Highest occupied molecular orbitals (HOMO) and lowest non-occupied molecular orbitals (LUMO) are most frequently mentioned FMOs. They provide important information for predicting the chemical activity of compounds owing to their special status.17-21 The energy gap between the HOMO and the LUMO is an expression of this information. Therefore, the values of HOMO, LUMO, and the energy gap (ΔELUMO-HOMO) were obtained from Gauss calculations and the results are summarized in Table 1. The maximum values of HOMO and LUMO were -4.89 eV (B6) and -0.56 eV (B6), respectively, while their minimum values were -8.89 eV (E8) and -4.61 eV (D8), respectively. Moreover, the maximum and minimum values of ΔELUMO-HOMO were 5.31 eV (A1) and 3.46 eV (B2), respectively. Therefore, we can make the conclusion that A1 was more stable than B2.
Figure 1 shows the variation trend of the HOMO and LUMO values of the designed compounds with different substituent groups and bridging. As shown in the figure 1, the variations in the HOMO and LUMO values were consistent. For the designed compounds with substituents -N3, -NH2, and -NHNH2, the HOMO and LUMO values increased. However, the HOMO and LUMO values decreased for the designed compounds with substituents -CN, -NO2, -NHNO2, -CH(NO2)2, and -C(NO2)3. In addition, Figure 1 shows the comparison between the HOMO values of the designed compounds with same substituents but different bridged connections. The compounds with –C=C-bridged connections were larger than those with other bridged connections. For the substituents –CN, –NO2, –NH2, –NHNO2, and –NHNH2, the HOMO value of the –N–N-bridged compounds was the lowest. Moreover, for the substituents –N3, –CH(NO2)2, and –C(NO2)3, the HOMO value of the –C–N-bridged compounds was the lowest. For same bridging connections, the HOMO values of the compounds with different substituents were compared. We found that for different bridging connections, the HOMO value of the compounds with the substituent –NHNH2 was the highest. Furthermore, the HOMO value for the compounds with the substituent –C(NO2)3 was the lowest. Therefore, our results indicate that the –NHNH2 energetic group and –C=C– bridge was the most effective combination for increasing the HOMO value of the designed compounds. For a same bridging connection, the LUMO values of the compounds with different substituents were compared. It was found that the LUMO value of the compounds was the highest when the substituent was –NHNH2 (except -C-C-) lowest when the substituent was –C(NO2)3. Hence, we believe that for the designed compounds, the –NHNH2 and –C(NO2)3 energetic groups could increase and decrease the LUMO values, respectively. The energy gap values of the compounds with a same substituent but different bridging connections, that is, the stability of the compounds, were compared. When the substituents were –N3, –NO2, –NHNO2, –NHNH2, and –C(NO2)2, the ΔELUMO-HOMO value of the designed compounds connected by –N–N– bridging was the largest. When the substituents were –CN, –NH2, and –NHNH2, the ΔELUMO-HOMO value of the compounds connected by –N=N– bridging was the lowest. Moreover, when the substituents were –N3, –NO2, –NHNO2, –CH(NO2)2, and –C(NO2)3, the ΔELUMO-HOMO value of the compounds connected by –C=C– bridging was the lowest. We can conclude that the –N–N– bridge could increase the stability of the compounds, while the –C=C– and –N=N– bridges could decrease the stability of the compounds. The ΔELUMO-HOMO values of the compounds with same bridging connections but different substituents were compared. The ΔELUMO-HOMO values of the compounds with –N3 substituent were the lowest. In the cases of –C–C–, –N–N–, and –C–N– bridging connections, the ΔELUMO-HOMO values of the compounds with the substituent –CN were the largest, thereby indicating that the –CN energetic group is the best, while the energetic group –N3 is the worst among the eight substituents in enhancing the stability of the compounds.
