210 nm; (e) 213 nm pump and 300 nm probe lasers. The
photoelectron signal generated from the fragment NO(A) appears at 0.35 eV.
be extensive: Kajimoto et al., from their analysis of the rotational state distribution of NO(A) fragments using phase
space theory, have suggested that the dimer mostly dissociates from its planar configuration [8,9]. The adiabatic potential energy surface of the valence state is correlated with the
NO(X) + NO(X) product channel. However, no experimental
study on the NO(X) + NO(X) channel has been reported so
far, and its examination seems quite important for elucidating
the dynamics.
In Fig. 12 an example of the time evolution of the PAD
of the ‘ridge’ component with photoelectron kinetic energy
between 0.3 and 0.4 eV is presented for a pump wavelength
of 200 nm and a probe wavelength of 300 nm, at pulse delay
times of 0 and 3 ps. For a (1 + 1 ) REMPI process the PADs are
generally given by I(θ k ) ∼ 1 + β2 P2 (cos θ k ) + β4 P4 (cos θ k ).
However, the obtained distribution could be nicely fitted to
the contracted form, I(θ k ) ∼ 1 + βP2 (cos θ k ), as shown in the
Fig. 12. PADs in the photoelectron kinetic energy range 0.3–0.4 eV. The
pump and probe laser wavelengths are 200 and 300 nm, respectively. The
delay times between both lasers are 0 ps (䊉) and 3 ps (). The solid lines
are least-squares fits to the functional form of I(θ k ) ∝ 1 + βP2 (cos θ k ).
204
M. Tsubouchi et al. / Journal of Electron Spectroscopy and Related Phenomena 142 (2005) 193–205
Fig. 13. Time dependencies of the anisotropy parameter β of the photoelectron angular distributions in the photoelectron kinetic energy range
0.3–0.4 eV. The probe laser wavelength is 300 nm. The asterisk shows the β
value determined in the 226 nm pump and 305 nm probe (1 + 1 ) resonanceenhanced two-photon ionization of the NO monomer via the A state at a
delay time of 2.8 ps.
solid lines in the same figure. Clearly, at short time delays the
angular distribution is quite isotropic, with β = 0.68 ± 0.10.
This situation is typical for ionization from a valence state.
For time delays longer than ∼2 ps the angular distribution is
quite anisotropic, with β = 1.35 ± 0.06. This is typical for ionization from an isolated NO(A) fragment in which removal of
the 3s Rydberg electron of the monomer in its A2 + state is
expected to possess a rather high β value. The anisotropy
parameter for a free NO(A), ν = 0, molecule was experimentally determined to be β ∼ 1.55 by using probe light
of ∼300 nm, as shown in Fig. 5(b).
In Fig. 13 the time dependencies of β obtained for a series
of pump–probe experiments performed at pump wavelengths
of 200, 203, 207, 210, and 216.5 nm and with a probe wavelength of 300 nm are presented. At all excitation wavelengths
the typical evolution from rather isotropic to quite anisotropic
PADs is apparent. This evolution takes place on the same
time scale as that of the formation of Rydberg states obtained
from the time-resolved PKEDs (Figs. 9 and 11). The asterisk shows the β value determined in an independent 226 nm
pump and 305 nm probe (1 + 1 ) REMPI experiment on the
NO monomer via the A2 + ν = 0 state at a delay time of
2.8 ps. This result again strongly supports the notion that at
very long time delays the photoelectron signal obtained in
photoionization of the NO dimer is predominantly due to
ionization of the isolated NO(A) fragment. The change of
the β parameter becomes faster at shorter pump wavelengths
in agreement with Fig. 9.
4. Conclusions
Femtosecond time-resolved pump–probe photoelectron
imaging (TR-PEI) spectroscopy is shown to be a powerful
tool for the elucidation of ultrafast processes arising from
optically excited states of molecular species. The observed
time dependencies of photoelectron kinetic energies and
photoelectron angular distributions contain much information about such decay processes. In this paper the NO dimer
is discussed as an illustrative example. For the range of
pump wavelengths employed (between 200 and 235 nm)
many excited states can be accessed whose details are essentially unknown. Experimentally we observe approximately
continuous behavior for the time constants of the relevant
decay processes obtained as a function of pump excitation
energy. Another observation is that for a pump wavelength
below 223 nm, at an energy which corresponds to the
dissociation threshold at which NO(X) + NO(A) fragments
can be formed, the formation of the 3s Rydberg state of
the dimer seems prohibited. For a detailed interpretation of
these observations results of advanced ab initio electronic
structure calculations on excited states of the NO dimer in
this energy region would be very valuable.
