A Transferable Intermolecular Potential 

for Nitramine Crystals 

by Dan C. Sorescu, Betsy M. Rice, and Donald L. Thompson 

AH.,-TR-23 72 December 2000 

,’ 

, 

,/” 

_/ 

Approved for public release; distribution is unlimited. 
The findings in this report are not to be construed as an offkial 

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authorized documents. 

Citation of manufacturer’s or trade names does not constitute an 

official endorsement or approval of the use thereof. 

Destroy this report when it is no longer needed. Do not return 

it to the originator. 
. Aberdeen Proving Ground, MD 2 1005-5066 

. 

Army Research Laboratory 

ARC-TR-2372 December 2000 

A Transferable Intermolecular Potential 

for Nitramine Crystals 

Dan C. Sorescu and Donald L. Thompson 

Department of Chemistry, Oklahoma State University 

Betsy M. Rice 

Weapons and Materials Research Directorate, ARL, 

I l 

ADDroved for public release; distribution is unlimited. 
Abstract 

We have analyzed the transferability of a previously proposed Buckingham 

repulsion-dispersion intermolecular potential for the explosive hexahydro- 1,3,5-trinitro- 1,3,5-striazine (RDX) (Sorescu, D. C., B. M. Rice, and D. L. Thompson, JournuZ of Physical 

Chemistry B, vol. 101, p. 798, 1997) to predict the crystal structures (within the approximation 

of rigid molecules) of a database of 30 nitramines. These include acyclic, monocyclic, and 

polycyclic molecules. It is shown that the proposed potential model is able to accurately 

reproduce the crystallographic structures and lattice energies (where available) of these crystals. 

For the majority of these crystals, the best agreement with experimental structural and energetic 

data is obtained in those cases when the electrostatic charges have been determined using ab 

initio methods that include electron correlations effects (namely MP2 and B3LYP). The use of 

the electrostatic charges calculated at the Hartree-Fock level results in large deviations of the 

predicted lattice energies from the experimental values.. The deviations of the lattice energies can 

be significantly decreased by scaling the electrostatic charges with a constant factor. 

ii 
Acknowledgments 

This work was supported by the Strategic Environmental Research and Development 

Program (SERDP). Donald L. Thompson gratefully acknowledgesupport by the U.S. Army 

Research Office (ARO) under grant number DAAG55-98-1-0089. 

. . . 

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iv 
Table of Contents 

. . . 

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..-......................................................... 111 

1. 

2. 

3. 

4. 

5. 

6. 

List of Figures ........................................................................................................... 

List of Tables ............................................................................................................ 

Introduction .............................................................................................................. 

Vii 

vii 

1 

Intermolecular Potential .......................................................................................... 

Computational Approach ........................................................................................ 

Results and Discussions.. ......................................................................................... 

Conclusions ............................................................................................................... 

References.. ............................................................................................................... 

Distribution List.. ..................................................................................................... 

Report Documentation Page ................................................................................... 

3 

5 

8 

22 

25 

29 

3 1 

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V 
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h’TENTIONALLY LEFT BLANK. 

vi 
List of Figures 

Page 

. 

. 

1. Illustration of Molecules Whose Crystal Structures Were Studied . . . . . . . . .._................ 

2. The Calculated Structural Shift Factor F (Equation [3]) for the Crystal 

Structures .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

3. The Percent Differences Between the Lattice Energies and Those Based on the 

MP2 Values .. . . . . . . . . . . . . . . . . . . . . . . . . . . ..I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

List of Tables 

Table 

1. Comparison of the Crystallographic Parameters as Determined in Molecular 

Packing Calculations to the Corresponding Experimental Values for Different 

Molecular Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

2. Comparison of the Experimental and Calculated Lattice Energies for Different 

Sets of Electrostatic Charges . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..-............... . . . . . . . . . . . . 

r 

vii 

9 

18 

21 

10 

20 
hTENTIONALLY LEFT BLANK. 

. I 

. . . 

VI11 
1. Introduction 

Atomistic simulation is increasingly gaining acceptance as a practical research tool in the 

investigation of the behavior of condensed-phase materials. In addition to providing information 

that is diflicult or impossible to measure, prediction leads to a reduction in unnecessary 

measurement or synthesis of candidates in the course of design of new materials. However, the 

power of atomistic simulation can only be realized if the description of the molecular system is 

accurate. The development of accurate intermolecular potentials is not a simple, straightforward 

procedure. Substantial work has been directed toward determining both simple functions that 

make large-scale simulation realizable, and correct parameterization such that the physical 

properties of the materials are properly described. In this work, an intermolecular potential that 

accurately describes nitramine crystals is presented. Also, the potential parameters effect on 

predictive ability is investigated. 

In initial studies of nonreactive processes in the nitramine explosive hexahydro-1,3,5,-trintro1,3,5-s-triazine (RDX), an intermolecular potential energy function was developed that would 

accurately reproduce the structure of the a-form of the RDX crystal [l]. This potential is 

composed of pair-wise atom-atom (6-exp) Buckingham terms with explicit inclusion of the 

electrostatic interactions between the charges associated with the atoms of different molecules. 

The parametrization of the potential function was done such that molecular packing calculations 

(MP) reproduced the experimental structure of the crystal and its lattice energy. 

Isothermal-isobaric molecular dynamics simulations (NPT-MD) using this potential energy 

function predicted crystal structures in excellent agreement with the experimental data [l]. 

It has been shown that this interaction potential energy function is transferable to two other 

nitramine crystals: the polycyclic nitramine 2,4,6,8,10,12-hexanitrohexaazaisowurtzitane (HNIW) 

[2] and the monocyclic nitramine 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX) [3]. Both 

Ml? and NFT-MD simulations predict geometrical parameters in good agreement with the 

experimental values for the different polymorphs of the HNTW and HMX crystals [2, 31. 

1 
Furthermore, the calculations indicate a stability ranking for HNIW in agreement with 

experimental measurements [4]. 

The success of these potential energy parameters in describing the RDX crystal and different 

phases of the HMX and HNIW crystals provides impetus for further investigations to determine 

the limits of the transferability of this interaction potential. Toward this end, MP calculations of 

30 nitramine crystals are reported here. This set of crystals is composed of monocyclic, 

polycyclic, and acyclic nitramine molecules. There was a particular interest to see if the 

geometrical and energetic parameters for these crystals could be reproduced by this proposed 

model. 

One of the main factors that contributes to the quantitative description of the molecular 

packing in a crystal is related to the representation of the electrostatic interactions. It was shown 

more than a decade ago [5, 61 that increased accuracy in structural predictions of the molecular 

crystals and in transferability of the potential parameters can be achieved by explicit use of the 

electrostatic interactions between the charges associated with the atoms. For example, many of 

the available force fields such as Amber [7], ECEPP [8], or Dreiding [9] use these kinds of 

potential terms in models of organic, biological, and main group inorganic crystals. Further 

improvement of the description of the electrostatic forces between molecules, particularly in 

crystals with substantial anisotropies, can be achieved by using sets of point multipoles (charge, 

dipole, quadrupole, etc.) on every atomic site. This distributed-multipole representation has been 

shown to be successful in the modeling of the crystal structures of polar and hydrogen-bonded 

molecules [lo]. 

The present study has found that, as in the cases of the RDX [l], HNIW [2], and HMX [3] 

crystals, the set of 30 crystals considered here can be accurately represented using the 

Buckingham potential plus Coulombic interactions. The assignment of the electrostatic charges 

poses a problem in that the atom-centered monopole charge is not an observable quantity and 

cannot be obtained directly from either experiment or first principles calculations. Currently, 

2 
. 

there are several schemes for evaluation of charges by empirical partition or by using a quantum 

mechanically derived wave function [l l-131. The Coulombic terms have been determined 

through fitting of partial charges centered on each atom of the molecules to a quantum 

mechanically derived electrostatic potential [13]. An investigation has been done on how the 

geometrical and energetic parameters predicted in MP calculations depend on charges determined 

from ab initio methods, which do or do not include electron correlation effects. Specifically, 

different sets of charges derived from the Hartree-Fock (HP’) wave function [14] and from 

methods that employ electron correlations such as second-order Moller-Plesset (MP2) 

[ 15-181 and B3LYP [ 19,201 have been used. 

