Next Article in Journal
Enantiopure Radical Cation Salt Based on Tetramethyl-Bis(ethylenedithio)-Tetrathiafulvalene and Hexanuclear Rhenium Cluster
Next Article in Special Issue
Crystal Structures of Two 1,4-Diamino-1,2,4-triazolium Salts
Previous Article in Journal
Constructor Graphs as Useful Tools for the Classification of Hydrogen Bonded Solids: The Case Study of the Cationic (Dimethylphosphoryl)methanaminium (dpmaH+) Tecton
Open AccessArticle

Electrostatic Potentials, Intralattice Attractive Forces and Crystal Densities of Nitrogen-Rich C,H,N,O Salts

by 1,2,*, 1 and 1,2
1
Department of Chemistry, University of New Orleans, New Orleans, LA 70148, USA
2
CleveProp, 1951 W. 26th Street, Cleveland, OH 44113, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Gerhard Laus
Crystals 2016, 6(1), 7; https://doi.org/10.3390/cryst6010007
Received: 9 December 2015 / Revised: 28 December 2015 / Accepted: 30 December 2015 / Published: 4 January 2016
(This article belongs to the Special Issue Nitrogen-Rich Salts)

Abstract

The computed electrostatic potentials on C,H,N,O molecular solids and nitrogen-rich C,H,N,O salts are used in analyzing and comparing intralattice attractive forces and crystal densities in these two categories of compounds. Nitrogen-rich C,H,N,O salts are not an assured path to high densities. To increase the likelihood of high densities, small cations and large anions are suggested. Caution is recommended in predicting benefits of nitrogen-richness for explosive compounds.
Keywords: nitrogen-rich; electrostatic potentials; C,H,N,O molecular and ionic compounds; crystal densities nitrogen-rich; electrostatic potentials; C,H,N,O molecular and ionic compounds; crystal densities

1. Why “Nitrogen-Rich?”

In the detonation of an explosive compound, an initial stimulus (input of energy) is followed by a series of steps culminating in self-sustaining highly exothermal chemical decomposition releasing large amounts of energy and gaseous products. This results in a high pressure, supersonic shock wave propagating through the system (detonation) [1,2,3,4,5]. Many explosives are composed of appropriate numbers of carbon, hydrogen, nitrogen and oxygen atoms. Their final decomposition products, apart from some solid carbon, are usually mainly large quantities of low molecular mass, very stable gases, e.g., N2, CO2, CO, H2O [6,7,8,9]. Due to their low masses, large amounts can be produced per gram of explosive, while their stabilities mean that a great deal of energy is liberated.
An important point is that many C,H,N,O compounds have relatively high densities compared to other organic compounds, in the range 1.50 g/cm3 to 2.00 g/cm3 [10,11,12]. This allows more explosive to be packed into the available volume. The density is in fact one of the primary factors affecting detonation performance [6,9].
During the past two decades, there has been a tendency to focus upon the design and synthesis of “nitrogen-rich” explosive compounds, whether molecular or ionic [13,14,15,16], [17] and references therein. While the term is somewhat ambiguous, basically it means replacing some C–H units in a molecular or ionic framework by nitrogens. This is expected to increase the compound’s heat of formation (its energy content) and possibly also its density, both of which would be desirable.
An increased density is plausible, because a nitrogen atom has a greater mass but smaller volume than a C–H unit [18]. An increased (more positive) heat of formation is expected because the hypothetical “formation reaction” requires breaking the very strong N≡N bond in N2 and creating much weaker C–N, C=N, N–N and/or N=N bonds in the explosive [19]. A high heat of formation suggests that the compound has a greater intrinsic energy content, which may result in a larger heat release during detonation.
It should be noted, however, that the effects of increasing the framework nitrogen content may not all be beneficial, as has recently been pointed out [19]. The overall heat release depends upon the compound’s stoichiometry as well as its heat of formation; furthermore, a capability for a very large heat release is likely to be accompanied by excessive sensitivity (vulnerability to accidental detonation). Another consideration is that diminishing the number of hydrogens adversely affects the number of moles of gaseous products per gram of explosive, since more of the heavier N2 and less of the lighter H2O are being formed. These issues will be further discussed in a later section.
Our present objectives are to compare molecular and ionic C,H,N,O solids in terms of intralattice forces, electrostatic potentials and crystal densities. At the same time we will consider the effects of nitrogen richness upon the ionic compounds.