Table 1
Calculated EHOMO and ELUMO (eV) and energy gaps (ΔELUMO–HOMO) of the designed compounds
Compd.
|
A1
|
A2
|
A3
|
A4
|
A5
|
A6
|
A7
|
A8
|
HOMO
|
-8.43
|
-6.65
|
-8.75
|
-5.70
|
-7.50
|
-5.42
|
-8.33
|
-8.85
|
LUMO
|
-3.12
|
-2.61
|
-3.96
|
-0.63
|
-2.88
|
-0.68
|
-4.06
|
-4.65
|
ΔELUMO-HOMO
|
5.31
|
4.04
|
4.79
|
5.07
|
4.62
|
4.74
|
4.27
|
4.20
|
Compd.
|
B1
|
B2
|
B3
|
B4
|
B5
|
B6
|
B7
|
B8
|
HOMO
|
-7.77
|
-6.11
|
-7.80
|
-5.10
|
-6.79
|
-4.89
|
-7.51
|
-8.04
|
LUMO
|
-3.49
|
-2.65
|
-3.96
|
-0.73
|
-2.91
|
-0.56
|
-3.98
|
-4.50
|
ΔELUMO-HOMO
|
4.28
|
3.46
|
3.84
|
4.37
|
3.88
|
4.33
|
3.53
|
3.54
|
Compd.
|
C1
|
C2
|
C3
|
C4
|
C5
|
C6
|
C7
|
C8
|
HOMO
|
-8.51
|
-6.69
|
-8.79
|
-5.91
|
-7.65
|
-5.68
|
-8.31
|
-8.84
|
LUMO
|
-3.24
|
-2.56
|
-3.87
|
-0.82
|
-2.74
|
-0.61
|
-3.94
|
-4.60
|
ΔELUMO-HOMO
|
5.27
|
4.13
|
4.92
|
5.09
|
4.91
|
5.07
|
4.37
|
4.24
|
Compd.
|
D1
|
D2
|
D3
|
D4
|
D5
|
D6
|
D7
|
D8
|
HOMO
|
-8.46
|
-6.61
|
-8.64
|
-5.58
|
-7.27
|
-5.31
|
-8.35
|
-8.86
|
LUMO
|
-4.38
|
-2.84
|
-4.42
|
-1.60
|
-3.26
|
-1.40
|
-4.13
|
-4.61
|
ΔELUMO-HOMO
|
4.08
|
3.77
|
4.22
|
3.98
|
4.01
|
3.91
|
4.22
|
4.25
|
Compd.
|
E1
|
E2
|
E3
|
E4
|
E5
|
E6
|
E7
|
E8
|
HOMO
|
-8.39
|
-6.74
|
-8.77
|
-5.80
|
-7.55
|
-5.48
|
-8.44
|
-8.89
|
LUMO
|
-3.17
|
-2.73
|
-3.93
|
-0.69
|
-3.07
|
-0.69
|
-4.28
|
-4.88
|
ΔELUMO-HOMO
|
5.22
|
4.01
|
4.84
|
5.11
|
4.48
|
4.79
|
4.16
|
4.01
|
Compd.
|
F1
|
F2
|
F3
|
F4
|
F5
|
F6
|
F7
|
F8
|
HOMO
|
-8.19
|
-6.42
|
-8.41
|
-5.40
|
-7.13
|
-5.16
|
-7.99
|
-8.52
|
LUMO
|
-3.80
|
-2.81
|
-4.03
|
-0.98
|
-3.07
|
-0.81
|
-4.28
|
-4.88
|
ΔELUMO-HOMO
|
4.39
|
3.61
|
4.38
|
4.42
|
4.06
|
4.35
|
3.71
|
3.64
|
2.2 Heats of formation
Heats of formation (HOF) is an indicator of energy content, which plays an important role in predicting the detonation characteristics of high-energy materials.22-25 Table 2 shows necessary data for the calculation of the HOF values, including total energies (E0), thermal corrections (HT), zero-point energies (ZPEs), molecular properties, and HOF (ΔHf) of the designed compounds. The gas-phase and solid-phase HOFs are expressed as ΔHf,gas and ΔHf,solid, respectively. Figure 2 shows that the trends of ΔHf,gas and ΔHf,solid variations are coincident. According to calculations, the ΔHf,solid values of the designed compounds were positive, and the ΔHf,solid values ranged from 1035.4 (A7) to 2851.4 kJ mol-1 (D2). The range of the ΔHf,solid values fulfils our aim for designing the energetic materials.
