Structure of liquid nitromethane: Comparison of simulation and diffractionstudiesTünde Megyes, Szabolcs Bálint, Tamás Grósz, Tamás Radnai, Imre Bakó et al. Citation: J. Chem. Phys. 126, 164507 (2007); doi: 10.1063/1.2721559 View online: http://dx.doi.org/10.1063/1.2721559 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v126/i16 Published by the American Institute of Physics. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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Structure of liquid nitromethane: Comparison of simulationand diffraction studies

Tünde Megyes,a� Szabolcs Bálint, Tamás Grósz, Tamás Radnai, and Imre BakóInstitute of Structural Chemistry, Chemical Research Center of the Hungarian Academy of Sciences,Pusztaszeri út 59-67, H-1025 Budapest, Hungary

László AlmásyOptics and Molecular Materials, Department of Engineering Physics and Mathematics, Helsinki Universityof Technology, P.O. Box 2200, FI-02015 HUT, Espoo, Finland

�Received 15 December 2006; accepted 12 March 2007; published online 26 April 2007�

Simulation �molecular dynamics and Car-Parrinello �Phys. Rev. Lett. 55, 2471 �1985��� anddiffraction �x-ray and neutron� studies on nitromethane are compared aiming at the determination ofthe liquid structure. Beyond that, the capabilities of the methods to describe liquid structure arediscussed. For the studied liquid, the diffraction methods are performing very well in thedetermination of intramolecular structure, but they do not give detailed structural information on theintermolecular structure. The good agreement between the diffraction experiments and the results ofmolecular dynamics simulations justifies the use of simulations for the more detailed description ofthe liquid structure using partial radial distribution functions and orientational correlation functions.Liquid nitromethane is described as a molecular liquid without strong intermolecular interactionssuch as hydrogen bonding, but with detectable orientational correlations resulting in preferentialantiparallel order of the neighboring molecules. © 2007 American Institute of Physics.�DOI: 10.1063/1.2721559�

I. INTRODUCTION

Nitromethane is one of the simplest nitrogen-containingmolecules belonging to the nitro compounds that are of greatinterest to the high explosives community. It has been inten-sively studied due to its use as a fuel and as a prototypemolecule for a class of high-energy materials and perhapsplays a role in the atmosphere1 as well. Shock wave induceddecomposition of nitromethane has been subject to manyinvestigations.2 Detailed studies of formation of negativeions,3 electron transfer processes,4 and gas phase solvationprocesses5 in nitromethane were also reported.

Nitromethane is a small highly polar molecule �dipolemoment of 3.46 D� for which pair association in the liquidstate has been claimed several times in the literature.6 Re-cently Cataliotti et al. concluded from their IR and Ramanspectroscopic experiments that liquid nitromethane has mol-ecules in monomeric state and is not associated in pairs asreported earlier.7

There exist various theoretical studies on the structureand properties of nitromethane. Byrd et al.8 performed abinitio study of solid nitromethane on four energetic molecu-lar crystals; they have found that the lattice vectors deter-mined display large errors possibly due to the lack of van derWaals forces in functionals applied in current density func-tional theories �DFTs� and further development of the meth-ods of DFT was suggested. Structural and vibrational prop-erties of solid nitromethane were also studied by DFTmethod.9 Correlated calculation of the interaction in the ni-

tromethane dimer was performed on a fixed monomerconfiguration.10 Ab initio study of nitromethane dimer andtrimer11 was performed by employing the density functionaltheory B3LYP method. For the optimized structure of ni-tromethane dimer the strength of C–H¯O–N bond rangesfrom −9.0 to −12.4 kJ mol−1 at MP2 level, while the B3LYPmethod underestimates the interaction strength comparedwith the MP2 method.

Molecular dynamics simulations were performed onboth crystalline and glassy nitromethane,12 on melting ofnitromethane,13 on nitromethane nanoparticles,14 and on liq-uid nitromethane.15–17

Diffraction techniques serve, in principle, as a directmethod to determine the structure of the matter in condensedstate. The crystalline structure of nitromethane has been de-termined using single crystal x-ray and neutron diffraction.18

To the best of our knowledge, diffraction study of liquidnitromethane was not performed yet. In the present study weconducted x-ray and neutron diffraction experiments for thefirst time on nitromethane, in combination with moleculardynamics simulation that uses the intermolecular interactionpotential of Sorescu et al.16 and a Car-Parrinello19 simula-tion. To learn more about the mutual orientation of ni-tromethane molecules, we have also performed an ab initiostudy of nitromethane dimer on MP2 level.

