Dissociation Reaction of N8 Azapentalene
to 4N2: A Theoretical Study
LAURA GAGLIARDI,1 STEFANO EVANGELISTI,2 ANDERS
BERNHARDSSON,3 ROLAND LINDH,3 BJÖRN O. ROOS3
1
Dipartimento di Chimica Fisica e Inorganica, Università di Bologna, Italy
Laboratoire de Physique Quantique, UMR 5626, Université Paul Sabatier, 118, Route de Narbonne,
31062 Toulouse Cedex, France
3
Department of Theoretical Chemistry, Chemical Center, P.O.B. 123, S-221 00 Lund, Sweden
2
Received 13 August 1999; accepted 27 August 1999
ABSTRACT: We present a theoretical study on the dissociation reaction of N8
azapantalene to four N2 molecules. The process proceeds via isomerization of N8
azapentalene to N8 azidopentazole, which then dissociates directly into four nitrogen
molecules. The calculations have determined the relative energies of the two isomers and
the two transition states involved in the dissociation process. The results show
azidopentazole to be 13 kcal/mol more stable than azapentalene. The barrier to
dissociation into four N2 molecules is computed to be 19 kcal/mol. It is concluded that N8
is not stable enough to be considered as a candidate for a high-energy density material.
The calculations have been carried out using multiconfigurational self-consistent field and
c 2000 John Wiley & Sons, Inc. Int J Quant Chem 77:
second-order perturbation theory. 311–315, 2000
Key words: CASSCF/CASPT2; nitrogen clusters; N8 ; structure; dissociation
Introduction
T
he model clusters composed by nonmetallic
light atoms (carbon, nitrogen, oxygen) have
been the object of a number of recent theoretical
investigations [1 – 18]. Among these compounds,
polynitrogen clusters (Nn with n > 4) have atCorrespondence to: L. Gagliardi.
Contract grant sponsor: Swedish Natural Science Research
Council (NFR).
Contract grant sponsor: Ministero dell’Università e della
Ricerca Scientifica e Tecnologia (M.U.R.S.T).
International Journal of Quantum Chemistry, Vol. 77, 311–315 (2000)
c 2000 John Wiley & Sons, Inc.
tracted attention because of their potential use as
high-energy density materials (HEDM), i.e., compounds with a high ratio between the energy released in a fragmentation reaction and the specific
weight. These studies have been summarized in one
of our previous works [19] and will not be discussed further. In our previous works on the hypothetical N8 system [19 – 21], we considered several
conformational isomers of this species. In particular, the isomerization path going from N8 with a
cubic structure to N8 azapentalene (1) was investigated. Azapentalene was found to be the most
stable species along the reaction path, in agree-
CCC 0020-7608 / 00 / 010311-05
GAGLIARDI ET AL.
ment with earlier studies [8]. Two studies in 1996
showed, however, that azidopentazole (2) was more
stable [10, 11]. Density functional studies gave an
energy difference of 15 kcal/mol [11], while the coupled cluster [CCSD(T)] results of Nguyen and Ha
obtained 16 kcal/mol [10]. No lower energy structure has been found for N8 , so this is considered to
be the global minimum. However, the recent synthesis of the N+
5 cation [22] suggests the possibility
−
of a pure nitrogen salt: N+
5 N3 , which may be lower
in energy. We shall return to this possibility in a future study.
Here, we initially investigated the isomerization
reaction of azapentalene (1) to azidopentazole (2),
and determined the transition state (TS12) between
the two isomers at the complete active space (CAS)
SCF and CASPT2 (multiconfigurational second order perturbation) levels of theory. The dissociation
of 2 was then investigated. The single bond in the
pentagonal ring opposite to the tail was broken and
a transition state (TS23) toward the dissociation of 2
to four N2 molecules was found.
