Photodissociation of HN3 at 248 nm and Longer Wavelength: A CASSCF Study

Article abstract of DOI:10.1021/jp993386c

In the present work, photodissociation of HN₃ at 248 nm and longer wavelength is investigated with the complete active space SCF (CASSCF) molecular orbital method. The stationary points on the ground- and excited-state potential energy surfaces are fully optimized at the CASSCF level with cc-pVDZ and cc-pVTZ basis sets. The potential energy profiles, governing HN₃ dissociation to NH + N₂ and H + N₃, are characterized with the multireference MP2 (CASPT2) algorithm. The pathways leading to different products are determined on the basis of the obtained potential energy surfaces of dissociation and their crossing points. A comparison is made among the present and previous theoretical results and experimental findings. The present study provides an insight into the mechanism of the UV photodissociation of HN₃ at a wavelength range from 355 to 248 nm.

Full text of DOI:10.1021/jp993386c

J. Phys. Chem. A 2000, 104, 4045-4050
4045
Photodissociation of HN3 at 248 nm and Longer Wavelength: A CASSCF Study
Wei-Hai Fang†
Department of Chemistry, Beijing Normal UniVersity, Beijing 100875, People’s Republic of China
ReceiVed: September 21, 1999; In Final Form: December 3, 1999
3
In the present work, photodissociation of HN at 248 nm and longer wavelength is investigated with the
complete active space SCF (CASSCF) molecular orbital method. The stationary points on the ground- and
excited-state potential energy surfaces are fully optimized at the CASSCF level with cc-pVDZ and cc-pVTZ
basis sets. The potential energy profiles, governing HN
3
dissociation to NH + N
2
3
and H + N , are characterized
with the multireference MP2 (CASPT2) algorithm. The pathways leading to different products are determined
on the basis of the obtained potential energy surfaces of dissociation and their crossing points. A comparison
is made among the present and previous theoretical results and experimental findings. The present study
provides an insight into the mechanism of the UV photodissociation of HN
to 248 nm.
3
at a wavelength range from 355
Introduction
In many ways the HN3 molecule is an ideal system for
investigating the photodissociation process. Single-photon pho-
Hydrazoic acid (HN3) is a member of a class of energetic
molecules. Although its bond energy relative to formation of
ground-state NH(X) and N2 is very small (∼4000 cm ), it is
fairly stable due to the fact that the dissociation of ground-
state HN3 to the lowest asymptote is spin-forbidden
8
9
8
todissociation experiments on HN3 at 308, 283, 266, and
1
0,11
2
48
nm show that the dominant product channel is
-
1
1
1
HN (X A′) + hν f HN (A A′′) f
3
3
1
+
1
N (X Σ ) + NH (a ∆) (5)
2
g
1
1
+
g
3 -
HN (X A′) f N (X Σ ) + NH (X Σ )
(1)
3
2
Measurements of vibrational and rotational state distributions
Decomposition according to reaction 1 can occur by a spin-
8-12
on both the NH and N2 fragments
find large rotational
orbit-induced crossing between the singlet surface, which
excitation of the N2 product but only modest internal excitation
of the NH fragment. The distribution of the available energy
among the various degrees of freedom of the fragments N2 and
HN, i.e., relative translation, rotation, vibration, and electronic
excitation, has been analyzed in great detail for reaction 5. The
UV photodissociation of HN3 at 193 nm was investigated in
1
+
1
correlates asymptotically to N2 (X ∑g ) + NH (a ∆), and the
lowest triplet surface. The crossing point can be considered as
the “transition state” of the spin-forbidden reaction 1. The barrier
-
1
1
height of 12 700 cm was estimated by Kajimoto et al. from
thermal dissociation studies in a shock tube. High-resolution
spectra for the predissociative N-H stretching overtone of HN3
have yielded a considerably different activation energy (∼15 100
3
-
detail in the bulk phase at 300 K. NH radicals in the X ∑ ,
1
l
+
3
1
a ∆, b ∑ , A Π, and c Π states were found to be formed
simultaneously, but with very different quantum yields. The N3
fragment and H atom as primary products of the HN3 photo-
dissociation at 248 and 193 nm were observed by Comes and
-
1 2,3
cm ) for reaction 1.
The spin-allowed process
1
1
+
g
1
HN (X A′) f N (X Σ ) + NH (a ∆)
(2)
13
3
2
co-workers
has been investigated by King and co-workers.4,5 The NH (a ∆)
1
1
1
HN (X A′) + hν f HN (A A′′) f
3
3
fragments were found to be translationally excited. This implies
2
2
-
1
N (X Π ) + H ( S) (6)
3 g
the existence of a barrier in the exit channel (∼1700 cm with
respect to the dissociation products). The relative enthalpy of
the other spin-allowed product channel
The photolysis of HN3/DN3 to give H/D and N3 was further
14
investigated at different photolysis wavelengths. Nascent H/D
atoms were characterized via Doppler and polarization spec-
troscopy using laser-induced fluorescence in the vacuum-
ultraviolet region. The quantum yields have been found to be
0.04, 0.2, and 0.14 at 266, 248, and 193 nm, respectively. State-
selected photodissociation of HN3 has been studied by vibra-
tionally exciting the molecule in the region of the second
overtone of its H-N stretching motion and then photodissoci-
ating it using 532 nm light. Measurement of the resulting NH
fragment rotational state distribution reveals that photodisso-
ciation from initial nuclear configuration with an extended N-H
bond leads to a substantially hotter rotational state distribution
1
2
2
HN (X A′) f N (X Π ) + H ( S)
(3)
3
3
g
plays an important role in determining the relative branching
ratios in the UV dissociation of HN3, as well as controlling the
exothermicity of the abstraction, reaction
2
2
1
+
3 -
H ( S) + N (X Π ) f N (X Σ ) + NH (X Σ )
(4)
3
g
2
g
1
5
which has been studied in Dagdigian’s laboratory.6,7
†
E-mail: fangwhgbnu.edu.cn.
