Topological Analysis of the Molecular Charge Density and Impact

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Topological Analysis of the Molecular Charge Density and Impact Sensitivy Models of Energetic Molecules Gilberto Anders and Itamar Borges, Jr* Departamento de Química, Instituto Militar de Engenharia, Prac-a General Tib
urcio, 80, Rio de Janeiro
Rj, 22290-270, Brazil ABSTRACT:

Important explosives of practical use are composed of nitroaromatic molecules. In this work, we optimized geometries and calculated the electron density of 17 nitroaromatic molecules using the Density Functional Theory (DFT) method. From the DFT one-electron density matrix, we computed the molecular charge densities, thus the electron densities, which were then decomposed into electric multipoles located at the atomic sites of the molecules using the distributed multipole analysis (DMA). The multipoles, which have a direct chemical interpretation, were then used to analyze in details the ground state charge structure of the molecules and to seek for correlations between charge properties and sensitivity of the corresponding energetic material. The DMA multipole moments do not present large variations when the size of the Gaussian basis set is changed; the largest variations occurred in the range 10
15% for the dipole and quadrupole moments of oxygen atoms. The charges on the carbon atoms of the aromatic ring of each molecule become more positive when the number of nitro groups increases and saturate when there are five and six nitro groups. The magnitude and the direction of the dipole moments of the carbon atoms, indicators of site polarization, also depend on the nature of adjacent groups, with the largest dipole value being for C
H bonds. The total magnitude of the quadrupole moment of the aromatic ring carbon atoms indicates a decrease in the delocalized electron density due to an electron-withdrawing effect. Three models for sensitivity of the materials based on the DMA multipoles were proposed. Explosives with large delocalized electron densities in the aromatic ring of the component molecule, expressed by large quadrupole values on the ring carbon atoms, correspond to more insensitive materials. Furthermore, the charges on the nitro groups also influence the impact sensitivity.

1. INTRODUCTION Explosives and propellants, energetic materials, have several civil and military applications.1 The ability of these materials to release large amounts of energy due to mechanical impacts, shock, and thermal or electrical stimuli in a short time interval are important and defining properties. Recent developments of energetic materials focused on reducing the sensitivity of these materials, mainly for military purposes, to prevent accidental explosion by shock, impact, or thermal effects during transportation or storage.2
5 Quantum chemistry computational methods have been used to investigate molecular properties of explosive compounds, mostly seeking to understand the characteristics and mechanisms of known substances. Application of these methods can also contribute to the development of new materials that combine high performance and low impact sensitivity.6 To measure the stability of an explosive compound, an experimental parameter, called impact sensitivity (h50%), can be used.7
9 This parameter is determined by the height (h) r 2011 American Chemical Society

where a given weight drops on a small amount of explosive material. The h50% corresponds to the value of the height with the likelihood of 50% of drops starting an explosion. Therefore, insensitive materials have large values of h50% and vice versa. The use of impact tests to measure sensitivity has several sources of uncertainty affecting the reproducibility and limiting the reliability of experimental h50% values. The multitude of possible errors includes atmospheric conditions, particle size distribution, humidity, and even the operator technique.7,8 However, it was shown before that the correlation of impact sensitivity with chemical structure depends on a large body of data of chemically related explosives and “individual out-of-line points tended to offset one another” in proposed models.7,8 Therefore, quantitative error evaluations are not available and the diversity of sensitivity-structure models presented in the Received: May 16, 2011 Revised: July 7, 2011 Published: July 11, 2011 9055

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The Journal of Physical Chemistry A literature assumes that; thus, error bars for h50% values are not taken into account.7
11,13
19 To minimize this problem, we have used in this work for 15 out of 17 molecules h50% values from the same laboratory;8 for the other two molecules, h50% values were taken from Wilson et al.12 Concerning previous works on sensitivity to impact, Kamlet and Adolph8 relate the impact sensitivity of some nitro compounds to the proportion of oxygen contained within an explosive material (OB100) which is needed for its complete oxidation, having obtained linear relationships between OB100 and log h50% for different types of organic explosives. Politzer and co-workers10 describe the impact sensitivity of seven nitramine and five nitroaliphatic explosives as a function of the molar mass and the reciprocals of the experimental and computed lengths of the N
NO2 and C
NO2 bonds. The reciprocals of bond lengths are a measure of bond strengths, and molar masses indicate molecular size. In another study, the Politzer’s group calculate the HF/STO/ 5-G* molecular surface electrostatic potential for 14 nitroaromatics and nitroheterocycles,11 which are stabilized by electronic charge delocalization. The authors employed two properties derived from the electrostatic potential in their models: the average deviation of the potential on the surface and their most positive values. It was suggested that a key factor in determining the impact sensitivity of a compound would be the degree to which the stabilization effect of the charge delocalization is balanced with respect to the characteristic electron-withdrawing effect of nitro groups. It was also suggested that impact sensitivity increases as the strength of the C
NO2 bond decreases. In other work, the same group relates the impact sensitivity of nitroaromatics, nitramines and nitroheterocyclics explosives also to other properties of the surface molecular electrostatic potential. Their main finding was that “impact sensitivities of the three classes of energetic compounds can be related to the degree of imbalance between their characteristically stronger positive surface electrostatic potentials and weaker negative ones”.13 Zhang et al. present another approach, the nitro group charge method, to assess the sensitivity of explosives compounds by means of BLYP/DNP optimized geometries and Mulliken charges.14
16 They could establish a correlation between sensitivity and electronic structures of 38 nitroaromatics through the Mulliken charges of the nitro groups (Qnitro). According to the authors, the greater the Qnitro negative charges, the lower their electron-attraction ability, the more stable is the nitro compound (i.e., the higher h50%). Su-Hong and co-workers consider impact sensitivity of explosives containing nitro and amine groups and B3P86/6-31G(d,p) molecular vibrational normal modes, the latter being used to emulate crystalline phonons.17 The rates of mechanical energy transfer given by shock are directly proportional to the number of vibrational (phonon) states in regions called doorway (doorway modes), corresponding to low frequency vibrational modes, estimated through a direct counting method of the molecular vibrational modes. Their energy transfer rates were linearly correlated to impact sensitivities. Song et al.18 sought a correlation between the impact sensitivity and the ratio between the dissociation energy of the C
NO2 and N
NO2 bonds (BDE) and the molecular energy, BDE/E, of nitramine and polynitro benzoate molecules. All molecular geometry and energy calculations used the B3LYP/ 6-31G* and UB3LYP/6-31G* methods for the explosive molecules and their fragments, respectively. According to their results,

