Orientational Correlations in Liquid Acetone and Dimethyl Sulfoxide: a Comparative Study Sylvia E

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2006 Orientational correlations in liquid acetone and dimethyl sulfoxide: A comparative study Sylvia E. McLain Rutherford Appleton Laboratories

Alan K. Soper Rutherford Appleton Laboratory

Alenka Luzar Virginia Commonwealth University

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McLain, S. E., Soper, A. K., Luzar, A. Orientational correlations in liquid acetone and dimethyl sulfoxide: A comparative study. The ourJ nal of Chemical Physics 124, 074502 (2006). Copyright © 2006 AIP Publishing LLC.

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Orientational correlations in liquid acetone and dimethyl sulfoxide: A comparative study ͒ Sylvia E. McLaina and Alan K. Soper ISIS Facility, Rutherford Appleton Laboratories, Chilton, Didcot, Oxon OX11 0QX, United Kingdom Alenka Luzar Department of Chemistry, Virginia Commonwealth University, Richmond, Virginia 23284-2006 ͑Received 10 August 2005; accepted 4 January 2006; published online 16 February 2006͒

The structure of acetone and dimethyl sulfoxide in the liquid state is investigated using a combination of neutron diffraction measurements and empirical potential structure refinement ͑EPSR͒ modeling. By extracting the orientational correlations from the EPSR model, the alignment of dipoles in both fluids is identified. At short distances the dipoles or neighboring molecules are found to be in antiparallel configurations, but further out the molecules tend to be aligned predominately as head to tail in the manner of dipolar ordering. The distribution of these orientations in space around a central molecule is strongly influenced by the underlying symmetry of the central molecule. In both liquids there is evidence for weak methyl hydrogen to oxygen intermolecular contacts, though these probably do not constitute hydrogen bonds as such. © 2006 American Institute of Physics. ͓DOI: 10.1063/1.2170077͔

I. INTRODUCTION separated resonance contributions playing only a small role in the ground-state description of the molecule. The differ- Understanding the relationships between the intermo- ence between these two bonding regimes is supported by the lecular interactions present in the liquid state is important in X–O ͑X=S,O͒ bond length, discussed below, as well as by providing a complete picture of any solvent. Dimethyl sul- the difference in the dielectric constant observed for these foxide ͑DMSO͒ and acetone are both common organic sol- two molecules as higher charge separation in a bond gener- 1 vents with wide industrial applications. Their efficacy as ally gives rise to higher dielectric constants. solvents is predominately attributed to their polar aprotic DMSO crystallizes in the monoclinic space group P21 /C nature where both liquids possess high dielectric constants at 5 K and shows a S–O bond length of 1.531 Å,19 which is ͑ ͒ acetone=20.7 at 20 °C; DMSO=47.2 at 20 °C and dipole shorter than the calculated single bond for DMSO but not ͑␮ ␮ moments DMSO=3.96 D; acetone=2.88 D in the gas sufficiently short to support a formal S O bond assign- ͒ 2–4 v phase . Both molecules possess the same molecular ment. Acetone on the other hand crystallizes in the ortho- groups differing only with respect to the central atom and as rhombic space group Pbca with a CvO bond length of such the differences observed between acetone and DMSO, 9 1.21 Å consistent with the C O double-bond formalism. both with regard to the macroscopic properties as well as in v In both crystalline DMSO and crystalline acetone, the mol- the structure itself, are due to the electronic differences be- ecules are layered along the c axis aligned in a configuration tween sulfur and carbon. that minimizes their dipole-dipole interactions. While DMSO In the gas phase DMSO and acetone adopt different ge- molecules are aligned in an antiparallel fashion consistently ometries which are easily predicted by valence shell electron 5 throughout the crystal, the structure of acetone beyond the pair repulsion rules. Gaseous DMSO adopts a pyramidal Cs geometry by virtue of a lone pair of electrons present on nearest-neighbor distance consists of perpendicular carbonyl interactions between each pair of antiparallel nearest neigh- sulfur while acetone shows a planar C2␯ geometry. Previous studies in the gas, liquid, and solid states show that this bors. When lowering the temperature or applying pressure to molecular geometry is conserved in all states for both acetone in the solid state, the antiparallel interactions are lost molecules.6–15 and only perpendicular carbonyl interactions are observed. The nature of the S–O bond in DMSO has been the This structural change which necessarily shortens the subject of several calculational investigations which show CvO¯CvO and C–H¯O contacts between acetone that a S+ –O− formulation is the best representation, rather molecules has been used to justify the broad heat-capacity 16–18 ͑ ϳ ͒ 9,20 than a formal double SvO bond. This formal charge transition over 60 K observed in solid-state acetone. separation will necessarily contribute strongly the dipole mo- Several structural studies of both DMSO and acetone ment of the molecule. In contrast to DMSO, there is a formal both as pure liquids and as components of mixtures have double bond between C and O in acetone, with charge- been performed by diffraction6–8,10,12,21–24 as well as simulation.10–12,25–45 DMSO has been the subject of the ma- ͒ a Author to whom correspondence should be addressed. Electronic mail: jority of these studies whereas the structure of pure acetone [email protected] has not been as widely reported. DMSO is more widely