It can be seen from Figure 2 that the compounds with same substituents but different bridging connections exhibit consistent changes in the HOF values. The HOF values for different bridging connections are in the following order: –C–C– < –C=C– < –C–N– < –C=N– < –N–N– < –N=N–. This proves that the HOF values of the compounds connected by the bridges containing N atoms were higher than those containing C atoms. The HOF values of the designed compounds were different when different substituents of the same bridge were attached. For the compounds linked by –C=C–, –N=N–, and –C=N– bridges, the HOF values were in the following order: –NH2 < –CH(NO2)2 < –NO2 < –C(NO2)3 < –NHNO2 < –NHNH2 < –CN < –N3. For the compounds linked by –C–C– and –C–N– bridges, the order of the HOF values was –CH(NO2)2 < –NH2 < –NO2 < –C(NO2)3 < –NHNO2 < –NHNH2 < –CN < –N3. This shows that the –N3 group was an excellent substituent for increasing the HOF of the designed compounds. In summary, for enhancing the HOF of a designed compound, the –N=N– bridge and –N3 substituent was the most effective combination, while the –C–C– bridge and –NH2/–CH(NO2)2 substituent was the most unfavourable combination.
Table 2
Calculated total energies (E0), thermal corrections (HT), zero-point energies (ZPE), molecular properties and heats of formation (ΔHf) of the designed compounds
Compd.
|
E0(a.u)
|
ZPE
(kJ mol-1)
|
HT
(kJ mol-1)
|
ΔHf,gas
(kJ mol-1)
|
A
(Å2)
|
ν
|
(kcal mol-1)2
|
ΔHsub
(kJ mol-1)
|
ΔHf,solid
(kJ mol-1)
|
A1
|
-1226.187475
|
475.4
|
58.2
|
1825.8
|
356.3
|
0.169
|
256.5
|
199.8
|
1626.0
|
A2
|
-1511.613309
|
520.7
|
69.0
|
2656.2
|
395.5
|
0.246
|
115.9
|
224.1
|
2432.1
|
A3
|
-1675.311254
|
515.1
|
66.8
|
1263.1
|
361.6
|
0.166
|
225.9
|
200.9
|
1062.2
|
A4
|
-1078.641448
|
673.9
|
54.2
|
1224.7
|
319.1
|
0.249
|
226.5
|
178.1
|
1046.6
|
A5
|
-1896.750323
|
695.4
|
78.8
|
1487.4
|
428.4
|
0.180
|
232.1
|
262.2
|
1225.2
|
A6
|
-1299.964997
|
853.1
|
66.4
|
1721.3
|
366.0
|
0.248
|
261.7
|
217.8
|
1503.5
|
A7
|
-2650.840866
|
838.7
|
108.9
|
1391.4
|
523.6
|
0.140
|
206.7
|
356.0
|
1035.4
|
A8
|
-3468.903380
|
843.9
|
137.9
|
1641.6
|
590.5
|
0.067
|
154.5
|
424.4
|
1217.2
|
B1
|
-1224.955055
|
411.6
|
57.0
|
1962.5
|
349.3
|
0.188
|
206.0
|
191.8
|
1770.7
|
B2
|
-1510.385246
|
457.5
|
67.6
|
2781.9
|
388.1
|
0.248
|
100.3
|
215.2
|
2566.7
|
B3
|
-1674.078428
|
451.0
|
65.7
|
1400.7
|
356.6
|
0.177
|
190.5
|
194.6
|
1206.1
|
B4
|
-1077.416035
|
610.9
|
52.8
|
1343.7
|
311.6
|
0.238
|
237.0
|
172.8
|
1170.9
|
B5
|
-1895.519808
|
631.5
|
77.8
|
1619.2
|
425.8
|
0.165
|
222.8
|
256.9
|
1362.3
|
B6
|
-1298.734184
|
788.4
|
66.4
|
1854.1
|
375.5
|
0.247
|
225.6
|
221.6
|
1632.5
|
B7
|
-2649.605741
|
774.2
|
108.2
|
1535.1
|
527.4
|
0.132
|
196.1
|
358.4
|
1176.7
|
B8
|
-3467.664624
|
778.8
|
135.3
|
1792.3
|
605.1
|
0.061
|
137.1
|
441.6
|
1350.7
|
C1
|
-1258.185010
|
412.9
|
57.0
|
2163.7
|
342.3
|
0.157
|
252.4
|
186.9
|
1976.8
|
C2
|
-1543.611802
|
458.8
|
67.4
|
2991.8
|
379.4
|
0.235
|
132.3
|
211.8
|
2780.0
|
C3
|
-1707.303688
|
451.3
|
65.8
|
1613.3
|
346.4
|
0.147
|
246.6