The paper is organized as follows. In Sec. II we describethe quantum chemical calculations and the simulation de-tails, and discuss the x-ray and neutron measurements anddata treatments in Sec. III. In Sec. IV we present the experi-mental and theoretical results and compare them in Sec. V.Section VI summarizes the main results.

a�Author to whom correspondence should be addressed. Electronic mail:megyes@chemres.hu

THE JOURNAL OF CHEMICAL PHYSICS 126, 164507 �2007�

0021-9606/2007/126�16�/164507/11/$23.00 © 2007 American Institute of Physics126, 164507-1

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II. COMPUTATIONAL DETAILS

A. Quantum chemical calculations

All calculations were performed by using the GAUSSIAN

03 program suite20 at DFT/B3LYP and MP2 level of theoryusing a 6-311+G** basis set. The behavior of the calculatedstationary points was characterized by their harmonic vibra-tional frequencies. The interaction energies for each mini-mum were corrected for basis set superposition error �BSSE�with the full counterpoise �CP� procedure, resulting in amore reliable estimate of the interaction energy.21 The mag-nitude of the BSSE correction at the energy minimum con-figuration is about 7%–8% and 25%–30% of the total inter-action energy at B3LYP and MP2 levels of theory,respectively. In principle, since the BSSE causes the inter-molecular interactions to be too attractive, the CP correctionis expected to make the complexes less stable.22

B. Molecular dynamics simulation

We have performed a classical molecular dynamics�MD� simulation in the NVT ensemble at 300 K temperature.The simulation box contained 500 rigid nitromethane mol-ecules. The intermolecular interactions were defined byBuckingham potentials, developed by Sorescu et al.16 Theside length of the cube was 35.56 Å, which corresponds tothe experimental density, �=1.14 g cm−3. During the 25 000time steps of equilibration the Nosé-Hoover thermostat wasused to control the temperature in the DLPOLY 2.15 software.23

The simulation was performed for 200 000 time steps, lead-ing to the total time of 400 ps.

C. Car-Parrinello simulation

Another simulation was performed by using theCar-Parrinello24 ab initio molecular dynamics scheme. Thevalence electronic wave functions were expanded in planewaves with a 25 Ry cutoff and the valence-core interactionwas described by the Vanderbilt ultrasoft pseudopotentials.

A liquidlike system was made up of 32 CD3NO2 mol-ecules enclosed in a cubic box with a density matching thatof the experiment. A classical molecular dynamics simula-tion using the potential model for liquid nitromethane ofSorescu et al.16 was used to generate the initial configuration.The CPMD simulation was run using a time step of �t=0.163 fs and the fictious electron mass ��� was 600 a.u. Acontinuous trajectory of 15 ps was obtained in the microca-nonical ensemble with the last 6 ps, and it was used for thecomputation of average properties. The temperature was setto 300 K.

Recently a series of Car-Parrinello and Bohr-Oppenheimer molecular dynamics simulations was carriedout for liquid water to investigate the reproducibility of thismethod.25–27 They showed that for structural properties thesize effects are rather small, but care is required in the choiceof an appropriate electron mass. In Car-Parrinello simula-tions it is important to maintain an adiabatic separation be-tween the electronic and ionic degrees of freedom. In ourcase this could be achieved using a mass ratio � /M =1/6�M: smallest atomic mass of the system�. We did not find any

energy drift in our simulation, and the conserved energy fluc-tuation was about 10−7% ��10−4 a.u.�. In order to verify theaccuracy of our model we analyzed the structure of the ni-tromethane molecule and the nitromethane dimer at differentlevels of theory. Our calculations, using plane-wave basisset, produced results which agree very well with the highlevel ab initio quantum chemical calculation findings.

The self-diffusion coefficient is a sensitive indicator ofthe accuracy of the applied model. The self-diffusion coeffi-cient was estimated from the Einstein relation, which usesthe long time limit of the mean-square displacements of thecenter of mass of the molecule. The value predicted from thesimulation is about 0.9�10−9 m2/s, which is about 70%smaller than the classical simulation value for pure CH3NO2

liquid at 298 K �1.52�10−9 m2/s�. Such a difference maybe an artifact caused by the small size of the simulation box,as it was already proven in earlier studies. Thus, applyingthe same classical potential model for a system containing32 molecules, the calculated diffusion constant was about1.1�10−9 m2/s. Both these values are still lower thanthe experimental result, which is 2.3�10−9 and 2.4�10−9 m2/s for proteated and deuterated nitromethane, re-spectively, at 298 K.28 Such deviations are not rare in simu-lations of liquids when the potentials are not fully optimizedfor reproducing thermodynamic properties.

III. DETAILS OF THE EXPERIMENTAL STUDIES

A. X-ray diffraction measurement and methodof structural analysis

X-ray diffraction measurement was carried out on liquidnitromethane, anhydrous, special grade, produced byAldrich. The physical properties of the nitromethane were asfollows: density �=1.14 g cm−3, linear x-ray absorptioncoefficient �=1.0329 cm−1, and atomic number density�0=0.0787�10−24 cm3.

The x-ray scattering measurements were performedat room temperature �24±1 °C�, with a Philips X’Pert goni-ometer in a vertical Bragg-Brentano geometry with a py-rographite monochromator in the scattered beam and propor-tional detector using Mo K� radiation ��=0.7107 Å�. Quartzcapillaries �1.5 mm diameter, 0.01 mm wall thickness� wereused as the liquid sample holder. The scattering angle rangeof measurement spanned over 1.28° �2��130.2° corre-sponding to a range of 0.2 Å−1�k�16.06 Å−1 of the scat-tering variable k= �4 /��sin �. Over 100 000 counts werecollected at each angle in �k�0.05 Å−1 steps.

