Electronic Energy Distributions in Energetic Materials - American

Department of Chemistry, UniVersity of Toledo, Toledo, Ohio, 43606, Quantum ... MendeleeV UniVersity of Chemical Technology, Moscow, Russia, and Karpo...
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J. Phys. Chem. B 2004, 108, 20173-20179

20173

Electronic Energy Distributions in Energetic Materials: NTO and the Biguanidinium Dinitramides Elizabeth A. Zhurova,† Vladimir G. Tsirelson,‡ Adam I. Stash,§ Mikhail V. Yakovlev,‡ and A. Alan Pinkerton†,* Department of Chemistry, UniVersity of Toledo, Toledo, Ohio, 43606, Quantum Chemistry Department, MendeleeV UniVersity of Chemical Technology, Moscow, Russia, and KarpoV Institute of Physical Chemistry, Moscow, Russia ReceiVed: July 1, 2004; In Final Form: September 29, 2004

The kinetic, potential, and electronic energy distributions were calculated from the experimental electron density using the DFT functionals for the energetic β-form of 5-nitro-2,4-dihydro-3H-1,2,4-triazol-3-one (NTO), biguanidinium dinitramide, (BIGH)(DN), and biguanidinium bis-dinitramide, (BIGH2)(DN)2. The spatial distribution of the electronic energy density is shown to be a useful descriptor of the chemical bonding and intermolecular interactions, in addition to the electron density and Laplacian distributions. Also, the kinetic energies and atomic charges have been integrated over the atomic basins. The examination of these spatial and integrated values allowed us to more completely describe the nature of atomic and molecular interactions.

Because of the growing interest in the development of new solid energetic materials1-3 and a need to relate their properties to fundamental parameters, we have initiated a program to experimentally and theoretically map the electron density distributions in energetic materials and to use this information to identify the energy-rich regions in the molecules of such compounds. The β-form of 5-nitro-2,4-dihydro-3H-1,2,4-triazol3-one (NTO) (Figure 1a) is an energetic compound that has been proposed as a replacement for RDX (cyclo-trimethylenetrinitramine) in bomb fill and for sodium azide for car air bag systems.4 The molecule is near planar with the largest out-ofplane deviation (0.11 Å) for the O(6) atom. The dinitramide (DN)- anion (Figure 1b) is a promising candidate in the development of energetic oxidizers5 since it forms stable oxygen-rich salts with high densities with a variety of cations. The (DN)- anion has a variable and asymmetric structure in different compounds.2-3 In the biguanidinium dinitramide, (BIGH)(DN), and biguanidinium bis-dinitramide, (BIGH2)(DN)2, crystals (Figure 1 c and d), the twist angle6 between two NO2 groups is 7.1 and 28.8°, and the difference of the anion N-N bond lengths is 0.023 and 0.037 Å, respectively. The monoprotonated (BIGH)+ and diprotonated (BIGH2)2+ biguanidinium cations are composed of two planar halves with one bridge nitrogen atom. The two halves of the cation are twisted with respect to each other with twist angles of 42.1 and 43.8° for (BIGH)+ and (BIGH2)2+, respectively. All bonds in these cations are relatively short because of extensive π-delocalization.7 As is shown below, the study of the electron density and electronic energy characteristics in these compounds helps in understanding their physical and chemical properties. Indeed, the features of the electron energy distributions reflect a general balance of the forces providing an equilibrium ground * Author to whom correspondence may be [email protected]. † University of Toledo. ‡ Mendeleev University of Chemical Technology. § Karpov Institute of Physical Chemistry.

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state of a molecule or crystal. The electron density defines8 the density of the electronic energy9-14

he(r) ) g(r) + V(r)

(1)

which is a sum of the kinetic, g(r) > 0, and potential, V(r) < 0, energy densities of a system under consideration. The kinetic energy density characterizes the local electron motion, while the electronic potential energy density exhibits the field of virial of the Ehrenfest15 force acting on an electron at point r.10,16 There is a one-to-one correspondence between the lines of maximally negative potential energy density connecting nuclei in this field and the lines of the maximal electron density, F(r), linking the same nuclei;10,17 the latter are called bond paths and represent the molecular graph. The he(rb) value at the saddle critical point in the electron density, rb, on the bond path (the bond critical point) may be used to more completely characterize the type of atomic interaction: he(rb) < 0 is typical for sharedtype (covalent) atomic interactions, while he(rb) > 0 is observed for closed-shell interactions.9,18 The critical point description is rather limited (for example, the electron lone pairs are not well accounted for), whereas the consideration of the total energy distribution can provide more information regarding the bonding mechanism. Our aim is to analyze the local energy features in the crystalline state using the experimental electron density, thus avoiding any wave function calculation. It is known19 that the kinetic and potential energy densities are connected via the Laplacian of the electron density, ∇2F(r):

