Molecular Design and Property Prediction for a Series of 3, 3-Bis(difluoroamino)-1, 5-substituted-pentane Derivatized as Energetic Plasticizers

Citation: Wang Wanjun, Li Huan, Pan Renming, Zhu Weihua. Molecular Design and Property Prediction for a Series of 3, 3-Bis(difluoroamino)-1, 5-substituted-pentane Derivatized as Energetic Plasticizers[J]. Chinese Journal of Organic Chemistry, 2019, 39(1): 170-176. doi: 10.6023/cjoc201808024 shu

含能增塑剂用系列3, 3-二(二氟氨基)-1, 5-取代戊烷衍生物的分子设计和性能预测

王万军 ^{a,b,
,} ,
李欢 ^a, ,
潘仁明 ^a, ,
朱卫华 ^a,

a.
南京理工大学化工学院南京 210094
b.
中国科学院上海有机化学研究所上海 200032

通讯作者: 王万军, wangwj@sioc.ac.cn

基金项目:
国家自然科学基金（No.51603103）资助项目

国家自然科学基金 51603103

摘要: 3，3-二（二氟氨基）-1，5-二硝酸酯基戊烷是一种高能低玻璃化转变温度的含能增塑剂.为了获得更多此类结构的新型二氟氨基含能化合物，设计了一系列3，3-二（二氟氨基）-1，5-取代戊烷衍生物作为新型含能增塑剂的候选品种.采用泛函密度理论（DFT）法研究了生成热、电子结构、能量特性和热稳定性.二氟氨基基团能增加标题化合物之间电子结构、密度和爆轰性质的能隙.特别是1，3，3，5-四（二氟氨基）戊烷（S₃）具有作为潜在含能增塑剂的显著价值.其晶体密度（1.91 g/cm³）、爆速（9.01 km/s）、爆压（37.31 GPa）和冲击灵敏度（h₅₀ 29.83 cm）均与奥克托今（HMX）非常接近.此外，S₃可以通过一些成熟的过程5步合成得到.

关键词:

English

Molecular Design and Property Prediction for a Series of 3, 3-Bis(difluoroamino)-1, 5-substituted-pentane Derivatized as Energetic Plasticizers

a.
School of Chemical Engineering, Nanjing University of Science and Technology, Nanjing 210094
b.
Shanghai Institute of Organic Chemistry, Chinese Academy of Sciences, Shanghai 200032

Corresponding author: Wang Wanjun, wangwj@sioc.ac.cn

Received Date: 20 August 2018
Revised Date: 22 October 2018
Available Online: 25 January 2019
Fund Project:
Project supported by the National Natural Science Foundation of China (No. 51603103)

Abstract: 3, 3-Bis(difluoroamino)-1, 5-dinitratopentane was used as energetic plasticizer with improving energy properties and low glass transition temperature. To obtain more new difluoroamino energetic compounds with similar sturctures, a series of 3, 3-bis(difluoroamino)-1, 5-substituted-pentane derivatives were designed as candidates of novel energetic plasticizers. The heats of formation (HOFs), electronic structure, energy property and thermal stability were studied using density functional theory (DFT) method. The difluoroamino groups can increase energy gaps of electronic structure, density and detonation properties among the title compounds. Especially, 1, 3, 3, 5-tetra(difluoroamino)pentane (S₃) has given outstanding values of potential energetic plasticizer. Its crystal density (1.91 g/cm³), detonation velocity (9.01 km/s), detonation pressure (37.31 GPa) and impact sensitivity (h₅₀ 29.83 cm) are very close to those of cyclotetramethylenetetranitramine (HMX). Furthermore, S₃ can be synthesized via some mature processes in five steps.

Key words:

1. Introduction

The intrinsically high energy of difluoroamino groups has attracted many attentions and interests in organic difluoramines which have been mainly due to their potential as energetic materials in rocket propellants and explosives.^[1] Many works on structure design and synthetic method development of difluoroamino-based energetic oxidizers, ^{[2, 3, 4, 5, 6, 7]} polymers^{[8, 9]} and plasticizers^{[10, 11]} with stable structures have been done since the late 1980s. Recently, our group have synthesized five difluoroamino energetic polymers with well-designed structure and good thermal stability.^{[12, 13, 14]} To meet the increasing demand for application of these difluoroamino energetic polymers, the design and development of novel difluoroamino plasticizers are worthwhile.