Theoretical Approach
Multiconfigurational wave functions (CASSCF)
[23] have been used to describe the electronic structure of the isomers of N8 and the transition states
between them. The reaction path studied passes
over transition states where near degeneracy occurs
between different electronic configurations. In such
situations, a multiconfigurational approach is the
safest way to describe the electronic structure accurately. Dynamic electron correlation is added using multiconfigurational second-order perturbation
theory (CASPT2) with the CASSCF wave function
as reference function [24, 25]. This approach has
in a number of earlier applications shown to give
estimates of relative correlation energies with an accuracy of a few kilocalories/mole (see, e.g. Refs. [26,
27]). The CASSCF and CASPT2 calculations were
performed using the MOLCAS-4 quantum chemistry software [28].
The geometries of the minima and transition
states were optimized at the CASSCF level using
analytical first derivatives. Single-point energy calculations were then performed at the optimized
geometries at the CASPT2 level. The minima and
transition states of the reaction were optimized
with some symmetry constraints when applicable,
namely 1 was optimized in D2h , 2 and TS23 in Cs ,
while no symmetry was used in the determina-
312
FIGURE 1. Azapentalene (1) and azidopentazole (2);
the transition state between (1) and (2), TS12; and the
transition state for dissociation of (2) into four N2 , TS23.
tion of TS12. Figure 1 shows the structures for the
two meta-stable energy minima, 1 and 2, and the
transition states, TS12 between 1 and 2, and TS23
between 2 and four N2 .
ANO-S-type basis sets have been used in all calculations [29]. All structures were studied with a
3s2p1d basis (112 basis functions for N8 ). Singlepoint energy calculations with a 4s3p2d1f ANO-L
basis set (240 basis functions) [30] were performed
for some of the optimized structures.
Calculations and Results
The choice of the active space is the crucial step
in a CASSCF calculation. In our previous study [19],
for azapentalene, 1, we used an active space of
12 electrons in 10 orbitals (12/10), the 8 π orbitals
(with 10 electrons) and the bonding and antibonding orbitals of the central bond, since the reaction
from octazacyclooctatetraene to azapentalene was
studied. The effect on the CASPT2 energy due to
VOL. 77, NO. 1
DISSOCIATION REACTION OF N8 AZAPENTALENE TO 4N2
the extension from a smaller (8/8) active space was,
however, small.
Here, we have studied the energy dependence
on the active space along the reaction path. The selection of the active spaces was based on restricted
active space SCF (RASSCF) calculation with 24 active orbitals and 24 electrons, allowing single and
double substitutions out of a closed-shell configuration. The occupation number of the corresponding
natural orbitals were used to select the active spaces.
For the two local minima, 1 and 2, we determined
the CASSCF and relative CASPT2 energy for several
active spaces of increasing dimension. In Table I we
report the CASSCF and CASPT2 energies as a function of the active space for structure 1. The results
show that, while the CASSCF energy decreases by
about 51 kcal/mol in going from the smallest active
space (8 electrons in 7 orbitals) to the largest one
(14 electrons in 13 orbitals), the CASPT2 energy, on
the other hand, is essentially stable, varying only by
1 kcal/mol.
In Table II the CASSCF and CASPT2 energy of
azidopentazole is reported for four different active spaces. The CASSCF energy varies by about
57 kcal/mol in going from 8 electrons and 8 orbitals
to 14 electrons and 13 orbitals. Here the variations
in the CASPT2 energy varies are somewhat larger
but stabilize at a change of about −1.5 kcal/mol for
the largest active space. This structure is more sensitive to the choice of the active orbitals. Not only
the size of the space is crucial, but the same active
space may give slightly varying total energies, depending on the convergence of the CASSCF wave
function. Thus, a somewhat larger uncertainty must
be attached to the total energy for this structure.
TABLE I
Azapentalene: CASSCF and CASPT2 energies for
different active spaces in D2h symmetry.a
ne
na
1ECASSCF
1ECASPT2
8
10
10
12
14
00002221
00003221
20002221
22002221
22202221
0.0
−6.4
−6.1
−19.1
−50.8
0.0
−0.3
−0.5
−1.3
−0.9
a Number
of active electrons: ne ; number of active orbitals
for the eight symmetry classes (the last four are π ): na ; the
energy difference (in kcal/mol) with respect to the first calculation (ne = 8, na = 7) at the CASSCF and CASPT2 levels:
1E.