|
188.1
|
1425.2
|
C4
|
-1110.644111
|
613.9
|
51.3
|
1550.0
|
291.2
|
0.248
|
223.8
|
158.6
|
1391.4
|
C5
|
-1928.747634
|
633.0
|
77.5
|
1825.9
|
417.4
|
0.141
|
243.2
|
247.6
|
1578.3
|
C6
|
-1331.958767
|
790.3
|
65.2
|
2068.7
|
358.8
|
0.243
|
244.9
|
209.6
|
1859.1
|
C7
|
-2682.832056
|
775.9
|
107.6
|
1745.6
|
515.3
|
0.124
|
228.7
|
346.0
|
1399.6
|
C8
|
-3500.893770
|
780.7
|
137.2
|
1998.1
|
583.1
|
0.061
|
160.5
|
414.0
|
1584.1
|
D1
|
-1256.961111
|
346.5
|
55.9
|
2259.0
|
344.9
|
0.183
|
203.7
|
187.5
|
2071.5
|
D2
|
-1542.396997
|
392.4
|
66.4
|
3063.4
|
383.1
|
0.250
|
106.0
|
212.0
|
2851.4
|
D3
|
-1706.076650
|
383.5
|
65.6
|
1716.4
|
353.1
|
0.154
|
199.2
|
190.0
|
1526.4
|
D4
|
-1109.430268
|
544.7
|
52.4
|
1618.3
|
306.6
|
0.250
|
268.4
|
174.1
|
1444.2
|
D5
|
-1927.530190
|
565.9
|
77.0
|
1904.2
|
419.9
|
0.163
|
227.8
|
251.6
|
1652.6
|
D6
|
-1330.749987
|
722.9
|
65.7
|
2125.0
|
370.2
|
0.237
|
237.4
|
217.4
|
1907.6
|
D7
|
-2681.615258
|
709.2
|
106.9
|
1822.4
|
524.4
|
0.108
|
210.5
|
352.7
|
1469.7
|
D8
|
-3499.674889
|
713.9
|
136.6
|
2080.3
|
598.1
|
0.060
|
131.9
|
431.7
|
1648.6
|
E1
|
-1242.197528
|
444.4
|
57.5
|
1969.3
|
339.7
|
0.150
|
290.9
|
187.0
|
1782.3
|
E2
|
-1527.618116
|
489.4
|
68.5
|
2813.4
|
393.4
|
0.232
|
137.4
|
224.4
|
2589.0
|
E3
|
-1691.319732
|
484.0
|
65.9
|
1410.4
|
347.7
|
0.154
|
252.7
|
190.6
|
1219.8
|
E4
|
-1094.645999
|
642.1
|
54.2
|
1382.6
|
316.8
|
0.250
|
233.7
|
177.4
|
1205.2
|
E5
|
-1912.757343
|
664.8
|
78.2
|
1639.3
|
423.6
|
0.171
|
228.6
|
256.1
|
1383.2
|
E6
|
-1315.971047
|
821.2
|
66.4
|
1875.1
|
362.5
|
0.245
|
260.2
|
214.4
|
1660.7
|
E7
|
-2666.850234
|
808.2
|
107.9
|
1536.9
|
506.4
|
0.135
|
218.8
|
336.6
|
1200.3
|
E8
|
-3484.911244
|
813.0
|
137.5
|
1791.2
|
589.6
|
0.064
|
168.8
|
423.6
|
1367.6
|
F1
|
-1240.972421
|
379.8
|
56.4
|
2073.4
|
346.7
|
0.176
|
226.7
|
190.4
|
1883.0
|
F2
|
-1526.405296
|
425.7
|
66.9
|
2885.6
|
385.3
|
0.250
|
117.3
|
215.7
|
2669.9
|
F3
|
-1690.094136
|
418.6
|
65.0
|
1515.2
|
345.1
|
0.163
|
184.1
|
183.4
|
1331.8
|
F4
|
-1093.437138
|
578.7
|
52.5
|
1444.6
|
308.7
|
0.249
|
270.4
|
175.6
|
1269.0
|
F5
|
-1911.537762
|
599.4
|
77.3
|
1728.3
|
422.8
|
0.169
|
252.6
|
257.3
|
1471.0
|
F6
|
-1314.755070
|
756.2
|
66.0
|
1955.5
|
372.6
|
0.239
|
275.7
|
223.6
|
1731.9
|
F7
|
-2665.625925
|
742.6
|
107.4
|
1638.5
|
522.9
|
0.121
|
209.5
|
352.8
|
1285.7
|
F8
|
-3483.684797
|
747.2
|
137.1
|
1898.3
|
598.8
|
0.066
|
152.1
|
435.0
|
1463.3
|
2.3 Detonation properties
Table 3 shows the values of oxygen balance (OB), density (ρ), heat (Q), detonation velocity (D), detonation pressure (P), and impact sensitivity (h50).26, 27 When the OB value is positive, oxygen is in surplus during the detonation process and consume a significant amount of energy. When the OB value is negative, oxygen cannot completely oxidize the energetic materials, which results in lower detonation performance. To highlight the properties of our synthetic materials, the data of RDX and HMX, which are the most classical explosives at present, were also listed in Table 3.