The studies described here representhe first stage in the development of a general model for 

nitramine crystals. The main limitations of the present model are due to the assumption of rigid 

molecules but further refinement of this model can be made to include the effects of 

intramolecular motions, particularly of low-frequency torsional motions of the nitro groups and 

the ring. 

The organization of the paper is as follows. In section 2, the intermolecular potential used to 

simulate the nitramine crystals is presented. In sections 3 and 4, the molecular packing methods 

and results, respectively, are described. The main conclusions are summarized in section 5. 

2. Intermolecular Potential 

The central problem in classical simulations of molecular crystals is the construction of 

realistic potentials that accurately predict the structural and thermochemical parameters. In this 

paper, the same general model is employed for the atom-atom potentials that proved to be 

successful in modeling of the RDX, HNIW, and HMX crystals [l-3]. In particular, it is assumed 

that (1) the intermolecular interactions depend only on the interatomic distances; (2) the 

interaction potential can be separated in contributions identified as van der Waals and 

electrostatic, and (3) the same type of van der Waals potential is used for the same type of atoms, 

3 
independent of their valence state. Moreover, in the present case, the transferability of the 

potential parameters determined for the case of RDX crystal to all the nitramines considered in 

this study is assumed. 

In the present treatment, the intermolecular interactions between the molecules of the crystal 

as the sum of pair-wise Buckingham (6-exp) (repulsion and dispersion) and Coulombic (C) 

potentials is approximated: 

Vliexp (r) = A,, exp(- Bapr)- C,, /r6, 

and 

(1) 

(2) 

where r is the interatomic distance between atoms a and p, qu and qp are the electrostatic charges 

on the atoms, and EO is the dielectric permittivity constant of vacuum. 

The parameters for the 6-exp potential in equation (1) are those previously determined for the 

case of the RDX crystal [ 11. The same combination rules are used for the calculation of the 

heteroatom parameters from homoatom parameters, as previously reported [ 11. 

The assignment of the electrostatic charges is made by using the set of atom-centered 

monopole charges for the isolated molecule that best reproduces the quantum mechanically 

derived electrostatic potential, which is calculated over grid points surrounding the van der 

Waals surface of the molecules. This method of fitting the electrostatic potential was proposed 

by Breneman and Wiberg [ 131 and is incorporated in the Gaussian 94 package of programs [2 13 

under the keyword CHELPG (electrostatic-potential-derived atomic charges). This method has 

the advantage of a higher density of points and a better selection procedure, which ensures a 

significant decrease in orientation effects compared to those observed with similar methods [ 121. 

4 
The CHJZLPG charges were found to be invariant to either the rotation of the molecular 

coordinates or internal bond rotations. These calculations have been done at both the HF [14] 

and second-order MP2 [15-l 81 levels to investigate the effect of electron correlation. 

For the purpose of comparison and as an alternative to the computationally demanding MP2 

method, density functional theory (DFT) has also been used in the Kohn-Sham formulation [22]. 

The DFI’ methods offer a less expensive but still accurate computational alternative to ab initio 

methods for including the electron correlation in post-HP treatments. In particular, the exchange 

functional, described by the fitted three-parameter hybrid of Becke [ 161 and the correlation 

functional of Lee, Yang, and Parr (B3LYP) [17] was employed. All the aformentioned theoretical 

calculations were done using a reasonable quality basis set (i.e., 6-31G** [split-valence plus dtype and p-type polarization functions]) [24]. 

It has been shown previously [25,26] that the neglect of electron correlation in self-consistent 

wave functions overestimates the electrostatic interactions; however, this is mainly a scaling 

effect. Cox and Williams [25] have suggested that a scaling factor of 0.9 can be used to improve 

agreement between the calculated and experimental values of the dipole moments for a set of 

eight small molecules. The same factor has been justified in a study of the electrostatic 

interactions of a dipeptide [26], as well as in a more recent work related to the role of 

electrostatic interactions in determinin gthe crystal structures of polar organic molecules [lo]. 

Such an electrostatic model has been employed to further evaluate the effects of this scaling 

procedure. Specifically, four electrostatic models were tested for each of the 30 crystals. Two of 

them use electron correlation methods (namely Ml?2 and B3LYP); the third one uses unscaled HF 

charges, and the last HP charges scaled by 0.9 (denoted as 0.9HF). 

3. Computational Approach 

A general procedure for testing intermolecular potential energy functions for organic crystals 

is based on the use of molecular packing calculations [5, 61. The basic idea is to minimize the 
lattice energy with respect to the structural degrees of freedom of the crystal. For crystals with 

one molecule in the asymmetric unit occupying an arbitrary position, the maximum number of 

degrees of freedom is 12 and corresponds to the six unit cell constants (a, b, c,‘a, j3, r), the three 

rotations (01, 02, (3s) and the three translations (71, 22, 2s) of the rigid molecule. A reduced 

number of structural degrees of freedom might be involved, depending on the symmetry 

restrictions of different space groups. For crystals with more than one molecule in the 

asymmetric unit, additional degrees of freedom are introduced to describe the rotation and 

translation of the additional molecules. 

Assuming that the crystal energy is known as a function of the structural lattice parameters, 

the equilibrium crystal configuration is determined by the conditions of zero force and torque, 

together with the requirement that there is a minimum. The search for such a minimum can be 

done using a combination of steepest-descent and Newton-Raphson procedures [27,28]. 

In the present study, it is assumed that the crystals can be represented as an ensemble of rigid 

molecules. The minimization of the lattice energy with symmetry constraints has been 

performed using the molecular packing program PCK91 [29] by taking the experimentally 

observed geometries as starting configurations. This program employs an accelerated 

convergence method [l, 281 for accurate evaluation of the crystal Coulombic and dispersion 

lattice sums, with the first and second derivatives of the crystal energy evaluated analytically. Jn 

all calculations, a cutoff distance of 19 A has been used with the parameters q that determines 

the relative contributions of the real- and reciprocal-space terms as defined in Sorescu et al. [l] 

having the values q I= 0.186 1 A- ’ and ‘& = 0.2304 A- ” The space-group symmetry is maintained 

throughout the energy minimization. This reduces the number of independent variables in the 

minimization procedure, resulting in a significant decrease in the computational time compared 

to unconstrained energy minimization. For example, for the b-phase of HMX crystal with space 

group P21/n (Z = 2), the crystallographic parameters that were varied in the minimization using 

the PCK91 program are the three dimensions of the unit cell and the angle p, while the angles 

a and y were frozen at 90”. Since the molecule in the asymmetric unit occupies an inversion 

6 
. 

. 

center, only the three rotations of this molecule were allowed to vary, while the three translations 

were not modified to maintain the symmetry imposed by the inversion center. It has been 

previously shown [ 1, 2, 301 that, despite the symmetry restrictions imposed in the PCIW 

program, the final lattice energies and crystallographic parameters are in good agreement with 

those obtained when symmetry constraints were removed (i.e., the predicted crystals maintained 

the observed space-group symmetry). 

The quality of the predicted geometrical crystallographic parameters relative to the 

experimental values has been done using a structural shift factor of the form [28,31] 

F= (A8/2)2+ (10Ax)2+ (100Aa/a)2+ (100Ab/b)2+ (~OOAC/C)~+ (A@‘+ (Ap)2+ (AY)~, (3) 

where A0 is the total root-mean-square (rms) rigid-body rotational displacement (in degrees) after 

minimization; Ax is the rms total rigid-body translational displacement (in angstroms); and a, b, c, 

and a, fi, y are, respectively, the lengths of the edges and the angles of the unit cell. 