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there is a small relation between BDE and the sensitivity of the explosive, but there is a clear correlation between h50% and the (BDE/E) ratio. Their first model correlates h50% and (BDE/E) of nitramine explosives with nitro alkyl groups. The second model is similar but it was applied to polynitro benzoates explosives also with nitro alkyl. Those researchers concluded that (BDE/E) would be a reasonable practical indicator of impact sensitivity. Rice and Hare analyzed the B3LYP/6-31G* molecular surface electrostatic potential of 34 polynitroaromatics and benzofuroxan molecules, probing different aspects of previous ideas from the Politzer’s group.13 They suggested that impact sensitivity would be connected to the degree of electron deficiency over covalent bonds within the inner skeleton of the molecular structure.19 For nitroaromatics and benzofuroxan the sensitivity would apparently be described by the degree of positive potential distribution located in the aromatic ring or on the C
NO2 bond. They found that build-up of positive charges located over covalent bonding regions of the compounds containing nitro groups is characteristic of highly sensitive explosives. In insensitive explosives this behavior is not apparent. The authors developed five models to correlate impact sensitivity h50% with parameters related to the electrostatic potential. The models were then applied to a test set of 15 CHNO explosives of a variety of chemical families to evaluate their predictive capacity, and relate h50% to (1) the average electrostatic potential in the center of the X
H bond (X = O, C, or N) in nitroaromatics systems; (2) positive and negative average values of the maximum electrostatic potential on the molecular surface; (3) a parameter that measures the degree of balance between positive and negative potentials in isosurfaces; (4) the heat of detonation of the studied molecules and; (5) a combination of the properties applied in the models 3 and 4. In a more recent work, Rice and collaborators9 looked for the origin of inconsistencies in the Atoms in Molecules (AIM) description of the electronic density of isolated molecules of energetic materials and assessed the feasibility of using the AIM method to model energetic materials sensitivity. The authors employed the Density Functional Theory (DFT) method to nine molecules of various chemical families, using the PW91, B3LYP, PBE functionals and the 6-31G*, 6-311++G(2d,2p), and 6-311+ +G(3df,3pd) Gaussian basis sets. According to their results, there is a significant variation in the electronic density AIM topology for molecules that form energetic materials crystals, and concluded that these calculations cannot currently be used to correlate the AIM results with impact sensitivity of energetic materials. We have just mentioned a diversity of attempts over the last thirty years to correlate impact sensitivity, a bulk property, and molecular properties of energetic materials components.20 Although these attempts may be subject to criticism,21 and as Brill and James pointed out,22 correlations of these type can mask the dominant chemical mechanisms of initiation reactions, we follow Rice and Hare advice: this approach should not be used to interpret them but “rather to identify molecular properties that indicate sensitivity to impact”.19 In this work, inspired by previous attempts, but employing a molecular property not used before, the distributed multipole analysis (DMA) decomposition of the molecular charge, we follow the idea of relating molecular properties to bulk macroscopic behavior, as the former can enlighten the origins of the latter. Along these lines, we recently studied the sensitivities of 9056

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The Journal of Physical Chemistry A energetic materials from the DMA decomposition of the molecular charge into multipoles localized on atomic sites.23 In that work, we decomposed the charge density of diazocyclopropanes, potential candidates of energetic materials, into monopoles, dipoles and quadrupoles using the distributed multipole analysis (DMA) of Stone.24
27 We then verified that electron withdrawing from the C ring atoms and charge build-up on the N atoms bonded to the ring increased with the number of diazo groups. We related these effects to a probable increased sensitivity to impact and ease of C
N bond breaking in the three compounds. As another illustration of the power of the DMA decomposition of charge densities to rationalize diverse molecular phenomena, in other works we studied microwave effects in hydrodesulfurization (HDS) catalytic processes27 and optimum cluster size for adsorption investigations.28 In the present effort, we apply the same approach previously used for the diazo compounds to molecules component of nitroaromatics energetic materials for a 2-fold purpose: (i) to carry out a detailed analysis of the charge density of the 17 molecules and (ii) to propose models, based on previous works, to relate principally some multipole moments of the molecules with experimental sensitivity measurements. In section 2, we discuss the DMA decomposition technique partition of the charge density and the computational methods used. Section 3 is dedicated to the analysis of the charge density of molecules while in section 4 we discuss and propose three models to predict impact sensitivity. Finally, the Conclusions are given in section 5.