It can be seen in Table 3 that all the OB values of A8 (3.81%), B8 (1.91%), C3 (18.78%), C7 (16.92%), C8 (5.70%), D3 (15.09%), D5 (19.83%), D7 (14.55%), D8 (7.62%), E8 (0.95%), F7 (-20.64%), and F8 (2.86%) were better than those of RDX and HMX (-21.6%). Among them, the OB values of A8, B8, C8, D8, E8, and F8 are closest to zero, which indicate that a compound burns fully when it contains –C(NO2)3. The values of ρ, Q, D, and P were in the ranges of 1.52 (A6) to 7.62 g cm-1 (D8), 822.82 (A4) to 1747.66 cal g-1 (B8), 6.23 (A1) to 9.65 km s-1 (D3), and 15.7 to 43.9 GPa (E8), respectively.
As shown in Figure 3, the substituent groups such as –N3, –NO2, –NHNO2, –CH(NO2)2, and –C(NO2)3 can increase the density, detonation heat, detonation velocity, and detonation pressure of the designed compounds. In contrast, the substituent groups such as –CN, –NH2, and –NHNH2 can decrease these quantities. In Figure 3(a), it can be seen that for a compound with same substituent group but different bridging groups, the rule is –C–C– < –C=C– < –C–N– < –N–N– < –C=N– < –N=N–. This indicates that the bridging group –N=N– can enhance the density of the designed compounds. Moreover, when the compounds are connected by the same bridge but have different substituents, the rule is –NHNH2 < –NH2 < –CN < –N3 < –NHNO2 < –NO2 < –CH(NO2)2 < –C(NO2)3, which indicates that the –C(NO2)3 substituent can increase the density of the designed compounds. From Table 3, the change trend of Q is basically the same as ρ, and the combination –N=N–/–C(NO2)3 plays an essential role in enhancing the explosion heat. We can conclude from Figure 3(b) and (c) that different bridges have the same influence on D and P, that is, in the following order: –C–C– < –C=C– < –C–N– < –C=N– < –N–N– < –N=N– (except for the –C(NO2)3 energetic group). When the bridging connections are –C–C–, –C=C–, –N–N–, –C–N–, and –C=N–, the effect of different substituents on the designed compounds was in the following order: –CN < –NH2 < –NHNH2 < –N3 < –NHNO2 < –NO2 < –CH(NO2)2 < –C(NO2)3. When the bridge was –N=N–, the effect of different substituents on the compounds was in the following order: –CN < –NH2 < –NHNH2 < –N3 < –NHNO2 < –CH(NO2)2 < –NO2 < –C(NO2)3. The combination of –N=N– and –C(NO2)3 can significantly affect the energy performance of the designed compounds and enhance their energy.
Figure 3(d) shows the comparison between the h50 values of the compounds with different substituents but same bridge. For the bridges –C–C–, –N–N–, and –C–N–, the h50 value of the compounds with the –NH2 substituent was the highest. Furthermore, for the bridges –C=C–, –N=N–, and –C=N–, the h50 value of the compound with the –N3 substituent was the highest. Besides, we found that the –C(NO2)3 substituent would decrease the h50 values of the designed compounds, while the –N3 and –NH2 substituents would increase the h50 values. The h50 values of the compounds with the –C(NO2)3 were the lowest. When the compounds were connected with same bridge but different substituents, the h50 values of the compounds bridged by –C–C– were the highest, while those of the compounds bridged by –N=N– were the lowest when the substituents were –NHNO2, –NHNH2, –CH(NO2)2, and –C(NO2)3.