1
0.1021/jp993386c CCC: $19.00 © 2000 American Chemical Society
Published on Web 04/06/2000

4046 J. Phys. Chem. A, Vol. 104, No. 17, 2000
Fang
than from nearly isoenergetic single-photon dissociation at 355
nm. Recently, the VUV photolysis of hydrazoic acid was
the MP2(FC) energy gradient, where FC denotes the frozen 1s
core of nitrogen atoms. The stationary structures are optimized
with the cc-pVDZ and cc-pVTZ basis sets. The intersection
16
24
reinvestigated by Stuhl and co-workers. The fragment NH/
1
ND (c Π) is formed with the same quantum yield below 147
point between the S0 and S1 or T1 surfaces is determined with
the state-averaged CASSCF method with the cc-pVDZ basis
set. Energies are calculated at the CASSCF-optimized structures
3
nm, while the relative production yield of NH/ND (A Π)
increases with decreasing wavelength. The near-ultraviolet
photolysis of HN3 has been investigated at a range of wave-
lengths, λ g 240 nm, using the technique of H Rydberg atom
2
5
with the multireference MP2 approach (CASPT2) which was
developed by Robb and co-workers. In calculation of barrier
17
26
photofragment translational spectroscopy. The deduced N3 (X)
product rotational energy disposal can be reproduced by an
impulse model, which yields a refined measure of the H-N3
height and adiabatic excitation energy, a factor of 0.85 is used
to scale the calculated zero-point energies. All the calculations
have been performed using the Gaussian 94 or G98W package
-
1
27
bond strength, D0(H-N3) ) 30 970 ( 50 cm . The N3 (X)
product vibrational progressions observed at each photolysis
wavelength “break off” at a low kinetic energy release. This is
interpreted by invoking a barrier to dissociation via H-N bond
of programs.
To determine the height of the barrier in the ground state as
well as the structure of the crossing point between the ground
2
0
and the lowest triplet states, Alexander et al. have used an
active space with 16 valence electrons in 11 orbitals for the
CASSCF calculations. Since the terminal N-N σ orbital is
doubly occupied with a very low orbital energy, this orbital is
excluded from the active space in the present CASSCF
calculations. In addition, the initial test CASSCF calculations
with 14 electrons in 10 orbitals for some geometries show that
there are 3 orbitals with occupancies near 2, which are deleted
from the molecular orbital space. Finally, an active space with
eight electrons distributed in seven orbitals is used here, referred
to as CAS(8,7). The energy of the separated fragments is
determined by a supermolecule calculation, including both
fragments at a large separation, with the same basis set and
active space as for the calculation of the bound fragments.
In the limit that energy flows rapidly and randomly among
all the vibrational degrees of freedom, the rate at which the
molecule passes through the transition state from reactants to
1
fission on the A A′′ state potential energy surface. Dissociation
of HN3 into HN and N2 was used as a model for studying the
specific phase correlations between reactive and nonreactive
1
8
modes during the final few vibrations prior to reaction.
In comparison, the HN3 photodissociation has received less
1
9,20
attention from a theoretical point of view. Alexander et al.
have carried out large-scale MCSCF and CI calculations, which
mainly concentrated on the crossing between the ground-state
singlet and the lowest triplet-state surfaces and on the barriers
and dissociation energies for the spin-forbidden and spin-allowed
2
1
decomposition of HN3 in the ground state. Yarkony has also
performed MCSCF and CI calculations for these two states and
has calculated the spin-orbit coupling matrix elements between
them in the crossing region. The potential energy curves of the
five lowest singlet and the five lowest triplet valence states of
HN3 along the interior N-N distance have been calculated by
Meier and Staemmler22 with ab initio CASSCF and valence CI
methods. The angular dependence of the energy for the first
excited singlet state was discussed. However, in their calculation
the terminal N-N and N-H bond lengths are kept fixed at the
ground-state equilibrium values, and the bond angles, N-N-N
and N-N-H, are varied independently. The resulting potential
energy profiles for dissociation of HN3 to NH and N2 are only
qualitatively reliable. For the interpretation of the absorption
28
products may be calculated with the RRKM theory. The rate
coefficient for reaction when the molecule contains total energy
E and has total angular momentum J is given by
k(E,J) ) W(E,J)/hF(E,J)
where F(E,J) is the density of states of the reactants as a function
of E and J, h is Planck’s constant, and W(E,J) is the number of
energy levels for vibration orthogonal to the reaction coordinate
at the transition-state configuration with energy less than E. They
can be, respectively, expressed as
1
6
spectrum, a series of quantum chemical ab initio calculations
at various levels of sophistication have been performed: SCF,
valence CI with different active spaces, CASSCF, and multi-
configuration coupled electron-pair approach (MC-CEPA). All
calculations were performed at the fixed equilibrium geometry
of the planar ground state of HN3. In the present paper, the
potential energy surfaces governing HN3 dissociation to HN +
N2 and H + N3 in the ground (S0), excited triplet (T1), and
singlet (S1) states are fully optimized with the CASSCF method.