2. Molecular vs. Ionic Crystal Lattices

The discussion in Section 1 applied to both molecular and ionic crystalline C,H,N,O explosives. However there is a major difference in the nature of the intralattice forces that stabilize these two categories of solids. The crystal lattices of molecular compounds are held together by relatively weak Coulombic attractions between molecules that are overall neutral, although having locally positive and negative regions of electrostatic potential. Figure 1 and Figure 2 are the computed electrostatic potentials on the molecular “surfaces” of the molecules 5-nitrotetrazole (1) and 3-nitro-1,2,4-triazole (2); the surfaces are taken to be the 0.001 au contours of the molecules’ electronic densities, as proposed by Bader et al. [20]. Such surfaces encompass roughly 97% of the electronic charge and have the advantage that they reflect features such as lone pairs, π electrons and atomic anisotropy that are specific to the particular molecules. Figure 1 and Figure 2 show regions of positive electrostatic potential to be associated with the hydrogens and the central portions of the molecules, and negative regions by the ring nitrogens and nitro oxygens. (All electrostatic potentials being discussed were computed at the density functional B3PW91/6-31G** level).
Figure 1. Computed electrostatic potential on 0.001 au molecular surface of 5-nitrotetrazole (1). Color ranges, in kcal/mol, are: red, greater than 30; yellow, between 30 and 15; green, between 15 and 0; blue, negative (less than 0). Circles show positions of atoms; NO2 group is on the left. Most positive potential is 73 kcal/mol by the hydrogen; most negative are −29 kcal/mol by the ring nitrogen at the bottom right.
Figure 1. Computed electrostatic potential on 0.001 au molecular surface of 5-nitrotetrazole (1). Color ranges, in kcal/mol, are: red, greater than 30; yellow, between 30 and 15; green, between 15 and 0; blue, negative (less than 0). Circles show positions of atoms; NO2 group is on the left. Most positive potential is 73 kcal/mol by the hydrogen; most negative are −29 kcal/mol by the ring nitrogen at the bottom right.
Crystals 06 00007 g001
Figure 2. Computed electrostatic potential on 0.001 au molecular surface of 3-nitro-1,2,4-triazole (2). Color ranges, in kcal/mol, are: red, greater than 30; yellow, between 30 and 15; green, between 15 and 0; blue, negative (less than 0). Circles show positions of atoms; NO2 group is on the lower right. Most positive potential is 71 kcal/mol by the N-H hydrogen; most negative are −33 to −39 kcal/mol by the ring nitrogens and the NO2 oxygens.
Figure 2. Computed electrostatic potential on 0.001 au molecular surface of 3-nitro-1,2,4-triazole (2). Color ranges, in kcal/mol, are: red, greater than 30; yellow, between 30 and 15; green, between 15 and 0; blue, negative (less than 0). Circles show positions of atoms; NO2 group is on the lower right. Most positive potential is 71 kcal/mol by the N-H hydrogen; most negative are −33 to −39 kcal/mol by the ring nitrogens and the NO2 oxygens.
Crystals 06 00007 g002
The crystal lattices of ionic solids are also held together by Coulombic attractions, but they are quite strong, involving the overall integral positive or negative charges on the ions. Consider the salts resulting from the interactions of 1 and 2 with a base such as NH3:
Crystals 06 00007 i001
Figure 3 and Figure 4 display the electrostatic potentials on the 0.001 au surfaces of the resulting 5-nitrotetrazolate anion (3) and 3-nitro-1,2,4-triazolate anion (4).
Figure 3. Computed electrostatic potential on 0.001 au anionic surface of 5-nitrotetrazolate anion (3). Color ranges, in kcal/mol, are: yellow, between −60 and −80; green, between −80 and −100; blue, more negative than −100. Circles show positions of atoms; NO2 group is on the left. Most negative potentials are −126 kcal/mol by the ring nitrogens closest to the carbon bearing the NO2 group.
Figure 3. Computed electrostatic potential on 0.001 au anionic surface of 5-nitrotetrazolate anion (3). Color ranges, in kcal/mol, are: yellow, between −60 and −80; green, between −80 and −100; blue, more negative than −100. Circles show positions of atoms; NO2 group is on the left. Most negative potentials are −126 kcal/mol by the ring nitrogens closest to the carbon bearing the NO2 group.
Crystals 06 00007 g003
Figure 4. Computed electrostatic potential on 0.001 au anionic surface of 3-nitro-1,2,4-triazolate anion (4). Color ranges, in kcal/mol, are: red, less negative than −60; yellow, between −60 and −80; green, between −80 and −100; blue, more negative than −100. Circles show positions of atoms; NO2 group is on the lower right. Most negative potentials are −133 and −136 kcal/mol by the ring nitrogens closest to the carbon bearing the NO2 group.
Figure 4. Computed electrostatic potential on 0.001 au anionic surface of 3-nitro-1,2,4-triazolate anion (4). Color ranges, in kcal/mol, are: red, less negative than −60; yellow, between −60 and −80; green, between −80 and −100; blue, more negative than −100. Circles show positions of atoms; NO2 group is on the lower right. Most negative potentials are −133 and −136 kcal/mol by the ring nitrogens closest to the carbon bearing the NO2 group.
Crystals 06 00007 g004
The surfaces of 3 and 4 are completely negative, although with some local variation, which will be discussed later; the surface of the cation NH4+ is completely positive (Figure 5), again with some variation. The magnitudes of the electrostatic potentials on the anions 3 and 4 (Figure 3 and Figure 4) and on NH4+ (Figure 5) are considerably greater than those on the neutral molecules 1 and 2 (Figure 1 and Figure 2) and on the ammonia molecule (on which they vary from −40 to +24 kcal/mol [21]). It follows that the Coulombic attractions between the ions in the two salts will be much stronger than between the neutral molecules in the molecular solids 1 and 2.
Figure 5. Computed electrostatic potential on 0.001 au cationic surface of NH4+ cation. Color ranges, in kcal/mol, are: red, greater than 178; yellow, between 178 and 174; green, between 174 and 168; blue, less than 168. Circles show positions of atoms. Most positive potentials are 181 kcal/mol by hydrogens.
Figure 5. Computed electrostatic potential on 0.001 au cationic surface of NH4+ cation. Color ranges, in kcal/mol, are: red, greater than 178; yellow, between 178 and 174; green, between 174 and 168; blue, less than 168. Circles show positions of atoms. Most positive potentials are 181 kcal/mol by hydrogens.
Crystals 06 00007 g005
The differences in the strengths of the intralattice attractive forces in molecular and ionic solids are reflected in the energies required to overcome them. The heat of sublimation of a molecular solid is the enthalpy for the transition from the crystal lattice to separate gas phase molecules. For C,H,N,O molecular explosives, the magnitudes of the heats of sublimation are mainly between 20 and 30 kcal/mol [22]. For ionic compounds, the analogue of the heat of sublimation is the lattice enthalpy, which is the enthalpy required to separate the lattice into free gas phase ions. Lattice enthalpies are generally much greater than heats of sublimation [23]. For C,H,N,O ionic explosives in which the ions have +1 and −1 charges, the estimated lattice enthalpies are between 100 and 200 kcal/mol [24]; for +1 and −2 they are roughly twice as large, and approach 400 kcal/mol for +2 and −2. The ionic charges are clearly a major factor.
Another interesting manifestation of the effects of overall ionic charges is evident in estimating “effective” molecular or formula unit volumes, Veff. These are defined for any molecular or ionic solid as,
Veff = M/ϱ
where M is the molecular or formula unit mass and ϱ is the crystal density. Veff is the hypothetical volume per molecule or per formula unit (in the case of an ionic compound) that would correspond to the unit cell of the lattice being completely filled. (In reality, there is of course always some free space.) Veff can also be determined by dividing the volume of the unit cell by the number of molecules or formula units that it contains.
For molecular C,H,N,O solids, Veff can be approximated quite well as the volume V(0.001) that is enclosed within the molecule’s 0.001 au surface [25,26,27]:
Veff (molecular solid) ≈ V(0.001)
This is surprising given that V(0.001) is computed for a single isolated molecule, with no consideration of intermolecular interactions within the crystal.
For an ionic C,H,N,O compound, the analogous procedure would be to compute V(0.001) for the positive and negative ions separately and then to estimate Veff for the formula unit by,
Veff (ionic solid) ≈ aV(0.001)cation + bV(0.001)anion
In Equation (3), a and b are the numbers of cations and anions, respectively, in one formula unit. However Equation (3) is not nearly as good an approximation to the actual Veff for ionic C,H,N,O compounds as Equation (2) is for molecular ones. The Veff obtained by Equation (3) are almost always too large [28,29], often quite significantly so.
Equation (2) is a reasonably good approximation for molecular C,H,N,O solids because the attractive forces between the molecules are relatively weak, and using the volume within the 0.001 au surface of the isolated molecule is therefore acceptable. However Equation (3) is a rather poor approximation for ionic C,H,N,O solids because the attractive forces between the oppositely-charged ions are quite strong, and bring the ions closer together than their 0.001 au volumes would predict.
For both types of solids, the Veff can be improved by taking explicit account of the electrostatic potentials on the molecular or ionic surfaces [24,25,26]. The corrected Veff can then be used to make reasonably good estimates of crystal densities via Equation (1).