Background and absorption corrections were appliedbased on an algorithm reported by Paalman and Pings29 forcylindrical sample holders. This algorithm assumes that sig-nificant coupling does not occur between the sample and thecell;30 therefore, the experimentally observed intensities areconsidered as linear combination of an independent compo-nent from the confined sample and a component from thesample cell. The correction procedure was applied using in-house software written in a Fortran language. The polariza-tion and Compton scattering corrections were applied usingstandard methods given in earlier works.31

The experimental structure function is defined as

164507-2 Megyes et al. J. Chem. Phys. 126, 164507 �2007�

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h�k� = I�k� − ��

x�f�2�k�M�k� , �1�

where I�k� is the corrected coherent intensity of the scatteredbeam normalized to electron units,32 f��k� and x� are thescattering amplitude and mole fraction for a type of � par-ticle, respectively, and M�k� is the modification function,1 / ��x�f��k��2. The coherent scattering amplitudes were cal-culated as previously described.31 The nitromethane mol-ecules were treated in atomic representation, and the neces-sary parameters were taken from the International Tables forX-ray Crystallography.33

The experimental radial distribution function was com-puted from the structure function h�k� by Fourier transforma-tion according to Eq. �2�,

g�r� = 1 +1

22r�0�

kmin

kmax

kh�k�sin�kr�dk , �2�

where r is the interatomic distance, kmin and kmax are thelower and upper limits of the experimental data, and �0 is theatomic number density. After repeated Fourier transforma-tions the nonphysical peaks present in the g�r� at small rvalues were removed, and the structure function was cor-rected for residual systematic errors.34

In order to characterize the structure of the liquid, as afirst step, a visual evaluation and a preliminary semiquanti-tative analysis of the observed structure functions kh�k� andradial distribution functions g�r� were performed. Further-more, the observed data were analyzed by geometrical modelconstructions and fitting the model structure functions to thecorresponding experimental ones by the nonlinear least-squares method. The fitting strategy was previouslydescribed in Refs. 31.

B. Neutron diffraction measurements

Neutron diffraction experiment on liquid nitromethaneCD3NO2 �99%� was carried out on the 7C2 diffractometerof the Laboratoire Léon Brillouin CEA-SACLAY in a rangeof 0.3�k�15.3 Å−1. The liquid was kept in a vanadiumcontainer of 6 mm diameter and 0.1 mm wall thickness. Theincident neutron wavelength was 0.70 Å. For standardcorrections and normalization procedures, additional runs�vanadium bar, cadmium bar, empty container, and back-ground� were also performed. The raw diffraction data werecorrected for background, container and sample absorption,and multiple scattering, and then the intensities were normal-ized to absolute scale, by using scattering of a vanadiumsample. A more detailed description of the correction proce-dure can be found elsewhere.35

The conversion of the observed total cross sectiond /d� to an r-space representation was performed with theMCGR method36 �Monte Carlo treatment of the experimentalradial distribution function�. In this method, the radial dis-tribution functions, either total or partial, are generated nu-merically and modified by a stepwise random Monte Carloprocess until its inverse Fourier transform agrees with theexperimentally scattering cross section within the limits ofexperimental error.

IV. RESULTS AND DISCUSSION

A. Quantum chemical calculations

The parameters obtained for the optimized structure ofnitromethane molecule with the methods employed in thiswork together with their experimental counterparts37,38 arepresented in Table I. It can be observed that all geometricalparameters obtained from two different levels of theory arein good agreement with experimental results. The two differ-

TABLE I. Characteristic values for eclipsed and staggered conformers of nitromethane molecule obtained withMP2 and B3LYP methods compared to experimental data from literature. Atom-atom distances are given in Å,while frequencies in cm−1. �Subscript s means symmetric, as means antisymmetric, and def means deformation�.

Expt.

Eclipsed Staggered

MP2 B3LYP MP2 B3LYP

rC–N 1.489a 1.497 1.503 1.491 1.503rN–O 1.224a 1.230 1.2209 1.230 1.221rC–H1 1.089a 1.087 1.086 1.0868 1.0886rC–H2 1.089a 1.090 1.090 1.091 1.0853rC–H3 1.089a 1.087 1.086 1.0868 1.0886

��O1NO2� 125.3a 125.6 125.6 125.8 125.6��H1CNO1� −179.9 −179.1 26.9 27.0

�as �CH3� 3048b 3254 3197 3254 3198�as �CH3� 3048b 3230 3166 3230 3165�as �CH3� 2965b 3120 3075 3120 3076�as �NO2� 1582b 1778 1623 1778 1624�s �NO2� 1413b 1441 1428 1439 1428�s,def �CH3� 1488b 1500 1474 1498 1475�as,def �CH3� 1449b 1491 1464 1494 1465�s,def �CH3� 1384b 1419 1400 1419 1399

aReference 37.bReference 38.