The picture of the UV photodissociation of the NO dimer
can be summarized as follows. After the initial optical excitation of one or more valence states in the dimer an evolution
on a time scale of <1 ps takes place to the dimer 3s Rydberg
state. This dimer Rydberg state then undergoes fragmentation on a time scale of a few ps into an NO ground state
fragment and an NO fragment in its 3s Rydberg A2 + state.
At every stage of this continuous process photoionization of
the dimer valence state, the dimer 3s Rydberg state, the separating NO(X) + NO(A) fragments, and the isolated NO(A)
fragment provide competing channels. With modern photoelectron imaging methods all these channels can be tracked
and compared in the same experiment.
Acknowledgements
We thank Professor Hanna Reisler for kindly providing
us with their preprints. This work was financially supported
by a Grant-in-Aid from the Ministry of Education, Culture,
Sports, Science and Technology of Japan under contract numbers 13127204, 14204063, and 15002011 and the Japan Science and Technology Agency. MT acknowledges the Special
Postdoctoral Researchers Program of RIKEN.
References
[1] A.L.L. East, J. Chem. Phys. 109 (1998) 2185;
R. Sayós, R. Valero, J.M. Anglada, M. González, J. Chem. Phys.
112 (2000) 6608.
[2] L. Krim, J. Mol. Struct. 471 (1998) 267;
L. Krim, N. Lacome, J. Phys. Chem. A 102 (1998) 2289.
[3] J.R. Hetzler, M.P. Casassa, D.S. King, J. Phys. Chem. 95 (1991)
8086;
E.A. Wade, J.I. Cline, K.T. Lorenz, C. Hayden, D.W. Chandler, J.
Chem. Phys. 116 (2002) 4755.
[4] H.J. Bernstein, G. Herzberg, J. Chem. Phys. 15 (1947) 77;
J. Mayence, Ann. Phys. 7 (1952) 453;
E. Forte, H. van den Bergh, Chem. Phys. 30 (1978) 325.
[5] J. Billingsley, A.B. Callear, Trans. Faraday Soc. 67 (1971) 589.
M. Tsubouchi et al. / Journal of Electron Spectroscopy and Related Phenomena 142 (2005) 193–205
[6] Y. Naitoh, T. Ibuki, O. Kajimoto, private communication.
[7] O. Kajimoto, K. Honma, T. Kobayashi, J. Phys. Chem. 89 (1985)
2725;
Y. Naitoh, Y. Fujimura, O. Kajimoto, K. Honma, Chem. Phys. Lett.
190 (1992) 135;
Y. Naitoh, Y. Fujimura, K. Honma, O. Kajimoto, Chem. Phys. Lett.
205 (1993) 423.
[8] O. Kajimoto, Prog. Theoret. Phys. Suppl. 116 (1994) 167.
[9] Y. Naitoh, Y. Fujimura, K. Honma, O. Kajimoto, J. Phys. Chem. 99
(1995) 13652.
[10] A.V. Demyanenko, A.B. Potter, V. Dribinski, H. Reisler, J. Chem.
Phys. 117 (2002) 2568;
A.B. Potter, V. Dribinski, A.V. Demyanenko, H. Reisler, J. Chem.
Phys. 119 (2003) 7197.
[11] V. Dribinski, A.B. Potter, I. Fedorov, H. Reisler, Chem. Phys. Lett.
385 (2004) 233.
[12] K. Sato, Y. Achiba, K. Kimura, Chem. Phys. Lett. 126 (1986) 306.
[13] J.L. Knee, in: I. Powis, T. Baer, C.Y. Ng (Eds.), High Resolution
Laser Photoionization and Photoelectron Studies, Wiley, New York,
1995, p. 369;
T. Suzuki, B.J. Whitaker, Int. Rev. Phys. Chem. 20 (2001) 313;
D.M. Neumark, Ann. Rev. Phys. Chem. 52 (2001) 255;
T. Seideman, Ann. Rev. Phys. Chem. 53 (2002) 41;
T. Suzuki, B.J. Whitaker, in: B.J. Whitaker (Ed.), Imaging in Molecular Dynamics, Cambridge University Press, Cambridge, 2003, p.