3. Electrostatic Potentials on Ionic Surfaces

On the 0.001 au surface of an ion, the electrostatic potential is everywhere positive or everywhere negative, in accordance with the overall integral charge on the ion (Figure 3, Figure 4, Figure 5 and Figure 6). However, it should be recognized that for polyatomic ions these surface potentials are frequently far from isotropic. To some extent, they may exhibit patterns that are qualitatively similar to those of the corresponding neutral molecules. (It should be kept in mind that the colors on the surfaces of the neutral molecules, the anions and the cations correspond to different ranges of potentials).
Consider the 5-nitrotetrazolate (3) and 3-nitro-1,2,4-triazolate (4) anions, Figure 3 and Figure 4. In the parent neutral molecules 1 and 2, the most positive features are the N-H hydrogens, with maximum potentials of about 70 kcal/mol (Figure 1 and Figure 2). These hydrogens are not present in the anions. However the other positive regions in the neutral molecules—above the rings and the C–NO2 bonds, as well as the C-H hydrogen in 2—are still in evidence, as being now the least negative regions in the anions. The most negative potentials in the anions (as in the neutral molecules) are associated with the nitrogens of the rings and the oxygens of the NO2 groups, reaching magnitudes in the neighborhood of −130 kcal/mol, roughly 100 kcal/mol more negative than in the neutral molecules.
In Figure 6 is the electrostatic potential on the 0.001 au surface of the positive 5-nitrotetrazolium cation, 5, formed by protonating one of the ring nitrogens in 1. Now there are two N–H hydrogens, and they have the most positive potentials, 174 kcal/mol. The regions above the ring and the C–NO2 bond are also strongly positive, with maxima of about 152 kcal/mol. The most negative (i.e., least positive) regions are by the non-protonated ring nitrogens and the NO2 oxygens. All of this is analogous to what is seen in the potential of the parent molecule in Figure 1 (except of course that the values of the electrostatic potential are now all positive).
Crystals 06 00007 i002
Figure 3, Figure 4, Figure 5 and Figure 6 show that it would be misleading to focus only upon the overall charges on polyatomic ions, ignoring the variations in the electrostatic potentials on their surfaces. What also needs to be taken into account are the polarizing effects of the ions upon each other. The influence of these factors upon crystal densities will be discussed in the next section.
Figure 6. Computed electrostatic potential on 0.001 au cationic surface of 5-nitrotetrazolium cation (5). Color ranges, in kcal/mol, are: red, greater than 150; yellow, between 150 and 120; green, between 120 and 90; blue, less than 90. Circles shown positions of atoms; NO2 group is on the left. Most positive potentials are 174 kcal/mol by hydrogens.
Figure 6. Computed electrostatic potential on 0.001 au cationic surface of 5-nitrotetrazolium cation (5). Color ranges, in kcal/mol, are: red, greater than 150; yellow, between 150 and 120; green, between 120 and 90; blue, less than 90. Circles shown positions of atoms; NO2 group is on the left. Most positive potentials are 174 kcal/mol by hydrogens.
Crystals 06 00007 g006