2. THEORETICAL BACKGROUND AND COMPUTATIONAL METHODS 2.1. Molecular Charge Density. The electron density is a central property, can be directly measured and provides a wealth of information on the electronic structure of molecules and solids.29 DFT further confirmed that electron density is a fundamental observable. From its fundamental theorem, the external potential is univocally determined by the electron density, thus by the charge distribution. As a corollary, the electron density ultimately determines the wave function.30 Both the measured and the computed electron density and, consequently, the molecular charge density, can be decomposed in several ways. The method of choice is determined by its utility.31 One possible partition scheme is the distributed multipole analysis (DMA) of Stone, developed with the main purpose to evaluate intermolecular interactions.24,25,32,33 The DMA method divides the molecular charge density into regions, each one represented by its own multipole moments. In the present work, a region is an atomic site of each one of the 17 molecules. The charge density is then divided into a sum of product of atom-centered Gaussian basis functions, with coefficients determined from the one-electron density matrix. Any individual product of the Gaussian basis functions “can be described exactly in terms of a sum of multipole moments of ranks up to the degree of its polynomial”.33 Therefore, the overlap of two s functions can be expressed as a pure charge (monopole), the product of an s with a p as a charge plus a dipole, the overlap of two p functions generates charge, dipole, and quadrupole values, and so on. If the orbitals are localized on different atoms, then each pair of Gaussian functions produces a finite multipole series at a point between the two atoms determined by the exponents of the Gaussian orbitals that

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constitute them. In this case, the multipoles are represented by a series on the nearest atom or other expansion site. The DMA evaluates these exact representations and approximates each of them by a multipole expansion, usually on the atomic nuclei and rapidly convergent due to the expansion on different points of the molecular charge distribution. The expansion terms of the DMA method have a chemically intuitive interpretation. From the monopole term, we evaluate the charges on the atomic sites, with bonds between adjacent atoms usually indicating some degree of charge separation. Bond densities can produce significant site dipole moments, which depend on the different nature, electronegativity, of the adjacent atoms and the remaining molecular environment. Dipole moments indicate atomic polarization, in general accompanied by charge separation in the opposite direction.34,35 The quadrupole moment is the first electrostatic moment to include contributions from the “out-of-plane density”, thereby usually being associated with delocalized electrons, π-electrons, and can also have contributions from lone-pair electrons.32 As DMA provides an accurate description of the molecular charge density, it can be used to study intermolecular interactions and to rationalize chemical bonding in different problems.23,26
28,36,37 The DMA decomposition of the charge density does not have the three great deficiencies of the Mulliken charges analysis method: orbital populations with nonphysical values smaller than zero, or greater than two, a patent violation of the Pauli Exclusion Principle; electrons shared in a bond are evenly distributed among the atoms, thus, ignoring electronegativity differences; and a considerable dependence on the basis set, a complicating feature for comparisons between different calculation levels.30 The reported dipole and quadrupole moment figures correspond to their magnitudes. Q0 is given in multiples of the fundamental electronic charge e (1.602  10
19 C), Q1 in multiples of ea0 (8.478  10
30 C 3 m), and Q2 in multiples of ea20 (4.486  10
40 C.m2). The dipole vectors point to regions of positive charge. 2.2. Computational Methods. The geometries of the 17 molecules were optimized with the DFT method38 and the B3LYP functional39 combined with the 6-311++G(2d,p) Gaussian basis set (Figure 1). All optimization calculations were done with the Gaussian 03 software.40 Normal mode vibration analysis of each structure did not show any imaginary frequency for the 3N
6 vibrational internal coordinates, where N is the number of atoms in the system, thereby indicating minima on the potential energy surface. The computed DFT electron density was decomposed into electric monopoles, dipoles and quadrupoles using the distributed multipole analysis (DMA) of Stone calculated with the GDMA2 software.33 Following Rice and Hare,19 the 17 molecules were separated in two sets. Ten of these molecules were used to propose correlation models to relate impact sensitivity and the charge density decomposed into multipoles and comprised the “training set”. The other seven molecules, the “test set”, were used to check the validity of the proposed correlation models. Additionally, to assess basis set effects on the multipole values, we also optimized the geometries of the ten molecules of the training set using the B3LYP method and the 6-31G(d) and 6-31+G(d,p) Gaussian basis sets; this discussion is presented in section3.1. The remaining results, to be dealt with in the following sections and subsections, will use optimized geometries and multipole values obtained only from the B3LYP/6-311++G(2d,p) method. 9057

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Figure 1. Chemical structures of the training (a) and test (b) sets. Sensitivity h50% values are from Kamlet and Adolph8 and Wilson et al. (HNB and PNB).12