The mechanism leading to different products is determined on
the basis of the calculated potential energy surfaces and their
crossing points. A comparison is made among the present and
previous theoretical results and experimental findings.
states
W(E) )
∑i H(E-Ei)
and
states
F(E) ) dW/dE )
δ(E-Ei)
∑i
where H(E-Ei) and δ(E-Ei) are the Heaviside and delta
functions, respectively. In practice the energy levels are obtained
by assuming a rigid rotor-harmonic oscillator approximation:
Computational Details
The stationary-point structures on the ground and the first
2
3
s
excited electronic states are optimized at the CASSCF levels
with the Cs symmetry constraint. The optimization was termi-
nated when the maximum force and its RMS were less than
ꢀn,J,K ) WJ,K
+
pω (n + 1/2)
i i
∑i
-
4
-4
4
.5 × 10 and 3.0 × 10 hartree/bohr, respectively. At the
As pointed out by Miller,28 the energy levels of most asymmetric
rotors are reasonably well approximated by assuming an “almost
symmetric top”; we invoke that approximation here, so that
CASSCF converged geometry, the harmonic frequencies are
calculated at the same level of theory with a cc-pVDZ basis set
to confirm the resulting geometry to be the minimum or the
first saddle point on the potential energy surfaces. Some
stationary structures on the S0 surface are also determined with
2
2
WJ,K ) (1/2)(A + B)[J(J + 1) - K ] + CK

Photodissociation of HN3
J. Phys. Chem. A, Vol. 104, No. 17, 2000 4047
and the terminal N-N bond lengths are increased by about 0.23
and 0.04 Å from S0 to S1, respectively. A natural orbital analysis
shows that there are two singly-occupied π orbitals for the HN3
molecule in S1. One is a bonding π orbital like the MO11 in
S0; the other is an antibonding π* orbital which is composed
of px atomic orbitals of the three N atoms. One electron
excitation from the π to π* orbital makes the interior N-N π
bond nearly broken and the terminal N-N π bond weakened,
which is responsible for a significant increase of the interior
N-N bond length and considerable change in the terminal N-N
bond length from S0 to S1. From the viewpoint of valence bond
theory, one electron excitation from S0 to S1 accompanies a
2
rehybridization of the middle N atom from sp to sp , which
results in a change in the N-N-N bond angle from 171.8° in
S0 to 118.3° in S1.
The adiabatic excitation energy from S0 to S1 is 73.0 kcal/
mol calculated with the CASPT2/cc-pVTZ approach on the
CAS(8,7)/cc-pVTZ optimized structures. It becomes 71.9 kcal/
mol with the scaled CAS(8,7)/cc-pVDZ zero-point energy
correction. This may be compared with the experimental 0-0
excitation energy, but the 0-0 energy gap for HN3 is not
experimentally reported up to date. Recently, the single-photon
Figure 1. Schematic structures of the stationary and crossing points
on the S
0 1 1 3
, T , and S surfaces of HN (bond lengths in angstroms and
bond angles in degrees).
1
5
UV photodissociation experiments at 355 nm produce an NH
A and B are chosen as the two most nearly equal rotation
constants of the three A, B, and C.
1
fragment in the ∆ electronic state. Compared with the corre-
sponding vertical excitation energy of 80.5 kcal/mol (355 nm),
one can expect that the calculated adiabatic excitation energy
is reasonable. It seems that an energy-minimum point was found
on the lowest triplet (T1) surface by Meier and Staemmler.22
Since the internal coordinates, except for the interior N-N
distance, were frozen in their calculations, the minimum
obtained in that study probably is not a real energy minimum.
An attempt to optimize the equilibrium geometry of HN3 in T1
does not converge; instead a transition state for reaction 4 is
found, which will be discussed below.
Results and Discussion
Equilibrium Geometries of HN3 in Its Ground and Excited
States. Although several ab initio studies1
6,19-22
of HN3 have
been performed, which always used the experimental structure,
the equilibrium geometry of HN3 in its ground electronic state
(
S0) was not optimized at a more advanced level of theory. The
equilibrium structure of HN3 in S0 is first optimized at the CAS-
8,7) and CAS(14,10) levels with the cc-pVDZ basis set. The
(
resulting geometric parameters are close to the experimental
values,29 but the CAS(14,10) optimization does not give a better
Spin-Forbidden and Spin-Allowed Decomposition of HN3
(S0). Reaction 1 is a spin-forbidden process, and one can expect
description of the equilibrium geometry than the CAS(8,7)
calculation, as compared with the experimental structure. With
increasing size of the basis set to cc-pVTZ, the optimized
structure is still not improved with respect to the experimental
geometry. The structure of HN3 (S0) is planar with a nearly
linear N3 moiety and the H-N bond strongly bent with respect
to the N3 backbone, as shown in Figure 1. It is of A′ symmetry.
