dan c. sorescu, betsy m. rice and donald l. thompson- theoretical studies of solid nitromethane

8/3/2019 Dan C. Sorescu, Betsy M. Rice and Donald L. Thompson- Theoretical Studies of Solid Nitromethane

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AbstractA classical potential to simulate the dynamics of a nitromethane crystal as a functionof temperature and pressure is described. The intramolecular part of the potential wastaken as superposition of bond stretching, bond bending, and torsional angles terms.These terms were parametrized on the basis of the geometric and spectroscopic(vibrational fr equencies and eigenvectors) data obtained using ab initio molecular orbitalcalculations performed at the B3LYP/6-31G level on an isolated molecule. Theintermolecular potential used is of the Buckingham 6-exp form plus charge-chargeCoulombic interactions and has been previously developed by us (Sorescu, D. C.; Rice,B. M.; Thompson, D. L. J. Phys. Chem. 1997, BlOl, 798) to simulate~crystalscontainingnitramine molecules and several other classes of nitro compounds. The analysesperformed using constant pressure and temperature molecular dynamics simulations andmolecular packing calculations indicate that the proposed potential model is able toreproduce accurately the changes of the structural crystallographic parameters asfunctions of temperature or pressure for the entire range of values investigated. Inaddition, the calculated bulk modulus of nitromethane was found in excellent agreementwith the correspond ing experimental results. Moreover, it was determined that thepresent potential predicts correctly an experimentally observed 45 change in methylgroup orientation in the high-pressure regime relative to the low-temperatureconfiguration. The analysis of the linear expansion coefficients and linear compressiondata indicate anisotropic behavior for the unit cell edges.


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Theoretical Studies of Solid NitromethaneDan C. Sorescu,Betsy M. Rice, and Donald1. ThompsonDepartmentof Chemistry,PklahomaState University,Stillwater,Oklahoma74078,and The U. S. Army Research.aboratory,Aberdeen rovingGround, Maryland21005

The Journal ofPhysicalChemistryB@Reprinted romVolume 104, Number 35, Pages 406-8419


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S406 J. Phys. Chem. B 2000,104, 8406-8419

Theoretical Studies of Solid NitromethaneDan C. Sorescu,~~~ Betsy M. Rice,*** and Donald L. Thompson*Depamnt of Chemistry, Oklahoma State University, Stillwa ter, Oklahoma 74078, andThe U. S. Army Research Laboratoq Aberdeen Proving Ground, Maryland 2100.5Received: March 13, 2000; In Final Form: June 13, 2OOQ

A classica l potential to simulate the dynamics of a nitromethane crystal as a function of temperature andpressure is described The intramolecula r part of the potential was taken as superposition of bond stretching,bond bending, and torsional angles terms. These terms were parametrized on the basis of the geometric andspectroscopic (vibra tional frequencies and eigenvectors) data obtained using ab initio molecular orbitalcalculat ions performed at the B3LYP/6-31G* level on an isolated molecule. The intermolecu lar potentialused is of the Buckingham 6-exp form plus charge-charge Coulombic interactions and has been previouslydeveloped by us (Sorescu, D. C.; Rice, B. M.; Thompson, D. L. J. Phys. Chem. 1997, BIN, 798) to simulatecrystals containing nitramiue molecules and several other classes of nitro compounds. The analyses performedusing constant pressure and temperature molecular dynamics simulations and molecular packing calculat ionsindicate that the proposed potential model is able to reproduce accurate ly the changes of the structuralcrystallographic parameters as functions of temperature or pressure for the entire range of values investigated.In addition, the calculated bulk modulus of nitromethane was found in excellent agreement with thecorresponding experimental results. Moreover, it was determined that the present potential predicts correc tlyau experimentally observed 45 change in methyl group orientation in the high-pressure regime relative tothe low-temperature configuration. The analysis of the linear expansion coefficients and linear compressiondata indicate anisotropic behavior for the unit cell edges.

I. IntroductionThis is the seventh in a series of papers describing ourdevelopment and assessmentof interaction potentials to be usedin the study of dynamic processes in energetic materia ls. Ouroriginal intent was to develop a model to study nonreactiveprocesses in the t&amine explosive RDX (1,3,5-hexahydro-1,3,5-s-triazine).1 The potential that was developed consisted

of atom-atom (6-exp) Buckingham potential terms plus elec-trostatic interactions. The Coulombic interactions were obtainedthrough fitting atom-centered partial charges to a quautum-mechanicaJly-determinedelectrostatic potential for a single RDXmolecule whose structure corresponded to that in the crystal atambient conditions. The remaining Buckiugham parameterswere adjusted to reproduce the experimental structure of theRDX crystal at ambient conditions. We found that this interac-tion potential could also describe the geometric parameters andlattice energies of different polymorph ic phases of two othernitramine crystals: the polyc yck r&amine 2,4,6,8,10,12-hexauitrohexaazaisowurtzitane (HNIW, or CL-20)2 and themonocyclic niaamine octahydro-1,3,5,7-tetrauiiro-1,3,5,7-tet-raazacyclooctane (H~vDZ).~sothermal-isobaric molecular dy-namics (NPT-MD) simulations for these crystals predicted cellparameters within a few percent of experimental values, andlittle translational or rotational disorder of the molecules. Furtherinvestigations to explore the limits of transferability of thisinteraction potential to other energetic molecular crystals wereundertaken through performing molecular packing (MP)

* Author to whom correspondence should lx addressed.+ Oklahoma State University.* The U.S. Army Research LaboIsltory, Aberdee n Proving Ground.8 Current mailin g address: Department of Chemistry, University of

Pittsburgh. Pittsburgh, PA 15260.

calculations for 30 r&amine crystals. These included severaltypes of man+ and polycyc lic n&u&es, particularly crystalsof importance in energetic materiak4 For most of the crystals,the predicted structural lattice parameters obtained from mo-lecular packing (IUP) calculations differ by less than 2% fromthe experimental structures, with small rotations and practicallyno translations of the molecules in the asymmetric unit cell. Afurther assessment on the limits of transferability of theinteraction potential was accomplished through molecularpacking calculations of 51 crystals containing non-nitraminemolecules with functional groups common to energetic materi-als? MF calculat ions using this interaction potential reproducedthe crystal structures to within 5% of experiment for these 51non-r&amine systems, ncluding the explos ives pentaerythritolteh-anitrate (PETN), nitromethaue, 2,4,6knitrotoluene (TNT),and several nitrocubane derivatives.More recently we have analyzed the dynamics of theimportaut energetic crystals FDX, HMX, HNTW, and PETNunder hydrostatic compression conditions using NPT-MDsimulations and this intermolecular potentiaL6 In that study wefound that the predicted lattice parameters for the RDX, HklX ,and HNIW crystals are in good agreement with experimentalvalues over the entire range of pressures investigated experi-mentally. For the PETN crystal, the calculated crystallographicparameters were in acceptable agreement with experimental datafor pressures up to 5 GPa. For higher pressures, the disagree-ments of predictions and experiment were attributed to theinadequacy of the rigid-body approximation used to simulatefloppy molecules such as PETN.

The valid ity of the rigid molecular approximation wasassumed n our previous studies.lB6As indicated by OUTesults,this model has been very successful in its ability to describe~0.1.021/jpOOO942q CC: $19.00 0 2000 American Chemical Socie tyPublished on Web 08/15/2000


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Solid Nitromethane

kFigure 1. Repmem ation of the ni tromerhane ctystal uni t cel l wi thodxhombic spacegroup p212121nd 2 = 4 moleculesper unit ce ll.Atom labels are consistentwith the indicesgiven in Table 1.the equilibrium structures of a variety of organic molecularcrysta ls under ambient conditions and with moderate inc reasesin pressureand temperature. However, the physical aud chemicalprocessesof energetic materials that are of most interest occurwithin the regime of high pressuresand temperatures, a regimein which conformational molecular changes become important.Consequently, further developments of the interaction potentialare necessary to describe more realistically the intramolecularmotion, molecular deformations, and the energy flow insidethesecrystals.For this purpose, n the present paper we eliminatethe p&iously used rigid-molecule approximationlm6 and extendthe current intermolecular potential to include a full intra-molecular potential for use n simulations of energetic materials.Particularly, in this work we consider he prototypical explosive,nitromethane.Nitromethane was selected or our first attempt at developinga fully flex ible model of an energetic molecular crystal sincenumerous experimental investigations of its properties under awide range of conditions have been performed, thus providingsignificant data for use in ass&sing the model potential.7-14Single-crystal X-ray diffraction and neutron powder diffractionmeasurements indicate that the low-temperature structure ofcrystalline nitromethane belongs to the orthorhombic spacegroup P2,2,21 with 2 = 4 molecules in the unit c ell (see Figurel). In this [email protected] the methyl group is in the staggeredsymmetric position with respect to the C-N& plane. Atambient pressure, the crystal sym metry was observed to remainunchanged when the tempemture was increased f?om 4.2 to 228K7+9 In the temperature range 243-244 K an intermediatecrystal phase (mesophase) was recently obser~ed,~ followedby transition to the liquid state at 244.73 K No crysta l-lographic details have been provided about the intermediatephase at 243 K.OThe internal rotation of the methyl group in the crystal has

1 received significant attention, since experimental evidenceindicates that th is motion is almost complerely governed byintermolecular interactions. Analyses of the neutron powderdiffmction patterns for deuterated nitromethane at temperaturesF ranging from 25 to 125 K provided temperature-dependentamplitudes of librations of the methyl group about the C-Nbond. Quasielastic neutron scattering spectra8 recorded attemperatures ranging from 50 to 150 K are consis tent withrotations of the methyl groups through 120 jumps ra ther thanthe 60 jumps observed in the gas phase. Furthermore, it wasfound8 that in the crys talline phase the activation energy forthe internal rotation of the methyl group is about 234 cal/mol,significantly higher than the corresponding gas-phase barrier