Properties could be often manipulated by making structural modifications. The primary step for design and synthesis of new energetic materials is the optimization of the candidates with high energy and less sensitivity.^[15] In the past several decades, theoretical studies based on quantum chemical treatments have been improved as an efficient research tool for structure optimization and property prediction of novel energetic materials.^[16~19] They could provide more understandings of the relationships between molecular structure and property without dangerous and expensive experimental tests.

As a promising candidate of difluoroamino-based plasticizers, 3, 3-bis(difluoroamino)-1, 5-dinitratopentane^[11] was designed and synthesized with low glass transition temperature and good energy properties. To Figure out if there are other 3, 3-bis(difluoroamino)-1, 5-substituted pentane derivatives with better energy property and low sensitivity, we report a systematic study of the heats of formation (HOFs), energetic properties, and thermal stability of a series of 3, 3-bis(difluoroamino)-1, 5-substituted pentane derivatives with different substituents by using density function theory (DFT).

2. Computational methods

Figure 1 presents the molecular frameworks of a series of 3, 3-bis(difluoroamino)-1, 5-substituted pentane derivatives. Based on the substituted energetic groups, the compounds can be divided into two series (S symmetric substituted in 1 and 5 position of pentane and A asymmetric substituted in 1 and 5 position of pentane).

Figure 1

Figure 1. Molecular frameworks of 3, 3-bis(difluoroamino)- 1, 5-substituted pentane derivatives

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Isodesmic reactions could be employed to calculate the heats of formation (HOFs) using total energies obtained from ab initio calculations.^{[20, 21]} Herein, isodesmic reactions (Figure 2) are designed in which the numbers of all types of bonds are invariable. Eq. 1 is used to calculate the heat of reaction ΔH₂₉₈ at 298 K.

Figure 2

Figure 2. Isodesmic reaction used to obtain the HOFs of title compounds

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$\Delta {H_{298}} = \Delta {H_{{\rm{f,P}}}} - \Delta {H_{{\rm{f,R}}}}$

(1)

Where ΔH_{f, P} and ΔH_{f, R} are the HOFs of products and reactants at 298 K, respectively.

The experimental HOFs of reference compounds CH₄, C₅H₁₂, CH₃ONO₂, CH₃NO₂ and (CH₃)₂NNO₂ are available, and the HOFs of CH₃NF₂ and CH₃N₃ are calculated by Ju et al.^{[22, 23]} The value of ΔH₂₉₈ can be also calculated via Eq. 2.

$ \begin{array}{l} \Delta {H_{298}} = \Delta {E_{298}} + \Delta \left( {PV} \right)\\ \;\;\;\;\;\;\;\;\; = \Delta {E_0} + \Delta {E_{{\rm{ZPE}}}} + \Delta {E_{\rm{T}}} + \Delta nRT \end{array} $

(2)

Where ΔE₀ is the change in total energy between the products and the reactants at 0 K, ΔE_ZPE is the difference between the zero-point energies (ZPE) of the products and reactants at 0 K, ΔE_T is the thermal correction from 0 to 298 K. For the isodesmic reaction in this calculation process, Δn＝0, so Δ(PV)＝0.

The calculation of detonation properties for most energetic compounds requires solid phase HOF (ΔH_{f, solid}) since their condensed phase is solid. According to Hess's low of constant heat summation^[24] and Politzer's research, ^{[25, 26]} ΔH_{f, solid} can be calculated via Eqs. 3 and 4.

$ \Delta {H_{{\rm{f}},{\rm{solid}}}} = \Delta {H_{{\rm{f}},{\rm{gas}}}} - \Delta {H_{{\rm{sub}}}} $

(3)

$ \Delta {H_{{\rm{sub}}}} = a{A^2} + b{(v\sigma _{{\rm{tot}}}^{\rm{2}})^{0.5}} + c $

(4)

Where ΔH_{f, ga}_s is the gas phase HOF, ΔH_sub is heat of sublimation, A is the surface area of the 0.001 electrons/bohr³ isosurface of the electronic density of the molecule, ν is the balance of charges between positive potential and negative potential on the isosurface, $v\sigma _{{\rm{tot}}}^{\rm{2}}$ is a measure of the variability of the electrostatic potential on the molecular surface. The coefficients a, b and c are reported by Rice et al., ^[27] a＝2.670×10^－4 kcal/(mol•Å⁴), b＝1.650 kcal/mol and c＝2.966 kcal/mol.