0021-9606/2006/124͑7͒/074502/12/$23.00124, 074502-1 © 2006 American Institute of Physics This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.172.48.58 On: Tue, 13 Oct 2015 15:21:27 074502-2 McLain, Soper, and Luzar J. Chem. Phys. 124, 074502 ͑2006͒

studied because of its extensive application in many disci- TABLE I. Weighting factor for partial structure factors present in measured plines such as biochemistry, organic chemistry, and DMSO and acetone samples where X=S for DMSO and X=Cc for acetone. biophysics.1,46,47 d6-DMSO d6-acetone h6-acetone 0.5h6 :0.5d6-acetone This study details the results of neutron diffraction measurements on acetone and DMSO in the liquid state. Addi- H–H 0.4170 0.3704 0.2202 0.0645 tionally computer simulation by empirical potential structure H–C 0.2771 0.2460 0.2609 0.1961 H–X 0.0750 0.1230 0.1305 0.0981 reﬁnement ͑EPSR͒ has been employed to model the diffrac- 48 H–O 0.1211 0.1075 0.1138 0.0855 tion data. Given the large number of interatomic distances C–C 0.0457 0.0409 0.0775 0.1484 in these molecules, it is difﬁcult to build a complete three- C–X 0.0198 0.0409 0.0775 0.1484 dimensional picture of either liquid through experiment C–O 0.0401 0.0356 0.0674 0.1291 alone. Using this combination of neutron diffraction mea- X–X 0.0002 0.0102 0.0193 0.0369 surements coupled with the EPSR method orientational cor- X–O 0.0009 0.0178 0.0337 0.0646 relation functions have been extracted from the resulting O–O 0.0009 0.0008 0.0149 0.0285 model which are consistent with the measured data for both 48 ␴ ␴ ␴ liquids. d d d 2 = + = ͚ c␣b ͑1+P͑Q,␪͒͒ + F͑Q͒, ⍀ ⍀ ⍀ ␣ d d self d distinct ␣ ͑1͒ ͑ ␪͒ ͑ ͒ where P Q, is the inelastic contribution and FN Q is the II. NEUTRON DIFFRACTION MEASUREMENTS total scattering structure factor arising from the “distinct A. Theory scattering” contribution, c␣ is the atomic fraction, and b␣ the scattering length of isotope ␣. F͑Q͒ is the sum of all Faber- Neutron diffraction with isotopic substitution is the pre- Ziman partial structure factors, S␣␤͑Q͒, present in the sample mier technique by which the structure of molecular liquids weighted by their composition and scattering intensity. F͑Q͒ 49–57 containing hydrogen has been determined. This is prima- and S␣␤͑Q͒ are related by the following equation: rily due to the lack of correlation between the atomic number and the strength of the nuclear scattering interaction where F͑Q͒ = ͚ ͑2−␦␣␤͒c␣c␤b␣b␤͑S␣␤͑Q͒ −1͒, ͑2͒ ␣␤ജ␣ light atoms, such as hydrogen, have scattering intensities on the same order of magnitude as heavier elements.58 The where Q is the magnitude of the change in momentum vector quantity measured in a neutron diffraction experiment is the by the scattered neutrons and Q=4␲ sin ␪/␭. For both ac- differential scattering cross section, d␴/d⍀, etone and DMSO, F͑Q͒ can be written as