‘ 

An important test of the validity of the model is the accuracy of the predicted lattice energies 

of the crystals. The lattice energies determine the relative stabilities of the different 

crystallographic phases. The calculated static lattice energy can be compared to the experimental 

sublimation enthalpy by the using the relationship [32] -AHsubl =E + & + 2RT, where E is the 

lattice energy and KO is the zero-point energy. Often, a rough estimation of the lattice energy is 

obtained by neglecting the KO term. Kitaigorodski [SJ has pointeZout that, considering the 

inaccuracy involved in the experimental determination of AH,b and with the neglect of zero-point 

energy, discrepancies up to 3-4 kcaVmo1 between the calculated and the observed enthalpies of 

sublimation are expected [5]. In the case of RDX crystals, it was found, using this approximation, 

that the predicted lattice energy (E = - 130.09 kJ/mol) is in very close agreement with the 

experimental sublimation enthalphy (-AHsub = - 130.1 kJ/mol) [ 11. 

7 
4. Results and Discussions 

The 30 nitrarnine molecules considered in this study are shown in Figure 1. They were chosen 

as representative examples of important acyclic and cyclic nitramines. Different types of monoand polycyclic nitramines have been included, particularly crystals that are important energetic 

materials. The structures of most of these crystals have been obtained by x-ray diffraction 

techniques. Despite the generally poorer resolution of hydrogen atom positions obtained by these 

techniques, no additional adjustment of these positions has been done to give, for example, the 

standard bond lengths .[33]. The crystal structures in Figure 1 are denoted fist by the common 

names of the molecules. Where available, the crystal abbreviation from the original reference is 

also included with the corresponding crystal “refcode” used in the Cambridge Structural Database 

[34] and indicated by the term in the second set of parentheses. The structures used for HNIW 

[35] and fi-HMX [36] crystals are not in the Cambridge database, so they do not have a refcode. 

In addition, different crystallographic phases of HMX and HNIW crystals have been studied, 

these are detailed in Table 1. The specific references for each of the 30 crystals in Table 1 are 

provided in brackets in the “Crystal” column and found in the reference section [35-571. 

The results of MP calculations using the PCK91 program are presented in Table 1. The 

predicted structural lattice parameters for the great majority of these crystals deviate by less than 

2% from the experimental structures. Also, for the majority of the crystals, there are small 

rotations and practically no translations for the molecules in the asymmetric unit cell. The 

accuracy of the predictions can be seen in Figure 2, where the overall structural drift factors 

described in equation (3) are given. Only 10% of the total number of crystals considered here 

have a structural shift factor larger than 2.0, and practically half of the crystals have shift factors 

that are less than 1.0. 

It is important to point out that, ideally, the predicted lattice structural parameters should be 

compared with the values determined at zero temperature. However, this is not possible due to 

. 

8 
I . 3 9v2 9 %Q ;px; ‘-0 

I I 2 2 NO2 I ’ 

NO2 

NO, 

1.3.5-Trinitro-1.3.5.triaza- 1,3.3-Trinitroazetidillr (TNAZ) 1.3-Dinitro-1,3-dia 2.4.6-Trimethyl-1.3.5-lrinitro- I.)-Dinitro-l,3-diazacyclocyclohesane (RDX) (CIWMEAIO) cyclohcsane henahydro-l.3.5-triaine hcptane 

CTMTNA) (KOFKAR) (NOHTAZ) (KOFKEV) 

13.5 ‘I-Tetranitm-I 3.5.7- 

&a&cvclo-octane ‘(HMX) 

1.3,3.5.7,7-Hcxanitro~l.5. cis-l,3.5.7-Tetanitro-1.3,5,7- vans I,4,5.8-Tetranitro- 1.3.7,9-Tctmnitro-l.3.7.9-tetra 

diazacyclo-octane tetra-azadccalin 1,4.5,8-tetra-azadecalin aaspiro(4.3)decane (lWD) 

(CATJIQ) (JEXLUT) 

2,4,8.10-Tetranitro-2.4.8.1~tetra- l.l’.3.3’-Tenaniuo-4,4’-biazarpiro(5.5)undccane (TNSU) imidazolidinc (TNBI) 

NO- WMTIF) (JEM) 

2.2’-Bis(l.3-dinitmhexahydropytimidine) 

(SECVOL) 

Dinitropertt&%hylenetetmmine (DPT) 

(DNPMTA) 

N-methyl-N.2.4.ktetra 

nitrotmiline (Tettyl) 

(MTNANL) 

l,5-Dinilro-3-nitroso1,3.S-triazncycloheptane 

(KOFKJZ) 

l,3-Dinitro-l.3-dia 

~ClOp~tan-2-OllC 

(JEDSUG) 

(JEXMEE) 

2.4,6.8.10-HexanitrohexaazaisowrQitatte (HNWJ 

2.5,7,9-Tewnino-8-0x0-1,5,7.9- 

tena-azabicyclo(4.3.O)nomme 

(JEHLAJ) 

“? 

\ NO2 NO2 

N-NO2 

/ 

th~~t44 

\ 

YC ‘6’ ?02 ?02 ‘“3 

> 

N.N-Dimethylninamine l.7-Dimetbyl-1.3.5.7.tetmnitm- 2,2’-Dinitmxy-diethyl- bis(2,2-Dinitropropyl)-nitramine (BDNON) 

(MEl-NAMOS) aimctbylcnetctramine (OHMX) nitmmine (NABMUYOI) 

(GEJXAUJ (NXENAMOI) COCH, 

d 

1.1.1.3.6.8.8.8-Octattitro-3,6-diaza-oclan (ONDO) 

(DILFUZ) 

bis(t.t,Z-Triniuoetbyl).nieaminc 

(NOETNAOZ) 

l,7-Diacetoxy-2,4.6-trinitro-2,4,6-. 

uiazahcptane (BSX) 

(ACENIH) 

Figure 1. Illustration of Molecules Whose Crystal Structures Were Studied. The Common 

Abbreviation of the Crystal Name Is Given in the First Set of Parentheses, and 

the Refcode Entry of the Cambridge Structural Database [34] Is Given in the 

Second Set of Parentheses. 

9 
Table 1. Comparison of the Crystallographic Parameters as Determined in Molecular Packing Calculations to the 

Corresponding Experimental Values for Different Molecular Structures 

Data 

Set 

Crystal symnl. z a (4 b 6% c (4 0” (“I x(&~ F” 