Modified Kamlet-Jacobs equations are used to estimate the detonation velocity and pressure^{[28, 29]} (Eqs. 5 and 6). And the theoretical crystal density is obtained from the Eq. 7 proposed by Polizer et al.^[30]

$D = 1.01{(N{\overline M ^{1/2}}{Q^{1/2}})^{1/2}}(1 + 1.30\rho )$

(5)

$P = 1.558{\rho ^2}N{\overline M ^{1/2}}{Q^{1/2}}$

(6)

$\rho = \alpha (\frac{M}{{V(0.001)}}) + \beta v\sigma _{{\rm{tot}}}^{\rm{2}} + \gamma $

(7)

Each term in Eqs. 5~7 is defined as follows: D, detonation velocity (km/s); P, detonation pressure (GPa); N, moles of detonation gases per gram explosives; $\overline M $, average molecular weight of the gases; Q, heat of detonation (cal•g^－1); ρ, loaded density of explosives (g/cm³); M, molecular mass (g/mol); V(0.001), volume of the 0.001 electros/bohr³ contour of electronic density of the molecule (cm³/molecule); $v\sigma _{{\rm{tot}}}^{\rm{2}}$, a measure of the variability of the electrostatic potential on the molecular surface [(kcal• mol^－1)²]. The values of α, β and γ in Eq. 7 are 0.9183, 0.0028 and 0.0443, respectively.

The impact sensitivity (h₅₀, cm) is defined as the height from which there is a 50% probability of causing an explosion. Impact sensitivity is generally reported either as this height in cm, designated h₅₀, or as the corresponding impact energy in J. With a 2.5 kg mass, an h₅₀ of 1 cm is equivalent to an impact energy of 0.245 J. The greater the value of h₅₀ or the impact energy, the less is the sensitivity. Eq. 8 presents a simple method to estimate the h₅₀ of energetic compounds.^[31]

${h_{50}} = \alpha \sigma _{\rm{ + }}^2 + \beta v + \gamma $

(8)

Where $\sigma _{\rm{ + }}^2$ is the strengths and variabilities of the positive surface potentials, ν is the degree of balance between the positive and negative potential on a molecular surface. The values of α, β and γ in Eq. 8 are －0.0064, 241.42 and －3.43, respectively.

The bond dissociation energy (BDE), which reflects the strength of bonding, is fundamental to understand chemical processes.^[32] The BDE and BDE with ZPE correction of reaction A-B(g)→A•(g)+B•(g) at 298 K and 101 kPa are given in terms of Eqs. 9 and 10.^{[33, 34]}

$ {\rm{BD}}{{\rm{E}}_0}({\rm{A}} - {\rm{B}}){\rm{ = }}{E_0}\left( {{\rm{A}} \cdot } \right) + {E_0}\left( {{\rm{B}} \cdot } \right) - {E_0}\left( {{\rm{A}} - {\rm{B}}} \right) $

(9)

${\rm{BDE}}{({\rm{A}} - {\rm{B}})_{{\rm{ZPE}}}}{\rm{ = BD}}{{\rm{E}}_0}({\rm{A}} - {\rm{B}}) + \Delta {E_{{\rm{ZPE}}}}$

(10)

where ∆E_ZPE is the difference between the ZPEs of the products and the reactions.

Gaussian 09 package^[35] is used to perform the calculations at B3LYP/6-311G++(d, p)^[36] and B3PW91/6-31G(d, p)^[37] level for different situations. The optimizations are performed without any symmetry restrictions, using the default convergence criteria in the program. All the optimized structures are characterized to the true local energy minima on the potential surface without imaginary frequencies. The total energy, zero-point energy and thermal correction are calculated with vibration frequencies analysis. The volume and surface electrostatic potential are calculated by Multiwfn program.^[38]

3. Results and discussion

3.1 Heats of formation

Here, the effects of different substituents in 1 and 5 positions of 3, 3-bis(difluoroamino) pentane on the gas-phase and solid phase HOFs of the title compounds are investigated. Table 1 presents the calculated total energy (E₀), zero-point energies (ZPE), thermal corrections (H_T) and heat of formation (HOFs) of the reference compounds in the isodesmic reactions at B3LYP/6-311++G(d, p) level. Table 2 shows the calculated E₀, ZPE, H_T, molecular properties, heat of sublimation and HOFs of the title compounds. S₄ has the highest ∆H_{f, gas} and ∆H_{f, solid} among the title compounds for the substitution of two azido groups. More clear evidence about the effects of the different substituents on ∆H_{f, gas} and ∆H_{f, solid} of the title compounds is presented in Figure 3. The calculated ∆H_{f, solid} has the same variation trend of ∆H_{f, gas}. The substitution of N₃ enhances the HOF values of the title compounds extremely. HOF values increase with the order of substituent species ONO₂ < NF₂ < NO₂ < N(NO₂)CH₃≪N₃. This can be attributable to the increase of the number of energetic N—N and C—N bonds in the title compounds, which is in agreement with the previous researches^{[41, 42]} that the more N—N bonds a compound has, the higher its HOF is.