͑ ͒ 2 2 ͓ ͑ ͒ ͔ ͓ ͑ ͒ ͔ ͓ ͑ ͒ ͔ ͓ ͑ ͒ ͔ F Q = bHcH SHH Q −1 +2bHbOcHcO SHO Q −1 +2bHbXcHcX SHX Q −1 +2bHbCcHcC SHC Q −1 ͓ ͑ ͒ ͔ ͓ ͑ ͒ ͔ ͓ ͑ ͒ ͔ 2 2 ͓ ͑ ͒ ͔ +2bObXcOcX SOX Q −1 +2bCbXcCcX SCX Q −1 +2bObCcOcC SOC Q −1 + bOcO SOO Q −1 2 2 ͓ ͑ ͒ ͔ 2 2 ͓ ͑ ͒ ͔ ͑ ͒ + bCcC SCC Q −1 + bXcX SXX Q −1 , 3

where X=S for DMSO and X=CC, signifying the carbonyl 4␲␳ ͑ ͒ ͵ ͓ ͑ ͒ ͔ ͑ ͒ ͑ ͒ S␣␤ Q =1+ r g␣␤ r −1 sin Qr dr, 4 carbon, for acetone. The neutron weights outside each partial Q structure factor for each sample are shown in Table I. In order to show the relative intensity of scattering from each where ␳ is the number density of the sample, 0.0819 and partial structure factor with respect to one another the 0.0844 atoms/Å−3 for acetone and DMSO, respectively. weighting factors shown in the table have been normalized Fourier transformation of the measured total structure factor by dividing each by the sum of the total scattering in the yields the total radial distribution function whereas the Fou- ͚ rier transformation of any partial structure factor yields the sample, ␣,␤c␣c␤b␣b␤. The Fourier transform of any structure factor yields the corresponding site specific RDF. associated radial distribution function, G͑r͒, which is the sum of the respective atom-atom radial distribution functions B. Experiment ͑RDF’s͒, g␣␤͑r͒’s, each weighted by concentration and scattering length of atomic species, ␣ and ␤, present in the In order to extract site-specific information in acetone sample. and DMSO, neutron diffraction experiments were performed S␣␤͑Q͒ is related to the radial distribution function on isotopomers of the two pure fluids at 298±3 K. All ͑ ͒ g␣␤ r via liquids—d6-acetone, h6-acetone, and d6-DMSO—were pur- This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.172.48.58 On: Tue, 13 Oct 2015 15:21:27 074502-3 Orientational correlations in acetone and dimethyl sulfoxide J. Chem. Phys. 124, 074502 ͑2006͒