In summary, six compounds (C3, C5, D3, D5, E3, and F3) were selected as candidates for energetic materials considering the detonation performance and impact sensitivity. For further analysis, their electronic structures, such as the FMO distribution and the electrostatic potential surface were simulated.
Table 3
Calculated oxygen balance (OB), densities (ρ), heats of detonation (Q), detonation velocities (D), detonation pressures (P) and impact sensitivity (h50) of the designed compounds
Compound
|
OBa
|
ρ (g cm-3)
|
Q (cal g-1)
|
D (km s-1)
|
P (GPa)
|
h50/cm
|
A1
|
-120.93
|
1.56
|
1129.69
|
6.23
|
15.7
|
36.2
|
A2
|
-70.59
|
1.66
|
1424.69
|
7.74
|
25.3
|
55.5
|
A3
|
-37.74
|
1.83
|
1536.83
|
8.44
|
31.9
|
35.5
|
A4
|
-115.79
|
1.52
|
822.82
|
6.66
|
17.7
|
55.8
|
A5
|
-39.67
|
1.77
|
1471.33
|
8.32
|
30.4
|
38.8
|
A6
|
-105.49
|
1.52
|
987.19
|
7.26
|
21.0
|
55.7
|
A7
|
-29.09
|
1.85
|
1580.24
|
8.68
|
34.0
|
29.2
|
A8
|
-3.81
|
1.98
|
1715.55
|
9.52
|
42.5
|
11.8
|
B1
|
-116.96
|
1.59
|
1237.42
|
6.27
|
16.1
|
41.1
|
B2
|
-67.00
|
1.69
|
1510.94
|
7.80
|
26.0
|
56.0
|
B3
|
-34.12
|
1.86
|
1600.08
|
8.57
|
33.2
|
38.4
|
B4
|
-111.26
|
1.55
|
926.64
|
6.82
|
18.8
|
53.2
|
B5
|
-36.51
|
1.80
|
1532.06
|
8.46
|
31.7
|
35.3
|
B6
|
-101.66
|
1.53
|
1077.81
|
7.34
|
21.6
|
55.5
|
B7
|
-26.75
|
1.87
|
1619.99
|
8.77
|
34.9
|
27.4
|
B8
|
-1.91
|
1.99
|
1744.86
|
9.57
|
43.0
|
10.5
|
C1
|
-97.11
|
1.62
|
1365.48
|
6.89
|
19.7
|
33.2
|
C2
|
-50.73
|
1.72
|
1620.54
|
8.34
|
30.0
|
52.7
|
C3
|
-18.78
|
1.89
|
1709.98
|
9.12
|
38.0
|
30.8
|
C4
|
-88.89
|
1.60
|
1086.75
|
7.58
|
23.7
|
55.7
|
C5
|
-23.05
|
1.82
|
1616.75
|
8.91
|
35.4
|
29.2
|
C6
|
-83.06
|
1.57
|
1214.00
|
7.97
|
25.9
|
54.9
|
C7
|
-16.92
|
1.89
|
1690.68
|
9.13
|
38.0
|
25.3
|
C8
|
5.70
|
2.02
|
1635.27
|
9.62
|
43.9
|
10.3
|
D1
|
-93.02
|
1.65
|
1439.21
|
6.86
|
19.8
|
39.8
|
D2
|
-47.06
|
1.75
|
1670.31
|
8.34
|
30.4
|
56.5
|
D3
|
-15.09
|
1.92
|
1747.66
|
9.23
|
39.2
|
32.7
|
D4
|
-84.21
|
1.62
|
1135.41
|
7.59
|
23.9
|
55.9
|
D5
|
-19.83
|
1.85
|
1637.85
|
9.00
|
36.6
|
34.9
|
D6
|
-79.12
|
1.59
|
1252.52
|
7.99
|
26.2
|
53.1
|
D7
|
-14.55
|
1.90
|
1704.86
|
9.15
|
38.3
|
21.5
|
D8
|
7.62
|
2.03
|
1588.71
|
9.54
|
43.3
|
10.2
|
E1
|
-108.99
|
1.59
|
1234.70
|
6.54
|
17.6
|
31.2
|
E2
|
-60.64
|
1.69
|
1512.89
|
8.03
|
27.5
|
51.9
|
E3
|
-28.24
|
1.87
|
1609.16
|
8.79
|
35.1
|
32.5
|
E4
|
-102.30
|
1.55
|
944.40
|
7.08
|
20.2
|
56.1
|
E5
|
-31.34
|
1.80
|
1535.05
|
8.62
|
33.0
|
36.7
|
E6
|
-94.25
|
1.54
|
1087.42
|
7.58
|
23.1
|
55.1
|
E7
|
-23.00
|
1.87
|
1629.33
|
8.89
|
35.9
|
27.9
|
E8
|
0.95
|
2.00
|
1721.89
|
9.65
|
43.9
|
11.1
|
F1
|
-104.96
|
1.62
|
1312.06
|
6.53
|
17.7
|
38.0
|
F2
|
-57.00
|
1.72
|
1567.83
|
8.04
|
27.9
|
56.5
|
F3
|
-24.59
|
1.90
|