2g(r) + V(r) ) (1/4)∇2F(r)

(2)

The electronic kinetic energy density, g(r), can be calculated from the electron density and its derivatives using the so-called gradient expansion

g(r) ) (3/10)(3π2)2/3F(r)5/3 + (1/72)[∇F(r)]2/F(r) + (1/6)∇2F(r) (3)

10.1021/jp0470997 CCC: $27.50 © 2004 American Chemical Society Published on Web 11/24/2004

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Zhurova et al. which is the well-known functional used in density functional theory.20-21 Then, the potential energy density may be calculated from expression 211

V(r) ) -(3/5)(3π2)2/3F(r)5/3 - (1/36)[∇F(r)]2/F(r) - (1/12)∇2F(r) (4) and the electronic energy density becomes

he(r) ) -(3/10)(3π2)2/3F(r)5/3 - (1/72)[∇F(r)]2/F(r) + (1/12)∇2F(r) (5)

Figure 1. (a) NTO (the O3 atom from the next molecule in the same plane associated with a hydrogen bond is also seen), (b) (DN)-, (c) (BIGH)+, and (d) (BIGH2)2+: the gradient fields, molecular graphs, and integrated atomic charges. Bond critical points (3,-1) are shown as circles, (3,+1) ring critical points are triangles, and (3,-3) maxima points are squares.

The approximations 3-5 provide energy densities at the Hartree-Fock level of accuracy12 and also the possibility for using the experimentally determined electron density under the assumption that the local virial theorem is valid in this case. In this work, the experimental electron densities, F(r), in NTO, (BIGH)(DN), and (BIGH2)(DN)2 compounds were obtained22,23 from low-temperature X-ray diffraction data using a model consisting of a superposition of aspherical pseudoatoms each modeled by a multipole expansion.24,25 The kinetic and potential energy density maps have been calculated from these model densities using expressions 3 and 4; such an approach was previously justified12 for crystalline systems with covalent, ionic, and van der Waals bonds. The WinXPRO program package26 has been used for the calculations in this work. For NTO, we have also checked27 the results by direct calculation of the g(r) and V(r) distributions from the nonempirical HartreeFock wave function (the 6-311G** basis set, the program GAMESS28 were used for the NTO experimental molecular geometry; the g(r) and V(r) functions have been calculated with the modified program PROAIM29). Averaged differences of the values of the functions at the bond CPs are 25% for g(r) and 17% for V(r). This, combined with the similarity of the corresponding contour maps, indicates semiquantitative agreement between the theoretical and “experimentally” obtained local electronic energies. Note that, in agreement with earlier findings,12 we observed small positive areas in the potential energy density around the atomic positions due to the divergence of the Laplacian term in expression 2 at r f 0. These areas have a maximal radius of 0.05 Å for the hydrogen atoms (Figure 2) and do not influence our conclusions. The potential energy density, V(r), maps are shown in Figure 2, and the g(r) maps are deposited. These distributions are, in general, topologically similar to the total electron density.22-23 At the same time, the distributions of the total electronic energy, he(r), look quite different (Figure 3); they are Laplacian-like shaped and reflect all the features of chemical bonding, being negative for the covalent interactions [Note negative electronic energy bridges all N-O bonds in the dinitramide anion (Figure 3B) even though narrow areas of slightly positive Laplacian are observed for some of them (ref 23, see Supporting Information).] and slightly positive for the hydrogen bond areas (Figure 3a). The he(r) map calculated for the NTO molecule directly from wave functions exhibits the same features. The positions of the saddle critical points on the interatomic lines in the electronic energy as well as electronic energy enhancements, which could be associated with lone pairs of N and O atoms, are clearly seen. It can be concluded that the he(r) distributions can serve as a descriptor of the bonding, showing explicitly the energy-rich and energy-depleted space regions of the molecule.