164507-3 Structure of liquid nitromethane J. Chem. Phys. 126, 164507 �2007�

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ent conformers eclipsed and staggered of nitromethane mol-ecule are shown in Fig. 1. These conformers have nearly thesame total energy. In the first minima of the O1NCH1 dihe-dral angle is about 180°, but in the other one it is about 30°.The rotation barrier between these two minima is less then0.01 kcal/mol, so it can be concluded that in gas phase therotation of NO2 group around the C–N bond is almost free.These results agree very well with the earlier findings.39,40

The rotational barrier between these two conformers, at T=0 K, in solid state is about 0.54 kcal/mol,41 and in gasphase it is about 0.006 kcal/mol.38,42

The optimized geometry for the dimer of nitromethanemolecules is shifted antiparallel, as shown in Fig. 2. Table IIreports resulting parameter values for the antiparallel struc-ture. Comparison between the geometries of the isolatedmonomer and the monomer geometry in the dimer shows nosignificant change. Table II reveals that the calculated O¯Hdistance is about 2.4–2.5 Å, which is slightly less than thesum of the van der Waals radii of hydrogen and oxygenatoms. From this distance it may be suggested that the ni-tromethane molecules interact with each other in the dimerby weak C–H¯O interaction. In previous works10,11 it was

found that in the nitromethane dimer weak C–H¯O interac-tion held together the two molecules. In our case the BSSEcorrected interaction energy is about 4.16 and 4.45 kcal/molat B3LYP and MP2 levels, respectively. It has already beenshown that the weak H-bonded interaction, if it appears, canbe detected by Bader analysis �atom in molecule method�AIM��, IR spectroscopy �change of CH stretching vibrationfrequency�, and natural orbital analysis �NBO�.

Eight AIM criteria have been proposed before to studyand characterize hydrogen bonds and decide whether theyare conventional or CH¯O bond.43,44 These properties areconnected to the topology of the electron density. When ap-plying these criteria in our case, however, we cannot detectany bond critical point along the CH¯O line.

The characteristic stretching frequencies of methyl groupin monomer and dimer are shown in Tables I and II. If theC–H¯O interaction in dimer would be hydrogen bond, theCH3 stretching frequency would show a redshift. It can beobserved that there are no significant differences between theCH3 stretching frequencies in monomer and dimer struc-tures, meaning that there is no hydrogen bonding interactionin nitromethane dimer.

It has also been shown that the NBO analysis is a usefultool in characterizing the electron transfer processes from theproton acceptor to the proton donor.45 Reed et al.46 investi-gated several typical H-bonded systems, demonstratingcharge transfer from the lone pairs of the proton acceptors tothe antibonding orbitals of proton donor. Specifically helpfulfor the characterization of the hydrogen bond is the secondorder perturbation energy lowering due to the interaction ofthe donor and acceptor orbitals. In our case this value ofenergy lowering is very small �less than 0.1 kcal/mol, butfor a typical H-bonded dimer it is about 1–2 kcal/mol�. The

FIG. 1. Ball and stick representation of nitromethane conformers: �a�eclipsed and �b� staggered. �H and O atoms are identified for the calculationof dihedral angle given in Table I.�

FIG. 2. Ball and stick representation of dimer structure.

TABLE II. Structural and energetic parameters for nitromethane dimer ob-tained with MP2 and B3LYP methods. Atom-atom distances are given in Å,while frequencies in cm−1. �Subscript s means symmetric, as means anti-symmetric, and def means deformation.�

MP2 B3LYP

−�E 7.34 4.45−�EBSSE 4.73 4.16rC–N 1.493 1.503rN–O 1.230 1.2209rC–H1 1.087 1.086rC–H2 1.093 1.090rC–H3 1.087 1.086

��O1NO2� 125.9 125.7��HCNO1� −89.2 −85.8

rCH¯O 2.45 2.43

�as �CH3� 3253 3198�as �CH3� 3231 3164�s �CH3� 3119 3072�as �NO2� 1770 1617�s �NO2� 1443 1432�s,def �CH3� 1499 1473�as,def �CH3� 1496 1469�s,def �CH3� 1429 1403

164507-4 Megyes et al. J. Chem. Phys. 126, 164507 �2007�

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conclusion from the above-mentioned considerations is thatin the nitromethane dimer the CH¯O interaction cannot beconsidered as H-bonded interaction.

B. MD and Car-Parrinello simulation results

1. Radial pair distribution functions „RDFs…

The structure of liquid nitromethane was analyzed interms of radial distribution functions �RDFs�, denoted asg� �r�, for the various atom-atom pairs. The correspondingrunning integration numbers n� �r� are defined by

n� �r� = 4� �0

r

g� �r�r2dr . �3�

The value of this integral up to the first minimum �rm1�

in g�r� is the number of coordinating atoms of type aroundatoms of type � and � is the number density of the atoms oftype at a distance r. The molecular dynamics simulationproduces individual pair distribution functions for each ofthe interactions and these can be analyzed to get an insightinto the arrangement of the molecules in the liquid. TheRDFs of the liquid nitromethane obtained from classical andCar-Parrinello simulations are presented in Fig. 3, and thecharacteristic values of RDFs obtained by classical methodare given in Table III.