4. Crystal Densities and Electrostatic Potentials

It has already been pointed out that replacing C-H units in molecular or ionic frameworks by nitrogen atoms could reasonably be expected to increase the crystal densities. The strongly attractive forces between oppositely-charged ions might be anticipated to have a similar effect. What is in fact observed?
In 2007, Rice et al. compiled a database of experimental crystal densities of 180 C,H,N,O molecular solids [26]. They were mainly nitroaromatics, nitroaliphatics, nitramines and nitrate esters. Many of them had all-carbon frameworks. In 2011, Gao and Shreeve tabulated the experimental densities of more than 230 C,H,N,O salts [15], in which one or both ions were usually tetrazole or triazole derivatives, with a few being derivatives of imidazole or pyrazole. Thus these can be viewed as largely nitrogen-rich salts.
Figure 7 compares the distributions of densities, on a percentage basis, within these two categories of compounds. The comparison shows clearly that nitrogen-rich salts do not represent an assured path to high densities. It has been suggested that a density greater than 1.80 g/cm3 is “an essential requirement for advanced energetic materials” [30]. This criterion is satisfied by about 22% of the molecular compounds in Figure 7 but only about 6% of the ionic ones, even though the latter were predominantly nitrogen-rich while many of the former were not.
Figure 7. Crystal density distributions of C,H,N,O molecular compounds (purple) and nitrogen-rich C,H,N,O ionic compounds (green). Vertical axes are percentages.
Figure 7. Crystal density distributions of C,H,N,O molecular compounds (purple) and nitrogen-rich C,H,N,O ionic compounds (green). Vertical axes are percentages.
Crystals 06 00007 g007
As Zhang et al. have pointed out [30], the interactions between polyatomic ions are directional, reflecting the nonisotropic natures of the electrostatic potentials on their surfaces (Figure 3, Figure 4, Figure 5 and Figure 6). Zhang et al. argued that closer packing and higher densities could be promoted by taking advantage of interactions such as hydrogen bonding, and drew attention to the hydroxylammonium ion, H3N-OH+, as being effective for this purpose.
It must be noted that Dunitz et al. found no general relationship between density and hydrogen bonding for a database of hydrocarbon, C,H,O and C,H,N molecular solids [31]. However that conclusion may not be relevant to the present systems of functionalized C,H,N,O salts.
It was demonstrated quite some time ago that hydrogen bonding ability can be related to the magnitude of the positive electrostatic potential on the hydrogen [32,33]. In Table 1 are listed the most positive calculated ionic surface potentials associated with the hydrogens in a series of monopositive cations that are commonly found in C,H,N,O salts. The hydroxylammonium ion clearly stands out; it has the single most positive potential, 190 kcal/mol near the hydroxyl hydrogen, plus three more of about 181 kcal/mol by the other hydrogens. There is in fact a continuous very strongly positive region encompassing all of the hydrogens, ranging in magnitude from 177 to 190 kcal/mol (Figure 8). The next most positive ion in Table 1 is the ammonium ion, NH4+, which has four hydrogen maxima of 181 kcal/mol, but they are separated by distinctly less positive regions (Figure 5).
The presence of several highly positive sites on H3N-OH+ shows it to be a likely candidate for strongly attractive directional interactions with polyatomic anions; NH4+ would be the next most likely in Table 1. Does this translate into higher densities? Dunitz et al. found no general relationship between density and lattice energies for their database of hydrocarbon, C,H,O and C,H,N molecular solids [31], mentioned above, but again this may not be relevant to the present functionalized C,H,N,O ionic solids.
We have surveyed 87 nitrogen-rich C,H,N,O salts that have been synthesized during the past five years [16,30,34,35,36,37,38,39,40,41,42,43,44,45,46]. (Only anhydrous salts were considered.) 41 of them, or 47%, have crystal densities ≥1.80 g/cm3. This is a remarkable increase over the 6% in the earlier work that is represented in Figure 7; some reasons for this will be proposed later.
In twelve of these 87 compounds, the cation is H3N-OH+. All twelve have densities ≥1.80 g/cm3. In four of them, the density is 1.90 g/cm3 or more. Thus, the hydroxylammonium ion does promote high densities in C,H,N,O salts, as is suggested by the electrostatic potential on its surface (Figure 8) and as was argued by Zhang et al. [30]. NH4+ is the cation in nine of the compounds surveyed, and six of them have densities ≥1.80 g/cm3, with one being 1.90 g/cm3. The H3N–OH+ and NH4+ cations clearly increase the likelihood of a C,H,N,O salt having a high density.
Figure 8. Computed electrostatic potential on 0.001 au cationic surface of NH3OH + cation. Color ranges, in kcal/mol, are: red, greater than 165; yellow, between 165 and 140; green, between 140 and 110; blue, less than 110. Circles show positions of atoms; OH group is on the left. Most positive potential is 190 kcal/mol by the OH hydrogen.
Figure 8. Computed electrostatic potential on 0.001 au cationic surface of NH3OH + cation. Color ranges, in kcal/mol, are: red, greater than 165; yellow, between 165 and 140; green, between 140 and 110; blue, less than 110. Circles show positions of atoms; OH group is on the left. Most positive potential is 190 kcal/mol by the OH hydrogen.
Crystals 06 00007 g008
Table 1. Most positive electrostatic potentials on the 0.001 au surfaces of some C,H,N,O monopositive cations.
Table 1. Most positive electrostatic potentials on the 0.001 au surfaces of some C,H,N,O monopositive cations.
CationMost Positive Potentials, kcal/mol
hydroxylammonium190, 181, 181, 180
ammonium181, 181, 181, 181
5-nitrotetrazolium174, 174, 153, 152
hydrazinium173, 173, 172
3,3-dinitroazetidinium172, 172
5-aminotetrazolium172, 172
methylammonium169, 169, 169
1,1-dimethylhydrazinium164, 164, 156
azidoformadinium165, 157, 143
t-butylhydrazinium161, 158, 154
1,5-diaminotetrazolium164, 141, 130, 130
1-isopropyl-3,3-dinitroazetidinium158, 158, 143
hydroxyguanidinium157, 152, 143, 136
guanidinium154, 154, 154
aminoguanidinium154, 151
1,5-diamino-4-methyltetrazolium149, 137
N,N,N-trimethylhydrazinium142, 142, 130
triaminoguanidinium136
In Table 2 are the most negative calculated ionic surface potentials of a series of mononegative anions often found in C,H,N,O salts. In general, their magnitudes are less than those of the most positive potentials on the cations in Table 1. It is further notable that the smaller ions tend to have the strongest potentials, whether positive or negative. This may be in part because the overall charge of the ion is not as delocalized [47]; another factor of course, for a given ionic framework, is the effects of the functional groups.
Table 2. Most negative electrostatic potentials on the 0.001 au surfaces of some C,H,N,O mononegative anions.
Table 2. Most negative electrostatic potentials on the 0.001 au surfaces of some C,H,N,O mononegative anions.
AnionMost Negative Potentials, kcal/mol
nitrate−151, −151, −151
nitroformate−142, −142, −123, −120, −120
azide−139, −139
5-aminotetrazolate−137, −137, −137
3-nitro-1,2,4-triazolate−136, −133
4-nitro-1,2,3-triazolate−132, −124, −124, −123
dinitramide−131, −126, −126, −121, −121
5-nitrotetrazolate−126, −126, −118, −118, −116
4,5-dinitroimidazolate−125, −125, −119
3,5-dinitropyrazolate−123, −123
3,5-dinitro-1,2,4-triazolate−119, −119, −119, −119
picrate−119, −119
2,4,5-trinitroimidazolate−116, −116, −115, −114
In using electrostatic potentials such as those in Figure 1, Figure 2, Figure 3, Figure 4, Figure 5, Figure 6 and Figure 8 to interpret and predict molecular and ionic interactions, it is important to keep in mind that these potentials are typically computed for the ground states of the molecules or ions, prior to any interaction [48,49,50]. Accordingly they do not reflect the polarizing effect that each molecule’s or ion’s electric field has upon the charge distribution of the other. This polarization, which is stabilizing, is of course particularly significant when resulting from the strong electric fields of ions.
The degree to which the charge distribution of a molecule, atom or ion is affected by an external electric field is determined by its polarizability. It is well known that polarizability generally increases with size [51,52,53,54,55,56,57] and in going from cations to neutral molecules to anions [58], as the outer electrons become less tightly bound. It is therefore to be expected that the intralattice attractive interactions in ionic compounds will be stronger when they have large polarizable anions in conjunction with cations having several highly positive polarizing sites. Hydroxylammonium and ammonium salts with large C,H,N,O anions fit this description, which helps to explain their frequently high densities.
Why are the recently-prepared nitrogen-rich salts more likely to have high densities than the earlier ones represented in Figure 7? Several factors may be involved. In the newer compounds, there is a greater emphasis upon small cations and large anions. This results in strong intralattice attractions due to the highly-positive potentials of small cations (Table 1) and the high polarizabilities of large anions, and evidently promotes higher densities. In contrast, a significant number of the salts represented in Figure 7 involved large cations, which have low polarizabilities and weaker positive potentials, and often large anions, which have weaker negative potentials (Table 2). Furthermore, even when these compounds did have a large anion and small cation, the latter was very rarely the hydroxylammonium while the anion was often relatively poor in oxygens or even just C,H,N in composition; all of this diminishes the opportunities for strong hydrogen bonding.
While C,H,N,O salts with large cations are less likely to have high densities, it is not precluded, as can be seen from the examples in Table 3. Note that the negative ion in three of the four compounds is NO3, which has the most negative potentials in Table 2.
Table 3. Some C,H,N,O nitrogen-rich salts with large cations and small anions that have experimental densities greater than 1.80 g/cm3.
Table 3. Some C,H,N,O nitrogen-rich salts with large cations and small anions that have experimental densities greater than 1.80 g/cm3.
SaltDensity, g/cm3Reference
oxalhydrazinium dinitrate1.94544
1-amino-3-nitroguanidinium nitrate1.9138
oxalhydrazinium nitrate1.84044
5-aminotetrazolium dinitramide 1.8331.83329