J. Phys. Chem. B, Vol. ,104, No. 35, 2ooO 8407of 6 cal/mol.15 Inelastic neutron-scattering measurements14 oftunneling splittings aud of the lowest rotational states ndicatedthat the methyl group activation ba rrier is significantly smallerthan the energy of the second excited rotational state by -170callmol. These findings have been confirmed by infrared16 andRamanl measurements, but the corresponding activation ener-gies reported in these studies are slightly higher, namely 401and 576 cal/mol, respectively. Several mechanisms have beenproposed to contribute to the dynamics of methyl groupsinclud ing the enhanced hopping due to interac tions withphonons, band tunneling through thermally broadened excitedstates, or changes of the barrier with temperature.14The influence of pressure on the interna l rotational motionof the methyl group has also been examined. The crystalstructure for iso tropically compressed nitromethane has beendetermined through X-ray diffraction at pressures anging from0.3 to 15.3 GPa, at room temperature.9J2 It was found that thespace group and the packing arrangement remain unchangedrelative to the low-temperature structure. However, the mea-surements indicate a continuous change in the orientation ofthe methyl group with the increase of pressure. For pressuresbelow 0.6 GPa the methyl group is freely rotating. At intermedi-ate pressures (between 0.6 and 3.5 GPa) the rotation of themethyl group is hindered., while for pressu res above 3.5 GPathe orientation of the methyl group becomes fixed. Moreover,it was determined that af pressures above 3.5 GPa, the methylgroup is rotated by 45 relative to the low-temperature config-uration.The ensemble of the above-presented experimental dataprovides many meirics against which to assess he performanceof our interaction potential by molecular dynamics simulations.In this work, we describe such an assessment. n Section II, weprovide a description of OUT otential model and our choice andparameuization of the intramolecular and intermolecular interac-tion terms. In Section III, we provide a brief description ofcomputational details. Section IV containa the results of ourMP and NPT-MD simulationa and a comparison of predictionsof crystal structural parameters with experimental values overa wide range of temperatures and pressures. Summary andconclusions are given in Section V.II. Potential Energy Fuutions

We have assumed that the potential energy for a system ofN niaomethane molecules can be described as the sum of inter-and intramolecular interaction terms:pGN 4 p-*-+&--Q- ) (1)i= l 1 1

The intermolecular potential is the same as described in theearlier stud ies,+ and consists of the superposition of a pairwisesum of Buckingham (6-exp) (repulsion and dispersion) andcoulombic (C) potentials of the form:

andV,(r) = Ati exp(--Btir) - C&r6 (2)

V,cr) = -g$ (3)0

where r is the interatomic distance between atoms a and p, qaand 4~ are the electrosta tic charges on the atoms, and EOs thedielectric permittivity constant of free space. The parameters


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8408 J. Phys. Chem B, Vol. 104, No. 35, 2ooO Sorescu et al.TABLE 1: Force PIeId Parameters for CrystallineNitromethane

atomb char&ewe do not require such a complex function in order toaccomplish the goals described in this work. Thus, we haveassumed a simpler form of the intramolecula r in teractionpotential:Cl -0.305342

N2 0.82060303 -0.47044504 -0.484277Bs 0.143365H6 0.155443H7 0.140652

Morse potential parametersbond D,(kI/mol) .&A-) fl(-QC-N 251.0419414 2.oos501 1.499574N-O 390.3702976 2.459942 1.226747C-H 426.7713101 1.892486 1.09OmO

bending potential p arame tersangle keoJlm ol rad-3 Weg)

C-N-O 294.5211162 117.039960O-N-O 657.8485114 125.890000N-C-H 2244.8140504 107.560708H-C-H 149.9402928 I1 1.3 12289torsionalpotential pammeters

angle v, (kJ/mol) We) mH&-N2-03 (i = 5,6,7) 0.27CQO (0.49y -90.0 3.0k&-C,-N z-04 (i = 5,6,7) 0.27000 (0.49) 90.0 3.0N 2 - ~ 4 - - 0 3 - c 1 240.37076 180.0 2. 0

a The elmtatic charges have been determined by the CHELPGpmxdure as implemented in Gaussian 9417 at the HlS-31G** level .bThe atom designationnumbersare detied in F igure 1. cThe choiceof a torsionalbarrierof 0.49 kJ/mol is also discussed iu tex t.AM, Ed. and CM for different types of atomic pairs have beenpreviously published and have been used in the present studywithout change.The set of partial charges used in these calculations weredetermined through fitting these to the quantum-mechanically-derived electrosta tic nteraction potential for an isolated moleculewhose atoms are arranged in the experimental crystallographicarrangement. These calculations have been done using theCHELPG procedure as implemented in the Gaussian 94package.l We have previously shown45 that for the majorityof the crys tals studied, the best agreement between simulationsand experiment occurs when the set of partial charges isdetermined using methods that employ electron correlationeffects such as second-order Mijuer-Plesset &WI) perturbationtl~eory.~~ owever, this was not true for nitromethane; the bestagreement between the measured and the predicted crystal-lographic lattice parameters was obtained when unscaled partialcharges derived from the Hartree-Fock (HP) wave functionwere used. The lack of improvement in the predicted latticeparameters when electron correlation effects are consideredmight bc due to omission of other important interactions. Thesecould include the omission of the polarization effects ofneighboring molecules in the crysta l when evaluating theelectrostatic charges or the isolated molecule, or the assumptionof a simple charge-charge interaction model when a multipolarinteraction description would be more accurate. Nevertheless,our choice for the set of charges determined at the HF leve l(see Table l), together with the rest of the potential parameters,give a very good representation of the crystallographic param-eters.In a previous study we have developed a complex intramo-lecular interaction potential to describe the unimoleculardecomposition reactions of gas-phase nitromethane.19 However,

to describe the bond stretching, angle bending, and torsionalmotions that occur witbin an isolated molecule. The bondstretches are represented by Morse potentials,Vsaelch i Dti(exp[-*&ri - rf)] - 2 exp[-&(ri - r;O)]}

i=l(5)

where r i are the bond distances, LJeiare the bond dissociationenergies, pi are the curvature parameters, and q arc theequilibrium bond lengths. The six bond stretches that aredescribed by this potential correspond to the six covalent bondsin nitromethane.The bending potentials are representedby harmonic functionsof the form

where ke is the force constant and 80 the equilibrium value ofthe angle. The nine angles used to describe these interactionscorrespond to the HCH, FEN, CNO, and ON0 angles innitromethane.Cosine-type torsional potentials have been used to describethe relative positions of the C-NO2 atoms and the orientationsof the H atoms relative to the C-N-O planes. The potentialshave taken the formvttion = 2 VJl + COS(rn@~ S)] (7)

i= iwhere Va is half of the intramolecular to rsional barrie r, @ isthe torsional angle, and m = 2 or 3. Six of the torsional anglesused to describe hese interactions correspond to HCNO angles,the seventh corresponds to the N-O-O-C torsional angle. Thecomplete l ist of potential parameters from eqs 5-7 is given inTable 1.The bond dissociation energies in eq 5 have been taken fromour previous study of nitromethane in the gas phase,t9 whilethe remaining set of geomeaical equilibrium values and forceconstants in eqs 5-7 were paramettized based on quantummechanical information generated using densiry fuuctionaltheory. These calculat ions have been done for the isolatedmolecule using Beckes three-parameter hybrid methodm incombination with the Lee, Yang, and Parrcorrelation functional~(B3LYP) and the basis set 6-31G**l using the Guussi~ 94package of progtams.r7 Our earlier molecular dynamics studies2*on reactions of gas-phase energetic molecules suggested that apotential energy function fitted to only the structural parametersand normal-mode frequencies could lead to a model thatproduced anomalous and unexpected results, such as nonstatis-tical behavior in the unimolecular decomposition of the mol-ecule. However, when the function was fitted to the ab initioCartesian second derivat ives of the energy, the potential modelproduced the expected statistical behavior in the unimoleculatdecomposition of the molecule. In this study, both the geo-metrica l parameters of the optimized nitromethane molecule and


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Solid Niuomethane J. P&s. Chkm B; Vol. 104, No. 35, Zoo0 8409TABLE 2: Comparison lxtweeu the Experimental, the Scaled Harmonic Vibrational Frequencies Calculated at B3LYP/6-31G*Lev4 and the Predictd Frequencies by Our Force Fields, the Corresponding Projdom (scalar hoduct) of thePredicted Eigenvectors on the Ab Initio F.igenvectors Are Also hdi&ecP

band ref ref ref re f ref B3LYPlw 24a 24b 24c 24d 24e 6-31G*" Me Pgas Ml Pl M2 I 2

Vt 51 50 0.94 117 0.94 157 0.94VS A; 476 477 480 415.2 461 459 0.99 461 0.99 461 0.99V6 A; 599 60s 607 602.5 584 596 0.94 601 0.94 605 0.94vs 4 647 658 656.0 655 657.4 636 602 0.92 605 0.92 605 0.92VA 4 921 918 917.1 917 917.9 892 828 0.93 821 0.92 821 0.92Vll F 1097 1087 1091.0 1103 1099.0 1076 1052 0.99 1053 0.99 1054 0.92VI1 IT 1153 1100 1146.0 1103 1119.0 1101 1098 0.99 1101 0.99 1103 0.99v3 4 1384 1377 1378.8 1379 1380.4 1364 1509 0.95 1508 0.95 1508 0.99v2 4 1397 1397.0 1402 1397.4 1388 1372 0.96 1368 0.96 1368 0.95VI0

z1449 1443 1426 1432 1432 I.00 1434 1.00 1437 0.99

no 1488 1482 1438.0 1426 1444 1434 0.99 1436 0.99 1439 0.99V7 A; 1582 1586 1583.3 1561 1583.8 1615 lH7 1.00. 1618 1.00 1618 1.00Vl 4 296s 2972 2964.3 2%7 2973.9 2981 2961 1.00 2961 0.98 2961 0.98VS 2984.0 3045 3044.0 3070 3083 0.98 3093 1.00 3093 0.98W