Electronic Energy Distributions in Materials

J. Phys. Chem. B, Vol. 108, No. 52, 2004 20175

Figure 2. Potential energy density, V(r), in (a) NTO (the O3 atom from the next molecule in the same plane associated with a hydrogen bond is also seen), (b) (DN)- anion, and (c) (BIGH)+/(BIGH2)++ cations. The contour interval is 0.2 au, all blue contours are negative.

Figure 3. Electronic energy density, he(r), in (a) NTO, (b) (DN)- anion, and (c) (BIGH)+/(BIGH2)2+ cations. The contours are -2 to +1 with interval 0.2 au, and -3.6 to -2 with interval 0.4 au; blue contours are negative, solid black are positive, and the zero line is black dash-dotted.

The positions of the saddle critical points in the electron density and in the electronic energy density do not coincide exactly; however, the he(rb) values at either critical point are

very similar and reflect the same tendencies. Therefore, in this paper, we will consider the g(r), V(r), and he(r) values at the critical points in the electron density.

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TABLE 1: Intramolecular Bond Critical Points in the Electron Densitya bond path

F, eÅ-3 ∇2F, eÅ-5

g, au

V, au

he, au

R, Å

-1.7994 -1.7029 -1.2994 -1.1255 -0.8332 -0.8464 -0.8078 -0.9449 -0.7041 -0.6934 -0.6531

-0.9350 -0.8760 -0.8061 -0.7055 -0.5243 -0.5161 -0.4942 -0.4896 -0.4401 -0.4263 -0.4172

1.2253 1.2279 1.2343 1.2987 1.3737 1.3556 1.3795 1.3658 1.4430 1.0090 1.0090

3.39(2) 3.27(3) 2.90(3) 2.67(3) 2.23(3) 2.23(3) 2.17(2) 2.30(2) 2.01(2) 1.98(2) 1.93(1)

NTO -6.8(1) 0.8645 -4.7(1) 0.8269 -30.1(2) 0.4934 -27.5(1) 0.4201 -20.8(1) 0.3089 -17.9(1) 0.3303 -17.4(1) 0.3136 -3.32(7) 0.4552 -16.97(9) 0.2640 -15.34(7) 0.2672 -17.47(4) 0.2360

O(1)-N(2) O(2)-N(2) O(4)-N(3) O(3)-N(3) N(1)-N(2) N(1)-N(3) O(1)‚‚‚O(4)

3.36(4) 3.28(4) 3.24(4) 3.22(4) 2.47(3) 2.34(3) 0.12(1)

(DN)- Anion -15.4(1) 0.7929 -12.3(1) 0.7769 -11.1(1) 0.7701 -10.9(1) 0.7605 8.22(8) 0.4813 -6.41(8) 0.4461 2.40(1) 0.0202

-1.7455 -1.6819 -1.6555 -1.6345 -1.0478 -0.9586 -0.0155

-0.9527 -0.9049 -0.8854 -0.8740 -0.5665 -0.5125 0.0047

1.2309 1.2475 1.2261 1.2357 1.3584 1.3809 2.5313

N(5)-C(1) N(7)-C(2) N(4)-C(1) N(8)-C(2) N(6)-C(1) N(6)-C(2) N(7)-H(5) N(7)-H(6) N(4)-H(2) N(5)-H(3) N(8)-H(8) N(8)-H(7) N(5)-H(4) N(4)-H(1)

2.52(4) 2.44(3) 2.38(3) 2.34(3) 2.38(4) 2.33(4) 2.16(4) 2.12(4) 2.11(4) 2.07(4) 2.09(4) 2.09(3) 2.02(4) 2.04(3)

(BIGH)+ Cation -29.6(2) 0.3512 -1.0096 -31.0(2) 0.3105 -0.9429 -29.3(2) 0.3030 -0.9097 -26.9(2) 0.3058 -0.8905 -22.0(1) 0.3538 -0.9362 -20.9(1) 0.3430 -0.9028 -34.1(2) 0.1944 -0.7427 -33.8(2) 0.1814 -0.7135 -32.2(2) 0.1991 -0.7214 -32.7(2) 0.1755 -0.6906 -28.4(2) 0.2100 -0.7146 -27.8(2) 0.2135 -0.7154 -27.9(2) 0.1914 -0.6721 -23.0(2) 0.2329 -0.7043