5. Discussion and Summary

Is nitrogen richness beneficial? For unsubstituted molecules, replacing a C–H unit by a nitrogen does tend to increase the density (Table 4). When functional groups are present, however, it is less straightforward; for example, 1,3,5-trinitrobenzene (6) and 2,4,6-trinitropyridine (7) have essentially the same densities, 1.76 g/cm3 [2] and 1.751 g/cm3 [59], respectively. Rice et al. compiled the densities of 38 “high-nitrogen” C,H,N,O molecular solids [26]; only four had densities greater than 1.80 g/cm3.
Table 4. Some experimental densities and heats of formation, ΔHf.
Table 4. Some experimental densities and heats of formation, ΔHf.
CompoundStructureDensity a g/cm3ΔHf b kcal/mol (cal/g)
1 H-imidazole Crystals 06 00007 i0041.030311.9 (175)
1 H-1,2,3-triazole Crystals 06 00007 i0051.1861---
1 H-tetrazole Crystals 06 00007 i0061.406056.4 (805)
cyclohexane Crystals 06 00007 i0070.7739−37.68 (−447.7)
piperidine Crystals 06 00007 i0080.8606−20.66 (−242.6)
a Reference [58]; b Reference [60].
Crystals 06 00007 i003
For C,H,N,O salts as well, nitrogen richness is not sufficient to make likely a density ≥1.80 g/cm3. This is shown by Figure 7. To increase the probability of a high density, the salt should also have a large anion and a small cation, preferably H3N-OH+ or NH4+.
A greater nitrogen/carbon ratio does frequently result in a more positive heat of formation, ΔHf (Table 4). Thus the values for 6 and 7 are −10.4 kcal/mol (−48.8 cal/g) and 18.8 kcal/mol (88.0 cal/g), respectively [2]. This may (or may not) lead to a greater heat release Q upon detonation, as shall be seen. For an explosive X, Q is typically taken to be the negative of the enthalpy change per gram of X in the overall detonation reaction:
Q = 1 M X [ i n i Δ H f , i Δ H f , X ]
In Equation (4), MX is the mass of X in g/mol, ni is the number of moles of final detonation product i, having molar heat of formation ΔHf,i, and ΔHf,X is the molar heat of formation of the explosive X.
From Equation (4), the detonation heat release Q is greater as the heat of formation ΔHf,X of the compound is more positive and as the heats of formation ΔHf,i of the products are more negative. Replacing C–H units by nitrogens is likely to increase ΔHf,X but it may also decrease the amounts of the three common detonation products that have negative heats of formation: CO2 (g), −94.05 kcal/mol; CO (g), −26.42 kcal/mol; H2O (g), −57.80 kcal/mol [60]. Producing one less mole of CO2 would negate a quite considerable increase of 94 kcal/mol in ΔHf,X; two fewer moles of H2O would cancel an increase of 115 kcal/mol! Of course, a larger N/C ratio means that more N2 is formed as a product, which may be viewed as desirable since N2 is (at the moment) considered to be environmentally benign; however its heat of formation is zero, so it does not contribute to the detonation heat release Q. Increasing the N/C ratio may therefore have two opposing effects, one making Q larger and the other making it smaller.
There are yet other factors to take into account. A larger value of Q is associated with a higher level of detonation performance [6], but it is also linked to greater sensitivity [5,19,61,62], i.e., undesirable vulnerability to accidental detonation caused by an unintended stimulus such as shock or impact. Finally, if the increase in N2 is accompanied by a decrease in the lighter product H2O, then the volume of gas produced per gram of compound will be less—adversely affecting detonation performance [6].
So, given all these conflicting factors, our answer to the question posed at the beginning of this section, “Is nitrogen richness beneficial?” is an unequivocal yes and no! Putting it more elegantly, one should not generalize; it depends upon the particular case.