;3048 306s 3080.4 306s 3080.0 3100 309s 0.98 309s 1.00 309s 1.00

u B3LYPK31G* values are scaled by 0.%13, as recommended in ref 23. b The columns denoted with Mgas, Ml, and M2 correspond to thereference force f ields for gas phase, for sol id phase (wi th tors ional HCN O barrier of 0.27 kT/mol), and for sol id phase wi th increased tors ionalbarrier (tors ional HCN O barrier of 0.49 Wm ol). reswctivelv. The corresponding project ions of the predicted eigenvectors a~ indicated in columnsPgas, Pi , and P2, rwpeft ively. The frequency&tzI are c&.the ab initio eigenvalues (scaled by a factor of 0.%1323) andthe corresponding eigenvectors of the ab initio Hessian matrixhave been used in the fitting procedure.Special attention was paid in this work to the choice of thetorsional barrier Va corresponding to the H-C-N-O torsionalangles. As indicated in previous experime ntal shldies,**1 0.*4-16au exact value for this barrier is not yet well-lmown and severalvalues have been prom The major difficulties in determininga precise barrier for the internal rotation of the methyl groupwere due to the existence of a complex mechanism thatincorporates enhanced hopping due to interactions with phonons,tunneling effects, and changes of the barrier with temperature.However, it is important to point out that independent ofexperimental technique used the numerical values of theactivation energy for the methyl rotation are quite smal18~10~16and represent only fractions of 1 kcal/mol. In the present studywe have investigated several values for Va potential parametersof H-C-N-O torsions and have analyzed their role on thecrystallographic parameters. The vibrational frequencies pre-dicted by our class ical potential for an isolated niu-omethanemolecule are given in Table 2 along with the corres~nding abinitio values and experimental data In this table we also indicatetbe values of the projections of the eigenvectors obtained fromthe normal-mode analysisusing the proposed potential onto theiiquantum mechanical counterpart. A projection whose magnitudeis one would indicate perfect agreement between the model andthe B3LYP/6-31G* eigcnvectors. A projection that has amagnitude near zero indicates that the atomic motion of thevibration that is predicted by the model i s extremely differentfrom that predicted by the quantum mechanical calculations.The projec tions of the normal-mode eigenvectors generated bydifferent potential models (see below) onto the quantummechanical cigenvectors are also indicated in Table 2.L In an initial attempt we described the interna l methy l grouprotational motion using a 6-fold torsional potential with a barrierof 6 cal/mol, in agreement *th the experimental gas-phasebarrier.15 The vibrational frequencies corresponding to thismodel are indicated in Table 2 where they are denoted as Mgas.As can be seen there is an overall very gd agreement betweenthe entire set of predicted vibrational frequencies and thecorresponding ab initio results. In particular, the frequency ofthe torsional mode vr is practicalIy identical to the corresponding

quantum mechanical value. The corresponding projection of theeigenvector predicted by the model onto the quantum mechan-ical eigenvector is 0.94, indicating also a very good predictionof the vibrational motion associated to this mode. However,when this potential was tested in NPT-MD simulations in theregime of low temperatures and pressures t was found that whiIethe unit cell size and shape of nitromethane were reasonablypredicted the methyl groups of the molecules in the unit cellwere rotated by approximately 30 relative to the experimentalorientation. This fact indicated the need to increase the barrierheight of the torsional H-C-N-O potentials in order toreproduce accurately the crystallographic structure.The second set of potentials we have considered is simila rto the Mgas model but we have changed the HCNO torsional.potential to a 3-fold form and increased the batrier parameterV&-C-N-O) to 0.27 kJ/mol, which corresponds to anoverall barrier for methyl rotation similar to that given in ref14. The complete list of intramolecular parameters for thispotential set is that indicated in Table 1. The modifications ofthe corresponding vibrational frequencies for this model areshown in columns denoted as Ml and Pl in Table 2. It can beseen that the most important variat ions of the vibrationalfrequencies take place for the mode vn which corresponds tothe internal rotation of the methyl group. Overall, exceptingmodes vT and vg (which describes the inversion of the methylgroup), there is good agreement between the predicted, the abinitio calculated, and the experimcnta124sets of vibrationalfrequencies with rm s deviations of 6.9 and 10.8 cm-t, respec-tively. In addition, the results indicate that the model reproducesthe quantum mechanical eigenvcctors very well, with thesmallest projection values being 0.92 for modes ~4 and vs. Aswill be described more fully hereafter, MP ca lculations andNFI-MD simulations using this potential model reasonablyreproduce the experimental crystal structure and molecularconformations for the entire range of temperatures and pressuresinvestigated. Consequently, all the results presented in the nextsections correspond to this choice of potential parametersdenoted as model Ml.

A final choice of torsional potential param eters we have testedcorresponds to an even larger value for Vm(H-C-N-O ) of0.49 kJ/mol. Our resu lts indicate that this potential change hasonly a very small influence on the predicted crystallographic


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8410 J. Phys. Chem. B, Vol. 104, No. 35, 2000TABLE 3: Latt ice Parametersclumge in lattice and molecularand is given in parenthese s)

Sorescu et al.and Energk Obtained in Crystal Packing without Symm etry Constraiuts ( the percentage* parameters after energy m inimization is determined as a fuucl ion of the exper imental geometry

Ianice energy lattice pammet&NE ES a b C a B Y

20.5-52.3 5.1832 6.2357 8.5181 90.000 90.000 9o.ooo

-25.0401 -35.0560 S.2369 6.2653 8.6214 90.001 89.989 89.997(1.W (0.48) (1.21) (0.00) (-0.01) (0-WAd AY A.2 A@ (dW A@ (deg) AY (deg)-0.037 -0.105 -0.014 3.44 3.02 6.41

aNonbonded (NB) and elec~ostatic ES) attice energiesper molecule n kJ/mol. b Lattice dimensionsu, b, and c in angstroms,and anglesa, fl,and y in degrees.c Cutoff pammeterasdescribedn text. d Experimenta l alues rom ref 7. eEstimatedusing he theoretical heat of sublimationof-47.3 kI/mol as provided by Politzer. f Change n titional coordinates f molecularcentroi& for ni&omethanemolecule. 8 Change n Euleranglesof mo lecular cen&oi& for nitromethane.parameters relative to the Ml model and that this influence i sparticu larly limited to the region of low temperatures. Conse-quently we will make only limited references to this potentialchoice in the present work. For completeness, we indicate inTable 2 columns M2 and F2, the predicted vibrational frequen-cies and the corresponding projections for this potential model.As can be seen only the value of the to rsional frequency vs isincreased by about 40 cm- relative to the Ml value while theprojection of its eigenvector on the corresponding ab initiovector remains 0.94. The large value of this projection, closeto unity, indicates that even for this high barrier value the modelis representing correctly the corresponding vibrational atomicmotions.KU. Computational Detai ls

Molecular Packing Calculations. A fu-st set of calculationsused to test the semiempirical intermolecular potential energyfunctions proposed here is based on the use of molecular packingcalculations,25 in which the lattice energy of the crystal isminimized with respect to the structural degrees of freedom ofthe crystal. These calculations have been done using thealgorithm proposed by Gibson and Schemgaz7 for efficientminimization of the energy of a fully variable lattice composedof rigid molecules and implemented in the program LIvfIN.=The nonbonded interactions were cut off with a cubic splinefunction from PO to Qo, to ensure the continuity of the functionand its frost derivative. Here o is the value of r in eq 2 at whichV&r ) = 0 and dV,&)/dr < 0. The parameters P and Q. whichspecify the start and the end of the cubic feather (see refs 1 and27 for details), were set to 20.5 and 20.0, respectively. Thecoulombic potential terms of the form given in eq 3 are summedover the lattice using the Ewald technique as previouslydescribed. Finally, the effect of pressure on the crystalJographicparameters has been simulated by adding a potential term ofthe form P (V - VO), where VO s the volume of a suitablychosen unit cell at zero pressure.coastant-pressure and -Temperature Mokcuhr Dynam-ics Cahdations. The dynamics of nitromethane as a functionof temperature and pressure have been investigated using NPT-MD simulations based on the total potential described in eqsl-7. For comparison we have also performed calculations usingthe rigid-body approximation1-6 of the molecules in the system.In all simulations we have used the Nos&Hoover thermo-stat-barostat algorithmz9 as implemented in the programDLJOLY-2.0,30 to simulate the crystals at various temper-atures and pressures. In this case, the equations of motion formolecules and the simulation cell are integrated using the Verlet

leapfrog scheme.31 In the case of rigid-molecu les simulationsthe molecular rotational motion is handled using Finchamsimplicit quaternion algorithm.32The MD simulation cells consist of boxes containing 5 x 4x 3 crystallographic unit cells. This choice of the simulationbox ensures the use of a cutoff distance for the intermolecula rpotentials of about 10 A. The initia l configuration comspondingto the lowest temperature was chosen to be identical to that forthe low-temperature experimental slructure. The system was thenequilibrated at that temperature and atmospheric pressure. Inall production runs done using the No&-Hoover implementationfor the NPT ensemble, the system was integrated for 34000time steps (1 time step = .75 x lo-l5 s), of which 4000 stepswere equilibration. In the equilibration period, the veloc itieswere scaled after every 5 steps so that the internal temperatureof the crysta l mimicked the imposed external temperature. Then,properties were calculated and accumulated for averaging overthe next 30000 integration steps n the simulation. In subsequentruns, performed at successively igher temperatures or pressures,the initia l configurations of the molecular positions and veloc i-ties were taken from the previous simulation at the end of theproduction mn.The lattice sums were calculated subject to the use ofminimum-image periodic boundary conditions in all dimen-sions.31 The interactions were determined between the s ites(atoms) in the simulation box and the nearest-image si tes withinthe cutoff distance. In these calculations, the coulombic long-range interactions were handled using Ewalds method.31The main quantities obtained from these simulations werethe average lattice dimensions and the corresponding volumeof the unit cell. Additional information about the structure ofthe crystal has been obtained by calculating the radial distribu-tion functions (RDF) between different atomic sites . Suchquantities have been calculated from recordings done at every10th step during the trajectory integrations.IV. Results and Discwwions