A natural orbital analysis of the total density based on the CAS-
that the minimum-energy crossing point (T1/S0) between the
lowest singlet and triplet surfaces would play an important role
in this process. The T1/S0 structure, as shown in Figure 1, is
optimized with the state-averaged CASSCF energy gradient
technique with the cc-pVDZ basis set. The structure of this
1
9,20
crossing point was also determined by Alexander et al.
and
2
1
Yarkony. Since the terminal N-N and N-H distances were
held to the equilibrium values in the isolated molecules in their
calculations, the full CAS(8,7)/cc-pVDZ optimization performed
here should provide a better description of the structure of the
crossing point. The crossing point lies 40.6 kcal/mol (14208.8
cm ) in energy above the ground-state minimum, which
provides an estimation of the barrier height of the nonadiabatic
reaction 1. From thermal dissociation studies in a shock tube,
(8,7)/cc-pVDZ calculated wave functions shows that there are
three doubly-occupied π molecular orbitals, numbered MO9,
MO10, and MO11. These orbitals can be approximately
represented as æ(MO9) ) 0.68(2pz(N2)) + 0.56(2pz(N3)) +
-
1
0
0
-
.05(2pz(N4)), æ(MO10) ) 0.15(2px(N2)) - 0.67(2px(N3)) -
.64(2px(N4)), and æ(MO11) ) 0.38(2pz(N2)) - 0.44(2pz(N3))
0.78(2pz(N4)). This is consistent with the HN3 molecular
-
1
the height of the barrier was deduced to be 12 700 cm by
valence bond structure, HsNdNtN. Finally, it should be
mentioned that an attempt to optimize a cis minimum of HN3
in S0 does not converge, and instead leads to formation of the
trans-HN3 shown in Figure 1.
1
2,3
Kajimoto et al. However, high-resolution spectra for the
predissociative N-H stretching overtone of HN3 have shown
that when the overtone pumping frequency is increased to
-1
1
5 100 cm , the lifetime of HN3 drops abruptly, which suggests
To our knowledge, no experimental or theoretical equilibrium
geometry of HN3 in its first excited electronic state (S1) has
been reported in the literature. This geometry is optimized here
at the CAS(8,7) level of theory with the cc-pVDZ and cc-pVTZ
basis sets. The obtained results with the two basis sets are close
to each other. HN3 (S1) has a trans planar conformation with
A′′ symmetry, as shown in Figure 1 where the CAS(8,7)/cc-
pVDZ parameters are also given. No cis minimum was found
on the S1 surface for HN3. Unlike that in the ground electronic
state, the N-N-N angle is close to 120° in S1, and the interior
that the activation energy of reaction 1 lies at about 43.1 kcal/
mol. This value is close to the present calculated result. The
previous theoretical calculations have estimated the activation
1
9-21
energy of 39.5-48.3 kcal/mol.
Reaction 1 is endothermic by 9.2-12.3 kcal/mol.30 The
endothermic character cannot be well described by the single-
reference SCF calculations, as pointed out by Alexander and
2
0
coworkers. On the basis of their CASSCF+CI calculations
and the previous experimental excitation energy, the bond

4048 J. Phys. Chem. A, Vol. 104, No. 17, 2000
Fang
on photodissociation of the isoelectronic HNCO molecule, a
1
barrier in the exit channel of the HNCO (S1) to NH (a ∆) +
1
+
-1
CO (X ∑ ) was estimated in the range of 500 cm . High-
3
5
level calculations by Schinke and co-workers have also
-
1
predicted a barrier height of about 550 cm (without zero-
point energy correction). The HN3 molecule with three elec-
tronegative N atoms is inherently less stable than the HNCO
molecule with a more electropositive element between the
electronegative ones. Therefore, the barrier of the HN3 dis-
sociation is expected to be lower than that of the HNCO
dissociation.
Figure 2. Schematic potential energy profiles of HN
in kcal/mol with zero-pont energy correction).
3
(relative energies
The interior N-N distance is increased by 0.162 Å from the
reactant of HN3 (S1) to the transition state of TS1 (S1), while
the other bond parameters are only slightly varied in TS1 (S1)
with respect to those in HN3 (S1). As anticipated by Hammond’s
postulate, the exothermic reaction has a transition-state
geometry close to that of the the reactant. The structures of HN3
3
-
dissociation energy (D0) for the N2 + NH (X ∑ ) asymptote
was determined to be about 12 kcal/mol by them. The present
CAS(8,7)/cc-pVTZ calculations give a dissociation energy of
36
6
.7 kcal/mol. With the dynamic correlation considered at the
(S1) and TS1 (S1), as in Figure 1, are both trans planar, which
CASPT2/cc-pVTZ level, it becomes 13.4 kcal/mol. The potential
energy profile of the spin-forbidden decomposition is plotted
in Figure 2.
have been confirmed to be minimum and saddle points on the
S1 surface, respectively. From the observed v-J and µ-v-J
8
,9,37
vector correlations,
however, the dissociation of HN3 (S1)
1
+
The spin-allowed decomposition of HN3 (S0) to N2 (X ∑g )
1
1
+
into NH (a ∆) and N2 (X ∑ g) is predicted to proceed via a
nonplanar motion of the NH rotor. The interior N-N bond
length is about 1.6 Å in TS1 (S1); the rotation of the NH moiety
is not completely free. Thus, TS1 (S1) maintains the planar
symmetry of the reactant. After the system passes through the
saddle point on the S1 surface, the interior N-N separation is
larger. In this case, it is easier for the NH moiety to distort
from the initial molecular plane. Therefore, the optimized planar
structures of HN3 (S1) and TS1 (S1) are not inconsistent with
the vector correlation experiments mentioned above.