Table 1

Table 1. Calculated total energy (E₀), zero-point energies (ZPE), thermal corrections (H_T) and heat of formation (HOFs) of the reference compounds at B3LYP/6-311++G(d, p) level

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Compd.	E₀/a.u.	ZPE^a/a.u.	H_T^a/(kJ•mol^－1)	HOF/(kJ•mol^－1)
H₄	－40.4894	0.04365	9.61	－74.60^b
C₅H₁₂	－197.6702	0.15650	20.30	－146.90^b
CH₃NF₂	－294.2638	0.04564	13.14	－115.23^d
CH₃ONO₂	－320.2390	0.05292	15.00	－124.40^b
CH₃NO₂	－245.0420	0.04864	13.35	－74.30^b
CH₃N₃	－204.1033	0.04908	13.64	296.54^e
(CH₃)₂NNO₂	－339.6683	0.09274	19.26	－0.84^c
^a The scaling factors for ZPE and H_T were 0.98 and 0.96, respectively.^[43] ^bExperimental values taken from Ref. [40]. ^cExperimental values taken from Ref. [39]. ^d Calculated values taken from Ref. [22]; ^e Calculated values taken from Ref. [23].

Table 2

Table 2. Calculated E₀, ZPE, H_T, molecular properties, heat of sublimation and HOFs of the title compounds at B3LYP/6-311++G(d, p) level

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Compd.	E₀/a.u.	ZPE^a/a.u.	H_T/(kJ•mol^－1)	∆H_{f, gas}/(kJ•mol^－1)	A/A²	$v\sigma _{{\rm{tot}}}^{\rm{2}}$/[(kcal•mol^－1)²]	∆H_sub/(kJ•mol^－1)	∆H_{f, solid}/(kJ•mol^－1)
S₁	－1264.7195	0.1697	50.21	－343.57	258.68	21.85	119.43	－463.00
S₂	－1114.3217	0.1617	45.92	－232.92	237.41	39.48	118.75	－351.67
S₃	－1212.7655	0.1555	46.70	－314.63	233.80	14.86	100.09	－414.72
S₄	－1032.4513	0.1625	47.05	490.73	253.08	17.10	112.51	378.22
S₅	－1303.5782	0.2495	59.11	－95.92	303.05	43.59	160.59	－256.51
A₁	－1189.5202	0.1656	48.16	－287.36	247.67	34.26	121.34	－408.70
A₂	－1238.7426	0.1626	48.73	－329.09	248.40	20.97	112.95	－442.04
A₃	－1148.5840	0.1660	48.64	77.00	255.60	19.60	115.96	－38.96
A₄	－1284.1505	0.2095	55.26	－223.74	283.45	39.48	145.54	－369.28
A₅	－1163.5438	0.1586	46.25	－274.36	235.64	33.11	114.16	－388.52
A₆	－1073.3879	0.1622	46.48	125.49	245.53	34.74	120.45	5.04
A₇	－1208.9516	0.2057	52.52	－168.48	270.41	44.86	140.33	－308.81
A₈	－1122.6073	0.1589	46.79	90.59	243.03	15.95	105.96	－15.37
A₉	－1258.1733	0.2025	53.02	－208.96	268.54	38.72	135.93	－344.89
A₁₀	－1168.0149	0.2061	53.04	197.23	278.12	38.32	141.56	55.67
^a The scaling factors for ZPE and H_T were 0.98 and 0.96, respectively.

Figure 3

Figure 3. Effects of different substituents on ∆H_{f, gas} (a) and ∆H_{f, solid} (b) of the title compounds

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3.2 Electronic structure

Table 3 presents the calculated highest occupied molecular orbital (HOMO) and lower unoccupied molecular orbital (LUMO) energies and energy gaps (∆E_LUMO-HOMO) of the title compounds at B3LYP/6-311++G(d, p) level. Figure 4 shows the effects of different substituents on ∆E_LUMO-OMO of the title compounds. For most of the A series, the substitution of NF₂ increases the LUMO-HOMO gaps comparing with the corresponding S series except for A₂. The symmetric substituted series behave higher energy gaps of LUMO-HOMO than the corresponding asymmetric substituted compounds except for A₁, A₅, A₈ and A₉. This indicates that the incorporation of NF₂ into NO₂, N₃ and N(NO₂)CH₃ substituted compounds and ONO₂ into NO₂-substituted compounds will decrease the reactivity, respectively. However, the LUMO-HOMO gaps are suggestive of reactivity only as approximation. In all, S₃ has the highest value of ∆E_LUMO-HOMO among the title compounds.