1 CTMTNA [37] Pbca 8 13.1820 11.5740 10.7090 90.0 

I 13.2862 (0.8) 11.6511 (0.7) 10.6081 (-0.9) 90.0 1.240 0.126 0.886 

II 13.2691 (0.7) 11.6341 (0.5) 10.6128 (-0.9) 90.0 1.470 0.129 0.863 

III 13.2600 (0.6) 11.6260 (0.4) 10.6103 (-0.9) 90.0 1.365 0.127 0.835 

Iv 13.2236 (0.3) 11.5853 (0.1) 10.5948 (- 1.1) 90.0 1.199 0.121 0.783 

2 CIWMEAlO [38] Pbca 8 5.7330 11.1270 2 1.4960 90.0 

I 5.7691 (0.6) 11.0676 (-0.5) 21.2537 (-1.1) 0.927 0.073 0.735 

II 5.7550 (0.4) 11.0602 (-0.6) 21.2597 (- 1.1) 0.886 0.063 0.679 

III 5.7366 (0.1) 11.0711 (-0.5) 21.2697 (-1.1) 1.067 0.055 0.624 

Iv 5.7007 (-0.6) 11.0707 (-0.5) 21.3017 (-0.9) 1.386 0.025 0.622 

3 KOFKAR [39] P21/c 4 6.630 21.390 6.060 120.0 

I 6.5556 (- 1.1) 20.3153 (-5.0) 5.9076 (-2.5) 115.60 (-3.7) 0.772 0.684 4.063 

II 6.5499 (- 1.2) 20.3381 (-4.9) 5.8968 (-2.7) 115.61 (-3.7) 0.775 0.669 4.021 

III 6.5468 (- 1.3) 20.3382 (-4.9) 5.8978 (-2.7) 115.60 (-3.7) 0.773 0.669 4.023 

Iv 6.5221 (- 1.6) 20.4265 (-4.5) 5.8775 (-3.0) 115.95 (-3.4) 0.519 0.615 3.792 

4 NOHTAZ [40] P2,2,2, 4 7.31 10.732 14.155 90.0 

I 7.2433 (-0.9) 10.8359 (1.0) 13.8592 (-2.1) 1.026 0.133 1.279 

II 7.2360 (- 1.0) 10.8401 (1.0) 13.8364 (-2.3) 1.039 0.143 1.372 

III 7.2340 (- 1.0) 18.8413 (1.0) 13.8330 (-2.3) 0.963 0.144 1.386 

Iv 7.2171 (- 1.3) 10.8402 (1.0) 13:7809 (-2.6) 0.874 0.150 1.553 

5 KOFKEV [39] P21/n 4 8.7380 11.200 8.3830 90.1 

I I 8.6594 (-0.9) 11.0612 (- 1.2) 8.3520 (-0.4) 90.5 (0.4) 0.755 0.123 0.846 

Note: The first line of every data set represents the corresponding experimental value, The Roman symbols I, II, III, and IV denote the results obtained for 

electrostatic charges calculated at MP2/6-3 lG**, B3LYP/6-3 lG**, HF/6-3 lG**, and scaled by 0.9, and respectively at HF/6-3 lG** and unscaled. The 

values in parentheses represent the procentual difference relative to experimental values, 

‘For monoclinic systems, only angles are given, For triclinic systems, the cell angles and the cell angle errors are given in the order. For orthorhombic crystal 

b 

systems, a value of 90.0 is indicated only for the experimental structure. 

x = the net rotation of the molecule and the net translation of the center of mass of the molecule. 

‘F = structural shift factor; defined in equation (3). 

I . 
. , 

Table 1. Comparison of the Crystallographic Parameters as Determined in Molecular Packing Calculations to the 

Corresponding Experimental Values for Different Molecular Structures (continued) 

1ata Crystal symm. z a C& b (A) c (A> (“Y (“) x(A)~ F” 

Set 

II 8.6657 (-0.8) 11.0522 (- 1.3) 8.3447 (-0.5) 90.48 (0.4) 0.885 0.122 0.862 

III 8.6623 (-0.9) 11.0531 (-1.3) 8.3464 (-0.4) 90.47 (0.4) 0.799 0.122 0.861 

Iv 8.6480 (- 1 .O) 11.0359 (- 1.5) 8.3312 (-0.6) 90.32 (0.2) 0.696 0.120 0.936 

6 -HMX [36] P21h 2 6.5347 11 SO296 7.3549 102.689 

I 6.4756 (-0.9) 10.8316 (- 1.8) 7.3733 (0.2) 99.91 (-2.7) 1.662 0.000 1.583 

II 6.4649 (-1.1) 10.8171 (- 1.9) 7.3836 (0.4) 100.05 (-2.6) 1.769 0.000 1.595 

III 6.4679 (- 1 .O) 10.8129 (-2.0) 7.3797 (0.3) 100.13 (-2.5) 1.696 0.000 1.567 

Iv 6.4563 (- 1.2) 10.7626 (-2.4) 7.3965 (0.6) 100.63 (-2.0) 1.957 0.000 1.602 

7 OCHTET [4 1 ] Fdd2 8 15.1400 23.8900 5.9130 90.0 

(HMX, -form) 

I 14.9760 (- 1.1) 23.6617 (- 1.0) 6.0191 (1.8) 2.502 0.019 1.314 

II 14.9775 (-1.1) 23.6502 (-1.0) 6.0115 (1.7) 2.321 0.018 1.256 

III 14.9668 (- 1.1) 23.6496 (- 1.0) 6.0065 (1.6) 2.268 0.017 1.239 

Iv 14.9452 (-1.3) 23.6373 (-1.1) 5.9819 (1.2) 1.840 0.012 1.117 

8 OCHTET03 [42] P61 6 7.7110 7.7110 32.5530 120.0d 

(HMX, -form) 

I 7.6681 (-0.6) 7.6681 (-0.6) 33.5947 (3.2) 2.404 0.111 1.645 

II 7.6647 (-0.6) 7.6647 (-0.6) 33.5503 (3.1) 2.394 0.110 1.597 

III 7.6688 (-0.5) 7.6688 (-0.5) 33.4853 (2.9) 2.266 0.095 1.482 

Iv 7.6666 (-0.6) 7.6666 (-0.6) 33.2954 (2.3) 2.023 0.084 1.233 

9 CATJIQ [43] Pbca 4 11.289 10.205 11.880 90.0 

I 11.5194 (2.0) 9.8602 (-3.4) 11.7061 (-1.5) 7.117 0.087 2.496 

Note: The first line of every data set represents the corresponding experimental value. The Roman symbols I, II, III, and IV denote the results obtained for 

electrostatic charges calculated at MP2/6-3 1G **, B3LYP/6-31G**, HF/6-31G**, and scaled by 0.9, and respectively at HF/6-31G** and unscaled. The 

values in parentheses represent the procentual difference relative to experimental values. 

aFor monoclinic systems, only angles are given, For triclinic systems, the cell angles and the cell angle errors are given in the order. For orthorhombic crystal 

systems, a value of 90.0 is indicated only for the experimental structure. 

by = the net rotation of the molecule and the net translation of the center of mass of the molecule. 

“F = structural shift factor; defined in equation (3). 

dFor P3 1 and P6 1, the angle = 120 is indicated. 
Table 1. Comparison of the Crystallographic Parameters as Determined in Molecular Packing Calculations to the 

Corresponding Experimental Values for Different Molecular Structures (continued) 

Data 

Set 

Crystal Symm. Z b (A) c (4 (“>” (“> x(A)~ F” 

II 11.5106 (2.0) 9.8526 (-3.5) 11.6979 (- 1.5) 6.992 0.091 2.497 

III 11.5114(2.0) 9.8190 (-3.8) 11.6898 (-1.6) 6.743 0.095 2.570 

Iv 11.4907 (1.8) 9.7801 (-4.2) 11.6735 (- 1.7) 6.530 0.103 2.656 

10 JEXLUT [44] P21 2 7.471 10.7770 7.6420 103.34 

I 7.3400 (- 1.8) 10.6501 (- 1.2) 7.6707 (0.4) 105.02 (1.1) 1.490 0.141 1.193 

II 7.3298 (- 1.9) 10.6430 (- 1.2) 7.6675 (0.3) 104.97 (1.1) 1.536 0.147 1.241 

III 7.3260 (- 1.9) 10.6426 (- 1.2) 7.6650 (0.3) 104.92 (1.0) 1.531 0.149 1.250 

Iv 7.3114 (-2.1) 10.6174 (- 1.5) 7.6604 (0.2) 104.81 (0.9) 1.560 0.162 1.354 

11 JEXMII [44] Pl 1 6.4610 6.8450 7.5420 74.01 

75.00 

68.53 

I 6.3721 (- 1.4) 6.9609 (1.7) 7.3407 (-2.7) 73.94 (-0.1) 2.146 0.194 1.796 

72.63 (-3.2) 

68.91 (0.6) 

II 6.3803 (- 1.2) 6.9531 (1.6) 7.3284 (-2.8) 74.04 (0.0) 1.867 0.215 1.888 

72.44 (-3.4) 

69.42 (1.3) 

III 6.3517 (- 1.7) 6.9355 (1.3) 7.3263 (-2.9) 74.17 (0.2) 2.036 0.183 1.756 

73.00 (-2.7) 

69.16 (0.9) 

Iv 6.3330 (-2.0) 6.9279 (1.2) 7.3052 (-3.1) 74.47 (0.6) 2.082 0.195 1.901 

73.14 (-2.5) 

Note: The first line of every data set represents the corresponding experimental value. The Roman symbols I, II, III, and IV denote the results obtained for 

electrostatic charges calculated at MP2/6-3 1G **, B3LYP/6-3 lG**, HF/6-3 lG**, and scaled by 0.9, and respectively at HF/6-3 lG** and unscaled. The 

values in parentheses represent the procentual difference relative to experimental values. 