-0.6584 -0.6324 -0.6067 -0.5847 -0.5824 -0.5598 -0.5483 -0.5321 -0.5223 -0.5151 -0.5046 -0.5019 -0.4807 -0.4714

1.3337 1.3365 1.3408 1.3344 1.3438 1.3397 1.0091 1.0091 1.0092 1.0100 1.0091 1.0092 1.0090 1.0091

N(5)-O(6) N(5)-O(5) C(3)-O(3) N(1)-C(5) N(2)-C(3) C(5)-N(4) C(3)-N(4) N(2)-N(1) N(5)-C(5) N(2)-H(2) N(4)-H(4)

(BIGH)(DN)

(BIGH2)(DN)2 O(2)-N(2) O(1)-N(2) O(4)-N(3) O(3)-N(3) N(1)-N(3) N(1)-N(2) O(1)‚‚‚O(4)

(DN)- Anion 3.47(2) -13.08(5) 0.8571 -1.8500 -0.9928 1.2303 3.45(2) -11.29(5) 0.8591 -1.8353 -0.9762 1.2195 3.34(2) -8.66(5) 0.8310 -1.7520 -0.9209 1.2288 3.16(2) -5.85(5) 0.7720 -1.6047 -0.8327 1.2476 2.50(1) -7.42(4) 0.4963 -1.0695 -0.5732 1.3537 2.22(1) -4.24(4) 0.4211 -0.8863 -0.4651 1.3908 0.12(1) 2.35(1) 0.0197 -0.0149 0.0048 2.5618

N(4)-C(1) N(5)-C(1) N(4)-H(1) N(5)-H(4) N(6)-C(1) N(4)-H(2) N(6)-H(6) N(5)-H(3)

2.61(2) 2.50(1) 2.12(2) 2.10(2) 2.20(1) 2.06(2) 1.97(2) 2.00(2)

(BIGH2)2+ Cation -28.15(6) 0.3963 -1.0847 -25.38(5) 0.3735 -1.0103 -33.2(1) 0.1880 -0.7207 -33.6(1) 0.1762 -0.7011 -18.75(5) 0.3124 -0.8193 -31.6(1) 0.1781 -0.6837 -34.7(1) 0.1274 -0.6151 -30.6(1) 0.1664 -0.6506

-0.6883 -0.6368 -0.5328 -0.5249 -0.5069 -0.5055 -0.4877 -0.4842

1.3119 1.3190 1.0090 1.0090 1.3700 1.0090 1.0090 1.0091

F is the electron density; ∇2F is the Laplacian, g, V, and he are the kinetic, potential, and total electronic energies at the bond critical point; R is the bond path length. R

The examination of the local energies at the critical points of the electron density for NTO shows that the highest g(r), V(r), and he(r) values are observed for the N-O bonds in the NO2 group (Table 1, Figures 2 and 3). The next are the values for the “double” C-O and C-N bonds. Additionally, taking into account the lone pair energy concentrations, we can conclude that the NO2 group is the most potentially energyrich region in this molecule. It is worth noting that the values of F(r), g(r), V(r), and he(r) for crystalline NTO correctly reflect the known tendency of the chemical decomposition of this molecule. Indeed, according to theoretical calculations,30 the

Figure 4. (a) Deformation kinetic energy density, δg(r); (b) deformation potential energy density, δV(r), and (c) deformation electronic energy δhe(r) in the NTO crystal. Contour interval is 0.1 au, blue contours are negative, solid black are positive, and the zero line is black dash-dotted.

C(5)-N(5) and N-H bonds should be the first to break during chemical decomposition in agreement with the observation that the electron density values and kinetic, potential, and total electronic energy values at these bonds are the lowest of all bonds in the molecule. Thus, it might be supposed that local energy characteristics provide information to predict the initial steps in the mechanism of the decomposition of this molecule. To reveal the subtle features of the atomic interactions in the studied crystals, we have also calculated the “deformation” kinetic, potential, and electronic energy densities:31

δg(r) ) g(r) - gprocrystal(r)

(6)

δV(r) ) V(r) - Vprocrystal(r)

(7)

δhe(r) ) he(r) - he procrystal(r)

(8)

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J. Phys. Chem. B, Vol. 108, No. 52, 2004 20177

