3.5 Results and Discussion
77
S 0 R 2 = 1.1865 Å), with the bond angle θ N N N = 180
◦ . This value is in very good
agreement with the experimentally-observed gas-phase equilibrium bond length
of 1.188 Å, as obtained from rotational spectroscopy [87]. If the optimisation is
performed with a full valence active space, CAS(16,12), the N-N bonds elongate,
with
S 0 R 1 =
S 0 R 2 = 1.2002 Å. This is only slightly longer than the experimental
bond length in the gas phase molecule, and for the molecule in the ionic azide materials (ca. 1.17–1.18 Å). Optimisation of the first triplet state, T 1 , leads to an increase
in the N-N bond lengths, with
T 1 R 1 =
T 1 R 2 = 1.2607 Å using a CAS(8,8) active
space, increasing to 1.2855 Å when optimised at CAS(16,12). The T 1 state remains
linear in all cases. Similarly, the bond lengths of the first singlet state, S 1 , expand from
1.2243 Å to 1.2475 Å when moving from a CAS(8,8) to CAS(16,12) calculation.
Importantly, when the active space is increased, the relative energies of the equilibrium structures change only slightly with E S1 − E S0 < −0.3 eV, E T 1 − E S0 , < +
0.03 eV. The same holds for comparison of structures with R 2 = 2.5 Å, i.e. beyond
the dissociation limit of the azido anion. The effect of increasing the active space is
therefore small relative to the additional computational costs, and as such the smaller
active space was used for the remainder of this work. To assess the effect of vibrational normal coordinates on the relative stabilities of the electronic states of N
−
3 ,
all excitations were performed as Frank-Condon (FC) transitions from perturbations
to the ground state (S 0 ) optimised geometry. Hence, rupture of bond R 2 along the
excited state PESs are investigated based on R 1 fixed at the optimised length of the
S 1 state.
Elongation of R 2 leads to bond dissociation at
S 0 R 2 > 2 Å, with a dissociation
energy of ca. 4.52 eV, Fig. 3.5A. The | S 0 , V 0 | S 1 , V 0 transition requires ca. 5.1 eV
energy, with the FC transition requiring 5.22 eV. In contrast to the dissociation energy
of the ground state, N-N dissociation in the S 1 state has an energy barrier of only
ca. 1 eV. This occurs with
S 1 R 2 > 1.75 Å. Importantly, once this energy barrier is
surpassed, dissociation is spontaneous, with E(
S 1 R 2,diss −
S 1 R 2,eqm ) ≈ −0.4eV.
The |S 0 , V 0 |T 1 , V 0 transition occurs at notably lower energy, 4.21 eV, with the FC
transition occurring at 4.46 eV. In the T 1 state, bond dissociation is met with a
similar energy barrier to the S 1 state (ca. 1 eV when
T 1 R 2 > 1.65 Å). Again, once
this energetic barrier has been surpassed, bond dissociation is spontaneous, with
E(
T1 R 2,diss −
T1 R 2,eqm ) ≈ −1.05 eV. The dissociation product of the T 1 state sits ca.
1.2 eV below that of the S 0 and S 1 states. The same general trend is observed for all
higher excited states. It therefore follows that excitation of the azido anion into any
of the excited states favours bond dissociation.
Based on energetic considerations, the T 1 state appears the most likely candidate
for bond dissociation given its low dissociation barrier. However, at equilibrium
geometry, the energies required to reach any of the excited states greatly exceeds
k B T. As described in Sect. 3.1, impact induced initiation results from mechanical
perturbation of the impacted material. This leads to excitation of the lattice modes,
and eventual localisation of this energy into vibrational modes [6]. The amount of
energy localised in this way can be greatly in excess of the energy achievable by bulk
temperatures, and sufficient to induce bond rupture [14]. Hence, it is necessary to
consider the effects of the vibrational normal coordinates on the electronic structure
77
S 0 R 2 = 1.1865 Å), with the bond angle θ N N N = 180
◦ . This value is in very good
agreement with the experimentally-observed gas-phase equilibrium bond length
of 1.188 Å, as obtained from rotational spectroscopy [87]. If the optimisation is
performed with a full valence active space, CAS(16,12), the N-N bonds elongate,
with
S 0 R 1 =
S 0 R 2 = 1.2002 Å. This is only slightly longer than the experimental
bond length in the gas phase molecule, and for the molecule in the ionic azide materials (ca. 1.17–1.18 Å). Optimisation of the first triplet state, T 1 , leads to an increase
in the N-N bond lengths, with
T 1 R 1 =
T 1 R 2 = 1.2607 Å using a CAS(8,8) active
space, increasing to 1.2855 Å when optimised at CAS(16,12). The T 1 state remains
linear in all cases. Similarly, the bond lengths of the first singlet state, S 1 , expand from
1.2243 Å to 1.2475 Å when moving from a CAS(8,8) to CAS(16,12) calculation.
Importantly, when the active space is increased, the relative energies of the equilibrium structures change only slightly with E S1 − E S0 < −0.3 eV, E T 1 − E S0 , < +
0.03 eV. The same holds for comparison of structures with R 2 = 2.5 Å, i.e. beyond
the dissociation limit of the azido anion. The effect of increasing the active space is
therefore small relative to the additional computational costs, and as such the smaller
active space was used for the remainder of this work. To assess the effect of vibrational normal coordinates on the relative stabilities of the electronic states of N
−
3 ,
all excitations were performed as Frank-Condon (FC) transitions from perturbations
to the ground state (S 0 ) optimised geometry. Hence, rupture of bond R 2 along the
excited state PESs are investigated based on R 1 fixed at the optimised length of the
S 1 state.
Elongation of R 2 leads to bond dissociation at
S 0 R 2 > 2 Å, with a dissociation
energy of ca. 4.52 eV, Fig. 3.5A. The | S 0 , V 0 | S 1 , V 0 transition requires ca. 5.1 eV
energy, with the FC transition requiring 5.22 eV. In contrast to the dissociation energy
of the ground state, N-N dissociation in the S 1 state has an energy barrier of only
ca. 1 eV. This occurs with
S 1 R 2 > 1.75 Å. Importantly, once this energy barrier is
surpassed, dissociation is spontaneous, with E(
S 1 R 2,diss −
S 1 R 2,eqm ) ≈ −0.4eV.
The |S 0 , V 0 |T 1 , V 0 transition occurs at notably lower energy, 4.21 eV, with the FC
transition occurring at 4.46 eV. In the T 1 state, bond dissociation is met with a
similar energy barrier to the S 1 state (ca. 1 eV when
T 1 R 2 > 1.65 Å). Again, once
this energetic barrier has been surpassed, bond dissociation is spontaneous, with
E(
T1 R 2,diss −
T1 R 2,eqm ) ≈ −1.05 eV. The dissociation product of the T 1 state sits ca.
1.2 eV below that of the S 0 and S 1 states. The same general trend is observed for all
higher excited states. It therefore follows that excitation of the azido anion into any
of the excited states favours bond dissociation.
Based on energetic considerations, the T 1 state appears the most likely candidate
for bond dissociation given its low dissociation barrier. However, at equilibrium
geometry, the energies required to reach any of the excited states greatly exceeds
k B T. As described in Sect. 3.1, impact induced initiation results from mechanical
perturbation of the impacted material. This leads to excitation of the lattice modes,
and eventual localisation of this energy into vibrational modes [6]. The amount of
energy localised in this way can be greatly in excess of the energy achievable by bulk
temperatures, and sufficient to induce bond rupture [14]. Hence, it is necessary to
consider the effects of the vibrational normal coordinates on the electronic structure