TABLE II. Isotopomers of acetone and DMSO measured on a SANDALS. well as the density of each sample to be confirmed. In each case the level of d␴/d⍀ was checked after the application of Sample Acetone Sample size ͑mm͒ corrections using GUDRUN by comparison with theoretical ͑ ͒ 58 d6-acetone CD3 2CO 2 values based on the known density and composition. In ͑ ͒ h6-acetone CH3 2CO 1 each sample measured the level of scatter measured by the ϳ 0.5h6 :0.5d6- ͓͑ ͒ ͔ ͓͑ ͒ ͔ transmission monitor was approximately 10% below the CH3 2CO 0.5 CD3 2CO 0.5 1 acetone expected level, likely due to machining uncertainties on the DMSO interior of the sample containers. For this reason in each ͑ ͒ d6-DMSO CD3 2SO 1 diffraction pattern the effective thickness of each sample was adjusted until the scattering level was within 1% of the expected value. chased from Sigma/Aldrich chemical company and were used without further purification. The diffraction data were III. EPSR AND ORIENTATIONAL CORRELATION obtained using the Small-Angle Neutron Diffractometer for FUNCTION ANALYSES ͑ ͒ Amorphous and Liquid Samples SANDALS located at the A. Methods ISIS pulsed neutron facility at Rutherford Appleton Labora- tory in the UK. SANDALS is an instrument well suited for 1. EPSR structural measurements of liquids containing hydrogen with EPSR was used to model the diffraction data collected detectors that range from 3.9° to 39°, giving a Q range from from isotopomeric samples of both liquids. EPSR is a com- 0.15 to 50 Å−1. In addition to the detectors, SANDALS is putational method created for modeling disordered materials equipped with a transmission monitor which measures the such as liquids and glasses,48,50 which allows the reconstruc- ␴ total cross section of the sample being measured, trans, relation of orientational correlation functions from a set of one- tive to the incident beam. Each of the samples measured was dimensional structure factor measurements in a manner contained in sample cells constructed from a Ti/Zr null alloy which is consistent with the measured data. metal where each cell has a 1 mm wall thickness. The use of EPSR begins with a standard Monte Carlo simulation this alloy allows for minimal coherent scattering from the using an initial reference potential where the potential con- sample cell leading to a more tractable data analysis for the sists of an intramolecular harmonic potential to define the samples themselves. The samples measured are listed in geometry of the molecules being modeled, and an intermo- Table II along with the size of the sample measured by neu- lecular potential, which, in the present case, consisted of tron diffraction. Lennard-Jones 12-6 potentials for the site-site interactions on The diffraction data collected for d6-DMSO have been different molecules as well as Coloumbic interactions for previously reported along with two different isotopomers of some sites. This reference potential is used to generate a DMSO, namely, h6-DMSO and a 0.67h6 :0.34d6-DMSO starting configuration of molecules. EPSR then iteratively mixture in a combined neutron diffraction and molecular- adjusts a perturbation to this reference potential to obtain the 10 ͑ ͒ dynamics study. Although the d6-DMSO data reported here best possible agreement between the computed F Q and the have been previously collected they have been reanalyzed in experimental diffraction data.48,50 the present work from the raw data to differential cross sec- While EPSR provides a molecular ensemble which is tion. The h6-DMSO and 0.67h6 :0.34d6-DMSO data were consistent with the diffraction data measured, it does not also analyzed; however, it was clear in a subsequent analysis necessarily provide a definitive model for the structure of the that both of the data sets collected from these two samples liquid in question. There may be several distinct structures were probably contaminated with water impurities, and so which give an equally reasonable agreement between the have not been used in the present analysis. The water was data and simulation. This is especially true in the present detected from the presence of a small negative peak at case where there are many more partial structure factors than r= ϳ0.98 Å in the Fourier transform of the data ͑the corre- available diffraction contrasts. Therefore it is imperative that sponding C–H peak is at ϳ1.08 Å͒ arising from the O–H the simulation box be constrained from the outset with as bond in water. A similar peak was not present in the much prior information regarding the properties of the liquid d6-DMSO sample. This feature of the older data was de- in question as is possible. For example, in the present study tected as a result of the present method of data interpretation the large dipole moments and dielectric constants observed using EPSR, and was not noticed with the earlier methods as in liquid acetone and DMSO are important factors to con- in the previous study the intramolecular contribution to the sider when defining the reference potential. diffraction pattern was subtracted prior to the analysis of the The purpose of EPSR analysis in the present instance is composite intermolecular radial distribution functions.10 not only to extract three-dimensional information from a For each measurement the raw data for each sample as model at the correct atomic number density which is consis- well as for each sample container have been converted to tent with the diffraction data but also to explore the validity differential scattering cross section, after correcting for ab- of some potential models against a set of diffraction data. sorption, multiple scattering, and inelasticity effects, by us- EPSR generates an effective site-site interaction potential ing a program, GUDRUN, which is a new version of the pre- which reproduces the measured diffraction data as close as 59 vious ATLAS suite of programs available at ISIS. possible. It has, however, so far proved impossible in EPSR ␴ The measurement of trans allows for the composition as to constrain both the energy and pressure in any reliable way This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.172.48.58 On: Tue, 13 Oct 2015 15:21:27 074502-4 McLain, Soper, and Luzar J. Chem. Phys. 124, 074502 ͑2006͒