3. RESULTS AND DISCUSSION 3.1. Basis Sets Effects on the Multipole Moments. As just described, we optimized the geometries of the 10 molecules in the training set and decomposed their electronic densities into electric multipoles using the 6-31G(d), 6-31+G(d,p), and 6-311

++G(2d,p) basis sets to investigate the dependence of the DMA results on the basis sets. To illustrate the results, we show in Figure 2 the computed multipole results of the TATB molecule. Increasing the basis set by adding diffuse and polarization functions almost does not change the magnitude of the multipole moments. Adding diffuse 9058

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Figure 2. Basis set effects on the magnitude of TATB multipole values. Green, red, and blue dots represent, respectively, the computed multipole values using the 6-31G(d), 6-31+G(d,p), and 6-311++G(2d,p) basis sets: (a) charges, (b) dipole moment values, and (c) quadrupole values. For the numbering of the carbon atoms, see Figure 4a.

functions to the heavy atoms and p functions to the hydrogen atoms, that is, change from the 6-31G(d) to the 6-31+G(d,p) basis set shows the largest variations. The largest differences occurred in the dipole and quadrupole moment values on the oxygen atoms with lone pairs, 10 and 13%, respectively. Some variation was expected, as diffuse functions are important to describe atoms containing isolated pairs. For the nitro group

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nitrogen atoms, the dipole and quadrupole moments discrepancies using different basis sets were even smaller. The charge values almost did not change. Therefore, at least for the 10 nitroaromatics of the training set and probably for the 7 molecules in the test set, the DMA decomposition of the molecular charge density as function of the Gaussian basis set is quite stable, a result which may be important for studies of larger systems using smaller basis sets and the DFT/B3LYP method. 3.2. Electronic Structure of the Molecules. The 17 molecules were grouped into sets according to their chemical groups and their molecular charge densities are analyzed below. The converged structures, the computed carbon dipole vectors, charge (Q0) and quadrupole (Q2) values are shown in Figures 3
7. The four molecules TNB, TETNB, PNB, and HNB, contain only nitro groups (NO2), see Figure 3. TNB is mildly sensitive (h50% = 100 cm), while TETNB (27 cm), PNB (11 cm), and HNB (11 cm) are very sensitive. The charges (Q0) on the carbon atoms of each molecule, either bonded to a hydrogen atom or a nitro group, get more positive with the increase in the number of nitro groups, with the PNB (five NO2 groups) and HNB (six NO2 groups) molecules having similar values, that is, the positive charges on the carbon atoms saturated. The magnitude of the dipole (Q1) vectors of the carbon atoms bonded to nitro groups, indicators of site polarization, decreases with the number of nitro groups. Thus, from the Q0 and Q1 values, we see that ring carbon electrons are transferred to the nitro groups, an expected behavior because the NO2 group is electron-withdrawing. This behavior leads to less stable energetic materials (i.e., more sensitive to impact), the situation of TETNB, PNB, and HNB. Rice and Hare have also found, using DFT molecular surface electrostatic potentials (nothing else than the integrated nuclear and electron densities over the volume) that for nitroaromatics electron deficiencies within the inner molecular structure correspond to more sensitive materials.19 The negative charges on the oxygen atoms in the nitro groups decrease with the addition of other nitro groups. There are two reasons for this effect: less availability of hydrogen atoms to donate electrons and a competition among the nitro groups for the ring carbon electrons. For these four nitroaromatics, we observe that dipole magnitudes of the ring carbon atoms bonded to hydrogen are larger than on the carbon atoms bonded to nitro groups. Moreover, the direction of the polarization (i.e., of the dipole vector) on the carbon atoms depends on the bonding type and also on the neighbor groups: for a C
H bond, the dipole vector points to the inner region of the ring, thus a positive region, while for a NO2 group it points outward, away from the nearest C
H bond, an inductive effect. For the symmetric HNB molecule, the dipole vectors are aligned with the C
NO2 bonds; for the also symmetrical TNB, there is bond alignment also for the C
H bonds. The presence of a C
H bond in the unsymmetrical PNB molecule destroys this alignment in the neighbor C-NO2 bonds, the exception being the exact opposite C
NO2 bond that preserves the symmetry due to the presence of neighbor nitro groups. The total magnitude of the quadrupole moment on the aromatic ring carbons, corresponding to the sum of the Q2 values of each carbon, decreases with the increase in the number of nitro groups indicating reduction in the ring π electron density. In the nitro groups, the largest Q2 values of the oxygen atoms are in the 9059

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Figure 3. Aromatic compounds containing only nitro groups: (a) TNB; (b) TETNB; (c) PNB; (d) HNB. Vectors correspond to the ring carbon dipoles. The dark numbers are the charge values (e units) and the red ones are the quadrupole values (ea20 units).