A. Molecular Packing Calculations. The results of MPcalculations without symmetry constraints are presented in Table3. As can be seen the predicted structural lattice parameters fornitromethane differ by less than 1.21% from the experimentalvalues reported by Trevino et al. Also, there are smalltransla ti&s but slightly larger rotations (with a maximumdeviation of 6.4 ) of the molecule in the asymmetric unit cell.Using the I-IF set of charges, the total latti ce energy is predictedto be -60.1 Wmol. This value compares acceptably well withthe lattice energy of -52.3 kJ/mol that has been estimated using


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Solid Nitromethane J. Phys.Chem. B; Vol. 104, No. 35, 2OCQ 8411TABLE 4: Lattice hramete rs Obtained in NPT-MD Cal&tions for Nitrometbane as a Function of Temperature; thecalculated TbermaI l3xpahon CNftkkslts (x) at 250 K Are Also lndiae

latt ice dimensions

,

T(K) a(A) HA) cc & a@&) i%d%) y(deg) volume(A3)4.2b 5.1832 6.2357 8.5181 275.312578.P 5.1983 6.2457 8.5640 278.0476

228-P 5.2440 6.3200 8.7300 289.33034.2 5.2116(0.54) 6.3416(1.69) 8.6464 (LSO) 89.998 89.999 9o.ooo 285.7666 (3.79)25.0 5.2134 6.3608 8.6935 90.012 90.018 89.996 288.300050.0 5.2184 6.3794 8.7266 90.001 90.034 9o.ooo 29O.sm78.0 5.2195 (0.40) 6.4032(2.52) 8.7543 (2.22) 89.991 89.996 89.991 292.5833 (5.22)100.0 5.2222 6.4173 8.7734 90.001 89.962 90.007 294.0166125.0 5.2267 6.4329 8.7979 89.987 89.994 90.002 295.8166150.0 5.2298 6.4605 8.8204 89.974 89.991 90.010 298.0166175.0 5.2373 6.4889 8.8606 89.995 90.005 89.987 301.1166200.0 5.2452 6.5167 8.8808 90.016 90.012 90.020 305.3166228.0 5.2534 (0.18) 6..5481(3 .60) 8.9195 (2.17) 90.015 90.020 ""~ 90.043 303.5667 (4.92)250.0 5.2620 6.5691 8.9561 90.001 89.993 89.946 306.8167f 68.9 x lo* 181.7 x 104 131.9 x 104 380.5 x 106a The values in mmUhe see represent the wntage di fferences relative to the avai lable exper imental m sults. Ir Expwimental data from ref 7.c The units for the &eat aucl volkne expansion coeff icients are K- l .

the relation U, w -A&,r - 2RT.33 n this analysis we haveused as the heat of sublimation for nitromethane the value of47.2 kJ/mol estimated theoretically by Politzer.B. NTT-MD Calculmtions. NPT-MD simulations of nitro-methane were used to predict the crystal structure of ni-tromethane over a large range of temperatures and pressures.We will first examine thermal effects on the crystallographiccell and molecular parameters at 1 atm, and compare themagainst experimental values.Bl. Temperature Efects. Average unit c ell edge lengths andvolumes determined from NPT-MD simulations for the flexiblemodel for temperatures ranging from 4.2 to 250 K are given inTable 4. These data are represented in Figure 2, along w ith thecorresponding experimental values and the NPT-MD resultsobtained using the rigid-body approximation. For the flexiblemodel, the NPT-MD lattice dimensions obtained at T = 4.2 Kare in very close agreement with those determined in the Mpcalculations and with the experimental values. At this temper-ature, the percentage differences between the predicted and theexperimental lattice dimensions arc 0.54% 1.69%, and 1.50%for the a, b, and c axes, respectively. The deviation of thepredicted unit cell volume from the experimental value at thistemperature is 3.79%. Tbis g& agreement is decreased onlysligh tly with an increase in temperature. At T = 78 K, the celledge lengths and the unit cell volume agree with the experi-mental values to within 2.52% and 5.22%, respective ly. At thehighest temperature where experimental data are available (228K), the deviations from experiment for the cell edges arc lessthan 3.60% while the difference is 4.92% for the unit ce llvolume. Also, the unit cell angles remain close to 90.0 for theentire temperature range analyzed, as expected for the orthor-hombic symmetry of the crystal. For comparison, calculationsusing the M2 potential model indicate slightly larger deviationsfor the predicted lattice parameters from experimental valuesof 1.3156, 1.038, and 1.72% at T = 4.2 K and OH%, 3.618,and 2.13% at T = 228 K for the a, b, and c axes, respect ively.The linear and volume thermal expansion coefficients ex-tracted from the data are also given in Table 4. The expansionof the lattice is highly anisotropic with the largest length changesalong the b and c axes. These effects can be partially attributedto the internal rotation of the methyl group. To illustrate ourargument, consider the limiting case n which a nitromethanemolecule is arranged in a unit c ell such that the C-N bond isparallel to the a axis. Changes in the positions of the hydrogen

a)

0 50 loo 150 200 250 300

330320 W

s 310e3w1

3 290=u 260=E3 270

250250

Tempentwe (K)

1l l UP

ElA M0.R0 MD.REL

0 50 100 150 200Temperature (K)

250 300

Fii 2 Variation of the lattice dimen sions (a) and unit cell volume(b) with temperature from NPT-M D simulations using the r igid-bodyapp-~ximafion (MD, R) and the f lexible model (MD, FJ The availableexper imenml data from fef 7 (FXP) ace also indicatedatoms due to the rotational motion of the methyl group aboutthe C-N bond would occur in the b-c plane only. Thus, theincreasingly large librational motion occurring with increasesin temperature would affect only the cell dimensions associatedwith the b and c axes. In the actual crys tal, the arrangement ofthe molecules in the unit cell is such that the C-N bonds of allfour are nearly perpendicular to the c axis (as can be seen inFigure 1). The angles that each C-N bond makes with the axesof the crystal cell are 40,51, and X6 for the a, b, and c axes,respectively. This alignment of the molecules relative to theseaxes ndicates that rotations of the methyl group about the C-Nbond would more strongly affect the b and c axes. Indeed, bycomparing the data in Figure 2a, it is clear that the majordifferences between NPT-MD data from the rigid and flexible


10/24

8412 J. Phys. Chem. B, Vol. 104, No. 35, Z&W sorescu et al.TABLE 5: Comparison of the Average Orientational Parameters ( fr ict ional coordinates sx, sy, sz and Euler angles 8, a, Y)for the Four Molecules in the Unit Cel l and of the Internal Geometr ical Parameters of Nitromethaue Molecule as Obtainedfrom Trajectory Calculations at Different Temp eratures; Corresponding Exper imental Values (where avai lable) Are Alsoindicated

temperature(K)parameter 4.2 4.2 4.2 78 78

7x 15 0-ptof NIT-MD ideal exptb NPT-MD ideal NPT-MD

-50ideal

sxl 0.3493SY l 0.41%SZ l 0.3750sx2 0.1507sY2 -0.41%sz2 -0.1250sx3 -0.3493SY3 -0.0804sz3 0.1250sx4 -0.1507SY4 0.0804$24 -0.375001 90.8@l 53.5VI. 238.902 -90.892 53.5V2 238.9:3 -53.59.2YJ3 58.904 -89.2Q4 -53.5Y4 58.9

0.35130.42840.36820.1487

-0.4284-0.1318-0.3513-0.0717

0.1317-0.1488

0.0716-0.368394.451.9

245.3-94.4

52.0245.3

85.5-52.065.3-85.6-52.0

65.3

0.1487-0-4284-0.1318-0.3513-0.0716

0.1318-0.1487

0.0716-0.3682

-94.451.9

245.385.6

-51.965.3-85.6-51.9

65.3

0.3475 0.34830.4188 0.42880.3803 0.37220.1525 0.1509

-0.4188 -0.4291-0.1197 -0.1279-0.3475 -0.3494-0.0812 -0.07110.1197 0.1277-0.1525 -0.1513

0.08 12 0.0708-0.3803 -0.371996.6 92.951.6 53.2

240.1 245.4-96.6 -92.9

51.6 53.1240.1 245.5

83.4 87.2-51.6 -53.160.1 65.4-83.4 -87.1-51.6 -53.2

60.1. 65.4

0.1517-0.4288-0.1278-0.3483-0.0712

0.1278-0.1517

0.0712-0.3722

-92.953.2

245.487.1

-53.265.4-87.1-53.2

65.4

0.34840.42900.37400.1512

-0.4290-0.1262-0.3488-0.0705

0.1260-0.1516

0.0703-0.373992.253.7

245.4-92.4

53.7245.4

87.7-53.865.4-87.7-53.7

65.4

0.1515-0.4290-0.1260-0.3485-0.0710

0.1260-0.1515

0.07 10-0.3740

-92.253.7

245.487.8

-53.76155.4-87.8-53.7

65.4

parameterC-NC-HN-4N-04HCHHCNcNo3cNo403NO4

4.2 4.2exptb m-m

1.481 1.4971.098 1.0881.209 1.2301.223 1.229

111.6 110.7107.3 108.2118.9 118.1117.8 117.7123.3 124.3

temperature(K)78

expLb1.4881.0771.1981.226

111.2107.7119.1116.8124.1

7x 150NPT-hlD Nm-MD

1.499 1.4991.089 1.0901.230 1.2311.230 1.231

110.6 110.5108.2 108.2117.8 117.8117.8 117.9124.2 124.2

u Jn the case of molecules 2-4 the ideal orientational parameters obtained based on F21212 1 space group symmetry operators and the oriemationparameters of molecu le 1, positioned in the asymmetric unit, are &WI. b Experimen tal values from ref 7. c Unit cell fractional values have hewshifted to fall within the m&e from -l/2 to k!.potent ial models arc in the expansions along the b and c axeswhile the variations for the case of the a axis are pract icallyabsent. The additional expansion due to the methyl grouprotation can be also Seen n Figure 2b where the volume valuesobtained using the flexible model are consistently larger thauthe corresponding data obtained for the rigid model.In Table 5 we compare first the results of the averagefractional coordinates and orientational Eu ler parameters of thefour molecules in the unit cell with the corresponding experi-mental data (where available). These values are averaged overtime and all unit cells in the simulation box. Additionally, inthe same table we provide the ideal orientational Eulerparameters for three of the four molecules of the unit cell relativeto the orientation of the reference molecule in the asymmetricunit cell. These parameters have been calculated assuming thesymmetry operations of the P212121 space group. In this waywe can analyze the degree of deviation of the predicted crystalstructure from the P212121 symmetry.It is evident that increasing the temperature from 4.2 to 150K does not produce any significant displacement of themolecular centers of mass and that the degree of rotationaldisorder is small. The largest deviations of the system from the