‘For monoclinic systems, only angles are given. For triclinic systems, the cell angles and the cell angle errors are given in the order. For orthorhombic crystal 

systems, a value of 90.0 is indicated only for the experimental structure. 

by = the net rotation of the molecule and the net translation of the center of mass of the molecule. 

‘F = structural shift factor; defined in equation (3). 
. . 

. 

Table 1. Comparison of the Crystallographic Parameters as Determined in Molecular Packing Calculations to the 

Corresponding Experimental Values for Different Molecular Structures (continued) 

C 

1 1ata 

[ 

Crystal symm. z a (A) b 6% c (A) (“I” (“1 x(A)~ FC 

Set 

69.74 (1.8) 

12 JEXMEE [44] P2,2*2, 4 7.8630 10.9890 14.4700 90.0 

I 7.7809 (- 1 .O) 10.9187 (-0.6) 14.5671 (0.7) 1.327 0.094 0.810 

II 7.7697 (-.12) 10.9007 (-0.8) 14.5770 (0.7) 1.314 0.096 0.889 

III 7.7660 (- 1.2) 10.8989 (-0.8) 14.5772 (0.7) 1.265 0.096 0.902 

Iv 7.7463 (- 1.5) 10.8664 (- 1.1) 14.5575 (0.60) 1.384 0.094 1.017 

13 KEMTIF [45] C2lc 8 12.8310 10.7260 19.6440 108.13 

I 12.8427 (0.1) 10.6040 (-1.1) 19.5672 (-0.4) 108.65 (0.5) 0.454 0.155 0.833 

II 12.8249 (0.0) 10.5976 (-1.2) 19.5465 (-0.5) 108.58 (0.4) 0.480 0.151 0.839 

III 12.8210 (-0.1) 10.5913 (-1.3) 19.5453 (-0.5) 108.56 (0.4) 0.478 0.152 0.885 

Iv 12.7957 (-0.3) 10.5541 (- 1.6) 19.5084 (-0.7) 108.39 (0.2) 0.527 0.149 0.957 

t; 14 JEXMAA [44] P2,2,2, 4 6.5480 9.89860 19.2990 90.0 

I 6.5 140 (-0.5) 9.8934 (0.0) 19.1302 (-0.9) 1.528 0.135 0.831 

II 6.5046 (-0.7) 9.8787 (-0.2) 19.1315 (-0.9) 1.593 0.139 0.869 

III 6.5066 (-0.6) 9.8729 (-0.2) 19.1448 (-0.8) 1.574 0.131 0.828 

Iv 6.4863 (-0.9) 9.8471 (-0.5) 19.1517 (-0.8) 1.561 0.138 0.918 

15 SECVOL [43] Pl 1 6.6020 7.3410 8.2310 89.54 

74.56 

66.15 

I 6.4829 (- 1.8) 7.2459 (- 1.3) 8.1550 (-0.9) 89.18 (-0.4) 0.648 0.102 1.032 

74.38 (-0.2) 

66.76 (0.9) 

Note: The first line of every data set represents the corresponding experimental value. The Roman symbols I, II, III, and IV denote the results obtained for 

electrostatic charges calculated at MP2/6-3 1 G **, B3LYP/6-3 lG**, HF/6-3 lG**, and scaled by 0.9, and respectively at HF/6-3 lG** and unscaled. The 

values in parentheses represent the procentual difference relative to experimental values. 

‘For monoclinic systems, only angles are given. For triclinic systems, the cell angles and the cell angle errors are given in the order. For orthorhombic crystal 

systems, a value of 90.0 is indicated only for the experimental structure. 

by = the net rotation of the molecule and the net translation of the center of mass of the molecule. 

‘F = structural shit? factor; defined in equation (3). 
Table 1. Comparison of the Crystallographic Parameters as Determined in Molecular Packing Calculations to the 

Corresponding Experimental Values for Different Molecular Structures (continued) 

Data 

Set C 

Crystal symm. a (4 b (A) c (4 (“)” x(ab FC 

II 

III 

Iv 

-HNIw [35] 

I 

II 

III 

Iv 

6.4802 (- 1.8) 7.2362 (- 1.4) 8.1431 (-1.1) 

(“1 

E 

0.756 0.110 1.106 

6.4663 (-2.1) 7.2347 (- 1.4) 8.1559 (-0.9) 0.115 1.156 

6.4332 (-2.6) 7.2131 (-1.7) 8.1506 (- 1.0) 0.149 1.419 

16 P2Jn 12.5166 

12.4881 (-0.2) 1.932 0.140 1.033 

12.4792 (-0.3) 1.964 0.137 1.009 

12.4924 (-0.2) 1.876 0.138 0.986 

12.4972 (-0.2) 1.780 0.141 0.945 

17 -HNIw [35] Pb2,a 13.0063 

I 12.9254 (-0.6) 0.690 0.113 0.972 

II 12.9137 (-0.7) 0.659 0.117 1.002 

III 12.9025 (-0.8) 0.626 0.120 1.017 

Iv 12.8807 (-1.0) 0.419 0.126 1.059 

18 -m [35] P2,/n 8.1700 109.17 

I 7.9099 (-3.2) 109.12 (0.0) 6.904 0.230 2.319 

II 6.714 0.232 2.274 C 7.9090 (-3.2) 109.10 (-0.1) 

8.8278 

8.8578 (0.3) 

8.8466 (0.2) 

8.8334 (0.1) 

8.8063 (-0.2) 

9.6764 

9.5342 (- 1.5) 

9.5285 (- 1.5) 

9.5257 (- 1.6) 

9.5171 (-1.6) 

13.2310 

13.5148 (2.1) 

13.4987 (2.0) 

89.10 (-0.5) 

74.47 (-0.1) 

66.79 (1.0) 

89.14 (-0.4) 

74.40 (-0.2) 

66.86 (1.1) 

89.16 (-0.4) 

74.55 (0.0) 

67.03 (1.3) 

106.752 

105.13 (- 1.5) 

106.75 (- 1.5) 

105.15 (- 1.5) 

105.21 (- 1.4) 

* 90.0 

0.891 

1.291 

13.3499 

13.463 1 (0.8) 

13.4489 (0.7) 

13.4371 (0.7) 

13.3963 (0.3) 

11.6493 

11.7522 (0.9) 

11.7469 (0.8) 

11.7382 (0.8) 

11.7154 (0.6) 

14.8760 

14.9339 (0.4) 

14.9148 (0.3) 

Note: The first line of every data set represents the corresponding experimental value. The Roman symbols I, II, III, and IV denote the results obtained for 

electrostatic charges calculated at MP2/6-3 1G **, B3LYP/6-3 lG**, HF/6-3 lG**, and scaled by 0.9, and respectively at HF/6-3 lG** and unscaled. The 

values in parentheses represent the procentual difference relative to experimental values. 

‘For monoclinic systems, only angles are given. For triclinic systems, the cell angles and the cell angle errors are given in the order. For orthorhombic crystal 

systems, a value of 90.0 is indicated only for the experimental structure. 

b 

x = the net rotation of the molecule and the net translation of the center of mass of the molecule. 

“F = structural shift factor; defined in equation (3). 

1 . 
. . 

. . 