TABLE 2: NTO: Results of Properties Integrationsa-c atom

q(Pv), e-

qAIM, e-

qproAIM, e-

δq, e-

ΩAIM, Å3

ΩproAIM, Å3

δΩ, Å3

-He, au

N(2) H(2) O(3) N(1) N(4) H(4) C(3) O(5) O(6) N(5) C(5) Σ Lerr,au Lmax,au

-0.203 0.227 -0.475 -0.063 -0.352 0.304 0.369 -0.142 -0.193 0.321 0.206 0.000

-0.643 0.410 -1.043 -0.397 -1.018 0.471 1.416 -0.377 -0.354 0.503 1.034 0.002 0.0003 -0.0005

-0.487 0.307 -0.580 -0.320 -0.704 0.335 0.949 -0.180 -0.182 0.141 0.725 0.004 0.0008 -0.0014

-0.156 0.103 -0.463 -0.077 -0.314 0.136 0.467 -0.197 -0.172 0.362 0.311 -0.002

12.578 3.669 16.089 13.862 13.445 2.661 5.275 16.328 15.221 6.723 6.538 112.388

12.019 4.758 14.308 13.237 12.475 3.740 7.206 15.245 14.205 7.601 7.544 112.338

0.559 -1.089 1.781 0.625 0.970 -1.079 -1.931 1.083 1.016 -0.878 -1.006 0.050

55.375 0.373 75.778 55.010 55.912 0.326 37.297 75.049 75.034 54.320 37.661 522.134

a q(Pv) is an atomic charge based on the monopole electron population of the multipole expansion of the electron density; qAIM is a charge integrated over an atomic basin; qproAIM is an integrated atomic charge in the atomic procrystal; δq ) qAIM - qproAIM; ΩAIM is an integrated atomic volume; ΩproAIM is an integrated atomic volume in the procrystal; δΩ ) ΩAIM - ΩproAIM; He is an integrated atomic electronic energy, He ) V/2 ) -G; Lerr ) (ΣLΩ2/Natoms)1/2, LΩ is the atomic integrated Lagrangian, au; Lmax is the maximal atomic integrated Lagrangian, au. b Total NTO energy from the molecular theoretical calculation (HF, 6-311G** basis set, experimental geometry) is -519.259 au, from the periodic calculation (DFT/B3LYP, 6-311G** basis set) it is -521.902 au. c NTO unit cell volume Ω ) 450.291 Å3, Ω/4 ) 112.57 Å3.

Here the suffix “procrystal” denotes the distributions of the kinetic, potential, and electronic energy densities of the atomic procrystal, a hypothetical system consisting of a set of spherical, chemically nonbonded atoms placed in the real positions of atoms in a crystal.32 These distributions disclose the details of the stabilizing enhancement in the local potential energy, and destabilizing increase in the local kinetic energy, resulting from formation of a crystal/molecule.12 The corresponding δg(r), δV(r), and δhe(r) maps for the NTO crystal are shown in Figure 4. Although, during the formation of the crystal from the nonbonded atoms, the potential and electronic energies (Figure 4 b and c) are enhanced for every covalent bond, this enhancement is different for different parts of the molecule. Being bond localized, it is maximal in bonds formed by the nitrogen atoms; it is also accumulated in the oxygen lone pairs, making the NO2 group energy rich. At the same time, enhancement in the kinetic energy density mainly takes place close to nuclei (Figure 4a). Deposited maps for the (BIGH)(DN) and (BIGH2)(DN)2 crystals exhibit similar features. Important quantitative information can be obtained from the integrations of various properties over the atomic basins that enclose the atomic nuclei. They are separated by the zero-flux surfaces defined33 as

∇F(r)‚n(r) ) 0,∀r ∈ Si(r)

(9)

and are usually associated with bonded atoms (or pseudoatoms) in molecules and crystals.33 By definition, the integration of any property A(r) over the volume of atomic basin Ω

〈A〉 )