TNB molecule, the most insensitive in this set and which have neighbor hydrogen atoms. For TETNB and PNB, the oxygen atoms closer to hydrogen atoms have also the largest Q2 values. Both situations are another manifestation of an inductive effect. The five aromatic molecules, TATB, DATB, TNA, TETNA, and PNA contain nitro and amine groups (NH2) as well as hydrogen atoms (Figure 4). The first three molecules are very insensitive (490 cm), DATB (320 cm), and TNA (177 cm), while the other two have the opposite behavior: TETNA (41 cm) and PNA (15 cm). The type of NO2 neighbor groups in this set especially determines the charge on the carbon atoms. When the two neighbors are amine groups, the charge on the carbon atoms is very small, almost zero; thus, the former groups compensate the ring negative charges lost to the NO2 group. On the other hand, when the neighbor groups are nitro groups or hydrogen atoms, or an amine group and a hydrogen atom, the charge on the carbons is positive, indicating domination of a charge transfer effect to the nitro group. Due to an inductive effect, the charges on the oxygen atoms in the nitro groups are greater when the closest group is a hydrogen atom or an amine group.

The ring carbon dipole values of the molecules in this group, as expected, are also influenced by their adjacent groups. The dipole vector directions follow the pattern of the previous group of molecules: the presence of a nearby C
H bond and/or an amine group break the bond alignment of the C
NO2 dipole vectors. The magnitude of the dipole values on the carbon atoms bonded to an amine group is very small, approximately 5 times smaller when compared to the carbon atoms bonded to the other groups; that is, the amine groups thus are much less effective to polarize the ring carbon atoms. In the PNA molecule, four out of five carbon dipole vectors on the C
NO2 bonds are not aligned to the bond, so even a far (second neighbor) amine group and the distorted nitro groups can break the dipole alignment. The magnitude of the quadrupole moments (Q2) on the ring carbons bonded to the nitro varies in the 1
1.3 ea20 range. The largest Q2 values are for the molecule with more NH2 groups, TATB, the most insensitive material. The other insensitive materials, DATB and TNA, have comparable quadrupole values. Thus, the multipole results showed that the amine groups can contribute both to the π system and localized charges of the ring carbon electrons, although the produced site polarization (i.e., the dipole magnitude) is quite small. 9060

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Figure 4. Aromatic compounds containing nitro and amine groups: (a) TATB; (b) DATB; (c) TNA; (d) TETNA; (e) PNA. Vectors correspond to the ring carbon dipoles. The dark numbers are the charge values (e units) and the red ones are the quadrupole values (ea20 units).

Note that the PNA and TETNA molecules, corresponding to very sensitive materials, have distorted nitro groups and carbon dipole vectors not aligned with the corresponding C
NO2 bonds. The TNAP and PA molecules contain a hydroxyl group (OH), in addition to the nitro groups and hydrogen atoms; the TNAP molecule also has an amine group (Figure 5). Both molecules correspond to mildly insensitive materials: TNAP (138 cm) and PNA (87 cm).

The carbon atoms bonded to an OH group have the largest positive charges and the smallest quadrupole values on both molecules due to the group electron-withdrawal effects. When the multipole values of the carbons bonded to the OH and NO2 groups are compared, it is seen that for the carbon atoms bonded to a nitro group the charge values are less positive and the quadrupole values are similar. Overall, the carbon dipole vectors 9061

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Figure 5. Converged geometries of a) TNAP and; b) PA. Vectors correspond to the dipole vectors and point to regions of positive density. The dark numbers are the charge values (e units) and the red one are the quadrupole values (ea20 units).

Figure 6. Converged geometries of (a) MTNB and (b) DMTNB. Vectors correspond to the dipole vectors and point to regions of positive density. The dark numbers are the charge values (e units) and the red one are the quadrupole values (ea20 units).

behave as the other sets of molecules. The dipole vector of the oxygen atom in the OH group is by far the largest, and point to a neighbor nitro group inducing on the closest oxygen an almost 50% higher negative charge when compared to the charge on the other oxygen atom. There is also in the TNAP molecule an inductive effect of the hydrogen atom in the amine group directed to the closest oxygen atom, but of smaller magnitude compared with the one due to the OH group. The MTNB and DMTNB molecules, in addition to nitro groups, have also methoxy groups (OCH3) bonded to the aromatic ring (Figure 6). The sensitivities are MTNB (192 cm) and DMTNB (251 cm).

The positive charge on the carbon atoms bonded to the methoxy group (OCH3) are larger than if the carbons were bonded to a nitro group. The dipole magnitudes of the carbon atoms bonded to a hydrogen in both molecules are larger than for the carbon atoms bonded to nitro groups, and the former dipole vectors point to the ring interior, the opposite direction of the local charge transfer. The direction of the carbon dipole vectors also depends on the neighbor groups, as expected. The magnitude of the carbon dipole vectors are smaller when compared to the dipole vectors of the molecules of the other sets. Inductive effects due to the hydrogens in the metoxy group are present for the closest oxygen atoms in a neighbor nitro group. 9062

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Figure 7. Converged geometries of (a) TBN, (b) TNT, (c) ClMTNB, and (d) TNBO. Vectors correspond to the dipole moments and point to regions of larger electronic density. The dark numbers are the charge values (e units) and the red one are the quadrupole values (ea20 units).