Author Contributions

P.P. and J.S.M. conceived and designed the plan for the paper and analyzed the data; P.L. and J.S.M. carried out the calculations; P.P. wrote the paper.

Conflicts of Interest

The authors declare no conflict of interest.

References

  1. Dlott, D.D. Fast Molecular Processes in Energetic Materials. In Energetic Materials. Part 2. Detonation, Combustion; Politzer, P., Murray, J.S., Eds.; Elsevier: Amsterdam, The Netherlands, 2003; Chapter 6; pp. 125–191. [Google Scholar]
  2. Meyer, R.; Köhler, J.; Homburg, A. Explosives, 6th ed.; Wiley: Weinheim, Germany, 2007. [Google Scholar]
  3. Shackelford, S.A. Role of Thermochemical Decomposition in Energetic Material Initiation Sensitivity and Explosive Performance. Cent. Eur. J. Energ. Mater. 2008, 5, 75–101. [Google Scholar]
  4. Klapötke, T.M. Chemistry of High Energy Materials; de Gruyter: Berlin, Germany, 2011. [Google Scholar]
  5. Politzer, P.; Murray, J.S. Some Molecular/Crystalline Factors that Affect the Sensitivities of Energetic Materials: Molecular Surface Electrostatic Potentials, Lattice Free Space and Maximum Heat of Detonation Per Unit Volume. J. Mol. Model. 2015, 21, 25. [Google Scholar] [CrossRef] [PubMed]
  6. Kamlet, M.J.; Jacobs, S.J. Chemistry of Detonation. I. A Simple Method for Calculating Detonation Properties of C,H,N,O Explosives. J. Chem. Phys. 1968, 48, 23–35. [Google Scholar] [CrossRef]
  7. Mader, C.L. Numerical Modeling of Explosives and Propellants, 2nd ed.; CRC Press: Boca Raton, FL, USA, 1998. [Google Scholar]
  8. Rice, B.M.; Hare, J. Predicting Heats of Detonation Using Quantum Mechanical Calculations. Thermochim. Acta 2002, 384, 377–391. [Google Scholar] [CrossRef]
  9. Politzer, P.; Murray, J.S. Some Perspectives on Estimating Detonation Properties of C,H,N,O Compounds. Cent. Eur. J. Energ. Mater. 2011, 8, 209–220. [Google Scholar]
  10. Klapötke, T.M.; Ang, H.-G. Estimation of the Crystalline Density of Nitramine (N-NO2 Bond) High Energy Density Materials. Propell. Explos. Pyrotech. 2001, 26, 221–224. [Google Scholar] [CrossRef]
  11. Eckhardt, C.J.; Gavezzotti, A. Computer Simulations and Analysis of Structural and Energetic Features of Some Crystalline Energetic Materials. J. Phys. Chem. B 2007, 111, 3430–3437. [Google Scholar] [CrossRef] [PubMed]
  12. Politzer, P.; Murray, J.S. Perspectives on the Crystal Densities and Packing Coefficients of Explosive Compounds. Struct. Chem. 2015. [Google Scholar] [CrossRef]
  13. Pagoria, P.F.; Lee, G.S.; Mitchell, A.R.; Schmidt, R.D. A Review of Energetic Materials Synthesis. Thermochim. Acta 2002, 384, 187–204. [Google Scholar] [CrossRef]
  14. Churakov, A.M.; Tartakovsky, V.A. Progress in 1,2,3,4-Tetrazine Chemistry. Chem. Rev. 2004, 104, 2601–2616. [Google Scholar] [CrossRef] [PubMed]
  15. Gao, H.; Shreeve, J.M. Azole-Based Energetic Salts. Chem. Rev. 2011, 111, 7377–7436. [Google Scholar] [CrossRef] [PubMed]
  16. Fischer, N.; Klapötke, T.M.; Reymann, M.; Stierstorfer, J. Nitrogen-Rich Salts of 1H,1′H-5,5′-Bitetrazole-1,1′-diol: Energetic Materials with High Thermal Stability. Eur. J. Inorg. Chem. 2013, 2013, 2167–2180. [Google Scholar] [CrossRef]
  17. Politzer, P.; Murray, J.S. Detonation Performance and Sensitivity: A Quest for Balance. Adv. Quantum Chem. 2014, 69, 1–30. [Google Scholar]
  18. Stine, J.R. Molecular Structure and Performance of High Explosives. Mater. Res. Soc. Symp. Proc. 1993, 296, 3–12. [Google Scholar] [CrossRef]
  19. Politzer, P.; Murray, J.S. Impact Sensitivity and the Maximum Heat of Detonation. J. Mol. Model. 2015, 21, 262. [Google Scholar] [CrossRef] [PubMed]
  20. Bader, R.F.W.; Carroll, M.T.; Cheeseman, J.R.; Chang, C. Properties of Atoms in Molecules: Atomic Volumes. J. Am. Chem. Soc. 1987, 109, 7968–7979. [Google Scholar] [CrossRef]
  21. Shields, Z.P.; Murray, J.S.; Politzer, P. Directional Tendencies of Halogen and Hydrogen Bonding. Int. J. Quantum Chem. 2010, 110, 2823–2832. [Google Scholar] [CrossRef]
  22. Byrd, E.F.C.; Rice, B.M. Improved Prediction of Heats of Formation of Energetic Materials Using Quantum Mechanical Calculations. J. Phys. Chem. A 2006, 110, 1005–1013. [Google Scholar] [CrossRef] [PubMed]