orientational parameters corresponding to a perfect crystal withI 212121 symmetry are O.OOIl and 0.2 for the fractionalcoordinates and Euler angles, respectively. A similar conclusionis obtained for temperatures between 150 and 250 K (notshown). At X = 4.2 K, the largest deviation between theexperimental and predicted molecular orientations is about 6.4for the Euler angle Y (see Table S), in agreement with previousMP fmdings. At T = 78 K this maximum deviat ion decreasesto about 5.4.Additiona l support for the smal l degree of translation of themolecules inside the unit cell with the temperature increase canbe obtained from the C*-*C RDFs given in Figure 3a . As canbe seen, the RDFs at these temperatures correspond to well-ordered structures with correlation at long distances. Thepositions of the major peaks do not change significantly andthe main temperature effect is the broadening of the peaks withpartial overlapping of some of them.The good agreement of the structural molecular parameterspredicted by the model with experiment can be also observedby analyzing the internal coordinates (bond lengths and angles)indicated in Table 5. At 4.2 K the maximum deviations for bondlengths is about 1.7% and about 1.0% for bond angles. This


11/24

Solid Nitromethane J. Phys. Chem? & Vol. ~104,No. 35, 2ooO 8413

I

86

cr4k2

20

0 2 4 6 8 10r(N

0 2 4 6 8 10

0-H b)T= 250 K,. 1. * - -. * - - * -

- - .T= ,50KpJ-----.*. .T=78K f___. .- __~._.f..f... *..*-.a...

. . . . . . . . . .

O...H .\ d)pz7,OGpa *.~.---s~m--m-.. I1P=5.4 GPaj fl/-fl-----: *_

P=3.5GPa . * * . + _ . . . f - ~ - f. . - * .. : * * . .-

T= 4.2 K P=O.3 GPa wpL

0 2 4 6 8 10 0 2 4 6 8 10r(N @v

P=3.5GPa

_ . . . . _ . . * . . . _ .

P--.3 GPa

Fii 3. Radial disnibntion functions or C--C and O--H as function s of tv (a-b) at atmospheric aad as function of ~~WUE(c-d) at T = 293 K.

level of agreement is particularly good taking into account thatin our potential parameuization, we have considered the internalgeometrical parameters of the nitromethane molecule determinedfrom gas-phaseab initio calculated values rather than parameterscorresponding to nitromethane in the c rysta lline phase. Theseresults suggest also a small influence of the latti ce field on theintemal parameters of the nitromethaue molecule. Changes inpredicted molecular structural parameters with temperature arenegligible, again in agreement with experiment. The mostsignificant change appears due to the interna l rotation of themethyl group as a function of temperature. This is evident byinspecting the behavior of the radial distribution functions(RDFs) for the 0**H intermolecular bonds given in figure 3b.There is a rapid destruction of tbe correlation at long distanceswith the increase of temperature and consequently the indi-vidual ity of the H atoms in the C-W-a bonds is lost. Theseeffects can be understood as being due to the increase inrotational disorder of the methyl group w ith the increase oftemperature.The increase in the librational motion of the methyl groupwith temperature is illustrated in Figure 4. This figure showsthe cumulative distributions of the Hi-Cl-Nz-03 (i = 5-7)dihedd angles at temperatures ranging from 4.2 to 150 K. Thesedistributions have been determined from the molecular con-figurations recorded at every tenth step during trajectories of16000 steps (12 ps). In this figure, the distributions are peakedat the angles corresponding to the equilibrium orientation ofthe methyl group in the low-temperature structure, namely,

-78, 42, and 161 respectively. These angles are within 10from those corresponding to the experimental structure deter-mined by the neutron diffraction technique. As can be seen inFgure 4 the increaseof temperature does not change the positionof these peaks. However, the distributions broaden with tem-perature, indicating an increase in librational motion withtemperacure. For the case of the potential model with theincreased HCNO torsional barrier (M2) we have found that theagreement between the predicted (-W, 34, 154) andexperimental ( -W, 31, 151) torsional angles is even better,with deviations within 3O. Similarly, in this case the increaseof temperarure did not mod ify the position of the peaks in thecumulative distributions.The magnitudes of the methyl group libration have beenpreviously determined experimenta lly for deuterated ni-tromethane in the temperature range 4.2- 125 K using neutrondiffraction powder experiments7 As can be seen in Figure 5where the experimental values are compared with our resultsthe agreement is quite good for the entire temperature range2% 125 K. For example, the experimental results indicate thatat 25 and 125 K the ruts amplitudes of libration of the CDsgroup are N 13O nd 25, respect ively. Our NPT-MD calculat ionsof deuterated niuomethane predict rms amplitudes of librationof 12 at 25 K and 23 at 125 K (see Figure 5). Comparison ofthe amplitude of libration at 4.2 K with experiment is notappropriate, since quantum mechanical effects would be sig-nificant at this temperature. The experiments suggest that theamplitude of libration at this temperature is as large as that at


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J. Phys. Chem B , Vol. 104, No. 35, 2000 Sorescn et al.

0.0060.0050.004

0.0030.0020.0010.000

-200 -150 -100 -50 0 50 100 150 20 0

Torsional Angle (deg.)

Torsional Angle (deg.)4. Distr ibution of the H,~-CI-N~-O~ ( i = 5,6,7) dihod.ml&romethane molocul~ in the simulation box as a function(a) and pressure b).

I V0 20 40 60 SO 100 120 140TempeFnbreK)

5. Roo-meau-square amplitude of l&ration of the methyl groupas a function of temperature.our class ical simulations predict a value that is smaller-7O. Previous quasielastic and inelastic neutron scatteringperformed on protonated nitromethane have providedinformation about the temperature dependence of thereorientation of the methyl groups. By assuming areorientation model and an Arrhenius dependencekr) of the mean residence times of methyl groups on therotation has been determined. However, more recentstudies based on infrared and Raman measure-indicated higher activation energies with values ofand 576 cal/mol,o respectively. We monitored

2

1

3s

0

-1 I0.002 0.006 0.010 0.014 0.018 0.022

l/l-- (K)Figure 6. Th e mean residence t imes r of the methyl group versusinverse tetnpemt ure. The activation energy of 387 cal /mol is obtainedfrom the slope of the least-squares l inear f i t to the data in the region ofhigher tempe ratures (125-250 K) indicated by a solid line.the frequency of 120 methyl group rotations for the durationof 12 ps in tra jectories integrated at temperatures rangiug from4.2 to 250 K. From these trajectories we have observed thatmethyl groups undergo large vibrationa l amplitudes, ind icativeof small barrier heights for torsional motions in agreement withexper imental f indings.To obtain a more quantitative description of the internalrotational motion we have considered the evaluation of tem-perature effects on the rates of reorientation of the methyl group.A rotational jump was defined in the following man ner. Atthe beginning of each trajectory, the Hi-Cl-NY-03 angles (i= 5-7) of each molecule were calculated. Each angle wasassigned to one of the three minima in the 3-fold rotationalpotential by virtue of its proxim ity to the minima, and the timedenoted as to- The minima corresponded to the values of theHi-Ct-N2-03 angles (i = 5-7) in the low-temperaturestructure, i.e., -78, 42, and 161, respectively. The assignmentof these angles to the minima are made at each subsequent stepin the trajectory and compared to the original assigument at to-When the assignments for all three of the H+Ir-Nz-@ anglesdiffer from the original assignments at b, it is assumed that arotational jump has occurred At this point, the time intervalbetween the time of the new assignments and to was recorded.The value of ro was reset to the tune of the new assignments,and the process repeated for the duration of the trajectory.Methyl group reorientation rates at each temperature weredetermined by extractiug fur&order rate coeff icients from l inearfits of plo ts of In(P) versus tune, where P is the fraction ofnitromethane molecules that have not jumped at time t. Thelifetimes indicate first-order behavior. Au Arrheuius plot of theresidence times, which are the inverse of the reorientation rates,is shown in Figure 6. Fitting a line to all the points in Figure 6predicts E, = 241 cal/mol. However, the nonlinearity of theArrhenius plot is a result of the statistical errors in the low-temperature rates, and if we base our prediction on the 7 pointsfor the.highest temperaures (100-250 K) we predict E, = 387cal/mol. These values are in accord with the reported experi-mental activation energies (234-576 caYmo1).*JJ6B2. Pressure Effects. The calculated lattice dimensions atdifferent pressuresare given in Table 6 and a visual comparisonwith the experimental data is presented in Figure 7. For theentire pressure range investigated (0.3-7 GPa) the di fferencesbetween the calculated NPT-M D data using the f lexible potential


13/24

Solid Nitromethane J. Phys. Ghem B; Vol . I@$, No. 35. Zoo0 Ml5TABLE 6: Lattice Parameters Obtained in Crystal Packing and NPT-MD Calculations for Nitromethaue as a Functi~rh ofPressure

pressmw0.300.330.501.002.003.003.504.005.005.456.006.507.00

NIT-MD molecularpackinglattice lengths (A) unit cell latfitx lengths A) unit cella b C vohlme (A> a b c volume 8,3)