165;
T. Suzuki, in: X. Yang, K. Liu (Eds.), Recent Advances in
Chemical Reaction Dynamics, World Scientific, Singapore, 2004
(Chapter 14);
A. Stolow, A.E. Bragg, D.M. Neumark, Chem. Rev. 104 (2004)
1719.
[14] V. Blanchet, A. Stolow, J. Chem. Phys. 108 (1998) 4371.
[15] M. Tsubouchi, C.A. de Lange, T. Suzuki, J. Chem. Phys. 119 (2003)
11728.
[16] M. Tsubouchi, T. Suzuki, Chem. Phys. Lett. 382 (2003)
418.
[17] M. Tsubouchi, T. Suzuki, J. Chem. Phys. 121 (2004) 8846.
[18] A.T.J.B. Eppink, D.H. Parker, Rev. Sci. Instrum. 68 (1997)
3477.
[19] K. Kimura, S. Katsumata, Y. Achiba, T. Yamazaki, S. Iwata,
Handbook of HeI Photoelectron Spectra of Fundamental Organic
Molecules, Japan Scientific Societies, Tokyo, 1981;
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
205
K. Kimura, J. Electron Spectrosc. Relat. Phenom. 100 (1999)
273.
B. Urban, A. Strobel, V.E. Bondybey, J. Chem. Phys. 111 (1999)
8939.
H. Katayanagi, Y. Matsumoto, C.A. de Lange, M. Tsubouchi, T.
Suzuki, J. Chem. Phys. 119 (2003) 3737.
P.M. Felker, J.S. Baskin, A.H. Zewail, J. Phys. Chem. 90 (1986)
724;
P.M. Felker, A.H. Zewail, J. Chem. Phys. 86 (1987) 2460.
A.B. Myers, R.M. Hochstrasser, J. Chem. Phys. 85 (1986)
6301.
C. Riehn, Chem. Phys. 283 (2002) 297.
C. Riehn, A. Weichert, B. Brutschy, Phys. Chem. Chem. Phys. 2
(2000) 1873.
K.L. Reid, T.A. Field, M. Towrie, P. Matousek, J. Chem. Phys. 111
(1999) 1438;
M. Tsubouchi, B.J. Whitaker, L. Wang, H. Kohguchi, T. Suzuki,
Phys. Rev. Lett. 86 (2001) 4500;
A.E. Bragg, R. Wester, A.V. Davis, A. Kammrath, D.M. Neumark,
Chem. Phys. Lett. 376 (2003) 767.
K.L. Reid, J.G. Underwood, J. Chem. Phys. 112 (2000)
3643.
J.G. Underwood, K.L. Reid, J. Chem. Phys. 113 (2000)
1067.
K.-P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules, Van Nostrand-Reinhold,
New York, 1979.
H. Nakatsuji, in: J. Leszczynski (Ed.), Computational Chemistry —
Reviews of Current Trends, World Scientific, NJ, 1997, p. 62.
M.J. Frisch, et al., GAUSSIAN’03 Revision B.04, Gaussian Inc.,
Pittsburgh, PA, 2003.
A. Witkowski, W. Moffitt, J. Chem. Phys. 33 (1960) 872;
R. Fulton, M. Gouterman, J. Chem. Phys. 35 (1961) 1059.
Y. Achiba, K. Sato, K. Kimura, J. Chem. Phys. 82 (1985) 3959;
S.R. Mackenzie, E.J. Halse, E. Gordon, D. Rolland, T.P. Softley,
Chem. Phys. 209 (1996) 127.
A. Giusti-Suzor, C. Jungen, J. Chem. Phys. 80 (1984) 986.
E. Miescher, K.P. Huber, in: A.D. Buckingham, D.A. Ramsay (Eds.),
International Reviews of Science, Phys. Chem. Ser. 2, vol. 3, Butterworths, London, 1976, p. 37.
I. Fischer, A. Strobel, J. Staecker, G. Niedner-Schatteburg, K. MüllerDethlefs, V.E. Bondybey, J. Chem. Phys. 96 (1992) 7171.