The essential features of the RDFs in the two types ofsimulations agree with each other. A small systematic shift ofall peaks toward larger r is apparent for the CP results. As thestatistical accuracy of the classical MD simulation is superiorto the Car-Parrinello simulation, we will use further the val-

ues obtained from the classical MD. The presently obtainedRDFs can also be compared to the results of earlier classicalcomputer simulations. We found our RDF functions to berather similar to those obtained in simulations by Alperet al.15 and Sorescu et al.16

The analysis of RDFs containing the intramolecular in-teractions obtained by the Car-Parrinello method revealedthat the molecular structure in the liquid state does notchange significantly compared to that in the gas phase. It iswell known that in the gas phase the rotation of the CH3

group is nearly free and in the solid state there is a barrier of0.6–0.86 kcal/mol between the two conformers of the ni-tromethane molecule.39

The angle distribution of the HCNO dihedral angle �Fig.4�, as obtained from the Car-Parrinello simulation, shows auniform distribution between 0 and /6, indicating that inthe liquid state the rotation of CH3 group is free.

In the crystalline state18�a� of nitromethane there areabout 18 short CH¯O distances per molecule �rCH¯O

�2.6 Å, which may correspond to the intermolecularCH¯O bonds�. In the O¯H partial radial distribution func-tion a first small peak at around 2.92 Å and an additional oneat 4.23 Å can be found �Fig. 3�. The featureless gOH�r� func-tion in the range of 2–2.6 Å serves as a strong evidence forthe nonexistence of a CH¯O-type hydrogen bond in theliquid state. Seminario et al.17 performed density functional/molecular dynamics study of liquid nitromethane and their

FIG. 3. Partial radial distribution functions obtained from simulations. Mo-lecular dynamics simulation, solid line; Car-Parrinello, dashed line.

TABLE III. Characteristic values for the radial distribution functions g� �r�.n� is the running integration number. Atom-atom distances are given in Å.

Bond type rmax g� �rmax� rmin n� �rmin�

C–C 5.17 1.89 6.57 13.2C–O 3.42 1.82 4.57 3.7C–N 4.27 2.04 5.07 5.8C–H 4.77 1.35 5.42 6.8O–O 3.47 1.06 4.37 2.5O–N 4.47 1.29 5.47 3.4O–H 2.92 1.15 3.67 4.7N–N 5.12 1.52 6.52 12.4N–H 3.62 1.27 4.37 8.7

FIG. 4. Angle distribution of the HCNO dihedral angle obtained in Car-Parinello simulation.

164507-5 Structure of liquid nitromethane J. Chem. Phys. 126, 164507 �2007�

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results clearly indicate the presence of CH¯O-type hydro-gen bond. The reason for this discrepancy could be in thedifference in the model potentials. We remark that thepresent Car-Parrinello simulation does not use any empiricalpotential parameter and gives the first peak of gOH�r� at3.1 Å. This distance is even longer than that obtained bymolecular dynamics simulation and does not support theexistence of CH¯O-type hydrogen bond in liquid.

2. Orientation of the nitromethane molecules

The orientations of the neighboring molecules can becharacterized by the angle dependent radial distribution func-tion. Specifically, we have calculated the angle between thedipole moment vector of center and neighboring moleculesas a function of N¯N distance. The calculated angular radialdistribution functions are shown in Fig. 5. It can be seen thatin liquid nitromethane only the first nearest neighbors tend tobe oriented in an antiparallel form. For N¯N distanceslonger than 4.0 Å, the angular distribution is almost constant,indicating that the preference in orientation is lost veryquickly.

The correlation of the relative orientation of the mol-ecules in the liquid state can be characterized by the coeffi-cients of a spherical harmonic expansion of the orientationalradial distribution function. The details of the spherical har-monics expansion as well as the orientational correlationfunction’s calculation using this expansion are givenelsewhere.47 Here we summarize the technique, followingthe notation used by Gray and Gubbins.48 According to thisformalism the total correlation function g�r ,�1 ,�2� can beexpanded by the following equation:

g�r,�1,�2� = �l1l2l

�n1n2

g�l1l2l:n1n2:r��l1l2l,n1n2��1,�2� , �4�

where �l1l2l,n1n2��1�2� are the generalized spherical harmon-

ics functions. g�l1l2l :n1n2 :r� functions are the r dependentexpansion coefficients, which can be written into the follow-ing form:

g�l1l2l:n1n2:r�

= 4�2l1 + 1��2l2 + 1�

�2l + 1�gcc�r��l1l2l,n1n2

* ��1�2� , �5�

where gcc�r� is the center-center �in our case the N¯N� ra-dial distribution function and �l1l2l,n1n2

* ��1�2� are the com-plex conjugates of the generalized spherical harmonics func-tions.