The aromatic ring carbon quadrupole total magnitude, corresponding to the sum of the values of each carbon for each molecule, increases with the addition of a second methoxy group in DMTNB. The rather insensitive behavior of both energetic materials seems to be related to the quite large quadrupole values on the ring carbon atoms, with the second metoxy group in DMTNB increasing its total quadrupole value resulting in a more insensitive material. Both features are consequences of the electron donating properties of the metoxy group, opposing the electron-withdrawing effects of the nitro groups. TBN has a nitrile group (CN), TNT has a methyl group (CH3), ClMTNB has a chloromethyl group (ClCH2) and TNBO has a carboxyl group (COOH)
see Figure 7. Their sensitivities are: TBN (140 cm), TNT (160 cm), ClMTNB (44 cm), and TBNO (109 cm). The four molecules have three nitro groups. TBN and TNBO also show similar trends of the first set, namely, the fact that electron-withdrawing groups, respectively CN and CH3, similar to NO2 groups, also lead to a decrease of

the ring electron density. This is seen by the positive charge values and a decrease of the magnitude of the quadrupole moments on the carbon atoms. The largest dipole vector is on the carbon atom bonded to the methyl group in TNT; in TBN the dipole vector on the carbon atoms bonded to hydrogen have similar magnitude. In the ClMTNB and TBNO molecules, the dipole vectors, thus the polarization, on the carbon atoms are considerable smaller than on the TNT and TBN molecules. The TNT and ClMTNB molecules, similar to the nitroaromatic compounds containing amine groups, also have electrondonor groups, thereby leading to an increase in the carbon electron density, especially of the delocalized electron component given by the quadrupole moments. Adding a CH3 (TNT) or ClCH2 (ClMTNB) group to trinitrobenzene (TNB) slightly increased the carbon quadrupole values, thus, resulting in increased delocalized ring electrons. The chloromethyl group (ClCH2) in the ClMTNB molecule lead to a 9063

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Figure 8. Comparison between the h50% results: theoretical (Model 1, eq 2) and experimental values. Correlation set (red squares) and test set (blue diamonds) represent h50% measurements.

Table 1. Experimental and Predicted Values of h50% (cm) for the Studied Molecules

compound

experimentala

Training Set model 1b

model 2b

model 3b

475(15) 329(
9)

493(
3) 319(1)

TATB DATB

490 320

470(20) 329(
9)

TNA

177

214(
37)

210(
33)

202(
25)

TNT

160

159(1)

152(8)

148(12)

TBN

140

79(61)

79(61)

96(44)

TNB

100

128(28)

124(
24)

127(
27)

TETNA

41

39(2)

48(
7)

45(
4)

TETNB

27

25(2)

30(
3)

34(
7)

PNA HNB

15 11

16(
1) 22(
11)

17(
2) 18(
7)

17(
2) 11(0)

12,2

12,0

8,9

standard deviation (cm)

DMTNB

251

Test Set 139(112)

37(214)

55(196)

MTNB

192

132(60)

30(162)

46(146)

TNAP

138

150(
12)

153(
15)

163(
25)

TNBO

109

91(18)

89(20)

104(5)

PA ClMTNB

87 44

123(
36) 61(
17)

121(
34) 20(24)

137(
50) 30(14)

PNB

11

16(
5)

17(
6)

17(
6)

a

Sensitivity h50% values are from Kamlet and Adolph8 and Wilson et al. (HNB and PNB).12 b Values in brackets correspond to differences (in cm) between the experimental and theoretical h50% values.

small negative charge on the ring C atom to which it is bonded, which may be a distinctive feature to explain its large sensitivity (44 cm) in comparison to the other molecules in the set.

4. CORRELATION MODELS FOR SENSITIVITY BASED ON THE MULTIPOLE MOMENTS OF THE MOLECULAR CHARGE DENSITY In this section, bearing in mind the limitations discussed in the Introduction, we propose and discuss three models to correlate

impact sensitivity and properties, mostly related to the DMA decomposition of the molecular charge density of the 17 molecules. The models were inspired by previous works.10,14,19 Because we used rather small samples and the impact sensitivity measurements have limited reliability,8 the correlations should be considered more as a new view on sensitivity
structure trends. 4.1. Model 1: Charges and Molar Masses of the Nitro Groups. This first model relates h50% to the sum of both DMA charges Q0 (e units) and the molar masses M (g 3 mol
1) of the nitro groups of each molecule in the training set. The two properties are combined according to eq 1, Γðq, MÞ ¼

∑jQ0ðNO2 Þj2 3 106 ½∑MðNO2 Þ

ð1Þ

where ∑|Q0(NO2)| and [∑M(NO2)]2 are, respectively, the sum of the DMA charge magnitudes and the molar masses; both terms are computed as a sum over the nitro groups present in each molecule. We described the sensitivity h50% dependence in Model 1 through the function h50% ¼ RðΓðq, MÞ Þ2
βðΓðq, MÞ Þ þ γ

ð2Þ

where the fitted constants R, β, and γ for the training set are, respectively, 0.1659 (g4 3 mol
4 3 e
2 3 cm), 5.0483 (g2 3 mol
2 3 e
1 3 cm) and 54.158. The correlation coefficient is 0.97 and the standard deviation equals 12.2 cm. The comparison between h50% predictions using Model 1 with the experimental values for the training and test sets are given in Figure 8 and a numeric comparison is given in Table 1. Considering the training set in Model 1, the only molecule with a large deviation in comparison to the experimental value was TBN, the only one with a CN group. The experimental and theoretical values of the TBN are, respectively, 140 and 79 cm. When this model was applied to the test set, the h50% values of the various molecules were rather well predicted, with the exception of the DMTNB and MTNB molecules, both having methoxy groups and being highly insensitive. The presence of the methoxy groups in these molecules, with their distorted geometry, high polarized oxygen atoms, and inductive effects on the neighbor nitro groups, are not prone to an analysis based only on nitro 9064

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Figure 9. Comparison between the h50% results: theoretical (Model 2, eq 4) and experimental values. Correlation set (red squares) and test set (blue diamonds) represent h50% measurements.

