76
3 Vibrational Up-Pumping: Predicting Impact Sensitivity of Some …
Table 3.4 Calculated band gaps for the crystalline azide materials by PBE (LBS) and HSE06
(LBS). The band gaps are labelled as being direct (D) or indirect (ID). Comparison of energies are
shown with literature and discrepancy in momentum conservation is shown. Values are given in eV
Material
PBE
HSE06
D/ID
Literature
N
−
3
5.64
7.06
–
–
α-NaN 3
4.02
5.34
D
5.38 ҂a ; 5.03 V
b
TAGZ
4.48
5.82
ID
–
NH 4 N 3
4.36
5.75
ID
5.08 (D) ҂b
LiN 3
3.56
4.75
D
4.98 ҂a ; 4.68 V
b
HN 3
3.78
5.20
ID
–
Ba(N 3 ) 2
4.12
5.32
D
3.65 V
c
AgN 3
1.57
2.77
D
1.72٣ a ; 2.5 ҂V
a
Zn(N 3 ) 2
3.41
4.78
ID
–
Sn(N 3 ) 2
0.66
1.51
ID
–
҂ TB-mBJ band gaps from (a) Ref. [60] (b) Ref. [80]; ٣ PBE band gap from (a) Ref. [81]; V PW91
band gap from (a) Ref. [82] (b) Ref. [83] (c) Ref. [84]
As expected, the magnitude of the band gap for each of the materials increases on
moving to the screened hybrid HSE06 functional, Table 3.4. Comparison to previously calculated band gaps, based on various functionals, for some of the azide materials agree well with the HSE06 values. A notable exception is NH 4 N 3 , for which
earlier works have suggested a direct band gap of ca. 0.7 eV lower than that calculated here [80]. Other theoretical studies support the present findings that NH 4 N 3 is
an indirect band gap material [85]. Experimental validation is therefore required. The
band gap of Ba(N 3 ) 2 is also considerably larger by HSE06 than previously reported
based on PW91 GGA DFT calculations. Despite this GGA functional performing
relatively well for other azides, it appears to fail in the case of Ba(N 3 ) 2 . Instead, the
PW91 result for Ba(N 3 ) 2 is much closer to the PBE band gap.
Interestingly, while the band gap criterion holds relatively well across the PBEbased band gaps, it is less prominent for the higher-level functional HSE06. Noting
that the latter is expected to be much more accurate, this suggests that the correlation
with the lower level functional was largely fortuitous. Some earlier works also show
discrepancy between sensitivity and band gap [86]. No obvious trend is seen between
the sensitivity and a material having a direct or indirect electronic band gap.
3.5.1.1 Dissociation of N
−
3
Throughout the following discussion, the symmetric N-N bonds are denoted R 1 and
R 2 , with the electronic state given as a preceding superscript. The S o bond length of
R 1 is thus denoted
S o R 1 .
In the closed-shell ground state of the N
−
3 anion, the optimised geometry
(CAS(8,8)/6-31 + G*) of the molecule shows two equivalent N-N bonds (
S 0 R 1 =
3 Vibrational Up-Pumping: Predicting Impact Sensitivity of Some …
Table 3.4 Calculated band gaps for the crystalline azide materials by PBE (LBS) and HSE06
(LBS). The band gaps are labelled as being direct (D) or indirect (ID). Comparison of energies are
shown with literature and discrepancy in momentum conservation is shown. Values are given in eV
Material
PBE
HSE06
D/ID
Literature
N
−
3
5.64
7.06
–
–
α-NaN 3
4.02
5.34
D
5.38 ҂a ; 5.03 V
b
TAGZ
4.48
5.82
ID
–
NH 4 N 3
4.36
5.75
ID
5.08 (D) ҂b
LiN 3
3.56
4.75
D
4.98 ҂a ; 4.68 V
b
HN 3
3.78
5.20
ID
–
Ba(N 3 ) 2
4.12
5.32
D
3.65 V
c
AgN 3
1.57
2.77
D
1.72٣ a ; 2.5 ҂V
a
Zn(N 3 ) 2
3.41
4.78
ID
–
Sn(N 3 ) 2
0.66
1.51
ID
–
҂ TB-mBJ band gaps from (a) Ref. [60] (b) Ref. [80]; ٣ PBE band gap from (a) Ref. [81]; V PW91
band gap from (a) Ref. [82] (b) Ref. [83] (c) Ref. [84]
As expected, the magnitude of the band gap for each of the materials increases on
moving to the screened hybrid HSE06 functional, Table 3.4. Comparison to previously calculated band gaps, based on various functionals, for some of the azide materials agree well with the HSE06 values. A notable exception is NH 4 N 3 , for which
earlier works have suggested a direct band gap of ca. 0.7 eV lower than that calculated here [80]. Other theoretical studies support the present findings that NH 4 N 3 is
an indirect band gap material [85]. Experimental validation is therefore required. The
band gap of Ba(N 3 ) 2 is also considerably larger by HSE06 than previously reported
based on PW91 GGA DFT calculations. Despite this GGA functional performing
relatively well for other azides, it appears to fail in the case of Ba(N 3 ) 2 . Instead, the
PW91 result for Ba(N 3 ) 2 is much closer to the PBE band gap.
Interestingly, while the band gap criterion holds relatively well across the PBEbased band gaps, it is less prominent for the higher-level functional HSE06. Noting
that the latter is expected to be much more accurate, this suggests that the correlation
with the lower level functional was largely fortuitous. Some earlier works also show
discrepancy between sensitivity and band gap [86]. No obvious trend is seen between
the sensitivity and a material having a direct or indirect electronic band gap.
3.5.1.1 Dissociation of N
−
3
Throughout the following discussion, the symmetric N-N bonds are denoted R 1 and
R 2 , with the electronic state given as a preceding superscript. The S o bond length of
R 1 is thus denoted
S o R 1 .
In the closed-shell ground state of the N
−
3 anion, the optimised geometry
(CAS(8,8)/6-31 + G*) of the molecule shows two equivalent N-N bonds (
S 0 R 1 =