Table 3

Table 3. Calculated HOMO and LUMO energies and energy gaps ∆E_LUMO-HOMO of the title compounds at B3LYP/6-311++G(d, p) level

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Compd.	E_HOMO/a.u.	E_LUMO/a.u.	∆E_LUMO-HOMO/a.u.
S₁	－0.3346	－0.0999	0.2347
S₂	－0.3281	－0.1048	0.2233
S₃	－0.3229	－0.0506	0.2723
S₄	－0.2777	－0.0553	0.2224
S₅	－0.2917	－0.0693	0.2224
A₁	－0.3266	－0.1012	0.2254
A₂	－0.3259	－0.0944	0.2315
A₃	－0.2799	－0.0979	0.1820
A₄	－0.2984	－0.0925	0.2059
A₅	－0.3264	－0.1016	0.2248
A₆	－0.2816	－0.0992	0.1824
A₇	－0.2984	－0.0986	0.1998
A₈	－0.2802	－0.0562	0.2240
A₉	－0.2973	－0.0717	0.2256
A₁₀	－0.2780	－0.0691	0.2089

Figure 4

Figure 4. Effects of different substituents on ∆E_LUMO-HOMO of the title compounds

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3.3 Detonation properties and impact sensitivity

Table 4 lists the calculated density, molecular and detonation properties and impact sensitivity of the title compounds at B3PW91/6-31G(d, p) level. Figure 5 presents the effects of different substituents on ρ, D, P and h₅₀ of the title compounds.

Table 4

Table 4. Table 4 Calculated uncorrected density [M/V(0.001)], corrected density (crystal density), detonation velocity (D), detonation pressure (P), molecular properties and impact sensitivity (h₅₀) of the title compounds at B3PW91/6-31G(d, p) level

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Compd.	M/V(0.001)/(g•cm^－3)	$v\sigma _{{\rm{tot}}}^{\rm{2}}$^a/[(kcal•mol^－1)²]	Crystal density/(g•cm^－3)	Q/(cal•g^－1)	D/(km•s^－1)	P/GPa	$v\sigma _ + ^{\rm{2}}$^b/[(kcal•mol^－1)²]	V^b	h₅₀/cm
S₁	1.90	23.54	1.85	1528.4	8.92	35.89	123.46	0.179694	39.16
S₂	1.86	32.57	1.84	1458.1	8.65	33.62	155.39	0.197494	43.25
S₃	1.99	14.39	1.91	1520.9	9.01	37.31	105.79	0.140591	29.83
S₄	1.71	18.73	1.67	1450.2	7.88	26.29	78.34	0.220414	49.28
S₅	1.71	38.06	1.72	1366.2	7.96	27.31	84.96	0.239974	53.96
A₁	1.88	32.27	1.86	1494.1	8.84	35.37	141.83	0.204702	45.08
A₂	1.94	23.36	1.89	1522.1	9.01	37.02	121.41	0.181812	39.69
A₃	1.81	21.75	1.77	1495.1	8.45	31.39	102.07	0.199145	43.99
A₄	1.79	36.15	1.79	1436.5	8.44	31.47	103.74	0.247193	55.58
A₅	1.92	32.07	1.90	1485.6	8.91	36.35	131.11	0.21593	47.86
A₆	1.78	30.90	1.77	1446.7	8.30	30.28	107.56	0.234407	52.47
A₇	1.77	39.38	1.78	1403.8	8.28	30.23	109.55	0.248915	55.96
A₈	1.85	16.79	1.79	1489.5	8.45	31.55	93.43	0.180208	39.48
A₉	1.83	34.56	1.82	1430.2	8.47	32.01	93.51	0.249796	56.28
A₁₀	1.71	34.83	1.71	1399.1	7.96	27.21	87.25	0.249176	56.17
HMX^c			1.91		9.10	39.60			30
^a The computed results pertain to 0.001 a.u. surfaces.^b The computed results pertain to 0.002 a.u. surfaces. ^c Calculated values taken from Ref. [44].