Figure 10. Comparison between the h50% results: theoretical (model 3, eq 6) and experimental values. Correlation set (red squares) and test set (blue diamonds) represent h50% measurements.

group charges. The experimental and theoretical values of the DMTNB are, respectively, 251 and 139 cm; the experimental and theoretical values of the MTNB are, respectively, 192 and 132 cm. 4.2. Model 2: Charges and Molar Masses of the Nitro Groups and Ring Carbon Quadrupoles. Model 2 corresponds to Model 1, including a new DMA term corresponding to the sum of the quadrupole moment Q2 (ea20 units) of the ring carbon atoms, according to Γðq, Θ, MÞ ¼

∑jQ0ðNO2 Þj 3 ∑½Q2 ðCring Þ 3 105 ½∑MðNO2 Þ2

ð3Þ

where ∑|Q0(NO2)|, ∑M(NO2), and ∑[Q2(Cring)] are, respectively, the sum of the DMA charge magnitudes, the molar mass of all nitro groups, and the sum of the DMA quadrupole moment values of the aromatic carbon atoms of each molecule. We recall that the quadrupole moment is a measure of the delocalized and

isolated-pair electrons, which depends on electron-donor or -acceptor properties of the groups bonded to the carbon atoms. The dependence of the measured h50% values of the training set is illustrated in Figure 9. The h50% dependence on the function Γ(q,Θ,M) in Model 2 is given by h50% ¼ RðΓðq, Θ, MÞ Þ2
βðΓðq, Θ, MÞ Þ þ γ

ð4Þ

where the fitted constants R, β, and γ are, respectively, 0.2965 2
2
2
2 (g4 3 mol
4 3 e
4 3 a
4 0 3 cm), 4.39055 (g 3 mol 3 e 3 a0 3 cm) and 32.935. The correlation coefficient is 0.97 and the standard deviation equals 12.0 cm. The results are given in Table 1. The comparison of Model 2 h50% predictions with the experimental values for the correlation and test sets are given in Figure 9 and a numeric comparison is given in Table 1. In this model, the TBN molecule in the training set showed a large deviation when compared to the experimental value. When this model was applied to the test set, the h50% values of various 9065

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molecules were well predicted, with the exception of the DMTNB and MTNB systems, as happened with Model 1. The experimental and theoretical (between brackets) values of the DMTNB are 251 cm (37 cm) and of MTNB are 192 cm (30 cm). Therefore, Model 2 still is not enough to deal with both molecules. 4.3. Model 3: Global Model. The last model combines the charges, dipole magnitudes and molar masses of the nitro groups in each molecule, the aromatic carbon atom quadrupoles and the average length of the C
NO2 bonds. The latter is a measure of the C
NO2 bond strengths. Following Rice and Hare,19 we call global a model of this type. These properties were combined according to Γðq, μ, Θ, M, RÞ ¼

∑jQ0 ðNO2 Þj 3 ∑½Q2ðCring Þ

∑jQ1ðNO2 Þj 3 ½∑MðNO2 Þ2 3 ½RðC
NO2 Þavg 3 3

ð1020 Þ
1 ð5Þ

where ∑|Q0(NO2)|, ∑|Q1(NO2)|, and ∑M(NO2) represent, respectively, the sum of DMA charge value, the dipole magnitudes and the molar masses; the three properties were computed for the nitro groups. ∑[Q2(Cring)] represents the sum of the aromatic carbon quadrupoles and R(C
NO2)avg corresponds to the average length of all C
NO2 bonds for each molecule. We denote this expression by Γ(q,μ,Θ,M,R), where Q0 represents the DMA charges (in e), Q1 the dipole moment magnitude (in ea0), Q2 is the quadrupole moment magnitude (in ea02), M is the molar mass (in g 3 mol
1), and R is the average distance of all the C
NO2 bonds in each molecule (in cm). The h50% relationship is described by the function h50% ¼ R½ðΓðq, μ, Θ, M, RÞ Þδ 2 þ βðΓðq, μ, Θ, M, RÞ Þδ þ γ

