A Facile Method for Assessing the Change in Detonation Properties during Chemical Functionalization: The Case of NH 2 → NHNO 2 and NH 2 → =N + =N − Conversions

: A simple and fast procedure for estimation of the effect of chemical functionalization on the change in detonation properties of energetic materials is reported. The procedure consists of two levels. Computations at Level 1 can be performed with a pocket calculator. At Level 2, quantum-chemical calculations are needed, but these include only three computational tasks: vacuum-isolated molecule relaxation (PBE/DND) → crystal structure prediction (COMPASSII) → crystal cell relaxation (PBE/DND). Thus, we have analyzed transformation of both aromatic and aliphatic amines into the corresponding nitramines and diazo compounds. The calculations at Level 1 indicated that both crystal density ( d c ) and solid-state enthalpy of formation ( ∆ H f ) are always positive and increase detonation properties, while the calculations at Level 2 revealed the amines that are the most sensitive to such chemical transformation.


Introduction
Recently, we have proposed a convenient method for estimation of crystalline density (d c ) and solid-state enthalpy of formation (∆H f ) on the basis of empirical formulas of C-H-N-O energetic materials; these were then applied for prediction of their detonation properties [1]. Using this method, we compiled a list of the predicted values of d c , ∆H f , detonation energy (Q), velocity (D) and pressure (P) for all compositions up to C 30 H 30 N 30 O 30 [1]. This method appeared to be very useful for predicting the influence of chemical transformation on changes in detonation properties, since one only needs find the interested compound in the table and crudely estimate its potential as an energetic material, or compare its potential with other molecule in the table. Thus, we have recently shown how this method performs for chemical transformation of energetic amines in corresponding triazenes [2] and pentazoles [3].
At the same time, due to a recent trend in the synthesis of nitrogen-rich heterocyclic energetic materials [4][5][6][7], the number of interesting and promising energetic amines demonstrates sustainable growth. Consequently, the area of its possible functionalization plays an increasingly important role. Apart from triazenes and pentazoles, it is interesting to estimate how the detonation properties change upon transformation into the corresponding nitramines and diazo compounds. Both these families of compounds are energetic and well known as conventional explosives [8][9][10]. The specific chemical route leading to these classes of compounds is also known and can be schematically illustrated as follows (Scheme 1) [11][12][13][14][15]: Scheme 1. Chemical routes from amines to diazo compounds (left) and nitramines (right).
Thus, in this work, we have applied a two-level scheme to estimate the potential of the aforementioned chemical reactions for enhancing the detonation properties of a number of heterocyclic nitrogen-rich amines.

Computational Method
Quantum-chemical calculations in this work were performed using the Materials Studio 2017 suite of programs [16]. Crystal structure predictions were done using ab initio forcefield condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASSII) [17]. The predicted values were then corrected using the previously developed regression model [2,3]: where is the uncorrected value obtained using the COMPASSII calculations. Geometry optimizations of vacuum-isolated molecules and crystals were carried out within all-electron approximation with pure GGA function due to Perdew-Burke-Ernzerhof (PBE) [18], together with a double numerical basis set, DND, as implemented in the DMol 3 code [19]. Enthalpies of formation were calculated using the following Equations (2) and (3): where EC i H j N k O l is the total energy of the crystal geometry optimization and EX are the corresponding atomic increments [2]. The ΔHf,pred values were then corrected using the following regression model [2]: ΔHf,theor = 1.1142 ΔHf,pred − 44.657, Detonation properties were calculated using the Kamlet-Jacobs scheme [20].

Calculation at Level 1
The changes in empirical formulas for transformation into nitramines and diazo compounds are expressed in Equations (4) and (5). Taking into account the general method for estimation of ΔHf [1], one can express the constant differences ΔΔHf, which are presented in Equations (6) and (7).
CxHyNzOw → CxHy-3Nz+1Ow It is clear that the studied reactions always increase the heat of formation that leads to increased detonation properties. On the other hand, the more important property is crystal density. Taking into account the previously developed equation for dc [1], the same difference Δdc, can be expressed as in Equation (8) and Table 1: Chemical routes from amines to diazo compounds (left) and nitramines (right).
Thus, in this work, we have applied a two-level scheme to estimate the potential of the aforementioned chemical reactions for enhancing the detonation properties of a number of heterocyclic nitrogen-rich amines.