Figure 5

Figure 5. Effects of different substituents on ρ (a), D (b), P (c) and h₅₀ (d) of the title compounds

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The substitution of NF₂ increases and has the highest values of ρ, D and P for almost the entire S and A series of 9 title compounds except for A₂. A₂ has the same value of D comparing with S₃. This indicates that NF₂ group is the most useful energetic substituent for improving the calculated density and detonation properties of 3, 3-bis(difluo- roamino)-1, 5-substituted pentane derivatives. The values of h₅₀ are on the range of 29~57 cm. S₃ has the smallest value among them, while A₉ had the largest one. The N(NO₂)CH₃ groups obviously improve the impact sensitivity among other mentioned energetic groups. S₃ has the similar stability compared with HMX. Besides, S₃ has the highest crystal density and detonation properties which could be considered as a promising energetic plasticizer.

3.4 Thermal stability

The values of BDE_ZPE of relatively weak bonds for the title compounds at B3LYP/6-311++G(d, p) level are listed in Table 5. The C—NF₂ bond locates in the central position of pentane had the lowest value of BDE_ZPE among the title compounds, which suggests that the cleavage of central C—NF₂ bond would be a possible initial thermal decomposition path for these compounds. Figure 6 shows the effects of different substituents on BDE_ZPE of central C—NF₂ bond. The substitution of ONO₂ and N(NO₂)CH₃ can increase the value of BDE_ZPE of central C—NF₂ bond. And A₄ has the highest BDE_ZPE. This could be caused by the relatively stronger steric hindrance of these two energetic groups. Considering the suggested energy barrier (80 kJ/mol), ^[45] most of these compounds can be thermal stable to some degree except for A₃ and A₈.

Table 5

Table 5. Bond dissociation energies (BDE) of the relatively weak bonds for the title compounds at B3LYP/6-311++G(d, p) level

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Compd.	BDE_ZPE/(kJ•mol^－1)
Compd.	C—NF₂^a	C—NF₂^b	C—ONO₂	O—NO₂	C—NO₂	N—NO₂	C—N₃	N—F^a	N—F^b
S₁	80.67		264.69	104.48				217.29
S₂	80.58				185.04			214.79
S₃	81.70	205.77						209.34	232.03
S₄	86.57						244.93	216.79
S₅	84.01					129.10		216.72
A₁	87.71		263.33	103.38	184.83			211.32
A₂	81.84	205.65	265.33	104.07				215.55	232.09
A₃	79.55		265.93	104.68			236.86	217.32
A₄	92.72		267	105.23		139.93		217.10
A₅	81.54	205.33			186.52			215.32	229.65
A₆	85.80				193.69		243.11	214.92
A₇	84.00				187.41	128.83		215.58
A₈	79.68	207.41					238.03	216.49	230.32
A₉	83.11	206.91				129.00		215.57	232.20
A₁₀	89.76					129.86	238.12	214.72
^a Bond located in the 3 position of the title compounds; ^b bond located in the 1 or 5 position of the title compounds.

Figure 6

Figure 6. Effects of different substituents on BDE_ZPE of the title compounds

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3.5 Synthetic route consideration of S₃

As S₃ has the outstanding energy properties, its syntheticroute is speculated via 5 steps (Figure 7). 1, 5-Dichloro- pentan-3-one can be synthesized via the reaction of 3-chloropropionyl chloride, ethylene and aluminum chloride.^[46] Then, by the following processes of amination, ^[47] amidation, ^{[8, 9]} fluorination^{[8, 9]} and difluoroamination, ^[48] S₃ could be gained.

Figure 7

Figure 7. Speculated synthetic route for S₃

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4. Conclusions

The HOFs, energy properties, and thermal stability of a series of 3, 3-bis(difluoroamino)-1, 5-substituted pentane derivatives with different energetic substituents are studied using DFT methods. The azido group significantly increases the HOFs both in gas and solid states. But the difluoroamino group obviously improves the values of crystal density, detonate velocity and detonation pressure. The weakest bond is the C—NF₂ bond located in the third position of the title compounds, which indicates that its cleavage could possibly be the initial thermal decomposi tion path. Most of the BDE_ZPE values are above the suggested energy barrier. Besides, S₃ is chosen as a potential energetic plasticizer for its highest detonation properties, lowest electronic reactivity and acceptable impact sensitivity. By using a five-step synthetic route, S₃ can be synthesized as a novel difluoroamino energetic plasticizer.