It is instructive to compare the orientational correlationsin nitromethane and another similar liquid, acetonitrile�CH3CN�. Both liquids have similar dipole moments �aceto-nitrile, 3.44 D; nitromethane, 3.46 D� and possess an identi-cal hydrophobic group �CH3�. Simulations and experimentsindicated that in the liquid acetonitrile the neighboring mol-ecules have a strong preference for antiparallel and slightpreference for parallel head-to-tail configurations.49

The orientational coefficients for the total correlationfunction were determined in liquid nitromethane from thepresent molecular dynamics simulation. Some of these coef-ficients are summarized in Fig. 6 together with the coeffi-cients for liquid acetonitrile calculated from a classical simu-lation using six site Bohm50 model.

The g00110 coefficient is proportional to −cos��� where

� is the angle between the dipolar axes of the two mol-ecules. This function shows a maximum around 4.0 Å,

FIG. 5. Distance dependent angular distribution function. �: angle betweenthe dipole moment vector of center and neighboring molecules.

FIG. 6. Orientational correlation functions: nitromethane �solid line� com-pared to acetonitrile �dashed line�.

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which is a sign of the preference of the molecular dipoles inan antiparallel alignment. This term is very similar to all ofthe investigated cases �classical MD of nitromethane and ac-etonitrile, and CPMD of nitromethane, not shown in Fig. 5�.The other term, which is connected to the angle of the dipolevectors, is the g00

220. In this case there is no significant differ-ence between the coefficients of liquid nitromethane and ac-etonitrile. The g00

101 and g00202 terms are proportional to the

cos��� and cos2��� terms, respectively, where � is theangle between the dipole vector of a central molecule and thevector connecting the two molecules. It is worth noting thatwe have calculated the orientational correlation functions forCar-Parrinello simulation as well �not shown here�, and theyagree well with those obtained from classical simulation ofnitromethane.

The significant difference in the g00101 and g00

202 terms be-tween the liquid nitromethane and acetonitrile can be ex-plained with the help of angular radial distribution function,when the angle distribution �cos���, angle between the di-pole moment of central molecule and the center-center vec-tor� as a function of N¯N distance was calculated �Fig. 7�.Figure 7�a� shows that in liquid acetonitrile the cos��� angledistribution has a symmetrical shape around 0, correspond-ing to the energy minimum configuration of acetonitriledimer. In the case of liquid nitromethane �Fig. 7�b��, thecenter of cos��� distribution is around 0.25, correspondingto the shifted antiparallel orientation of nitromethane dimer.

On the basis of simulation study, it can be concluded thatthe local structure of liquid nitromethane is determined by

dipolar forces, with a slight preference to antiparallel and nopreference to parallel or head-to-tail configurations. It shouldbe mentioned that we have obtained this structural informa-tion based on the detailed analysis of the molecular dynamicssimulations. The previous MD studies15,16 did not provideany comprehensive structural information, for they were fo-cused mainly on testing the newly developed model poten-tials and comparing their predictions with the experimentallyaccessible vibrational quantities and the overall thermody-namic behavior of the liquid. Given the obvious limitation ofthe information contained in angle-averaged RDFs, it is evi-dent from the present study that for deeper understanding ofthe liquid structure by using computer simulations, it is nec-essary to analyze the obtained configurations as deeply aspossible.

C. Structural results from x-ray diffraction

At first a semiquantitative analysis was done at the levelof the radial distribution functions; as a second step a least-squares fitting method was used to determine the intra- andintermolecular structural parameters. The average scatteringweighting factors of the different partial distribution func-tions were as follows: C–C, 0.04; C–N, 0.08; C–O, 0.18;N–O, 0.21; N–N, 0.05; and O–O, 0.25. After examination ofthe weights of the contributions to the structure function onecontribution for each type of interatomic distance listed inTable II was involved in the fitting procedure.

The experimental and theoretical x-ray structure func-tions, derived from experiment, are shown in Fig. 8, and theradial distribution functions are shown in Fig. 9.

For the first peak centered around 1.20 Å, intramolecularC–N and N–O interactions are responsible. The small secondpeak can be observed in the range 1.85–2.70 Å. This peakcan be assigned to C–O and O¯O distances. Another broadpeak appears in the range 3.50–5.85 Å. This peak is difficultto resolve because of its complexity, and can be attributed tovarious intermolecular atom-pair interactions.

The structural parameters obtained from the least-squares fit of the structure functions kh�k� shown in Fig. 8are given in Table IV. The fitting procedure resulted in1.49±0.01 and 1.22±0.01 Å for the intramolecular C–N andthe N–O distances, respectively. The O¯O distance wasfound to be 2.17±0.02 Å and C–O distances 2.32±0.01 Å.