  23. Gálvez-Ruiz, J.C.; Holl, G.; Karaghiosoff, K.; Klapötke, T.M.; Löhnwitz, K.; Mayer, P.; Nöth, H.; Polborn, K.; Rohbogner, C.J.; Suter, M.; et al. Derivatives of 1,5-Diamino-1H-tetrazole: A New Family of Energetic Heterocyclic-Based Salts. Inorg. Chem. 2005, 44, 4237–4253. [Google Scholar] [CrossRef] [PubMed]
  24. Byrd, E.F.C.; Rice, B.M. A Comparison of Methods to Predict Solid Phase Heats of Formation of Molecular Energetic Salts. J. Phys. Chem. A 2009, 113, 345–352. [Google Scholar] [CrossRef] [PubMed]
  25. Qiu, L.; Xiao, H.; Gong, X.; Ju, X.; Zhu, W. Crystal Density Predictions for Nitramines Based on Quantum Chemistry. J. Hazard. Mater. 2007, 141, 280–288. [Google Scholar] [CrossRef] [PubMed]
  26. Rice, B.M.; Hare, J.J.; Byrd, E.F.C. Accurate Predictions of Crystal Densities Using Quantum Mechanical Molecular Volumes. J. Phys. Chem. A 2007, 111, 10874–10879. [Google Scholar] [CrossRef] [PubMed]
  27. Politzer, P.; Martinez, J.; Murray, J.S.; Concha, M.C.; Toro-Labbé, A. An Electrostatic Interaction Correction for Improved Crystal Density Prediction. Mol. Phys. 2009, 107, 2095–2101. [Google Scholar] [CrossRef]
  28. Politzer, P.; Martinez, J.; Murray, J.S.; Concha, M.C. An Electrostatic Correction for Improved Crystal Density Predictions of Energetic Ionic Compounds. Mol. Phys. 2010, 108, 1391–1396. [Google Scholar] [CrossRef]
  29. Rice, B.M.; Byrd, E.F.C. Evaluation of Electrostatic Descriptors for Predicting Crystalline Density. J. Comput. Chem. 2013, 34, 2146–2151. [Google Scholar] [CrossRef] [PubMed]
  30. Zhang, J.; Zhang, Q.; Vo, T.T.; Parrish, D.A.; Shreeve, J.M. Energetic Salts with π-Stacking and Hydrogen-Bonding Interaction Lead the Way to Future Energetic Materials. J. Am. Chem. Soc. 2015, 137, 1697–1704. [Google Scholar] [CrossRef] [PubMed]
  31. Dunitz, J.D.; Filippini, G.; Gavezzotti, A. A Statistical Study of Density and Packing Variations among Crystalline Isomers. Tetrahedron 2000, 56, 6595–6601. [Google Scholar] [CrossRef]
  32. Murray, J.S.; Politzer, P. Correlations Between the Solvent Hydrogen-Bond-Donating Parameter α and the Calculated Molecular Surface Electrostatic Potential. J. Org. Chem. 1991, 56, 6715–6717. [Google Scholar] [CrossRef]
  33. Hagelin, H.; Murray, J.S.; Brinck, T.; Berthelot, M.; Politzer, P. Family-Independent Relationships between Computed Molecular Surface Quantities and Solute Hydrogen Bond Acidity/Basicity and Solute-Induced Methanol O-H Infrared Frequency Shifts. Can. J. Chem. 1995, 73, 483–488. [Google Scholar] [CrossRef]
  34. Thottempudi, V.; Shreeve, J.M. Synthesis and Promising Properties of a New Family of High-Density Energetic Salts of 5-Nitro-3-trinitromethyl-1H-1,2,4-triazole and 5,5′Bis(trinitromethyl)-3,3′-azo-1H-1,2,4-triazole. J. Am. Chem. Soc. 2011, 133, 19982–19992. [Google Scholar] [CrossRef] [PubMed]
  35. Gao, H.; Joo, Y.-H.; Parrish, D.A.; Vo, T.; Shreeve, J.M. 1-Amino-1-hydrazino-2,2-dinitroethene and Corresponding Salts: Synthesis, Characterization, and Thermolysis Studies. Chem. Eur. J. 2011, 17, 4613–4618. [Google Scholar] [CrossRef] [PubMed]
  36. Klapötke, T.M.; Petermayer, C.; Piercey, D.G.; Stierstorfer, J. 1,3-Bis(nitroimido)-1,2,3-triazolate Anion, the N.-Nitroimide Moiety, and the Strategy of Alternating Positive and Negative Charges in the Design of Energetic Materials. J. Am. Chem. Soc. 2012, 134, 20827–20836. [Google Scholar] [CrossRef] [PubMed]
  37. Fischer, N.; Fischer, D.; Klapötke, T.M.; Piercey, D.G.; Stierstorfer, J. Pushing the Limits of Energetic Materials—The Synthesis and Characterization of Dihydroxylammonium 5,5′-Bistetrazole-1,1′-diolate. J. Mater. Chem. 2012, 22, 20418–20422. [Google Scholar] [CrossRef]
  38. Fischer, N.; Klapötke, T.M.; Stierstorfer, J. 1-Amino-3-nitroguanidine (ANQ) in High-Performance Ionic Energetic Materials. Z. Naturforsch. 2012, 67b, 573–588. [Google Scholar] [CrossRef]
  39. Fischer, N.; Gao, L.; Klapötke, T.M.; Stierstorfer, J. Energetic Salts of 5,5′Bis(Tetrazole-2-oxide) in a Comparison to 5,5′-Bis(Tetrazole-1-oxide) Derivatives. Polyhedron 2013, 51, 201–210. [Google Scholar] [CrossRef]
  40. Fischer, D.; Klapötke, T.M.; Reymann, M.; Stierstorfer, J. Dense Energetic Nitraminofurazanes. Chem. Eur. J. 2014, 20, 6401–6411. [Google Scholar] [CrossRef] [PubMed]