∫ΩA(r)dV

(10)

gives its mean value, and the sum of atomic contributions provides the total value of the property under examination. In particular, the integration of the electronic energy over atomic basins yields the energy of molecular functional groups. The sum of these contributions represents the total electronic energy of a molecule in a crystal.34,35 Tables 2, 3, and 4 list the atomic volumes, integrated atomic charges, and kinetic energies for all three compounds. Although the integrated Lagrangian (L ) -1/4∇2F(r)) for every atom has to be exactly zero, in practice a reasonably small number (0.0015 au or less) was obtained. All the atomic charges36 in Tables 2, 3, and 4 sum to small nonzero values, showing that the bounded

molecules are practically electroneutral as required. The sums of atomic volumes reproduce the unit cell volume per molecule with a maximum error of 0.2%.37 The net atomic charges were calculated as differences between the integrated total electron densities and nuclear charges. These charges (Figure 1) are significantly enhanced compared to the charges calculated from the monopole electron populations of the multipole expansion q(Pv) as previously observed and discussed.23 Following ref 38, we have also calculated the atomic charges and volumes for procrystals using a zero-flux surface partitioning of the procrystals. The procrystal “atomic charges” are far from zero, except for the central nitrogen in the (DN)- anion; they all have the same signs as charges of the atoms in a real crystal, but their values are smaller. The differences between these charges,38 δq ) qAIM - qproAIM, “deformation charges”, are closer in value to the charges based on the monopole electron populations q(Pv). This results from the fact that qAIM charges contain the contribution related to the intra-atomic redistribution of the electron density due to chemical bond formation, while δq values reflect mainly interatomic electron transfer. In the same way, the differences in atomic volumes, δΩ , reflect how the atomic volumes change after the formation of chemical bonds in crystals; when atoms become more negative, their volumes increase, and vice-versa. The integral form of the virial theorem connects the average atomic kinetic energy, G, with the average potential energy, V, and the average total electronic energy, He, of a system:

G ) -V/2 ) -He

(11)

For the NTO crystal, the total integrated He value (Table 2) is lower than the corresponding energy from our molecular calculation (-519.259 au, see above), which correctly reflects the energy decrease due to crystal formation. The (DN)- anion in the (BIGH2)(DN)2 crystal shows the same tendency (Table 4). The reported2 single (DN)- anion energy at the (BIGH)(DN) crystal geometry (-465.134 au) is a little higher than that shown in Table 3. Therefore, we have performed single (DN)anion theoretical calculations (DFT, B3LYP functional, 6-311+G* basis set, Gaussian9839 program) and obtained the (DN)- energy values of -465.141 and -465.142 au at the (BIGH)(DN) and (BIGH2)(DN)2 crystal geometries, respectively, in excellent agreement with the previously reported values.2 To verify the values of the integrated energies, we have performed three-

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TABLE 3: (BIGH)(DN): Results of Properties Integrationsa-c atom

q(Pv), e-

qAIM, e-

qproAIM, e-

δq, e-

ΩAIM, Å3

ΩproAIM, Å3

δΩ, Å3

-He, au

O(1) O(2) O(3) O(4) N(1) N(2) N(3) N(4) N(5) N(6) N(7) N(8) C(1) C(2) H(1) H(2) H(3) H(4) H(5) H(6) H(7) H(8) Σanion Σcation Σmolecule Lerr,au Lmax,au

-0.329 -0.397 -0.258 -0.168 -0.151 0.119 0.182 -0.271 -0.228 -0.304 -0.305 -0.272 0.208 0.257 0.201 0.228 0.268 0.275 0.259 0.254 0.224 0.209 -1.002 1.002 0.000

-0.472 -0.604 -0.422 -0.341 -0.229 0.648 0.707 -1.355 -1.409 -0.981 -1.435 -1.319 1.385 1.415 0.469 0.569 0.637 0.553 0.578 0.591 0.481 0.538 -0.714 0.716 0.002 0.0006 -0.0015

-0.209 -0.212 -0.196 -0.195 -0.001 0.289 0.300 -0.798 -0.798 -0.529 -0.795 -0.806 0.741 0.747 0.298 0.313 0.310 0.308 0.315 0.299 0.310 0.318 -0.224 0.233 0.009 0.0005 -0.0011

-0.263 -0.392 -0.226 -0.146 -0.228 0.359 0.407 -0.557 -0.611 -0.452 -0.640 -0.513 0.644 0.668 0.171 0.256 0.327 0.245 0.263 0.292 0.171 0.220 -0.490 0.483 -0.007

14.725 15.701 14.518 17.243 12.884 6.071 6.349 16.850 17.998 14.755 20.172 16.006 5.323 5.708 2.888 2.368 2.051 2.402 2.239 3.043 2.549 2.431 87.491 116.783 204.274