Table 1. Comparison of the Crystallographic Parameters as Determined in Molecular Packing Calculations to the 

Corresponding Experimental Values for Different Molecular Structures (continued) 

1ata Crystal symm. 2 a (4 b (A> c (4 0” (“I x(A)~ FC 

Set 

III 13.4836 (1.9) 7.9094 (-3.2) 14.8961 (0.1) 109.08 (-0.1) 6.591 0.233 2.241 

Iv 13.4486 (1.6) 7.9096 (-3.2) 14.8584 (-0.1) 109.01 (-0.1) 6.225 0.241 2.175 

19 DNPMTA [47] P2,lc 4 9.345 8.284 11.566 105.6 

I 9.2282 (- 1.3) 8.2258 (-0.7) 11.4319 (-1.2) 105.37 (-0.2) 1.204 0.030 0.807 

II 9.2415 (- 1.1) 8.2346 (-0.6) 11.3959 (- 1.5) 105.34 (-0.2) 1.222 0.036 0.848 

III 9.2377 (-1.1) 8.2298 (-0.7) 11.4089 (-1.4)’ 105.40 (-0.2) 1.221 0.034 0.828 

Iv 9.2202 (- 1.3) 8.2020 (- 1 .O) 11.4041 (-1.4) 105.57 (0.0) 1.372 0.038 0.943 

20 MTNANL [48] P21/c 4 14.1290 7.3740 10.6140 95.07 

I 13.7905 (-2.4) 7.3776 (0.0) 10.65 15 (0.4) 94.35 (-0.8) 0.302 0.166 1.236 

II 13.7998 (-2.3) 7.3607 (-0.2) 10.6446 (0.3) 94.33 (-0.8) 0.259 0.165 1.212 

III 13.7958 (-2.4) 7.3532 (-0.3) 10.6319 (0.2) 94.36 (-0.7) 0.323 0.163 1.216 

Iv 13.8256 (-2.1) 7.3265 (-0.6) 10.5854 (-0.3) 94.42 (-0.7) 0.388 0.159 1.160 

21 KOFKIZ [39] PC 4 11.300 6.340 12.230 102.40 

I 11.5003 (1.8) 6.2393 (- 1.6) 12.3482 (1.0) 102.58 (0.2) 4.443 0.180 1.508 

0.420 0.104 

II 11.4945 (1.7) 6.2486 (- 1.4) 12.3206 (0.7) 102.71 (0.3) 4.372 0.147 1.406 

0.603 0.106 

III 11.5197 (1.9) 6.2452 (- 1.5) 12.3198 (0.7) 102.90 (0.5) 4.453 0.140 1.482 

0.583 0.125 

Iv 11.4859 (1.6) 6.2486 (- 1.4) 12.2657 (0.3) 103.04 (0.6) 4.406 0.096 1.346 

0.817 0.121 

22 JEDSUG [49] P21212, 4 5.9120 7.9280 13.9510 90.0 

Note: The first line of every data set represents the corresponding experimental value. The Roman symbols I, II, III, and IV denote the results obtained for 

electrostatic charges calculated at MP2/6-3 1G **, B3LYP/6-3 lG**, HF/6-3 lG**, and scaled by 0.9, and respectively at HF/6-3 lG** and unscaled. The 

values in parentheses represent the procentual difference relative to experimental values. 

aFor monoclinic systems, only angles are given. For triclinic systems, the cell angles and the cell angle errors are given in the order. For orthorhombic crystal 

systems, a value of 90.0 is indicated only for the experimental structure. 

by = the net rotation of the molecule and the net translation of the center of mass of the molecule. 

‘F = structural shift factor; defined in equation (3). 
Table 1. Comparison of the Crystallographic Parameters as Determined in Molecular Packing Calculations to the 

Corresponding Experimental Values for Different Molecular Structures (continued) 

Data 

Set 

Crystal symm. z a (4 b (A) c (4 0” (9 am F” 

I 5.9731 (1.0) 7.8660 (-0.8) 13.7991 (-1.1) 2.614 0.096 1.049 

II 5.9646 (0.9) 7.8495 (- 1.0) 13.8041 (- 1.1) 2.469 0.093 1.027 

III 5.9576 (0.8) 7.8449 (- 1.0) 13.7986 (-1.1) 2.399 0.097 1.026 

Iv 5.9220 (0.2) 7.8140 (- 1.4) 13.8098 (- 1.0) 2.029 0.089 0.994 

23 JEHLAJ [50] P31 3 10.9230 10.9230 7.8880 1 20.0d 

I 10.8959 (-0.2) 10.8959 (-0.2) 7.93 15 (0.6) 1.463 0.037 0.369 

II 10.8808 (-0.3) 10.8808 (-0.4) 7.9234 (0.4) 1.436 0.027 0.467 

III 10.8737 (-0.5) 10.8735 (-0.5) 7.9132 (0.3) 1.367 0.021 0.451 

M”EkN~O8 [51] 

10.8417 (-0.7) 10.8417 (-0.7) 7.8970 (0.1) 1.208 0.009 0.547 

24 P21/m 2 6.540 6:195 6.060 123.65 

I 6.6364 (1.5) 6.2481 (0.9) 6.2207 (2.7) 124.08 (0.3) 0.212 0.084 1.472 

II 6.6380 (1.5) 6.2391 (0.7) 6.2211 (2.7) 124.09 (0.4) 0.255 0.083 1.465 

III 6.6345 (1.4) 6.2424 (0.8) 6.2273 (2.8) 124.07 (0.3) 0.186 0.089 1.502 

Iv 6.6179 (1.2) 6.2 179 (0.4) 6.2092 (2.5) 123.94 (0.2) 0.105 0.082 1.294 

25 GEJXAU [52] P21fc 4 20.9520 9.4770 6.5710 96.29 

I 20.8355 (-0.6) 9.3867 (- 1 .O) 6.4843 (- 1.3) 96.80 (0.5) 1.706 0.098 0.905 

II 20.8601 (-0.4) 9.3693 (- 1.1) 6.4801 (- 1.4) 96.64 (0.4) 1.734 0.102 0.941 

III 20.8566 (-0.5) 9.3744 (-1.1) 6.4740 (- 1.5) 96.73 (0.5) 1.637 0.099 0.914 

I&NAM01 [53] 

20.8399 (-0.5) 9.3484 (- 1.4) 6.4494 (- 1.4) 96.89 (0.6) 1.274 0.097 1.100 

26 P21lc 4 9.060 9.150 12.330 109.940 

I 9.0568 (0.0) 9.0915 (-0.6) 12.3615 (0.3) 110.50 (0.5) 1.705 0.027 0.515 

II 9.0452 (-0.2) 9.0928 (-0.6) 12.3436 (0.1) 110.40 (0.4) 1.678 0.03 1 0.491 

Note: The first line of every data set represents the corresponding experimental value. The Roman symbols I, II, III, and IV denote the results obtained for 

electrostatic charges calculated at MP2/6-3 1G **, B3LYP/6-3 1 G**, HF/6-3 lG**, and scaled by 0.9, and respectively at HF/6-3 lG** and unscaled. The 

values in parentheses represent the procentual difference relative to experimental values. 

aFor monoclinic systems, only angles are given. For triclinic systems, the cell angles and the cell angle errors are given in the order. For orthorhombic crystal 

b 

systems, a value of 90.0 is indicated only for the experimental structure. 

x = the net rotation of the molecule and the net translation of the center of mass of the molecule. 

‘F = structural shift factor; defined in equation (3). 

dFor P3 1 and P61, the angle = 120 is indicated. 

. 

. 
. . 