FIG. 7. Distance dependent angular distribution function. �: angle betweenthe dipole moment of central molecule and the center-center vector. �a�Acetonitrile and �b� nitromethane.

FIG. 8. Structure functions h�k� multiplied by k for nitromethane obtainedby x-ray diffraction. Circles, experimental values; solid line, fitted values.

164507-7 Structure of liquid nitromethane J. Chem. Phys. 126, 164507 �2007�

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Once the intramolecular structure was found, various modelswere tested to determine the intermolecular structure of theliquid. Trial models containing nitromethane dimers in par-allel and/or antiparallel orientations failed completely. Then,a decision has been made not to assume any initial intermo-lecular geometrical picture for the structure at the beginningof the fitting procedure. Due to their low contribution to thetotal scattering picture, intermolecular interactions �C¯C,C¯N, N¯N� could not be determined. The three other in-termolecular distances, C¯O, N¯O, and O¯O, contributewith nearly similar weights to the total scattering intensityand it is not possible to resolve the interactions one by one.Consequently, no suggestions could be made on the intermo-lecular structure of liquid nitromethane on the basis of x-raydiffraction alone. The solution for this problem might be toperform a comparison of the intermolecular radial distribu-tion functions obtained by x-ray diffraction and moleculardynamics simulation �see Sec. V�.

D. Structural results from neutron diffraction

The total cross section d /d� of liquid deuterated ni-tromethane and the structure function I�Q� together with theresults of MCGR procedure are presented in Fig. 10. The total,

intramolecular, and intermolecular radial distribution func-tions are shown in Fig. 11. The intramolecular distances weredetermined using a least-squares fitting procedure and re-sulted in 1.19±0.01, 1.47±0.03, 2.12±0.02, and2.26±0.02 Å for the N–O, C–N, O–O, and C–O bonds, re-spectively. Least-squares refined values for the X–H dis-tances were 1.07±0.01 Å for C–H, 2.06±0.03 Å for N¯H,and 1.74±0.01 Å for H¯H. The results are shown in TableII. Previous neutron diffraction studies on various molecularliquids resulted in the following values: C–H distance in me-thyl group of 1.06–1.09 Å,51 H¯H distance in methyl groupof 1.73–1.79 Å,35�d�,51�d� and N¯H distances in formamideof 2.04–2.09 Å.52

Overall, the intramolecular distances obtained by least-squares fitting agree fairly well with similar distances inother compounds determined from neutron diffraction data.They also agree with the results of our x-ray diffraction studyon proteated nitromethane. The intermolecular distributionfunction determined from the neutron data is, however,rather featureless, and just like in the case of the x-ray dif-fraction, no suggestions could be made on the intermolecularstructure of the nitromethane on the basis of neutron diffrac-

FIG. 9. Radial distribution functions for nitromethane obtained from x-raydiffraction. Circles, experimental values; dashed line, intramolecular contri-bution; open circles, intermolecular contribution; solid line, intermolecularcontribution obtained from MD simulation.

TABLE IV. Structural parameters from the x-ray and neutron diffractionrefinement with estimated errors in the last digits. n is the coordinationnumber. Distances �r� and their mean-square deviations �� are given in Å.

Bond type r n

X-ray diffractionC–N 1.49�1� 0.08�2� 1C–O 2.32�1� 0.10�1� 2N–O 1.22�1� 0.05�1� 2O–O 2.17�2� 0.10�2� 1

Neutron diffractionC–N 1.47�2� 0.12�1� 1C–O 2.26�2� 0.13�2� 2N–O 1.19�1� 0.09�2� 2O–O 2.12�2� 0.12�1� 1C–H 1.07�1� 0.07�1� 3N–H 2.06�3� 0.13�2� 3H–H 1.74�1� 0.13�1� 2

FIG. 10. Total differential cross section and structure function �inset� ofnitromethane obtained from neutron diffraction experiment �cross and opencircles, experimental values; solid line, fit by the MCGR procedure�.

FIG. 11. Radial distribution function g�r� obtained from the neutron diffrac-tion. Circles, experimental values; dashed line, intramolecular contribution;open circles, intermolecular contribution; solid line, intermolecular contri-bution obtained from MD simulation.

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tion data. In Sec. V a comparison of the total radial intermo-lecular distribution function obtained from molecular dy-namics simulation and neutron diffraction is described.

V. COMPARISON OF EXPERIMENTSAND SIMULATIONS

The radial distribution functions obtained from the x-rayand neutron diffraction experiments are compared with thoseobtained from simulation in Figs. 9 and 11, respectively.

The total structure function relevant to the liquid struc-ture �not including the intramolecular contribution� has beencalculated from the partial radial distribution functions ac-cording to the equation

H�k� = ���

� �2 − �� �x�x f�f h� �k�M�k�

, �6�

where f� is the scattering length or scattering factor of the�-type atom �which depends on k in the case of x-ray dif-fraction�, and x� is the mole fraction of the � atom. h� �k� isdefined according to the following equation:

h� �k� = 4��0

rmax

r2�g� �r� − 1�sin�kr�

krdr . �7�

The total radial distribution function is defined as the Fouriertransform of the structure function.