13.098 13.378 12.982 14.343 11.585 7.176 7.582 14.390 14.773 12.445 17.128 13.768 7.933 8.191 4.284 4.614 4.667 4.095 4.298 5.739 3.694 4.025 80.144 124.044 204.188

1.627 2.323 1.536 2.900 1.299 -1.105 -1.233 2.460 3.225 2.310 3.044 2.238 -2.610 -2.483 -1.396 -2.246 -2.616 -1.693 -2.059 -2.696 -1.145 -1.594 7.347 -7.261 0.086

75.125 75.359 74.844 74.576 54.741 54.048 53.870 55.955 55.941 55.573 56.183 55.936 37.294 37.199 0.348 0.304 0.299 0.293 0.286 0.285 0.332 0.318 462.563 356.546 819.109

a For the definitions, see Table 2. b The (DN)- single anion energy from our theoretical calculation (DFT/B3LYP, 6-311+G* basis set, (BIGH)(DN) experimental geometry) is -465.141 au; from ref 2 (same conditions) it is -465.134 au; the energy per the (BIGH)(DN) molecule in the crystal from our periodic calculation (DFT/B3LYP, 6-311G** basis set) is -819.622 au. c (BIGH)(DN) unit cell volume Ω ) 409.1 Å3, Ω/2 ) 204.55 Å3.

TABLE 4: (BIGH2)(DN)2: Results of Properties Integrationsa-c atom

q(Pv), e-

qAIM, e-

qproAIM, e-

δq, e-

ΩAIM, Å3

ΩproAIM, Å3

δΩ, Å3

-He, au

O(1) O(2) O(3) O(4) N(1) N(2) N(3) N(4) N(5) N(6) C(1) H(1) H(2) H(3) H(4) H(6) Σanion Σcation Σmolecule Lerr,au Lmax,au

-0.374 -0.324 -0.356 -0.377 -0.039 0.071 0.066 -0.115 -0.168 -0.251 0.344 0.276 0.296 0.333 0.299 0.383 -1.330 2.660 0.000

-0.575 -0.525 -0.539 -0.590 -0.092 0.639 0.595 -1.287 -1.168 -1.133 1.295 0.602 0.636 0.623 0.619 0.669 -1.087 2.176 0.002 0.0006 -0.0012

-0.190 -0.185 -0.190 -0.193 -0.025 0.308 0.292 -0.822 -0.812 -0.711 0.770 0.314 0.313 0.308 0.315 0.319 -0.183 0.380 0.014 0.0006 -0.0010

-0.385 -0.340 -0.349 -0.397 -0.067 0.331 0.303 -0.465 -0.356 -0.422 0.525 0.288 0.323 0.315 0.304 0.350 -0.904 1.796 -0.012

15.156 14.367 15.407 14.564 12.481 6.311 6.374 15.342 15.637 14.467 4.925 1.804 1.864 2.133 1.930 1.685 84.660 103.422 272.742

13.563 12.796 13.242 12.714 10.986 7.569 7.448 13.683 13.832 12.253 7.000 3.631 3.958 4.181 3.946 3.218 78.318 115.933 272.569

1.593 1.571 2.165 1.850 1.495 -1.258 -1.074 1.659 1.805 1.107 -2.075 -1.827 -2.094 -2.048 -2.016 -0.766 6.342 -12.511 0.173

75.625 75.449 75.473 75.617 54.639 54.260 54.305 56.142 56.030 56.071 37.495 0.278 0.265 0.253 0.266 0.213 465.368 357.742 1288.478

a For the definitions, see Table 2. b The (DN)- single anion energy from our theoretical calculation (DFT/B3LYP, 6-311+G* basis set, (BIGH )(DN) 2 2 experimental geometry) is -465.142 au; from ref 2 (same conditions) it is -465.137 au; the energy per the (BIGH2)(DN)2 molecule in the crystal from our periodic calculation (DFT/B3LYP, 6-311G** basis set) is -1285.070 au. c (BIGH2)(DN)2 unit cell volume Ω ) 1092.51 Å3, Ω/4 ) 273.13 Å3.