Supporting Information Details of the Kamlet-Jacobs equation are included, especially, the formula derivation of the parameters N, $\overline M $, and Q in more detail. The Supporting Information is available free of charge via the Internet at http://sioc-journal.cn.

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Figure 1 Molecular frameworks of 3, 3-bis(difluoroamino)- 1, 5-substituted pentane derivatives

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Figure 2 Isodesmic reaction used to obtain the HOFs of title compounds

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Figure 3 Effects of different substituents on ∆H_{f, gas} (a) and ∆H_{f, solid} (b) of the title compounds

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Figure 4 Effects of different substituents on ∆E_LUMO-HOMO of the title compounds

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Figure 5 Effects of different substituents on ρ (a), D (b), P (c) and h₅₀ (d) of the title compounds

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Figure 6 Effects of different substituents on BDE_ZPE of the title compounds

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Figure 7 Speculated synthetic route for S₃

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Table 1. Calculated total energy (E₀), zero-point energies (ZPE), thermal corrections (H_T) and heat of formation (HOFs) of the reference compounds at B3LYP/6-311++G(d, p) level

Compd.	E₀/a.u.	ZPE^a/a.u.	H_T^a/(kJ•mol^－1)	HOF/(kJ•mol^－1)
H₄	－40.4894	0.04365	9.61	－74.60^b
C₅H₁₂	－197.6702	0.15650	20.30	－146.90^b
CH₃NF₂	－294.2638	0.04564	13.14	－115.23^d
CH₃ONO₂	－320.2390	0.05292	15.00	－124.40^b
CH₃NO₂	－245.0420	0.04864	13.35	－74.30^b
CH₃N₃	－204.1033	0.04908	13.64	296.54^e
(CH₃)₂NNO₂	－339.6683	0.09274	19.26	－0.84^c
^a The scaling factors for ZPE and H_T were 0.98 and 0.96, respectively.^[43] ^bExperimental values taken from Ref. [40]. ^cExperimental values taken from Ref. [39]. ^d Calculated values taken from Ref. [22]; ^e Calculated values taken from Ref. [23].

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Table 2. Calculated E₀, ZPE, H_T, molecular properties, heat of sublimation and HOFs of the title compounds at B3LYP/6-311++G(d, p) level

Compd.	E₀/a.u.	ZPE^a/a.u.	H_T/(kJ•mol^－1)	∆H_{f, gas}/(kJ•mol^－1)	A/A²	$v\sigma _{{\rm{tot}}}^{\rm{2}}$/[(kcal•mol^－1)²]	∆H_sub/(kJ•mol^－1)	∆H_{f, solid}/(kJ•mol^－1)
S₁	－1264.7195	0.1697	50.21	－343.57	258.68	21.85	119.43	－463.00
S₂	－1114.3217	0.1617	45.92	－232.92	237.41	39.48	118.75	－351.67
S₃	－1212.7655	0.1555	46.70	－314.63	233.80	14.86	100.09	－414.72
S₄	－1032.4513	0.1625	47.05	490.73	253.08	17.10	112.51	378.22
S₅	－1303.5782	0.2495	59.11	－95.92	303.05	43.59	160.59	－256.51
A₁	－1189.5202	0.1656	48.16	－287.36	247.67	34.26	121.34	－408.70
A₂	－1238.7426	0.1626	48.73	－329.09	248.40	20.97	112.95	－442.04
A₃	－1148.5840	0.1660	48.64	77.00	255.60	19.60	115.96	－38.96
A₄	－1284.1505	0.2095	55.26	－223.74	283.45	39.48	145.54	－369.28
A₅	－1163.5438	0.1586	46.25	－274.36	235.64	33.11	114.16	－388.52
A₆	－1073.3879	0.1622	46.48	125.49	245.53	34.74	120.45	5.04
A₇	－1208.9516	0.2057	52.52	－168.48	270.41	44.86	140.33	－308.81
A₈	－1122.6073	0.1589	46.79	90.59	243.03	15.95	105.96	－15.37
A₉	－1258.1733	0.2025	53.02	－208.96	268.54	38.72	135.93	－344.89
A₁₀	－1168.0149	0.2061	53.04	197.23	278.12	38.32	141.56	55.67
^a The scaling factors for ZPE and H_T were 0.98 and 0.96, respectively.