Computational Method
Quantum-chemical calculations in this work were performed using the Materials Studio 2017 suite of programs [16]. Crystal structure predictions were done using ab initio forcefield condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASSII) [17]. The predicted values were then corrected using the previously developed regression model [2,3]: where d pred is the uncorrected value obtained using the COMPASSII calculations. Geometry optimizations of vacuum-isolated molecules and crystals were carried out within all-electron approximation with pure GGA function due to Perdew-Burke-Ernzerhof (PBE) [18], together with a double numerical basis set, DND, as implemented in the DMol 3 code [19]. Enthalpies of formation were calculated using the following Equations (2) and (3): where E CiHjNkOl is the total energy of the crystal geometry optimization and E X are the corresponding atomic increments [2]. The ∆H f,pred values were then corrected using the following regression model [2]: Detonation properties were calculated using the Kamlet-Jacobs scheme [20].

Calculation at Level 1
The changes in empirical formulas for transformation into nitramines and diazo compounds are expressed in Equations (4) and (5). Taking into account the general method for estimation of ∆H f [1], one can express the constant differences ∆∆H f , which are presented in Equations (6) and (7).
It is clear that the studied reactions always increase the heat of formation that leads to increased detonation properties. On the other hand, the more important property is crystal density. Taking into account the previously developed equation for d c [1], the same difference ∆d c , can be expressed as in Equation (8) and Table 1: where V M (atoms) are the previously estimated atomic volumes [1]. As it follows from Equation (8) and Table 1, the expected ∆d c are about 0.2 g/cm 3 for compositions of typical energetic materials and are always positive, too. Thus, fast calculations at Level 1, which can be performed without involvement of quantum-chemical methods, endorse the transformation of amines into nitramines and diazo compounds.

Calculations at Level 2
On the basis of calculations at Level 2, we have identified those chemical compositions that are sensitive to the studied transformations and selected the corresponding experimentally available energetic amines from the literature. Chemical structures of the potential products of the amine transformations into nitramines (1-15) and diazo compounds (16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) are illustrated in Figure 1, and the calculated absolute values of detonation properties and their changes caused upon the transformation are listed in Table 2. As one can see in Table 2, the calculations at both levels demonstrate an increase in detonation properties. At Level 1, the mean absolute and relative differences in Q, D and P values under the formation of nitramines are 166 cal/g (13.8%), 680 m/s (8.7%) and 6.0 GPa (23.2%), respectively. For diazo compounds, these differences for Q, D and P are the following: 266 cal/g (26.2%), 459 m/s (6.5%) and 3.9 GPa (18.7%), respectively. The differences obtained at Level 2 are generally comparable. For example, in the case of the nitramine formation, the Q, D and P values are the following: 323 cal/g (47.9%), 1191 m/s (15.5%) and 10.6 GPa (39.2%), respectively. Finally, for diazo compounds, these differences are the following: 597 cal/g (225.1%), 1041 m/s (20.1%) and 5.1 GPa (46.2%) for Q, D and P, respectively.
where VM(atoms) are the previously estimated atomic volumes [1]. As it follows from Equation (8) and Table 1, the expected Δdc are about 0.2 g/cm 3 for compositions of typical energetic materials and are always positive, too. Thus, fast calculations at Level 1, which can be performed without involvement of quantumchemical methods, endorse the transformation of amines into nitramines and diazo compounds.

Entry
Ref. The absolute predicted values of D and P indicate that transformation into the nitramines is most effective for the precursor of compound 8 (Figure 1). In this case, one can expect an increase in detonation properties up to 2028 m/s and 13.8 GPa (Table 2). At the same time, for the diazo compounds, a significant gain in detonation properties was observed only for precursors with a very low detonation profile, namely, compounds 19, 20, 24 and 25 ( Table 2). The transformation of amines into diazo compounds can even slightly reduce detonation properties, such as in the case of compounds 17 and 18 (Table 2). This is mainly caused by the lower crystal density of the resulting diazo compounds due to the vanishing of intermolecular hydrogen bonds (Figure 1). The only compound that demonstrates a significant rise in detonation properties and has high absolute values is compound 16 ( Table 2).

Conclusions
Thus, in this article, we have presented an example of using our two-level scheme to evaluate the effectiveness of changes in the detonation properties of energetic amines that have undergone two types of chemical functionalization. Since this family of nitrogen-rich energetic compounds demonstrates intensive growth, it is of current interest to study possible routes for the enhancement of their detonation profiles by means of a simple functionalization. Thus, in this work, we have found that transformation of amines into corresponding nitramines increases their detonation properties by up to 15 and 40% for D and P, as an average. At the same time, transformation into diazo compounds generally has a little effect on highly energetic amines. A significant enhancement is observed only for low-energy density precursors. Nevertheless, in this work, we have revealed the energetic amines whose detonation properties can be easily enhanced via a simple one-pot functionalization. These are the amine precursors of the compounds 8 and 16.
Funding: This work was supported by the Ministry of Education and Science of Ukraine, Research Fund (Grant No. 0122U000760).