TABLE II
Azidopentazole: CASSCF and CASPT2 energy for
different active spaces in Cs symmetry.a
ne
na
1ECASSCF
1ECASPT2
8
12
14
14
44
66
75
76
0.0
−30.7
−30.6
−57.4
0.0
+3.9
−2.3
−1.6
a Number
of active electrons: ne ; number of active orbitals
for the two symmetry classes: na ; the energy difference
(in kcal/mol) with respect to the first calculation (ne = 8,
na = 8) at the CASSCF and CASPT2 levels: 1E.
The first transition state, TS12, was optimized
with the active space (12/11). This transition state
is rather close to structure 1, the energy of which is
stable with respect to further increase of the active
space. The structure of TS23 was first optimized using the (12/12) active space. A single-point energy
calculation was then performed with the (14/13)
space.
In Table III the energetics of the reaction are reported. At the CASPT2 level of theory with the
small basis set 2 lies 13.3 kcal/mol below 1, and
the transition state between the two structures,
TS12, lies 8.8 kcal/mol above 1 and 22.1 kcal/mol
above 2. The CCSD(T)/DZP value of the energy
difference was computed by Nguyen and Ha to
be 16.3 kcal/mol [17.7 when the zero-point energy (ZPE) is added] [10]. Glukhovtsev et al. obtains 14.8 kcal/mol at the DFT/B3LYP level of theory [11]. Nguyen and Ha have also computed the
barrier between 1 and 2 and obtained the result
of 13.4 kcal/mol (11.8 with ZPE). All these results
are similar. However, when the CASPT2 calculations are repeated with the more extended basis set
ANO-L 4s3p2d1f , the energy difference between 1
and 2 is reduced to 1.5 kcal/mol. Adding the zeropoint correction given by Nguyen and Ha increases
the value to 2.9 kcal/mol. Thus, 2 is still the most
stable compound, but the energy difference is considerably reduced. It is azapentalene, which is most
affected by the extension of the basis set, probably
due to the strong π conjugation in that molecule.
The transition state has not been treated at this level
of theory. Because it is intermediate in structure between the two equilibria, we can expect an effect of
about 5 kcal/mol from a basis set extension, leading
to a prediction of about 14 kcal/mol for the barrier.
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
313
GAGLIARDI ET AL.
TABLE III
Energy difference (in kcal/mol) between the two local minima, 1 and 2, between each transition state and the
preceding minimum, and between 2 and 4 N2 , 3, at CASSCF and CASPT2 levels of theory.a
1E (kcal/mol)
Structure
2-1
TS12-1
TS23-2
3-2
CASSCF
CASPT2
CCSD(T)b
DFT/B3LYPc
−53.5(55.8)
+5.0
+12.4(15.2)
−338.5(−352.8)
−13.3(−1.5)
+8.8
+14.1(+19.3)
−195.7(−197.2)
16.3
13.4
—
−233.2
14.8
—
—
−187.0
a Basis
set: ANO-S 3s2p1d, active space (14/13). Results obtained with the larger ANO-L 4s3p2d1f basis are given within parentheses.
b From Ref. [10].
c From Ref. [11].
A similar basis set effect has in fact been found for
the barrier between 2 and the dissociated product.
It has been found in the present study that 2 in
turn dissociates directly into four N2 molecules via a
transition state of Cs symmetry. This transition state
was computed to lie 14.1 kcal/mol above the equilibrium energy of 2, a number which increased to
19.3 with the large basis set (cf. Table IV). To our
knowledge, this is the first time that the dissociation
path from N8 to four N2 molecules has been fully explored. We note from the results in Table IV that the
energy difference between 2 and four N2 molecules
varies somewhat between the different correlated
methods. Our CASPT2 energies are rather close to
the density functional theory (DFT) results, while
CCSD(T) seems to give a somewhat larger energy
difference.