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Table 3. Calculated HOMO and LUMO energies and energy gaps ∆E_LUMO-HOMO of the title compounds at B3LYP/6-311++G(d, p) level

Compd.	E_HOMO/a.u.	E_LUMO/a.u.	∆E_LUMO-HOMO/a.u.
S₁	－0.3346	－0.0999	0.2347
S₂	－0.3281	－0.1048	0.2233
S₃	－0.3229	－0.0506	0.2723
S₄	－0.2777	－0.0553	0.2224
S₅	－0.2917	－0.0693	0.2224
A₁	－0.3266	－0.1012	0.2254
A₂	－0.3259	－0.0944	0.2315
A₃	－0.2799	－0.0979	0.1820
A₄	－0.2984	－0.0925	0.2059
A₅	－0.3264	－0.1016	0.2248
A₆	－0.2816	－0.0992	0.1824
A₇	－0.2984	－0.0986	0.1998
A₈	－0.2802	－0.0562	0.2240
A₉	－0.2973	－0.0717	0.2256
A₁₀	－0.2780	－0.0691	0.2089

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Compd.	M/V(0.001)/(g•cm^－3)	$v\sigma _{{\rm{tot}}}^{\rm{2}}$^a/[(kcal•mol^－1)²]	Crystal density/(g•cm^－3)	Q/(cal•g^－1)	D/(km•s^－1)	P/GPa	$v\sigma _ + ^{\rm{2}}$^b/[(kcal•mol^－1)²]	V^b	h₅₀/cm
S₁	1.90	23.54	1.85	1528.4	8.92	35.89	123.46	0.179694	39.16
S₂	1.86	32.57	1.84	1458.1	8.65	33.62	155.39	0.197494	43.25
S₃	1.99	14.39	1.91	1520.9	9.01	37.31	105.79	0.140591	29.83
S₄	1.71	18.73	1.67	1450.2	7.88	26.29	78.34	0.220414	49.28
S₅	1.71	38.06	1.72	1366.2	7.96	27.31	84.96	0.239974	53.96
A₁	1.88	32.27	1.86	1494.1	8.84	35.37	141.83	0.204702	45.08
A₂	1.94	23.36	1.89	1522.1	9.01	37.02	121.41	0.181812	39.69
A₃	1.81	21.75	1.77	1495.1	8.45	31.39	102.07	0.199145	43.99
A₄	1.79	36.15	1.79	1436.5	8.44	31.47	103.74	0.247193	55.58
A₅	1.92	32.07	1.90	1485.6	8.91	36.35	131.11	0.21593	47.86
A₆	1.78	30.90	1.77	1446.7	8.30	30.28	107.56	0.234407	52.47
A₇	1.77	39.38	1.78	1403.8	8.28	30.23	109.55	0.248915	55.96
A₈	1.85	16.79	1.79	1489.5	8.45	31.55	93.43	0.180208	39.48
A₉	1.83	34.56	1.82	1430.2	8.47	32.01	93.51	0.249796	56.28
A₁₀	1.71	34.83	1.71	1399.1	7.96	27.21	87.25	0.249176	56.17
HMX^c			1.91		9.10	39.60			30
^a The computed results pertain to 0.001 a.u. surfaces.^b The computed results pertain to 0.002 a.u. surfaces. ^c Calculated values taken from Ref. [44].

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Table 5. Bond dissociation energies (BDE) of the relatively weak bonds for the title compounds at B3LYP/6-311++G(d, p) level

Compd.	BDE_ZPE/(kJ•mol^－1)
Compd.	C—NF₂^a	C—NF₂^b	C—ONO₂	O—NO₂	C—NO₂	N—NO₂	C—N₃	N—F^a	N—F^b
S₁	80.67		264.69	104.48				217.29
S₂	80.58				185.04			214.79
S₃	81.70	205.77						209.34	232.03
S₄	86.57						244.93	216.79
S₅	84.01					129.10		216.72
A₁	87.71		263.33	103.38	184.83			211.32
A₂	81.84	205.65	265.33	104.07				215.55	232.09
A₃	79.55		265.93	104.68			236.86	217.32
A₄	92.72		267	105.23		139.93		217.10
A₅	81.54	205.33			186.52			215.32	229.65
A₆	85.80				193.69		243.11	214.92
A₇	84.00				187.41	128.83		215.58
A₈	79.68	207.41					238.03	216.49	230.32
A₉	83.11	206.91				129.00		215.57	232.20
A₁₀	89.76					129.86	238.12	214.72
^a Bond located in the 3 position of the title compounds; ^b bond located in the 1 or 5 position of the title compounds.

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