1654.58
|
8.91
|
36.3
|
35.0
|
F4
|
-97.69
|
1.59
|
1000.96
|
7.17
|
21.1
|
55.8
|
F5
|
-28.16
|
1.82
|
1562.54
|
8.69
|
33.7
|
36.1
|
F6
|
-90.36
|
1.56
|
1140.29
|
7.63
|
23.6
|
53.5
|
F7
|
-20.64
|
1.89
|
1648.89
|
8.96
|
36.6
|
24.5
|
F8
|
2.86
|
2.01
|
1684.36
|
9.59
|
43.5
|
11.6
|
RDX
|
-21.6
|
1.82
|
1590.7
|
8.75
|
34.0
|
28.0
|
HMX
|
-21.6
|
1.91
|
1633.9
|
9.10
|
39.0
|
32.0
|
aFor the explosive CaHbOcNd: OB = (c-2a-0.5b)/Mw, where Mw is the molecular weight. |
2.4 Electronic structures
To investigate the electronic structure and properties of these compounds, the LUMO–HOMO and electrostatic potential (ESP) orbitals were studied. Figure 4 shows the LUMO and HOMO distributions of the selected compounds (C3, C5, D3, D5, E3, and F3). It can be clearly seen that the LOMO and HOMO distributions of each compound are different. The LUMOs of C3, C5, and E3 were mainly distributed on the energetic groups and rings on one side, while those of D3, D5, and F3 were mainly distributed on the energetic groups and bridging structures. The HOMOs of C3, C5, D3, D5, and F3 were mainly distributed on the parent structure, while that of E3 was mainly distributed on the energetic group and ring on one side. The ΔELUMO-HOMO values of the six screened compounds (C3, C5, D3, D5, E3, and F3) were in the range of 4.01 eV(D5) to 4.92 eV (C3), which were relatively stable. Therefore, we conclude that the compound C3 has the most stable structure.
The molecular surfaces of the six screened compounds were quantitatively analysed using the Multiwfn software, and then the distribution of the ESP was obtained using the VMD software. The molecular interactions and chemical reaction sites could be visualized on the ESP surface.28-30 Figure 5 shows the ESP analysis of the selected compounds (C3, C5, D3, D5, E3, and F3). In Figure 5, the positive and negative potentials are represented by red and blue colours, respectively. In addition, the area ratio of the positive and negative potentials is also provided. The positive potential was mainly distributed on the ring and the hydrogen atoms, while the negative potential was mainly distributed on the outer ring and the energetic groups. Global maximal ESPs of C3, C5, D3, D5, E3, and F3 were calculated as 62.05, 57.86, 44.86, 60.49, 62.69, and 45.12 kcal mol-1, respectively. Moreover, all the global maximal ESPs of these compounds were distributed around the substituent group. The global minimal ESPs of the compounds C3, C5, D3, D5, E3, and F3 were calculated as -25.32, -30.40, -23.42, -31.16, -25.65, and -23.13 kcal mol-1, and these ESPs were distributed around nitrogen of the heterocycle. Besides, there were more positive ESP regions than the negative ones, which suggests that it is a nucleophilic reaction.