1
2
2
+
NH (a ∆) or N3 (X Πg) + H ( S) has been studied by
20
Alexander and co-workers with the complete active space self-
consistent field and multireference configuration interaction
(
CASSCF+MRCI) method and large basis sets. The resulting
dissociation energies (D0) of reactions 2 and 3 were 48.1 and
7.8 kcal/mol, respectively. The present CASPT2/cc-pVTZ
8
calculations give dissociation energies of 48.4 for reaction 2
and 85.3 kcal/mol for reaction 3. Compared with the experi-
mental estimations of 45.6-48.6 kcal/mol for reaction 2 and
2-5,17
8
6.8-96.9 kcal/mol for reaction 3,
both the present and
On the basis of the optimized structures of HN3 (S1) and TS1
the previous theoretical values are in excellent agreement with
the experimental findings. No energy barrier above the endo-
thermicity is found for reaction 3; however, a small barrier exists
(S1), the available energy distribution in the nascent fragments
can be roughly estimated with a simple impulse dissociation
38
model. More than half of the available energy is changed into
translational energy of the fragments. The rest is mainly dumped
into rational states of N2 and vibrational states of NH. Less than
in the exit channel (reaction 2). The height of the barrier is
estimated to be 4.1 kcal/mol.20 The potential energy profiles of
reactions 2 and 3 are summarized in Figure 2. The results from
the present calculations are consistent with the previous theoreti-
cal and experimental findings where available, which gives us
a reason to expect that the dissociation of HN3 on the excited
electronic states can be well described by the CAS(8,7)
calculation.
1
% of the available energy is distributed in vibrational states
of N2 and rotational states of NH. These clearly show that the
nascent N2 is in its vibrational ground state and rotational excited
states, whereas the nascent NH is in its vibrational excited states.
All of these are consistent with the experimental findings.
Decomposition of HN3 on the Excited Electronic States.
Hydrazoic acid in its ground state is stable, due to the existence
of the conjugation π system and the fact that the decomposition
In addition to dissociation to HN and N2, the HN3 molecules
2
2
in S1 can also decompose into N3 (X Πg) + H ( S), namely,
pathway 6. A transition state on this pathway [TS2 (S1)] is found,
as shown in Figure 1. Again, optimizations with the cc-pVDZ
and cc-pVTZ basis sets provide nearly the same structural
parameters for TS2 (S1), in which the H-N bond is almost
broken and the N-N-N moiety is close to the N3 radical in
structure. Analysis of the N3 (X) product vibrational progres-
3
-
to the asymptote N2 + NH (X ∑ ) is spin-forbidden. However,
when the molecule is excited to the S1 state, the interior N-N
π bond is nearly broken and the direct dissociation, pathway 5,
is spin-allowed. This gives us a hint that the dissociation of
HN3 in S1 is much easier than that in S0. A transition state [TS1
1
7
(
(
S1)] is found on pathway 5 at the CAS(8,7)/cc-pVDZ and CAS-
8,7)/cc- pVTZ levels of theory. Figure 1 shows the CAS(8,7)/
sions shows that a barrier exists on the S1 pathway, HN3 f
H + N3. The observed energy disposals and the deduced impact
parameters predict that the departing H atom is directed at ∼90°
to the near linear N3 chain. The optimized structure of TS2 (S1)
in Figure 1 is in agreement with this experimental prediction.
It should be pointed out that an attempt to search for a trans
transition state does not converge, and instead leads to formation
of TS2 (S1) that has a cis conformation. The optimization process
of TS2 (S1) shows that departure of the hydrogen atom
accompanies an isomerization from the trans to cis conforma-
tion. In fact, there is little difference between the trans and cis
conformations, when the N-H separation is large and the
N-N-N configuration is close to being linear. The dissociation
cc-pVDZ-optimized TS1(S1) structure. Relative to the S1
minimum of HN3, the CAS(8,7)/cc-pVDZ and CAS(8,7)/cc-
pVTZ calculations provide the same barrier height of 1.1 kcal/
-
1
-1
mol (385 cm ). It becomes 0.2 kcal/mol (∼70 cm ) with the
scaled CAS(8,7)/cc-pVDZ zero-point energy correction. The
modest modulation on the absorption spectrum3
1,32
of HN3, S1
r S0, is a hint for an insignificant potential barrier of reaction
. No strong potential barrier was found along the interior N-N
5
11
separation in the photofragmentation dynamics of hydrazoic
acid from its lowest excited singlet state. A direct dissociation
1
9
mechanism of HN3(A A′′) was deduced by Chu et al. and also
by Hawley and co-workers.12 In a set of recent experiments
33,34
of HN3 (S1) into N3 (X Πg) and H ( S) is endothermic by 12.4
2
2

Photodissociation of HN3
J. Phys. Chem. A, Vol. 104, No. 17, 2000 4049
kcal/mol with a barrier of 39.7 kcal/mol at the CAS(8,7)/cc-
pVTZ level, including the scaled CAS(8,7)/cc-pVDZ zero-point
energy correction. On the CAS(8,7)/cc-pVTZ-optimized station-
ary structures, the endothermic character and barrier height of
the reaction are further calculated to be 13.4 and 41.3 kcal/
mol, respectively, with the multireference MP2 approach. The
potential energy profile of the reaction is depicted in Figure 2.