ð6Þ

where the fitted values of R, β, γ, and δ are, respectively, 1.5 7 2
2 4 (g4 3 mol
4 3 e
2 3 a
2 0 3 cm ), 422.82 (g 3 mol 3 ea0 3 cm ), 7.8401, and 1.4. The correlation coefficient was 0.98 and the standard deviation was 8.9 cm. The graphical comparison between model 3 h50% predictions and the experimental values for both sets are in Figure 10 and numeric comparisons are in Table 1. In this model, no molecule in the training set presented large deviations when compared to the experimental value. When this model was applied to the test set, similarly to the other two models, it also did not predict well only DMTNB and MTNB h50% values. The experimental and theoretical (between brackets) values of the DMTNB are 251 cm (55 cm) and of MTNB are 192 cm (46 cm). Therefore, the model 3 still does not handle adequately both molecules. The simplest model (model 1), which involved only nitro charges and molecular masses, gave the best, though still deviating, results for DMTNB and MTNB. In Figures 8
10 we observe a strong correlation between the impact sensitivity and the DMA decomposed molecular charge density in the training set. The three correlation models predicted h50% successfully for the molecules in the test set, with the exception of the MTNB and DMTNB molecules. Possibly, the ability of these models to predict the h50% impact sensitivity failed for MTNB and DMTNB because these molecules have OCH3 groups, which can interact with other regions of the molecule, as discussed, and their hydrogen bonding in the crystal probably lead to an increased stability, similar to the one Meents et al. verified in the energetic material FOX-7 (1,1-diamino-2, 2-dinotroethylene).41 Therefore, our molecular approach is not

sufficient to infer properties for the MTNB and DMTNB materials in crystalline form.

5. CONCLUSIONS The molecular charge density, decomposed into electric distributed multipoles according to the DMA, was used to analyze the charge structure of 17 molecules component of energetic materials. The multipoles were considered as a structural parameter to evaluate the impact sensitivity (h50%). Concerning the charge density (Q0), we showed that the charges on the carbon atoms of the aromatic ring of each molecule become more positive with the increase of the number of nitro groups, an indication that the carbon electrons are being transferred to the electron-withdrawing nitro groups. The behavior of the dipole moments of the carbon atoms bonded to nitro groups depends also on the adjacent groups, with the largest dipole value being associated to the C
H bonds. The total magnitude of the quadrupole moment of the aromatic ring carbons, corresponding to the sum of the values of each atom, decreases with the increase of the number of nitro groups. This effect points to a decrease in the π electron density of the ring carbon atoms due to the electron-withdrawing effect. We verified that the magnitude of this decrease is particularly influenced by the type of neighbor groups, in addition to the influence of the group directly bonded to the ring carbon. In order to investigate possible relationships between molecular properties and energetic materials sensitivity, three models inspired on previous works were suggested. Our models sought to correlate the molecular electron density decomposed through DMA into charge, dipole and quadrupole moments, nitro molar masses and average C
NO2 distances, combined in different forms, with the experimental parameter h50% to look for sensitivity-structure trends; the models were initially applied to a training set of 10 molecules. The proposed models predicted quite accurately the impact sensitivity of the explosives of a test set composed of 7 molecules; the exception was the DMTNB and MTNB molecules, components of highly insensitive materials and containing metoxy groups. The more sophisticated models, model 2 combining the nitro groups charge values, molar masses and carbon quadrupole moment magnitudes, and Model 3 involving combinations of the charge and dipole moment magnitudes of the nitro groups and the ring carbons quadrupole moment magnitudes, gave the best results (standard deviations 12.0 and 8.9 cm, respectively). The model 1, which only includes nitro group charges, despite its simplicity, predicted the experimental h50% values of the test set molecules with similar quality of model 2. The results for model 1 indicate that indeed the nitro group charge is the main molecular property related to the impact sensitivity of nitraromatics. This pattern of model 1 is in complete agreement with the proposal of Zhang and co-workers using the not so accurate Mulliken charges.15 Despite the drawbacks of the Mulliken analysis, Zhang et al. have captured the essence of the molecular basis of the sensitivity of the energetic materials composed of molecules with nitro groups, which our work using a more accurate representation of the molecular charge density, has confirmed and extended. Our approach is a step forward over previous works because the DMA is an accurate and stable method, the latter as function of Gaussian basis set size, to decompose the molecular charge density into multipole moments, each one with a straight 9066

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The Journal of Physical Chemistry A chemical interpretation. The result is a wealth of details of the molecular charge of each molecule, which can be used to develop other sensitivity or property models. We showed that an explosive compound will have a large value of h50%, thus will be less sensitive, if its delocalized electron densities in the aromatic ring, represented in our work by the quadrupole (Q2) total magnitude values of the ring carbon atoms, have large values. The charge values on the nitro groups also play an important role. Our results agree with the discoveries of Politzer and co-workers which, through the study of features of the molecular electrostatic potential (the integrated nuclear and electron densities over the volume), identified that the balance between charge delocalization and NO2 electron-withdrawing effects is crucial for the impact sensitivity of an energetic material compound. Our results also agree with the work of Rice and Hare that identified “the level of sensitivity to impact to the degree of charge build-up over covalent bonds within the inner framework” of explosives. The idea of a positive electrostatic potential buildup over nitroaromatic C
NO2 bonds was first established in the literature by Politzer et al. in 198442 and recently revisited.43 To summarize, in this work we have applied the DMA to decompose the molecular charge density of nitroaromatic molecules, components of explosive compounds, and used these results to analyze in details the electronic structure of the molecules and to propose models to correlate them with the material sensitivity. The DMA method, being a general and accurate approach, has a considerable potential to be applied to other explosive molecules and other molecular problems.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by CAPES, CNPq, Faperj, Brazilian Agencies, the Ministry of Defense, and the Basic Plan for Science and Technology of the Brazilian Army. ’ REFERENCES (1) Sikder, A. K.; Sikder, N. J. Hazard. Mater. 2004, 112 (1
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