5.2070 6.4829 8.8597 299.0666 5.2068 6.1989 8.5628 276.37585.2005 6.4814 8.8416 298.2833 5.2040 6.1929 8.5576 275.79275.1713 6.4236 8.7800 291.6500 5.1861 6.1561 8.5172 27 1.76495.0997 6.3001 8.6595 278.2166 5.1397 6.0786 8.4295 26294984.9827 6.1706 8.4936 261.1500 5.0656 5.9716 8.3055 250.53474.8963 6.0797 8.3826 249.5166 5.0051 5.8988 8.2150 241.63014.8603 6.0448 8.3392 245.0000 4.9792 5.8684 8.1772 237.93974.8245 6.0139 8.2955 240.6833 4.9536 5.8447 8.1421 234.64724.7652 5.9600 X.2265 233.6500 4.9054 5.8085 8.0780 228.88754.7426 5.9412 8.2001 231.0500 4.8843 5.7969 8.0517 226.59964.7116 5.9145 8.1% 227.5833 4.8527 5.7982 8.0161 223.94484.6898 5.8925 X.1404 224.9666 4.7698 5.9133 7.9484 221.27194.6666 5.8733 8.1162 222.4500 4.7171 5.9801 7.8992 218.8226

--*, UP+, Dm0 UP. MD.R-o- M0.F

LW - .0 2 4 6 s1-.05 , ,.-,DtP0 MPl-. HD.Rq- MD.F1.w. 0)0.950* 0.60.0.6!3-

o.so0.75

0 2 4 6 sPressure(GPa)

FTgure 7. FVesure variat ion of the latt ice dimensions (a), t i t cel lvolurrae (b), and volume compression WV0 on the external pressure.The dcul6Ied data hum nmlexlarpackhg (MP), NFT -MD hnulat ionsusing the rigid-body approximation (MD ,R) and the f lexible model(MD m 2x6 repiesented T he Corresponding exprimmtal data kom re fs9 (F.XP) ad 12 (EXPZ ), -l ively, are also indicated.and the experimental crysta llographic parameters are small. By* considering as reference the experimental data determined byCromer et aL9 we find that in the low-pressure region (0.3 GPa)the percentage errors for lattice dimensions z+ b, and c are 0.3%,3.44, and 2.99, respectively. A s imi lar good cof iespondenceis found in the high-pressure region (6.0 GPa) where thepercentage errors are 0.4%, 3.5%, and 2.4% for the a, b, and clattice dimensions, respectively. Moreover, for the entire pres-sure range investigated the NPT-MD predicted volume com-pression closely follows the corresponding variation observed

experimentally (see Figure 7b). In Figure 7b we have alsorepresented the experimental values reported by Yarger andOlinger.12 As can be seen in this case the agreement with ourcalculated unit cell volumes is even better than that found withdata provided by Cromer et aL9 with decreasing deviations fromabout 3.6% at 1 GPa to 1.4% at 7 GPa.The MP results obtained using the rigid body approximationgenerally follow the predictions obtained using the flexible

potentials, particularly in the low-pressure region. Also, theagreement between the NPT-MD data obtained using the rigidmolecular assumption is surprising ly good with NFT-MD datausing the flexible model. This fact indicates that for the pressureregion investigated, the compression of the lattice is almostentirely due to a reduction of intermolecular distances. Theseeffects can be also seen from the inspection of the normalizeddependence of the unit c ell volume on pressure given in Figure7c. In this plot the experimental curve9 and those predicted bythe flexible and rigid models are practically superimposed forthe entire range of pressures nvestigated. The values obtainedin the Mp calculations start to deviate more significantly fromthe experimental results, particularly for pressuresabove 5 GPa.These facts indicate that the lattice compressibility becomes lesswell represented in these calculations as the pressure isinct~ased. However, the present set of results support ourprevious tidings6 that in the region of low to moderate pressures(-5 GPa) the MF calculations can be used as an alternativetool to describe the changes of the unit cell geometricalparameters but at a fraction of the computational cost involvedin MD simulations.

Further comparison of the predicted and experimental latticeparameters can be obtained by extrapolating to zero pressureand 293 K the results of different studies, which in principleshould coincide. As in previous experimental studies,7,9.12heexbapolation is taken becauseat rOOm emperature nitromethaneis in the liquid phase. The coefficients of cubic fits in pressureof the predicted lattice parameters and unif cel l volume to thedata predicted by our flexible potential are given in Table 7. InTable 8 we compare the zenpressure extrapolated data obtainedin this work to those of previous experimental investigations.Particularly , we have considered both the low-temperature dataobtained by Trevino et al. and extrapolated to room temperatureas well as the high-pressure values determined previously9+ 2and extrapolated to zero pressure. As can be seen in Table 8,our crystal lattice dimensions are within 2.2%, 2.9%, and 3.4%from the data given in refs 7,9, and, 12, respectively. This levelof agreement is satisfactory t&ng into account the relative largedeviations between different sets of experimental values.


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J. Phys. Chem. B, Vol. 104, No. 35, 20007: CoetI icients of the Cubic Fi t in Prwnwe @Pa) o f the Latt ice Constants and Unit CelJ Volume

Sorescu et al.

a1 a3a(A) -1.601 x 10-l 8, GPa-*b& l -2.475 x 10-l 8, GPa-1c(-Q 8.911 A -2.711 x 10-l A GPa-W-Q, 305.17 A -2.885 x IO+A3GPa-

Comparison of the Latt ice Constan ts for Sol idExtrapolated to 293 K and 0 GPa aud of them Equation Coeff icients (eq 8) from Presentons and Var ious Studies

ref7 ref9 ref 10Qow @W Oligh presentparameter temperature) P=.==) pres=) workao


15/24

Solid Nitromethane J. Phys. Chem B, Vol.. 104, No. 3 5, 20# &i17

150e looz

= 50zF 0a=-5O$g -100

-150

-200

4 6 8 10 12fime (ps)

W

14

0 2 4 6 8 IO 12 14Time (ps)

Figpre 9. The time history of the variation of &-C,-&-03 (i =5,6,7) dibedrd angles or one of the nitromethane molecules tiorntrajectories performed at P = 0.3 GPa (a), and P = 7. 0 GPa b). an dT = 293 K. For vi-on pqses some of the angles have beenshifted by f36O.

different pressures (T = 293 K) are represented. In the low-pressure case, the methyl group rotation i s slightly hindered, asmethyl group jumps from one equilibrium corQura tion toanother are seen at times 0.5 and 5 ps in the time histories. Inthe high-pressure regime the torsional angles oscillate aroundwell-defined equilibrium values and the jumps between theequilibrium wells are absent. Also , the equilibrium confrgumtionfor the methyl group changes with pressure, as illustrated bythe time histo ries in Figure 9. To determine these equilibriumvalues we have analyzed the cumulative distributions of theHi-CL-Nz-03 (i = 5-7) torsional angles for all the moleculesin the simula tion box during tmjectories executed at differentpressures, T = 293 K. The correspond ing data obtained in theseanalyses ate repmented in Figure 4b. When compared to thedistribut ions of these angles as a timction of temperature (seeHgure 4a), the increase of pressure has a totally different effecton the distribution of torsional angles. In this case there is acontinuous shift of the peak positions with pressure such thatbetween 0.3 and 5.4 GPa this shift amounts to about 41 whileb between 0.3 GPa and 7.0 GP the corresponding variation isabout 50. These data agree very well with the experimentalfindings obtained by Cromer et aL9 in which the methyl groupwas found to be rotated by about 45 relative to the low-temperature configurationWe next explore the basis for the rotational reorientation withpressure by comparing properties of two c rysta ls, one in whichthe methyl groups are rotated and one in which the methylgroups are in the arrangement corresponding to the low-

temperature, low-pressure con@uration. Both crysta ls haveEL12121 ymmehy and use the shuctural parameters corrcspond-ing to averagesobtained in our simulations. The only differencebetween the two models is iu the arrangement of the hydrogensof the methyl group. In one model, the methyl group is rotatedby 50 relative to the low-temperature, low-pressure crystal. Inthe second model, the methyl group is in the same arrangementas the low-temperature, low-pressure crystal. We firs t comparedthe total potential energy for the two systems using structuralparameters for T = 4.2 K at 0 atm pressure The model in whichthe methyl group is not rotated has a total potential energy thatis lower by 3.5 kVmo1 per molecule. In that model, the repulsiveN-H contributions to the total potential arc greater (by 4.9 kJ/mol), but the repulsive H-H interactions are lower by 1.4 kJ/mol. The attractive C-H contribution is larger for the modelin which the methyl group is rotated by 0.9 kJ/mol. The largestdifference in contribution to the total potential is due to theO-H contributions, which are more attractive by 6.1 kJ/molfor the low-energy crystal. These combined effects account forthe difference in energy between the two models.

For model crystals using structural parameters correspondingto a pressure of 7 GPa and tempcrantre of 293 K, the model inwhich the methyl groups are rotated by 50 has a total potentialenergy that is lower by 35 kJ/mol per molecule than the modeliu which the methyl groups are not rotated. The energydifference (per molecule) is due mainly to the H-N, O-H, andH-H interactions. For the model in which the methyl group isrotated by 50, there is a net decrease of 17.0 kJ/mol for theN-H repulsive interactions, a net increase of 1.1 kJ/mol forthe C-H attractive interactions, and a net increase of 26.8 kJ/mol for the O-H attractive interactions. H-H repulsions arcgreater in the rotated crys tal model by 10 kJ/mol. For bothpressures, the largest differences in the total potential energyarc due to the contributions of O-H and N-H interactions.The result8 ndicate that the methyl group rotation with pressureallows for the enhancement of the O-H attractions whilereducing the N-H repulsions.Structural molecular parameters predicted by the model andexperimental values (where available ) as a function of pressureare given Table 9. The most significant changes in molecularstructure with p ressure are the compression of the C-N bondand the distortion of the Cl-Nz-04 angle. These trends werealso seen in experiment; however, the effects were morepronounced. In the experimental results, the C-N bond iscompressed by 0.08 A at 3.5 GPa, and the heavy atom angleshave changed by -4. In our model, the corresponding C-Nbond compression is only 0.01 A , and the heavy atom angleshave not significantly changed.