Table 1. Comparison of the Crystallographic Parameters as Determined in Molecular Packing Calculations to the 

Corr&ponding Experimental Values for Different Molecular Structures (continued) 

)ata Crystal symm. z a (& b @I c (4 (“I” (0) x (A)b F” 

Set 

III 9.0467 (-0.1) 9.0813 (-0.8) 12.3390 (0.1) 110.42 (0.4) 1.589 0.032 0.509 

Iv 9.0444 (0.2) 9.0477 (- 1.1) 12.3149 (-0.1) 110.40 (0.4) 1.465 0.039 0.605 

27 NABMUYOl [54] C2 2 10.7260 5.9920 10.4000 110.01 

I 10.5180 (-1.9) 5.9524 (-0.7) 10.3705 (-0.3) 109.77 (-0.2) 0.333 0.011 0.935 

II 10.5058 (-2.10) 5.9488 (-0.7) 10.3650 (-0.3) 109.72 (-0.3) 0.228 0.012 0.996 

III 10.4796 (-2.3) 5.9423 (-0.8) 10.3658 (-0.3) 109.63 (0.3) 0.000 0.014 1.117 

Iv 10.4440 (-2.6) 5.9223 (- 1.2) 10.3586 (-0.4) 109.50 (-0.5) 0.307 0.019 1.322 

28 DILFUZ [55] P21/n 2 5.9716 12.0170 11.8407 97.114 

I 5.9169 (-0.9) 12.0507 (0.3) 11.4238 (-3.5) 95.98 (- 1.2) 0.786 0.017 1.720 

II 5.9120 (-1.0) 12.0456 (0.2) 11.4207 (-3.5) 95.97 (- 1.2) 0.741 0.014 1.737 

III 5.9094 (- 1 .O) 12.0530 (0.3) 11.3882 (-3.8) 95.78 (- 1.4) 0.829 0.018 1.883 

Iv 5.8901 (-1.4) 12.0476 (0.3) 11.3627 (-4.0) 95.65 (- 1.5) 0.754 0.015 2.027 

29 NOETNA02 [56] P21/n 4 11.8200 6.1620 18.2290 96.10 

I 11.7226 (-0.8) 6.0508 (- 1.8) 17.7506 (-2.6) 95.49 (-0.6) 1.258 0.17 1.570 

II 11.7311 (-0.8) 6.0453 (- 1.9) 17.7284 (-2.7) 95.42 (-0.7) 1.308 0.187 1.638 

III 11.7152 (-0.9) 6.0407 (-2.0) 17.7191 (-2.8) 95.36 (-0.8) 1.254 0.197 1.697 

Iv 11.6977 (- 1 .O) 6.0219 (-2.3) 17.7022 (-2.9) 95.30 (-0.8) 1.291 0.219 1.846 

30 ACENIH [57] c2/c 4 26.9350 9.1740 6.1220 101.90 

I 26.783 1 (-0.6) 9.2170 (0.5) 5.9955 (-2.1) 101.78 (0.4) 0.204 0.036 0.925 

II 26.7718 (-0.6) 9.2189 (0.5) 5.9895 (-2.2) 101.77 (0.4) 0.221 0.083 0.968 

III 26.7416 (-0.7) 9.2046 (0.3) 5.9938 (-2.1) 191.67 (0.3) 0.103 0.037 0.936 

Iv 26.6814 (-0.9) 9.1524 (-0.2) 5.9979 (-2.0) 101.44 (0.1) 0.133 0.043 0.935 

late: The first line of every data set represents the corresponding experimental value. The Roman symbols I, II, III, and IV denote the results obtained for 

electrostatic charges calculated at MP2/6-3 1G **, B3LYP/6-3 lG**, HF/6-3 lG**, and scaled by 0.9, and respectively at HF/6-3 lG** and unscaled. The 

values in parentheses represent the procentual difference relative to experimental values. 

aFor monoclinic systems, only angles are given. For triclinic systems, the cell angles and the cell angle errors are given in the order. For orthorhombic crystal 

systems, a value of 90.0 is indicated only for the experimental structure. 

by = the net rotation of the molecule and the net translation of the center of mass of the molecule. 

‘F = structural shift factor; defined in equation (3). 
4.5 

r 

4.0 4 I 

1 

-T 

3.5 - 

I 

IL I 

6 z 3.0 - 

I2 

c' 25- 

.- - _ 

l MP2 

n BJLYP I 

. 0.9"HF ' ; 

VHF 14 

0 5 10 15 20 25 30 35 

Crystal Index 

Figure 2. The Calculated Structural Shift Factor F (Equation [3]) for the Crystal 

Structures. The Crystal Index Corresponds to the Number of the Crystal in 

Table 1. The Horizontal Lines at 1 and 2 Are Marked for a Clearer View of the 

Distribution of Points. 

lack of data at low temperatures. Consequently, the aforementioned comparison considers the 

deviations of the predicted geometrical parameters from the experimental values obtained at 

room temperature. It can be observed from the data given in Table 1 that the predicted lattice 

dimensions either underestimate or overestimate the experimental values. Consequently, there is 

not a general trend of the relationship between the predicted and the experimental geometric 

lattice periods, despite the small deviations between the two sets of values. 

The influence of the level of ab initio calculations on the final crystallographic paramenters is 

also illustrated by the results in Table 1. The difference in the predicted geometrical parameters 

is less than 1.0% when correlated and uncorrelated ab initio methods are used. In addition, there 

is not a clear trend of the degree of accuracy with the ab initio level of calculations. In 19 of the 

systems, the accuracy increases when the HF charges are replaced with those obtained at the 

. 

18 
B3LYP and MP2 levels, but, in the other 11 cases, the accuracy decreases. The maximum 

difference of the structural shift factors with the different levels of calculation is less than 0.27%. 

It can also be seen from the results in Table 1 that, when the electrostatic charges calculated 

at HF level are scaled by the 0.9 factor, the corresponding predicted geometrical parameters are 

very close to those obtained at MF2 level. Moreover, the corresponding structural shift factors 

have values intermediate between the MP2 and HF values. 

The lattice energies predicted by different models are given in Table 2. As can be seen by 

comparing the results for MP2, B3LYP, and HF methods, the use of the correlated methods 

result in a decrease in the absolute lattice energy. This effect can be understood as a consequence 

of the decrease in the absolute value of the electrostatic energy, which is attractive. The 

variations in the absolutes values of the HF lattice energies are between 8.5 and 17.5%, relative 

to the MP2 energies, with the average deviation 12.8% (see Figure 3). The use of the 0.9 scaling 

factor reduces these deviations to the range O-7.8%, with the average deviation 4.1%. Finally, 

the B3LYP lattice energies are, as expected, much closer to the MP2 energies, with the range of 

variations 1.5-3.9% and average deviation 2.6%. These results indicate that the lattice energies 

differ significantly for sets of electrostatic charges calculated with ab initio methods that do not 

include electron correlation. These differences can be decreased by a factor of -3 by scaling the 

HF charges. Another important result is that DFT can provide charges that give an accuracy 

(within 2.6%) for the lattice energy that is comparable to those determined at the MP2 level. 

These results are important since the computational times for_ B3LYP calculations are 

significantly lower than those for MP2. 

The calculated lattice energies can also be compared to experimental sublimation enthalpies 

in Table 2. For RDX (CTMTNA), HMX @-HMX, OCHTETO3) and dimethylnitramine 

(METNAMO8) crystals the agreement of the MP2 energies to the experimental values is very 

good, while for tetryl (NTNANL) the difference of 15.7 kJ/mol is within the range 12-17 kJ/mol 

considered acceptable by Kitaigorodsky [5]. Despite the limited number of experimental values 

19 
Table 2. Comparison of the Experimental and Calculated Lattice Energies for Different 

Sets of Electrostatic Charges 

” I 

1 ~CTMTNA 

2 CIWMEAlO 

3 KOFKAR 

4 NOHTAZ 

5 KOFKEV 

6 B-M 

7 OCHTET 

8 OCHTET03 

9 CATJIQ 

10 JEXLUT 

11 J-Exhm 

12 JEXMEE 

13 KEm 

14 JEXMAA 

15 SECVOL 

16 HNW (s-phase) 

17 HNTW (B-phase: 

18 mlw (Ir-ph=e) 

19 DNPMTA 

20 h4TNANL 

21 KOFKIZ 

22 JEDSUG 

23 JEHLAJ 

24 MJZTNAMO8 

25 GEJXAU 

26 NXEiNAMOl 

27 NAEMUYOl 

28 DILFUZ 

29 NOETNA02 

30 ~ACENIH 

&ub 

(kT/mol) 