as well as fit the diffraction data, so the simulation cannot be ͑ ␻ ␻ ͒ ͑ ͒ g r, 1, 2 = ͚ ͚ ͚ g l1l2l;n1n2;r relied upon to reproduce the correct thermodynamics as well. l1l2l m1m2m n1n2 Obtaining a fit to the measured data does not ensure the ϫC͑l l ;m m m͒ potential model is correct, but it is a necessary condition for 1 2 1 2 ϫ l1 ͑␻ ͒* l2 ͑␻ ͒* l ͑␻ ͒ ͑ ͒ any chosen potential model of the liquid. This direct com- Dm n 1 Dm n 2 Dm0 L , 5 parison with the diffraction data in Q space is rarely done 1 1 2 2 ͑ ͒ with conventional molecular dynamics and Monte Carlo where C l1l2l;m1m2m are the Clebsch-Gordan coefficients, ␻ ␻ simulations of molecular liquids. Ideally a wide range of 1 represents the Euler angles of molecule 1, 2 represents ͑ ␻ ͒ initial reference potentials should be explored, for example, the Euler angles of molecule 2, and r= r, L represents the those which include three-body or many-body forces such as position of molecule 2 relative to molecule 1 in the labora- polarizability. Unfortunately such a task is still beyond most tory coordinate frame. computing strategies, and as such the most likely potentials In order to reconstruct the orientational correlation func- must be selected from the literature for each individual case tion it is convenient to set molecule 1 at the origin and orient ␻ and tested against the experimental data. it so that 1 =0. This serves to define the coordinate system Having found, through EPSR, a model liquid structure about which the spatial density and orientation of second consistent with the diffraction data, it is useful to extract ͑neighboring͒ molecules will be plotted. It also leads to an ͑ ͒ l ͑ ͒ structural information from the simulation box concerning immediate simplification of Eq. 5 in that Dmn 000 the intermolecular distributions, such as the individual site- =␦͑mn͒, so that combining this with the requirement from site RDF’s, vide infra, as this information is not directly the Clebsch-Gordan coefficients that m=m1 +m2, the orienta- available from the experimental data. Because the site-site tional pair-correlation function relative to a central molecule RDF’s only give a one-dimensional representation of the at the origin is given by fluid, it is difficult to use these distances to visualize the local g͑r,␻,␻ ͒ = ͚ ͚ ͚ g͑l l l;n n ;r͒ spatial and orientational orders in three dimensions. For this M 1 2 1 2 l l l m n n reason, spatial density functions ͑SDF’s͒,60,61 which allow a 1 2 1 2 ϫ ͑ ͒ l2 ͑␻ ͒* l ͑␻ ͒ ͑ ͒ C l l l;n m m D M D L , 6 three-dimensional representation of the liquid structure to be 1 2 1 2 m2n2 m0 constructed, were used to help determine the most probable nearest-neighbor positions for both fluids in the present where m2 =m−n1. The spatial density function is generated study. Although the SDF’s show the most probable location by averaging the full orientational pair-correlation function ␻ of nearest-neighbor molecules they do not necessarily give over the orientations of the second molecule, M ϵ͑␸ ␪ ␹ ͒ direct orientational information about the surrounding mol- M M M , which immediately eliminates any terms in the ͑ ͒ ecules. In light of this some aspects of the orientational pair- summation shown in Eq. 6 for which l2 ,m2 ,n2 0. Hence correlation function ͑OCF͒ are also shown.59 These tasks are the spatial density function is expressed as achieved via spherical harmonic expansion of the full orien- ͑ ␻͒ ͑ ͒ ͑ ͒ l1 ͑␻ ͒ g r, = ͚ ͚ g l 0l ;n 0;r C l 0l ;n 0n D L , 62,63 1 1 1 1 1 1 1 n10 tational pair-correlation function, using the simulation l1 n1 box to derive the positional and orientational coordinates of ͑7͒ the molecules, and are described in more detail in the following section. from the closure relations for the Clebsch-Gordan coeffi- ͑ ജ ജ͉ ͉͒ cients l1 +l2 l l1 −l2 . In general the full orientational pair-correlation function 2. Spatial density and orientational pair-correlation ͓Eq. ͑6͔͒ is difficult to visualize because it is a function of six functions coordinates. To assist in this visualization, the spatial density The details of the spherical harmonic expansion as well function can be plotted to gauge the most likely places of as the orientational correlation function calculation using a finding neighboring molecules, then the orientational corre- ␻ spherical harmonic expansion are given in detail lation function can be plotted for a specified L, after aver- elsewhere.62,63 Here a summary of these techniques which aging over one of the remaining angular coordinates, e.g., ␹ follow the notation used by Gray and Gubbins explicitly is M, as is done in the present work. This eliminates from ͑ ͒ presented.63 Eq. 6 all terms for which n2 0, leaving an average orien- A set of Euler angles within the laboratory reference tational pair-correlation function which is a function of three ␸ ␪ frame ␻ ϵ͑␸ ␪ ␹ ͒ for each molecule M is calculated variables, r, M, and M, for a specified direction M M M M ␻ ϵ͑␪ ␸ ͒ using a predefined set of molecular coordinate axes. The cor- L L L away from the central molecule. Other averages responding set of generalized spherical harmonic functions, of the orientational pair-correlation function over angular co- Dl ͑␻ ͒, are calculated for each molecule and for a range of ordinates can be obtained by eliminating other terms in the mn M ͓ ͑ ͔͒ ͑l,m,n͒ values ͑up to l=4 in the present instance͒. The set of full expression Eq. 6 . such functions is then correlated taking into account the relative position rϵ͑r,␻ ͒ϵ͑r,␪ ␸ ͒ of the second molecule L L L B. Simulation with respect to the first, yielding a set of orientational corre- ͑ ͒ 63 lation function expansion coefficients, g l1l2l;n1n2 ;r . EPSR simulations were performed for both acetone and From these coefficients the full orientational pair-correlation DMSO by constructing a box containing 500 molecules at function is obtained as an expansion of the form the appropriate density for each liquid. Table III shows the This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.172.48.58 On: Tue, 13 Oct 2015 15:21:27 074502-5 Orientational correlations in acetone and dimethyl sulfoxide J. Chem. Phys. 124, 074502 ͑2006͒