coupling between S1 and T1 in HN3 is strong, the ground-state
products of N2 (X ∑g ) and NH (X ∑ ) should be experimen-
1
+
3
-
tally observed, as the T1 surface is repulsive with respect to the
1
+
1
interior N-N separation. However, N2 (X ∑g ) and NH (a ∆)
were exclusively observed as the primary products in the single-
photon dissociation of HN3 at the 355-266 nm. Recently,
4
0
Reisler and co-workers have investigated fragment recoil
anisotropies on the photoinitiated decomposition of HNCO.
They concluded that direct S1 f T1 coupling is much weaker
Single-photon photodissociation experiments on HN3 at 355,
3
08, 283, and 266 nm find that the products are exclusively N2
1
+
1
1 0
than S f S internal conversion (IC). All of these give us a
(X ∑g ) + NH (a ∆). The corresponding vertical excitation
reason to expect that the ISC from S1 to T1 takes place with
very low efficiency and is negligible with respect to the direct
dissociation on S1.
energy is in the range from 80.5 to 107.4 kcal/mol. Upon
inspection of Figure 2, one can see that the TS1 (S1) and TS2
1
(
S1) lie 72.1 and 113.2 kcal/mol in energy above the HN3 (X A′)
zero-point vibrational level. It is obvious that channel 5 is
energetically accessible, but channel 6 not accessible in energy
The third pathway involves IC to the ground state. The
intersection point between the S and S surfaces (S /S ) plays
an important role in the IC process. The S /S point is optimized
1 0
1
0
1
0
2
to photodissociation at 355-266 nm. The N3 (X Πg) and H
2
(
S) were found as minor products at 248 nm photodissocia-
with the state-averaged CAS(8,7)/cc-pVDZ approach. The
resulting structure is depicted in Figure 1 along with its
geometric parameters. Obviously, the S /S point is closer to
10,11
tion.
In this case the excitation energy of 115.3 kcal/mol is
a little higher than the barrier energy of channel 6; thus, reaction
can occur, but with lower yield compared with reaction 5.
1
0
6
1 0
the S minimum in structure than to the S minimum. It should
The energies calculated above are in excellent agreement with
the photodissociation experiments of HN3.
1 0
be pointed out that the S /S point is not on the dissociation
1
+
1
pathway of HN (S ) to N (X ∑ ) and NH (a ∆), although
3
1
2
g
Mechanism of HN3 Photodissociation. After photoexcitation
in a wavelength range from 355 to 248 nm, the HN3 molecules
populate in the first excited electronic state (S1). From this state,
in addition to radiative decay, there are three possible pathways
for HN3 to deactivate. The first pathway involves the dissocia-
the interior N-N separation in the S1/S0 structure lies between
the corresponding values in the S1 and TS1 (S1) structures. This
is because the terminal N-N separation in the S1/S0 structure
is longer than that in the S1, TS1 (S1), or N2 structure. The S1/
S0 point is 29.0 kcal/mol lower in energy than the S1/T1 point,
but 6.9 kcal/mol higher than the barrier height of the direct
dissociation reaction 5. The S1 f S0 IC occurs more easily than
the S1 f T1 ISC, but the dissociation reaction 5 still prevails,
due to a very small barrier on the pathway. The rate of the IC
1
+
1
2
2
tion to N2 (X ∑g ) + NH (a ∆) or N3 (X Πg) and H ( S) on
the S1 surface. Since some excess energy is dumped into
vibrational modes, the reactions cannot be viewed correctly as
rolling along the minimum-energy path of the potential energy
surface with locally zero kinetic energy. The RRKM theory can
be used to estimate the rates of these processes. On the basis of
the calculated vibrational frequencies, rotational constants, and
energies, the RRKM rate coefficients of reactions 5 and 6 as a
function of total energy and total angular momentum are
computed. When the molecule contains the total energy of 43
kcal/mol [relative to the zero-point vibrational level of HN3 (S1)],
and has total angular momentum J ) 20, the rate coefficient of
41
from S1 to S0 in ketene (H2CCO) was experimentally estimated
9
13 -1
to be in the range of 2.5 × 10 to 4.0 × 10 s . Since H2CCO
is an isoelectronic molecule of HN3, and their electronic and
geometric structures are similar to each other, one can assume
that the IC rate from S1 to S0 for HN3 is in a similar range. The
lower limit of the IC rate is negligibly small, as compared with
1
+
the rate of the direct dissociation of HN3 (S1) to N2 (X ∑g )
1
and NH (a ∆). In this case, the HN3 molecule is excited to S1
2
2
the HN3 (S1) dissociation to N3 (X Πg) and H ( S) is 3.72 ×
and followed by the direct dissociation, which is the most
probable mechanism of the HN3 photodissociation at a wave-
length range from 355 to 248 nm.