Finally, a few words about the geometries. The
most significant bond distance and angles are
shown in Table IV with atom labeling taken from
Figure 1. Structure 1 is planar and the N—N bond
distances are similar, due to the π delocalization,
varying between 1.30 and 1.32 Å. The bond angles
vary between 110.0◦ and 113.1◦. In going from 1
to 2, one bond between a two-coordinated and a
three-coordinated nitrogen is broken. This implies a
general rearrangement of the molecule. In the pentagonal ring there are two double (1.29 Å), two
equal single bonds, 1.36, and one conjugated bond,
1.32 Å. The tail of the molecule contains a triple
bond, 1.11 Å, between the two end atoms, one single bond, 1.37, and one shorter conjugated bond,
1.31 Å. The pentagonal ring remains planar, and
the tail lies almost perpendicular to it. The transition state between 1 and 2 presents an intermediate
TABLE IV
Significant bond distances (R) and bond angles (A) of the local minima 1 and 2, and the transition states TS12
and TS23.a
1
2
TS12
TS23
R12 = 1.30
R13 = 1.30
R37 = 1.32
A124 = 110.03
A137 = 103.42
R37 = 1.36
R13 = 1.29
R12 = 1.32
R26 = 1.37
R68 = 1.31
R85 = 1.11
A374 = 108.74
A213 = 105.35
A268 = 107.92
A685 = 169.09
R37 = 1.28
R13 = 1.32
R12 = 1.30
R26 = 1.38
R68 = 1.26
R85 = 1.09
A137 = 109.44
A213 = 102.28
A268 = 106.04
A685 = 167.39
R37 = 1.89
R13 = 1.17
R12 = 1.49
R26 = 1.37
R68 = 1.32
R85 = 1.11
A374 = 115.86
A213 = 114.58
A268 = 107.19
A685 = 170.16
a The
314
distances are in angstrom and the angles in degrees. For the atom numbering, see Fig. 1.
VOL. 77, NO. 1
DISSOCIATION REACTION OF N8 AZAPENTALENE TO 4N2
geometry. It is almost planar like 1, with a substantial rearrangement of the bond distances and angles.
The structure shows that the isomerization reaction
from 1 to 2 implies breaking the bond between a
two- and a three-coordinated nitrogen atom (1 and 5
in Fig. 1) and a subsequent the rotation out of plane
of the tail, which occurs after the transition state has
been crossed.
In the second part of the reaction, 2 is transformed into four nitrogen molecules by first breaking the bond between the end atoms of the fivemembered ring followed by a simultaneous rupture
of the three long NN bonds. The transition state
is characterized by an increase of four of the NN
bonds, while the other four bonds either do not
change or decrease their distance (cf. Table IV).
The barrier to this reaction was computed to be
19 kcal/mol, using the largest active space and the
largest basis set.
Conclusions
CASSCF/CASPT2 calculations have been performed on two structures of the N8 cluster, azapentalene and azidopentazole and the transition
state between them. The dissociation of azidopentazole into four nitrogen molecules has also been
studied. The results show that azapentalene transforms into azidopentazole via a barrier of about
15 kcal/mol and that the azido form is 3 kcal/mol
more stable. The barrier for dissociation of the more
stable com- pound into 4 N2 molecules was, however, found to be less than 20 kcal/mol. Since only
a Cs , pathway was explored, this value must be considered as an upper limit only. It is thus possible
that a pathway with an even smaller barrier exists. We conclude that N8 in the forms studied here
are not good candidates for HEDM. Whether it is
possible to form more stable compounds starting
−
from N+
5 and N3 will be studied in a forthcoming
work.
ACKNOWLEDGMENTS
This contribution is dedicated to Mike Zerner on
his 60th birthday. One of us (B.O.R.) would like to
express his deep gratitude for a long and lasting
friendship. It is only a pity that it has not resulted in
more than one joint fishing trip so far. Maybe some
time in the future?
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
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