130.1 [58] 

175.2 [SS] 

161.9 [59] 

133.8 f 1.6 [60] 

69.87 [61] 

T 

W2/6-31G”’ 

- 130.09 

- 113.01 

- 116.55 

- 141.45 

- 120.00 

- 180.23 

- 179.15 

- 168.24 

- 182.50 

- 178.54 

- 169.22 

- 172.98 

- 184.42 

- 176.33 

- 187.66 

- 186.77 

- 181.29 

- 175.31 

- 140.60 

- 149.53 

-262.18 

- 124.22 

- 180.70 

- 70.26 

- 171.87 

- 131.84 

- 169.28 

-216.09 

- 166.55 

- 186.20 

Lattice Energies 

WI1 

B3LYP/6-31G”” 

- 133.68 

-116.40 

- 119.40 

- 145.35 

- 122.66 

- 185.02 

- 184.66 

- 173.44 

- 187.59 

- 184.32 

- 172.11 

- 178.48 

- 190.46 

- 182.29 

- 192.30 

- 192.82 

- 186.28 

- 180.90 

- 142.78 

- 153.81 

-267.98 

- 128.89 

- 187.76 

-71.20 

- 174.31 

- 134.80 

- 173.70 

- 220.50 

- 163.68 

- 188.32 

31) 

0.9 HF/6-3 lG** 

- 136.05 

- 118.81 

- 119.61 

- 145.99 

- 122.20 

- 187.01 

- 188.74 

- 178.11 

- 196.88 

- 186.70 

- 177.36 

- 179.86 

- 192.56 

181.97 

- 193.63 

- 196.52 

- 190.54 

- 186.15 

- 142.60 

- 158.30 

- 265.78 

- 131.24 

- 192.29 

-70.21 

- 175.69 

- 137.57 

- 180.86 

- 209.57 

- 172.29 

- 191.61 

IHF/~-~~G**I 

- 148.18 

- 129.07 

- 129.26 

- 157.25 

- 131.95 

- 204.45 

- 208.75 

- 197.67 

-213.26 

- 200.43 

- 190.98 

- 196.13 

- 208.80 

- 196.64 

- 209.42 

-210.88 

-201.81 

- 198.61 

- 154.30 

- 170.57 

- 288.98 

- 145.14 

-209.63 

- 76.25 

- 191.41 

- 148.40 

- 196.26 

-241.50 

- 181.04 

- 205.65 

available for comparisons, it can be seen that a significant improvement in the accuracy of the 

predicted lattice energies can be obtained by using the electrostatic charges determined by 

electron correlated methods. The scaling of the HF charges also leads to improvements of the 

predicted energies, but the differences from the experimental values are larger than those obtained 

when the charges are calculated with electron correlation methods. 

. 

20 
I 

I I 

I 

i . 

24 

-2 

0 B3LYP 1 

I 

q 0.9*HF 

AHF , 

Figure 3. The Percent Differences Between the Lattice Energies and Those Based on the 

MP2 Values. The Crystal Index Corresponds to the Number of the Crystals in 

Table 1. The Three Horizontal Lines Indicate the Average Deviations for the 

Energies Calculated Using the B3LYP (<pl> = 2.6%), 0.9*HF (<p2> = 4.1%) 

and HF (cp3> = 12.8%) Sets of Charges. 

21 

Crystal Index 
The relative stability of different polymorphic phases of the HMX and HNIW crystals has also 

been investigated. The calculated MP2 lattice energies for the @, a, and 6 phases of HMX are 

- 180.23, - 179.15 and - 168.24 kJ/mol, respectively. These values support the polymorph 

stability ranking p > a > 6 found experimentally by McCrone [62]. Also, the calculated lattice 

energies per molecule for the E-, p-, and y-HNIW phases of - 186.77, - 181.29, and 

- 175.3 1 kJ/mol, respectively, are consistent with the stability ranking E > p > y reported by 

Russell et aL [4]. 

5. Conclusions 

An investigation has been done on the transferability of a 6-exp Buckingham potential 

previously developed for the a-RDX crystal [l] to 30 crystals, consisting of acyclic, monocyclic, 

or polycyclic nitramines. The intermolecular potential includes Coulombic interactions between 

electrostatic charges. These charges were determined from fits to ab initio electrostatic potentials 

calculated for the individual molecules in the experimental configurations. 

The tests of this potential for the set of 30 crystals have been performed using molecular 

packing calculations. Accurate values of the crystal lattice energy have been obtained by 

employing the accelerated convergence technique for the dispersion and Coulombic lattice sums. 

Four different electrostatic models, have been considered with charges determined at HF, B3LYP, 

and MP2 levels, and with charges obtained at HF level uniformly scaled by a factor of 0.9. The 

predicted geometries indicate a good agreement with the experimental values for the great 

majority of the crystals in the study. For 90% of the crystals, the structural shift factor was less 

than 2.0, while for 50% of them it is less than 1.0. 

There is only a small influence, generally below l%, on the crystallographic parameters by the 

set of electrostatic charges used. However, the lattice energies are strongly dependent on the 

electrostatic model. In particular, the best overall agreement with the experimentalattice 

energies was obtained by using Ml?2 calculated charges. The lattice energies calculated using the 

. 

22 
B3LYP charges overestimate the MP2 energies by about 2.6%, while the overestimation in the 

case of HF charges is about 12.8%. The procedure of uniformly scaling the HF charges, [lo, 251 

decreases the differences to about 4.1%. It was also shown that this intermolecular potential 

correctly describes the order of stability of different phases. The predicted stability j3 > a > 6 is 

in accord with the experimental findings [62]. Also, the calculated stability ranking E > b > y for 

HNIW agrees with the previously reported results [4]. 

The success of the present potential energy parameters in describing different types of 

nitramines and different phases at moderate temperatures and low pressure provides incentive to 

further investigate the transferability of this model to other classes of crystals. Incorporation of 

intramolecular motion by relaxing the rigid molecular model will also be investigated in future 

studies. 

23 
INTENTIONALLY LEFT BLANK. 

24 
. 1. 

. 2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

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622618.HSOOO 

A Transferable Intermolecular Potential for Nitramine Crystals 

6. AUTHOR(S) 

Dan C. Sorescu,*t Betsy M. Rice, and Donald L. Thompson* 

7. PERFORMING ORGANWTION NAME(S) AND ADDRESS 

U.S. Army Research Laboratory 

AT-IN: AMSRL-WM-BD 

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*Department of Chemistry, Oklahoma State University, Stillwater, OK 74078 

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Approved for public release; distribution is unhmited. 

13. ABSTRACT(Maximum 206 words) 

We have analyzed the transferability of a previously proposed Buckingham repulsion-dispersion intermolecula 

potential for the explosive hexahydro-1,3,5-trinitro-1,3,5-s-triazine (RDX) (Sorescu, D. C., B. M. Rice, an 

D. L. Thompson, Journal of Physical Chemistry B, vol. 101, p. 798, 1997) to predict the crystal structures (within th 

approximation of rigid molecules) of a database of 30 nitramines. These include acyclic, monocyclic, and polycyclil 

molecules. It is shown that the proposed potential model is able to accurately reproduce the crystallographic structure 

and lattice energies (where available) of these crystals. For the majority of these crystals, the best agreement wit! 

experimental structural and energetic data is obtained in those cases when the electrostatic charges have bee] 

determined using ab initio methods that include electron correlations effects (namely MP2 and B3LYP). The use o 

the electrostatic charges calculated at the Hartree-Fock level results in large deviations of the predicted lattice energie 

from the experimental values. The deviations of the lattice energies can be significantly decreased by scaling th 

electrostatic charges with a constant factor. 

14. SUBJECT TERMS 

nitramine, intermolecular potential energy function, molecular packing 

15. NUMBER OF PAGES 

37 

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