8
-1
1
0 s which is negligibly small in comparison with the rate
1
3 -1
coefficient of 2.17 × 10
s
for reaction 5. If the IC rate from
13
-1
S1 to S0 is in the higher limit, which is discussed below, the
RRKM rate coefficients of both reactions 5 and 6 will be
decreased, as the state density of the ground-state reactant makes
an important contribution to the RRKM-calculated rate coef-
ficient. In addition, the rate coefficient of reaction 5 has
approached the applicability limit of the RRKM theory, which
assumes the species are vibrationally equilibrated, as the time
scale of vibrational relaxation, in general, is in the range of a
picosecond or a subpicosecond. Although there is an error in
the calculated rate coefficients, we can say that channel 6 cannot
compete with channel 5 at 248 nm and longer wavelength
photodissociation of HN3.
If the IC rate lies in the higher limit of 4.0 × 10 s , the
direct dissociation on S and the IC to the ground electronic
1
state are a pair of competitive pathways. The HN molecules
3
which return to the ground state are left with sufficient internal
1
+
energy to undergo the spin-conserved dissociation to N2 (X ∑g )
1
1
+
+
+
NH (a ∆) and the spin-forbidden dissociation to N2 (X ∑g )
3
-
2
NH (X ∑ ), but the spin-allowed dissociation to N3 (X Πg)
2
and H ( S) cannot compete with the above two ground-state
processes, due to its high endothermic character. Time-domain
measurements of dissociation rate in S0 have been reported for
3
different vibrational levels. It has been found that the rate of
the spin-forbidden dissociation is overestimated by a factor of
4
The second possible pathway is intersystem crossing (ISC)
to the lowest triplet state (T1) and followed by dissociation. An
intersection point between the S1 and T1 surfaces (S1/T1) is found
with the state-averaged CAS(8,7)/cc-pVDZ method. Its structure
is shown in Figure 1. The S1/T1 point lies 36.1 kcal/mol in
energy above the S1 minimum, therefore much higher than the
barrier height of the direct dissociation reaction 5. A qualitative
about 10 if the dissociation is treated as a spin-allowed process.
That is, the S0 f T1 ISC occurs with probability close to a
-
4
value of 10 . So, the spin-forbidden dissociation reaction 1
cannot compete with the spin-allowed process 2, although the
T1/S0 intersection point is a little lower in energy than TS1 (S0),
as seen in Figure 2. The HN3 molecules populated in S1 relax
back to the ground electronic state; thus, the dominant product
3
9
1
1
+
1
analysis by Turro predicted the ISC from S1 ( ππ*) to T1
(
channel is still N2 (X ∑g ) and NH (a ∆), due to a very small
S0 f T1 probability which decreases the rate of the spin-
forbidden dissociation reaction 1. This provides a good explana-
3
ππ*) to be inefficient, since there is no first-order spin-orbit
coupling between the two states. On the other hand, if the

4050 J. Phys. Chem. A, Vol. 104, No. 17, 2000
Fang
1
tion of the experimental fact that NH (a ∆) is formed with a
(5) Casassa, M. P.; Foy, B. R.; Stephenson, J. C.; King, D. S. J. Chem.
Phys. 1991, 94, 250.
3
-
quantum yield of 0.4, while the NH (X ∑ ) yield is less than
(
6) Chen, J.; Quinones, E.; Dagdigian, P. J. J. Chem. Phys. 1989, 90,
603.
(7) Sauder, D. G.; Patel-Misra, D.; Dagdigian, P. J. J. Chem. Phys.
989, 91, 5316.
0
.002 in the UV photolysis10 of HN3 at 193 nm.
7
1
1
2
2
As shown in Figure 2, when N3(X Πg) and H ( S) approach
each other, there exist three spin-conserved pathways leading
to HN3 (S0), HN3 (S1), and N2 (X ∑g ) + NH (X ∑ ). The
first two have been discussed before. The last one is reaction
(8) Gericke, K.-H.; Theinl, R.; Comes, F. J. Chem. Phys. Lett. 1989,
1
+
3
-
64, 605. Gericke, K.-H.; Theinl, R.; Comes, F. J. J. Chem. Phys. 1990,
92, 6548.
(9) Chu, J. J.; Marcus, P.; Dagdigian, P. J. J. Chem. Phys. 1990, 93,
57.
4
. A transition state [TS (T1)] shown in Figure 1 is found on
2
this triplet pathway. The optimized TS (T1) is similar in structure
to that of reaction 6. The barrier height of reaction 4 is 20.8
kcal/mol, which is 7.1 kcal/mol lower in energy than that of
the reverse process of reaction 6.
(10) Rohrer, F.; Stuhl, F. J. Chem. Phys. 1988, 88, 4788.
(11) Gericke, K.-H.; Haas, T.; Lock, M.; Theinl, R.; Comes, F. J. J.
Phys. Chem. 1991, 95, 6104.
12) Hawley, M.; Baronavski, F.; Nelson, H. H. J. Chem. Phys. 1993,
9, 2638.
(
9
(
13) Gericke, K.-H.; Haas, T.; Lock, M.; Comes, F. J. Chem. Phys. Lett.
Summary
1
991, 186, 427. Haas, T.; Gericke, K.-H.; Maul, C.; Comes, F. J. Chem.
Phys. Lett. 1993, 202, 108.
14) Lock, M.; Gericke, K.-H.; Comes, F. J. Chem. Phys. 1996, 213,
385.