dimensional periodic (DFT, B3LYP functional, 6-311G** basis set, Crystal9840 program) calculations for all three crystals and also found good agreement between the integrated (based on experimental data) and theoretical (from the wave function) energy values (Tables 2-4). Physical properties of explosive materials, such as detonation pressure and velocity, depend on energy release that accompanies the combustion and decomposition processes41 that directly relate to the energy accumulated by a crystal or molecule. It is the energy-rich dinitramide anion that makes the (BIGH)(DN) and (BIGH2)(DN)2 crystals explosive. Note that

the electronic energy, He, is a significant part of the thermodynamic free energy function41 of a system. Our study allows us to compare the electronic energies of the dinitramide anion in both crystals (Tables 3 and 4). We observe that, in the (BIGH)(DN) and (BIGH2)(DN)2 crystals, the (DN)- anion itself stocks significantly more energy than the (BIGH)+ and (BIGH2)2+ cations (Table 3, Figure 2 b and c). The (DN)- electronic energy in (BIGH2)(DN)2 is lower than in the (BIGH)(DN) crystal; thus, this anion in the (BIGH2)(DN)2 crystal accumulates more energy. The average NO2 group electron energy is also lower in (BIGH2)(DN)2 {-205.4 au} compared to those of (BIGH)-

Electronic Energy Distributions in Materials (DN) {-203.9 au} and NTO {-204.4 au}. The energy of the second protonation of the monoprotonated biguanidinium cation (BIGH)+ in solution was reported42 to be significant (∆H) -21 kJ/mol, -0.008 au). In a qualitative agreement with this observation, the (BIGH2)2+ cation energy in the crystal is lower than that of (BIGH)+ by -1.2 au. Conclusion On the basis of multipole analysis of the experimental electron density of three energetic materials, we have obtained important information relevant to the electronic energy distribution previously available only from theoretical calculations. We have demonstrated that the spatial distribution of the local electronic energy can serve as a new “old” descriptor of chemical bonding, having the advantage of being reference-model independent and providing direct information of bond strength in crystals and molecules. The examination of the local kinetic, potential, and electronic energy distributions, combined with the integrated atomic energies and the multipole and topological analyses of the electron density, allows us to examine more deeply the nature of atomic and molecular interactions in energetic materials directly from the X-ray diffraction experiment. We confirmed experimentally the likely initial steps in the mechanism of NTO decomposition as previously predicted theoretically,30 that is, the C(5)-N(5) and N-H bonds are most susceptible to break first during the chemical decomposition. The formation of NTO, (BIGH)(DN), and (BIGH2)(DN)2 crystals from neutral nonbonded atoms is found to be accompanied by the most significant enhancement of (negative) local potential and electronic energies around the nitrogen atoms and the oxygen lone pairs. The dinitramide anion as a whole and its NO2 groups in particular in the (BIGH2)(DN)2 crystal were found to be the most energy rich among the molecules studied. Thus, the energy analysis is able to provide a useful tool for the study of the physical and chemical properties of energetic materials. Acknowledgment. E.A.Z. and A.A.P. appreciate the financial support of the Office of Naval Research through Contracts N00014-99-1-0392 and N00014-03-1-0533. V.G.T. and A.I.S. acknowledge the financial support of Russian Foundation for Basic Research (Grant 04-03-33053). V.G.T. thanks the Alexander von Humboldt Foundation (Germany) for a Research Award. We appreciate the help of Dr. D. Shorochov with the Gaussian98 calculations. Supporting Information Available: NTO critical points extended table, NTO energy density maps from the molecular calculation, energy density, and Laplacian maps. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Energetic Materials. Theoretical and Computational Chemistry Series; Politzer, P., Murray, J. S., Eds; Elsevier: New York, 2003; Vol. 12. (2) Pinkerton, A. A.; Ritchie, J. P. J. Mol. Struct. 2003, 657, 57-74. (3) Tanbug, R.; Kirschbaum, K.; Pinkerton, A. A. J. Chem. Crystallogr. 1999, 29, 45-55. (4) Lee, K.-Y.; Gilardi, R. Mater. Res. Soc. Symp. Proc. 1993, 296, 237-242. (5) Christe, K. O.; Wilson, W. W.; Petrie, M. A.; Michels, H. H.; Bottaro, J. C.; Gilardi, R. Inorg. Chem. 1996, 35, 5068-5071. (6) The twist angles used to describe the mutual arrangement of the two nitro groups can be calculated from the two torsion angles of the NO2 groups out of the NNN plane and then averaging these two values.

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