A comparison of the average fractional coordinates andorientational Euler parameters for the four molecules in the unitcel l is given in Table 9. All orientational parameters of the fourmolecules in the unit cell were averaged over time and all unitcel ls in the simulation space. We have also generated orienta-tional parameters or the four molecules in the unit cell assumingperfect P212121 ymmetry in the manner described earlier. Theonly complete set of fractional coordinates for all atoms in theCromer et a.Lgstudy corresponded to 3.5 GPa, 293 K , with theassumption that the C-H bonds and H-H distances are 1.0and 1.63 A, respectively. The simulation results arc in goodagreement with these experimental data, indicating that themodel reasonably epresents he crystal under moderate pressureComparison of the averages of the four molecules in the unitcel l with those with P212t2t symmetry indicate that the space


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8418 J. Phys. Chem. B, VoL 104, No. 35, 2000 Sorescu et al.TABLE 9: Comparison of the Average Orier~tatioti Parameters ( fractional coordinates sx, sy, sz and Euler augles 8, a, W)for the Four Molecules in the Unit Cel l and of the Internal Geometr ical Parameters of Nitromethane Molecule as Obtainedfrom Trajectory Calculations at Ditkent Pressures; Cornspoudiog Exper imental Values (where avai lable) Are Also IndicaW

pressure(GPa)

parameter0.3

NPT-MD0.3

ideal3.5

expt3.5

NPr-MD3.5

ideal7.0

NFT-MO7.0

idealsxlSY lszlsx2SY 2sz2SX 3SY 3SC43sx4SY 4sz401@lYl02E03@3Y3zv4

0.34880.42840.37650.1519

-0.4243-0.1235-0.3479-0.0687

0.1233-0.1525

0.0686-0.376991.454.7

245.3-91.4

54.7245.3

88-4-54.8

65.2-88.6-54.6

65.2

0.1512-0.4284-0.1235-0.3488-0.0716

0.1235-0.1512

0.0716-0.3765

-91.454.7

245388.6

-54.765.3-88.6

-54.765.3

0.3453 0.33910.4055 0.43110.3844 0.38550.1547 0.1609

-0.4055 -0.4300-0.1156 -0.1139-0.MS3 -0.3388-0.0945 -0.0688

0.1156 0.1149-0.1547 -0.1614

o.Ow5 0.0700-0.3844 -0.385391.3 90.655.8 56.2

242.9 248.0-91.3 -89.9

55.8 56.3242.9 247.7

8X.7 89.6-55.8 -56.3

62.9 67.8-88.7 -89.9-55.8 -56.2

62.9 67.7

0.1609-0.4311-0.1145-0.3391-0.0689

0.1145-0.1609

0.0689-0.3855

-90.656.2

248.089.4

-56.268.0-89.4

-56.268.0

0.33160.43040.39380.1684

-0.4295-0.1059-0.3314-0.0693

0.1060-0.1685

0.0706-0.394089.557.0

249.3-89.1

57.0249.0

90.7-57.1

69.0-90.7-57.0

69.0

0.1684-0.4304-0.1062-0.3316-0.0696

0.1062-0.1684

0.0696-0.3938

-89.S57.0

249.390.5

-57.069.3-90.5

-57.069.3

pressure(GPa)0.3 0.3 3.5 3.5 7.0

parameter exptb NPT-MD exptb N-R-MD m-MDC-N 1.55 1.500 1.47 1.489 1.481C-H 1.092 1.088 1.084N-03 1.21 1.231 1.21 1.228 1.224N-O., 1.20 1.231 1.26 1.228 1.226HCH 110.5 110.7 110.6 110.8HCN 108.1 107.9 107.9 107.7(SNOS 117.7 117.7 118.4 117.0 115.9m0 4 116.2 117.9 119.9 118.8 119.903No4 125.9 124.1 121.6 123.9 123.9

a In the case of molecules 2-4, the ideal orientational pammeters obtained based on P2121 21 space group symmehy operators and the orientationparameters f molecule 1, positioned n the asymmetricunit, arealso ndicated b Exper imental values from ref 9. Since tbe hydrogen atom positionscould n ot be resolved at 0.3 GPa, the orientationa l parameters for nitromethane at this pressure are not available for comparison. c Unit c ell tictionalvalues have been sblfted to fall. within the range from -l/2 to ILL

group symmetry is conserved with pressure, as observed inexperiment.9Also, as opposed to the temperature effects, which tend toincrease the degree of disorder in system, the increase ofpressure has the opposite effect. As can be seen in Figure 3cthe peaks of RDFs for C***C intermolecular distances shifttoward smaller distance values with increasing pressure, ndicat-iug the compression of the material. Moreover, more and more

peaks regain their individuality with pressure ncreases, ndicat-ing an increase n the degree of rotational and translational order.V. Conclusions

We have developed a classica l potential for simulation ofsolid nitromethane containing both intra- and intermolecularpotential terms. The parametrization of the intramolecularpotential has been done on the basis of the results of ab initiocalculations performed on the isolated nitromethane moleculeat the B3LYP/6-31G* level. Both structural geometrical pa-rameters as well as data about the vibrational frequencies andtheir eigenvectors have been used in the fitting procedure. The

intermolecular potential used in these calculations is of theBuckingham 6-exp form and was previously developed for RDXcrys tals aud showed to be transferable to 30 nitramiue crysta ls4and to 51 other non-nit&nine crystak5Molecular packng calculations using the proposed set ofintermolecular parameters and the set of I-IF charges indicatean accurate prediction of crystallographic parameters withdeviations less than 1.21% for the lattice edges. Additionally,the predicted lattice energy of nitromethane is in acceptableagreement with previous theoretical estimationkUThe tests of this potential in NFp-MD simulations indicatethat the prediction of the crystallograph ic parameters is alsowell reproduced as a function of temperature with deviationsbetween 1.7 and 3.6% from the experimental data~~ or thetemperature range 4.2-228 K. Moreover, the present potentialis able to predict changes of the crystallographic parameterswith pressure similar to those observed experimentaLly.g Asimi lar good agreement is found for the bulk modulus and itspressurederivative. At zero pressure the predicted bulk modulusis BO= 6.78 GPa while the corresponding experimenta l valueis 7.0 GPa9


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Solid NitromethaneThe results of MD and NPT-MD simulations performed us ingthe rigid-body approximation indicate that the predicted va luesin these cases are simila r to those obtained from the flexib lemodel particula rly for pressures up to about 5 GPa.Both RDFs as well as the analyses of the HCNO dihedralangle distributions during ttajtiories calculat ions obtained usingthe flexible model indicate two distinctive regimes for methylgroup rotational dynamics. There is an increase of the degreeof rotation of the methyl group with temperature increase (at

ambient pressure) without signikant changes of the averageequilibritm~positions. On the other band, at ambient temperature,the increase of pressure causesa continuous shift of the averageequilibrium positions of the H atoms relative to the C-N@plane. A comparison of the contributions of the individualintermolecular interactions to the total potential energies forcrystals in which the methyl groups are in the low-temperature,low-pressure co@uration or arranged in the high-pressurecor@uration show that at high pressures, the O-H attractiveinteractions are enhanced upon methyl group rotation in thecrystal while the N-H repulsive interactions are decreased, theremaining intermolecular interactions do not change significantlybetween the two models.The success of the present potential model to describe theprototypical explosive, nitromethane, conjugated with theperformances of the present intermolecular potential to describea large number of important energetic materials, provides furtherincentives to develop these models and to extend their applica-tions to more subtle effects such as the enerq transfe$738 andreactions in condensed phases.

AcknowMgmen~ We are pleased to acknowledge manyinspiring and helpful discussions with Dr. S. F. Trevino. Thiswork was supported by the Strategic Envirorunental Researchand Development Program (SERDP). D.L.T. gratefully ac-knowledges support by the U.S. Army Research Of&e underGrant DAAG55-98-I-0089.Referents and Nob

(1) Sorescu, D. C.; Rice, B. M.; Thompson, D. L. .f. Phyx Gem. 1997,BIOI,798.(2) So tem, D. C.; Rice, B. M; Tbornpson, D. L. J. Phys. Chcm. 1998,BIOZ, 948.(3) Sorescu, D. C.; Rio% B. M.: lhompsor~ D. L. 1. Phys. Chetn 1998,B 102,6692.

(4) Sorcscu, D. C.: R&x. B. M.: Thompson, D. L. .I. Phys. Chem 1998,A 102,83&S.(5) SOKS CU, D. C.; Rice. B . M.; Thompson D. L. .I. Phys. Chem 1999,A 103,989.(6) So-u, D. C.; Rice, B. M.; Thompson D. L. J Phys. Chem 1999,B 103,6783.(7) Trevino, S. F.: Prince, E.; Hubbard C. R. J. C/tern Phys. 1 980,73.2996.(9) Trevino, S. F.; Rymq W. H. 1. Chem Phys. 1980, 73, 3001.(9) Crotrer, D. T.; Ryan, R R; Schiferi, D. J. Phys. C/rem. 1985.89,2.315.

(10) Grokv, V. M-z; Steker, F.; Jochar& D. J. I&L Smrcrum 1999,476,181.