In the present work, photodissociation of HN3 at long
wavelength (355-248 nm) is investigated with the complete
active space SCF molecular orbital method. The mechanism
leading to different products is determined on the basis of the
optimized ground- and excited-state potential energy surfaces
of dissociation and their crossing points. After the HN3
molecules are excited to the S1 state, the most probable pathway
(
(
15) Barnes, R. J.; Gross, A.; Lock, M.; Sinha, A. J. Phys. Chem. A
1
997, 101, 6133-6137.
(16) Schoennenbeck, G.; Biehl, H.; Stuhl, F.; Meier, U.; Staemmler, V.
J. Chem. Phys. 1998, 109, 2210.
(17) Cook, P. A.; Langford, S. R.; Ashfold, M. N. R. Phys. Chem. Chem.
Phys. 1999, 1, 45.
(
18) Wright, K. R.; Hutchinson, J. S. Phys. Chem. Chem. Phys. 1999,
1
+
1
is direct dissociation of HN3 (S1) into N2 (X ∑g ) and NH (a ∆),
due to a very small barrier on the pathway. A high barrier exists
1
, 1299.
(19) Alexander, M. H.; Werner, H.-J.; Dagdigian, P. J. J. Chem. Phys.
2
2
1988, 89, 1388.
20) Alexander, M. H.; Werner, H.-J.; Hemmer, T.; Knowles, P. J. J.
Chem. Phys. 1990, 93, 3307.
21) Yarkony, D. R. J. Chem. Phys. 1990, 92, 320.
on the S1 pathway to N3 (X Πg) + H ( S), which is nearly
(
inaccessible in energy at the long-wavelength region. Thus, the
decomposition of HN3 (S1) to N3 (X Πg) + H ( S) cannot
compete with the direct dissociation to N2 (X ∑g ) and NH
2
2
(
1
+
(22) Meier, U.; Staemmler, V. J. Phys. Chem. 1991, 95, 6111.
(23) Yamomoto, N.; Vreven, T.; Robb, M. A.; Frisch, M. J.; Schlegel,
J. B. Chem. Phys. Lett. 1996, 250, 373.
1
(
a ∆). If the IC rate constant lies in the estimated higher limit,
the S1 f S0 IC is in competition with the direct dissociation.
The HN3 molecules in S1 which return to the ground electronic
state are left with sufficient internal energy to overcome the
(24) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007.
(25) McDouall, J. J.; Peasley, K.; Robb, M. A. Chem. Phys. Lett. 1988,
48, 183.
1
1
+
(26) Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502.
barrier of the spin-allowed dissociation to N2 (X ∑g ) + NH
(27) Gaussian 98 (Revision A.3): Frisch, M. J.; Trucks, G. W.; Schlegel,
1
1
+
(
a ∆) or the barrier of the spin-forbidden pathway to N2 (X ∑g )
H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.;
Montgomery, J. A.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam,
J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.;
Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Promelli, C.; Adamo,
C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.;
Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman,
J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.;
Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith,
T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.;
Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M.
W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A., Gaussian,
Inc.: Pittsburgh, PA, 1998.
-
+
NH (X3∑ ). A very small S0 f T1 probability reduces the
rate coefficient of the spin-forbidden dissociation by a factor
4
of about 10 . Therefore, the dominant product channel is still
N2 (X ∑g ) + NH (a ∆), as in S1. The present calculations
provide a good elucidation that the NH fragments are exclusively
1
+
1
1
in the a ∆ state in the UV photodissociation of HN3 at a
wavelength range from 355 to 248 nm. The triplet potential
energy surface is repulsive with respect to the interior N-N
2
2
separation. When N3 (X Πg) and H ( S) approach each other
(28) Eyring, H; Lin, S. H.; Lin, S. M. Basic Chemical Kinetics; Wiley:
along the triplet pathway, reaction 4 can occur, forming the
New York, 1980. Miller, W. H. J Am. Chem. Soc. 1979, 101, 6810.
(29) Winnewisser, B. P. J. Mol. Spectrosc. 1980, 82, 220.
1
+
3
-
ground-state products of N2 (X ∑g ) + NH (X ∑ ), but it is
2
2
(30) Okabe, H. Photochemistry of Small Molecules; Wiley: New York,
978.
more efficient for N3 (X Πg) and H ( S) to combine, forming
1
the ground-state reactant of HN3.
(
(
31) Okabe, H. J. Chem. Phys. 1968, 49, 2726.
32) McDonald, J. R.; Rabalis, J. W.; McGlynn, S. P. J. Chem. Phys.
Acknowledgment. This work was supported by the National
Natural Science Foundation of China (Grant No. 29673007). I
am grateful to the Alexander von Humboldt Foundation for
donation of an IBM/RS6000 workstation.
1970, 52, 1332.
33) Droz-Georget, T.; Zyrianov, M.; Reisler, H.; Chandler, D. W. Chem.
Phys. Lett. 1997, 276, 316.
34) Brown, S. S.; Berghout, H. L.; Crim, F. F. J. Chem. Phys. 1996,
105, 8103.
(
(
(35) Klossika, J.-J.; Floethmann, H.; Beck, B.; Schinke, R.; Yamashita,
K. Chem. Phys. Lett. 1997, 176, 325.
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(
29.
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4
(
2) Foy, B. R.; Casassa, M. P.; Stephenson, J. C.; King, D. S. J. Chem.
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9, 1378.
(
(
8
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