74
3 Vibrational Up-Pumping: Predicting Impact Sensitivity of Some …
Fig. 3.3 Electronic structure of the azido anion by HSE06 in a periodic box, N 3
− . a Projected
Crystal Overlap Hamilton population (pCOHP) for a TZVP (blue) and STO-6G (black) basis set. A
high-level basis set leads to spurious results, [71] hence use of a minimal basis set. b The ‘density
of states’ for the azido anion, with visualisation of the associated molecular orbitals. Figure from
Ref. [1], https://doi.org/10.1021/acs.jpcc.8b05285. Copyright 2018 American Chemical Society
The electronic structure of the azido anion, present in all the energetic azides
studied here, is given in Fig. 3.3. The Projected Crystal Overlap Hamilton Population (pCOHP) weights each orbital by the overlap matrix component associated
with neighbouring N atoms. Hence, it identifies orbitals in which directly bonded N
atoms are stabilised or not. The first excited state associated with the azido anion
involves excitation of an electron from a non-bonding π g orbital (i.e. –pCOHP close
to zero) to an antibonding π u molecular orbital (i.e. −pCOHP is negative). Hence
excitation should yield considerable weakening of the N-N covalent bonds. Analysis
of the crystalline band structures in Fig. 3.4 suggests that for all azides, the top of
the conduction band and bottom of the valence bands are both primarily azide in
character. This suggests that direct excitation of the N
−
3 molecule is the dominant
transition mechanism.
This concept has led to the ‘band gap criterion’ for predicting impact sensitivity
in some materials (Chap. 1.3.2.2) [78]. Despite interest in the energetic azides, no
data on the experimental band gaps could be found. As such, band gaps presented
here are compared against literature calculated values, where possible, Table 3.4.
The electronic band structure was calculated for each of the nine crystalline azide
materials listed in Fig. 3.1 using the PBE and HSE06 (Shown in Fig. 3.4) DFT
functionals. It is first worth noting that all of the crystalline materials have smaller
band gaps than the isolated molecule [79]. This is expected and due to the periodicity
of the former. It is generally found that the ionic azide materials (NaN 3 , TAGZ,
NH 4 N 3 , LiN 3 and BaN 6 ) exhibit larger band gaps than the polymeric (SnN 6 , AgN 3 ,
ZnN 6 ) or molecular (HN 3 ) systems. Noting that the ionic azide materials are typically
less sensitive to mechanically-induced initiation than the polymeric and molecular
systems (Sect. 3.3), the trend in PBE band gaps generally agree with the band gap
criterion. However, it is worth noting a discrepancy in this trend, where the sensitivity
of BaN 6 NaN 3 despite their band gaps being similar.
3 Vibrational Up-Pumping: Predicting Impact Sensitivity of Some …
Fig. 3.3 Electronic structure of the azido anion by HSE06 in a periodic box, N 3
− . a Projected
Crystal Overlap Hamilton population (pCOHP) for a TZVP (blue) and STO-6G (black) basis set. A
high-level basis set leads to spurious results, [71] hence use of a minimal basis set. b The ‘density
of states’ for the azido anion, with visualisation of the associated molecular orbitals. Figure from
Ref. [1], https://doi.org/10.1021/acs.jpcc.8b05285. Copyright 2018 American Chemical Society
The electronic structure of the azido anion, present in all the energetic azides
studied here, is given in Fig. 3.3. The Projected Crystal Overlap Hamilton Population (pCOHP) weights each orbital by the overlap matrix component associated
with neighbouring N atoms. Hence, it identifies orbitals in which directly bonded N
atoms are stabilised or not. The first excited state associated with the azido anion
involves excitation of an electron from a non-bonding π g orbital (i.e. –pCOHP close
to zero) to an antibonding π u molecular orbital (i.e. −pCOHP is negative). Hence
excitation should yield considerable weakening of the N-N covalent bonds. Analysis
of the crystalline band structures in Fig. 3.4 suggests that for all azides, the top of
the conduction band and bottom of the valence bands are both primarily azide in
character. This suggests that direct excitation of the N
−
3 molecule is the dominant
transition mechanism.
This concept has led to the ‘band gap criterion’ for predicting impact sensitivity
in some materials (Chap. 1.3.2.2) [78]. Despite interest in the energetic azides, no
data on the experimental band gaps could be found. As such, band gaps presented
here are compared against literature calculated values, where possible, Table 3.4.
The electronic band structure was calculated for each of the nine crystalline azide
materials listed in Fig. 3.1 using the PBE and HSE06 (Shown in Fig. 3.4) DFT
functionals. It is first worth noting that all of the crystalline materials have smaller
band gaps than the isolated molecule [79]. This is expected and due to the periodicity
of the former. It is generally found that the ionic azide materials (NaN 3 , TAGZ,
NH 4 N 3 , LiN 3 and BaN 6 ) exhibit larger band gaps than the polymeric (SnN 6 , AgN 3 ,
ZnN 6 ) or molecular (HN 3 ) systems. Noting that the ionic azide materials are typically
less sensitive to mechanically-induced initiation than the polymeric and molecular
systems (Sect. 3.3), the trend in PBE band gaps generally agree with the band gap
criterion. However, it is worth noting a discrepancy in this trend, where the sensitivity
of BaN 6 NaN 3 despite their band gaps being similar.