  41. Klapötke, T.M.; Preimesser, A.; Stierstorfer, J. Energetic Derivatives of 2-Nitrimino-5,6-dinitro-benzimidazole. Propell. Explos. Pyrotech. 2015, 40, 60–66. [Google Scholar] [CrossRef]
  42. Zhang, J.; Shreeve, J.M. 3,3′-Dinitroamino-4,4′-azoxyfurazan and Its Derivatives: An Assembly of Diverse N-O Building Blocks for High-Performance Energetic Materials. J. Am. Chem. Soc. 2014, 136, 4437–4445. [Google Scholar] [CrossRef] [PubMed]
  43. Klapötke, T.M.; Mayr, N.; Stierstorfer, J.; Weyrauther, M. Maximum Compaction of Ionic Organic Explosives: Bis(hydroxylammonium) 5,5′ Dinitromethyl-3,3′-bis(1,2,4-oxadiazolate) and Its Derivatives. Chem. Eur. J. 2014, 20, 1410–1417. [Google Scholar] [CrossRef] [PubMed]
  44. Fischer, D.; Klapötke, T.M.; Stierstorfer, J. Oxalylhydrazinium Nitrate and Dinitrate—Efficiency Meets Performance. J. Energ. Mater. 2014, 32, 37–49. [Google Scholar] [CrossRef]
  45. Fischer, D.; Klapötke, T.M.; Stierstorfer, J. 1,5-Di(nitramino)tetrazole: High Sensitivity and Superior Explosive Performance. Angew. Chem. Int. Ed. 2015, 54, 10299–10302. [Google Scholar] [CrossRef] [PubMed]
  46. Yin, P.; Parrish, D.A.; Shreeve, J.M. Energetic Multifunctionalized Nitraminopyrazoles and Their Ionic Derivatives: Ternary Hydrogen-Bond Induced High Energy Density Materials. J. Am. Chem. Soc. 2015, 137, 4778–4786. [Google Scholar] [CrossRef] [PubMed]
  47. Robbins, A.M.; Jin, P.; Brinck, T.; Murray, J.S.; Politzer, P. The Electrostatic Potential as a Measure of Gas Phase Carbocation Stability. Int. J. Quantum Chem. 2006, 106, 2904–2909. [Google Scholar] [CrossRef]
  48. Politzer, P.; Murray, J.S.; Clark, T. σ-Hole Bonding: A Physical Interpretation. Top. Curr. Chem. 2015, 358, 19–42. [Google Scholar] [PubMed]
  49. Politzer, P.; Murray, J.S.; Clark, T. Mathematical Modeling and Physical Reality in Noncovalent Interactions. J. Mol. Model. 2015, 21, 25. [Google Scholar] [CrossRef] [PubMed]
  50. Andrić, J.M.; Misini-Ignjatović, M.Z.; Murray, J.S.; Politzer, P.; Zarić, S.D. Hydrogen Bonding Between Metal Ion Complexes and Non-coordinated Water. Electrostatic Potentials and Interaction Energies. ChemPhysChem. submitted for publication.
  51. Glasstone, S. Text-Book of Physical Chemistry; Van Nostrand: New York, NY, USA, 1940. [Google Scholar]
  52. Teixeira-Dias, J.J.C.; Murrell, J.N. The Calculation of Electric Polarizabilities of Hydrocarbons with Particular Attention to the Bond-Additive Property. Mol. Phys. 1970, 19, 329–335. [Google Scholar] [CrossRef]
  53. Gough, K.M. Theoretical Analysis of Molecular Polarizabilities and Polarizability Derivatives in Hydrocarbons. J. Chem. Phys. 1989, 91, 2424–2432. [Google Scholar] [CrossRef]
  54. Laidig, K.E.; Bader, R.F.W. Properties of Atoms in Molecules: Atomic Polarizabilities. J. Chem. Phys. 1990, 93, 7213–7224. [Google Scholar] [CrossRef]
  55. Brinck, T.; Murray, J.S.; Politzer, P. Polarizability and Volume. J. Chem. Phys. 1993, 98, 4305–4306. [Google Scholar] [CrossRef]
  56. Jin, P.; Murray, J.S.; Politzer, P. Local Ionization Energy and Local Polarizability. Int. J. Quantum Chem. 2004, 96, 394–401. [Google Scholar] [CrossRef]
  57. Politzer, P.; Murray, J.S.; Janjić, G.V.; Zarić, S.D. σ-Hole Interactions of Covalently-Bonded Nitrogen, Phosphorus and Arsenic: A Survey of Crystal Structures. Crystals 2014, 4, 12–31. [Google Scholar] [CrossRef]
  58. Lide, D.R. Handbook of Chemistry and Physics, 87th ed.; CRC Press: Boca Raton, FL, USA, 2004. [Google Scholar]
  59. Li, J.-R.; Zhao, J.-M.; Dong, H.-S. Crystal Structure of 2,4,6-Trinitropyridine and its N-oxide. J. Chem. Cryst. 2005, 35, 943–948. [Google Scholar]
  60. Linstrom, P.J.; Mallard, W.G. NIST Chemistry Webbook, NIST Standard Reference Database No. 69. Available online: http://www.nist.gov (accessed on 31 December 2015).
  61. Rice, B.M.; Hare, J.J. A Quantum Mechanical Investigation of the Relation between Impact Sensitivity and the Charge Distribution in Energetic Molecules. J. Phys. Chem. A 2002, 106, 1770–1783. [Google Scholar] [CrossRef]
  62. Pepekin, V.I.; Korsunskii, B.L.; Denisaev, A.A. Initiation of Solid Explosives by Mechanical Impact. Combust. Explos. Shock Waves 2008, 44, 586–590. [Google Scholar] [CrossRef]
Back to TopTop