Figure 12�a� shows the contributions of each interactionto the total intermolecular radial distribution function, ob-tained from molecular dynamics simulation. It can be ob-served that the three interactions, C–X, O1–X, and N–X,contribute in nearly the same ratio to the total intermolecularradial distribution function. That is the reason for the note-worthy uncertainty of the x-ray diffraction method in thedetermination of intermolecular structure of liquid ni-tromethane and the only suggestion could be the comparisonbetween the x-ray diffraction and the theoretical radial dis-tribution functions.

The agreement between the radial distribution functionobtained by x-ray diffraction and the theoretical radial distri-bution function is very good, meaning that the averagepicture of the structure of liquid nitromethane obtained bymolecular dynamics simulation is confirmed by x-raydiffraction.

Figure 12�b� shows the contributions of each interactionto the total intermolecular radial distribution function, ob-tained from molecular dynamics simulation, for the case ofneutron data. It can be observed that the situation is evenworse than in the case of x-ray diffraction because all theinteractions considered, except O–O, contribute with about20% to the total intermolecular radial distribution functionand there is not a real chance to resolve them. Comparing thetotal radial distribution functions that resulted from neutrondiffraction experiment and the simulation, a slight shift be-tween them can be observed, which may originate from thenot perfect separation of the inter- and intramolecular partsof the experimental structure factor.

VI. CONCLUSIONS

A combined theoretical and experimental study of liquidnitromethane was carried out. The results of molecular dy-namics simulations and diffraction experiments were com-pared in order to obtain a more reliable picture of the struc-ture of the liquid. The limitations of the applied methods arealso discussed.

The diffraction methods are known for the solutionchemists as “direct methods for structural determination.”This would mean that the parameters obtainable from radialdistributions are characteristic of local structures in the liquiddirectly and no further speculation is needed for extractingthem from the experimental data. However, the nitromethaneis a very good example when one can see that the localstructure of the liquid cannot be determined only on the basisof the diffraction data.

Quantum chemical calculations showed that there aretwo different conformers, eclipsed and staggered, of ni-tromethane molecule, with nearly the same total energy. Therotation barrier between these two minima is less then0.01 kcal/mol; therefore, the rotation of NO2 group aroundthe C–N bond is almost free. The optimized geometry for thedimer of nitromethane was obtained to be molecules shiftedantiparallel and it has been found that in the nitromethanedimer the CH¯O interaction cannot be considered asH-bonded interaction.

The essential features of the RDFs in molecular dynam-ics and Car-Parrinello simulations agree with each other andare similar to the results of earlier classical computer simu-lations. The Car-Parrinello method revealed that the molecu-lar structure in the liquid state does not change significantlycompared to that in the gas phase. The angle distribution ofthe HCNO dihedral angle, as obtained from the Car-Parinellosimulation, shows a uniform distribution between 0 and /6,indicating that in the liquid state the rotation of CH3 group isfree. According to the molecular dynamics simulation studyno predominated occurrence of nitromethane dimers in theliquid nitromethane could be detected; however, the position

FIG. 12. Contribution of different interactions to the total radial distributionfunction measured by �a� x-ray diffraction and �b� neutron diffraction.

164507-9 Structure of liquid nitromethane J. Chem. Phys. 126, 164507 �2007�

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and orientation of the nearest neighbor molecules resembleto some extent the configuration of the theoretically calcu-lated energy-minimized dimer. Neighboring C–N bond vec-tors slightly prefer an antiparallel orientation over a parallelone and there is no evidence for parallel or head-to-tail con-figurations in the liquid. In the liquid state CH¯O-typeweak hydrogen bonds could not be detected.

The radial distribution functions of MD simulation andx-ray diffraction agree very well. The small discrepancy be-tween the radial distribution functions obtained by simula-tion and neutron diffraction results may be due to both thepotential model applied in the simulation and to the experi-mental uncertainties, but the theoretical and experimentalfindings are in general accordance.

It is important to mention that while x-ray diffractionand neutron diffraction fail in determining the bulk structure,both methods are performing very well in the determinationof intramolecular distances. It should be emphasized that wehave obtained structural information of liquid nitromethaneon the detailed analysis of the molecular dynamics simula-tions and comparison with diffraction experiments; therefore,for deeper understanding of the liquid structure it is advis-able to apply simultaneous theoretical and experimentalmethods.

ACKNOWLEDGMENTS

This research was supported by the project NAP VE-NEUS05 �OMFB-00650/2005� and the Hungarian ScientificResearch Fund �OTKA�, Project Nos. F 67929, K 68498, andK 68140. Support from the Hungarian/Austrian WTZ col-laboration project A9/2004 is gratefully acknowledged. Theauthors wish to thank to Marie-Claire Bellisent-Funel herhelp with the neutron diffraction measurements on the dif-fractometer 7C2 of the Laboratoire Léon Brillouin CEA-SACLAY.

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