. I . Phys. Chenr. B; Vol., 104, No. 35, 2ooO 8419(11) Jones. W. M.: Giauque, W. F. J. Am Chem Sot. 1947, 69,983.(12) Yarger, F. L.; Ohnga, B. 1 Ckem Phys. 198 6 85, 1534.(13) Piermarin i. G. J.: Block S.; Miller, P. J. Phys. Ch em. 1989, 93,457.(14) CawgnaL D.; Magerl, A.; Vetoer, C.; Anderson, I. S.; Trevino, S.F. Phys. Rev. fat. 1!%5,54+ 193.(15) T armebaum. E.: Myers, R. J; Gwinn, W. D. J. Chem Phys. X954 ,25, 42.(16) Remiwv, A. B.; Musayakaev~ R H. Opt Spdeosk 1975, 38,226.(17) Frisch, M. J.: Trucks. G. W.: Schleeel. H. B.: Gill. P. M. W.Johnson, B. G.: Robb. M. A.; Cheeseman , J. k; Keith, T.; Patersson, G.

A.; Montgomery, J. A.: Raghavachati, K; Al-Lahatn M. A.; Zaktzewski,V. G.; Chtiz, J. V.; Fortsman, I. B.; Cioslowski, J.; Stefanov, B. B.;Nanyakhq A: Chdlawm be, M.; Peng, C. Y.; AyaJa P. Y.: Chen, W.;Wang, M. W.; At&es, J. L.; Replog le, E. S.; Gxnpks, R.; Martin, R L.;Fox, D . J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart. J. P.; Head-Gordon, M.; Go- C.; Pople , J. A. &ussk 94. Revision C.3: Gaussian.Inc.: Pit&burgh , PA, 1995.

(18) Mijlle r, C. M. S. Phvs. Rev. 1934,46. 618.(19) Rice. B . M; Tbomp-so~ D. L. J. Chenr Phys. 1990,93,79 86.(20) (a) Beck A. D. J. Chem Fhvs. 199 3.98.564s. (b) Lee. C.: Yang,W.; Parr, R G. Phys. Reu. 1988, B 43, 78 5.(21) Hehre, W.; Radom. L.; Schleyer, P. v. R.; Pople . J. A Ab InitioMobcular Orbitd Theory; Wiley-Interscience: New Y0t-R 1986.(22) Rice, B . M.; Chabalow sld, C. F.; Adams, G. F.; Mowrey, R C.;Page, M. Chem Phys. L&t. 1991, 184, 335.(23) Forscrrm. I. B.; F&h, A In Exploring Chemisr~ with Ekc~onicSrmcture Metlwak Gaussiau, Inc.: Pittsburgh, PA, 19%.(24) (a) Wells, A J.; Wilson, E. B. J. Chem Phys. 1941, 9. 314. (b)

Smith. D. C.; Pan. C.; Nielsen. I. R. I. C&m Phvs. X950. 18. 706. cc1Jones. W. J.; Sheppard N. Proc. R Sot. London Sk. A 1968,304, 1%.(d) Trinouecoste, C.; Rev-Lafon. M.: FoteL M.-T. Surztnxhirn Acta A1974 30,-813. (e) McKea& D. C.; Watt+ R A. J. Mol. $ZC~TOSC. 1976,61,184.

(25) Pertsin A, I.; Kitaigonadsky, A. L Zk Atom-Atom Pore&yh&d Applica lio~ to organic Mokdorsolidr, SpingeT-vetiag: Berliq(26) kaitaju,G.RCysmlEngkeetig: TheDesignofOrgmicSol~Ekevier: knsterda~~ 1989.(27) Gibson. K D.; Scheraga, H. A. I. Phys. Chem. 1995, 9 9,3752.(28) Gibson, K D.; Sctmaga, I-L k LMIN: A Program for Crystal

Packing, QCPE, No. 664.(29) Melchionna. S.; Ciccotti, G.; Holian, B. L. MoL P/zysics 1993, 78,533.(30) DL_wLY is a package of molecular simulation routines writtenby W. Smith and T. R. Forester, copyright Tbe Counc il for the CentralLalmatoty of tk Research Councils, Daresbury Laboratory at Daresbury,Nr. Warrington, 1996.(31) Allen, M. P.: Til&ley, D. J. Compruer Sim& rion of Liquids,Oxford University Press: New York. 1989.(32) Fincham D. Mokcukr Simulo tfon 1992, 8, 165.

(33) Fwukwwntals of Gystdlography, Giacovazzo. C., Ed.; OxfordUniversity Ress: New York, 1992.(34) The enthalpy of sublima tion for nitronxctbane has been corn-municated by P. Politzr and has ken obtained based on the method

dealbe d in Pohtzer, P.; Murray, J. S.; G&e, M. E.; LkSalvo, M.; Miller,E. M. MoL Phys. 1997,92,923.(35) Mumagb an,F.D.In Fin& &fommio nofmE kmicSo lti DoverPublications: New York, 1951: p 73.(36) Cook M. D.; Fellows, J.; Ha&us, P. J. In Decompos ition,Combus tion and Detonation Chew&y of Energetic M aterials; Brill, T.

B., Russell, T. P., Tao, W. C., Wmile. R B., Eds.; M-r. Res. Sot. Symp.Proc. 1995.418,267-275.(37) A ubuchon, C. M.; Rector, K D.; Holmes, W.; Fayer, M . D. ChamPhys. L&t. 1999,200 , 84.(38) D e&, J. C.; Iwaki, L. K.; Dlott D. D. J. Phys. Chem A lm,103, 971.

c


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NO. OF

.

NO. OFCOPIES ORGANIZ4TIONDEFENSETECHNICALINFORMATIONCENTERDTIC DDA8725 JOHN J KINGMAN RDSE0944FT BELVOIR VA 22060-6218HQDADAMOFDT400 ARMY FENTAGONWASHINGTONlX20310-0460OSDOUSD(A&T)/ODDDR.&E(R)RJTREWTHEPENTAGONWASHINGTON DC 20301-7100DFl-Y CG FOR RDAUSARMYMATERIELCMDAMCRDAso01 EISENHOWER AVEALEXAkDRIA VA 22333-01MST FOR ADVNCD TCHNLGYTHE UNIV OF TEXAS AT AUSTINPO Box 202797AUSTIN TX 7872@2797DARFAB KASPAR3701 N FAIRFAX DRARLINGTON VA 22203-1714US MILITARY ACADEMYMATH SCI CTR OFEXCELLENCEMADNMATHMAJHUBERTHAYERHALLWEST POINT NY 109961786DIRECTORUS ARMY RESEARCH LABAMSRLDDRSMlTH28wmwDERMILLRDADELPHI MD 20783-l 197

COPIES ORGANIZATION

1 DIRECTORusARMYREsEARcHLABAMSRL DD28mmwDERMLLRDADELPHI MD 20783-l 197

1 DIRECTORusARMYRIlmzARcHLABAMSRLCIAIR(RECORDSMGMT)28mpowDERMIILRDADELPHI MD 20783-l 1453 DIRECTORusARMYREsEARcHLABAMSRLCILL28alPowDERMlLLRD

ADELPHI MD 20783-l 1451 DIRECTORusARMYREsEARcHLABAMSRLCIAP28mImvDERMILLRDADELPHI MD 20783-l 197

BB4 DIR USARLAMSRL CI LP @Lx 305)


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NO. OFCDPJESB

22 DIR USARLAMSRLWMB RINGERSAMSRL WM BDB E PORCHWR ANDERSONSWBUNTEC FCHABALOWSKIA COHENRDANIELD DEVYNCKRAFIFERBEHOMANAJKOTLARKLMCNBSBYM MCQUAIDMSMJILERAWMLZIOIEKJ B hORRJSR A PESCE-RODRIGUEZBMRICER C SAUSAMA SCHROEDERJ A VANDERHOFFAMSRLWMMBBFINK


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of Solid Nibomethane

Dan c. s-, Betsy lvl Rice, and Donald L. Thompson*

ATlTk AlWWzWM-BDAberdeen proving Ground, MD 210055066

Deparunent of Chemistry, Oklahoma State University, Stillwater, OK 74078A reprint froan the Journal ofPhysical Chemistry B, vol. 104, no. 35, pp. 8406-8419.lb msTRImnlowAVAY*BlLm~AlEMENTApproved for public release; distribution is unlimited la DErR lBu lmu eQ#

13. ABSTRACT@nxhBm =J*wds)A classica l potential to simulate the dynamics of a nitromethzme crystal as a function of temw and pressure isrlcscriw. The intramolecular part of the potential was taken as superposition of bond stretching, bond bending, aud

torsional angles terms. l&se terms were parametrized on the basis of the geometric and wit (vihtionalfrequencies and eigenvectors) data obtained using ab hitio molecular orbital calculations peaformed at theB3LYP/&3 1G level on an isolated molecule. The intermolecular potential used is of the Buckingham &exp form plus:hargecbarge CouIombic interactious and has been previously developed by us (Sorezcu, D. C.; Rice, B. M.;Thompson, D. L. J. Phys. Chem. 1997, BlOl , 798) to simulate crystals containing nitmmine molecules and sev&her classes of nitro compouuds. -Ike analyses performed usiug constant pressure and temjEmtlue molecularQnamics simulations and molecular packing calculations indicate that the pqosed potential model is able toreprduce accmately the changes of the structural crystallographic parameters as functions of tempeaanrre or pressurebr the entire range of values investigated. In addition, the calculated bulk modulus of uhmehne was found inexcellent mment with the corresponding experimental results. Mclreova, it was de&mmed that the presentpMential predicts correct ly au experimentally observed 45 change in methyl group orientation in the high-pressureregime dative to the low-temperature configuration.14.au- lERys 1s. MUMBER OF PAQEShromethane, molecular dynamics, intennokcular interaction potential 20

lB .PR I#eQOE

17. EcuRrrY clA!s!aMTloR 16. SECURITV CIASSIFICATION is. SEcuRrw clA!sslFlcATloR 26. LlUITAllON ff ABSTRACToFREml?T OF l l i I PAQE OFABSTRACrUNCLASSIFIED UNCLASSIFIED UNCLASSIFIED ULJSN 7a.o-o1-2845500

298102


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dan c. sorescu, betsy m. rice and donald l. thompson- theoretical studies of solid nitromethane

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