TABLE III. Intramolecular geometries used to construct the EPSR simulation boxes for acetone and DMSO.

Acetone Bond ͑Å͒ Angle ͑°͒

H–Cm 1.10 H–Cm –H 110.0 Cm –CC 1.50 Cm –CC –Cm 118.0 CC –O 1.21 CC –CC –H 113.0 O–CC –Cm 121.0

DMSO Bond ͑Å͒ Angle ͑°͒

H–C 1.10 H–C–H 110.0 C–S 1.74 C–S–C 99.0 S–O 1.53 S–C–H 111.0 114.0

intramolecular angles and distances used for the input mol- ͑ ͒ ͑ ͒ FIG. 1. F Q data circles for d6-acetone, 0.5h6 :0.5d6-acetone, and ecules for each set of EPSR simulations. In each simulation, ͑ ͒ h6-acetone at T=298 K and subsequent EPSR fits solid lines to the data the methyl hydrogens were allowed to freely rotate around using the ͑a͒ FHMK reference potential ͑Ref. 27͒ and ͑b͒ the WR reference ͑ ͒ the CC –Cm axis in acetone and the S–C axis in DMSO. potential Ref. 40 . The 0.5h6 :0.5d6-acetone data have been shifted by 0.6 For acetone, the three measured structure factors were and the h6-acetone data have been shifted by 1.1 in each case for clarity. simultaneously fit using the acetone potential developed by 27 Ferrario et al. as the reference potentials, hereafter termed Clearly, both the WR and FHMK reference potentials pro- FHMK, as well as a potential developed by Wheeler and 40 vide good starting points for the EPSR fits to the three data Rowley, hereafter termed WR. Both of these potentials are sets measured. The only exception is at low values of Q͑Q listed in Table IV where Cm refers to the methyl carbons and Ͻ3Å−1͒ where the background and inelasticity corrections CC refers to the central carbonyl carbon in acetone. Table IV to the data are most difficult to remove when the isotopomers also lists two separate potentials for DMSO, P1 and P2, de- contain light hydrogen, as is the case with the h -acetone and et al.10,11 6 veloped by Luzar which were used as reference the 50:50 mixture. Although the starting potentials are differ- potentials for EPSR fits to the DMSO diffraction data. ent, the fits to the data show no obvious differences, indicating that the EPSR procedure is able to counteract differences IV. RESULTS between the two reference potentials with regard to repro- ducing the structure. Figure 2 shows the site-site RDF’s ob- The total structure factor data for the three acetone mea- tained from both of these models and as expected from the surements are shown in Fig. 1 along with the two EPSR fits fits in Fig. 1, there are negligible differences in these func- to the data using the FHMK and WR reference potentials. tions between the two fits. Additionally, Table V shows the coordination numbers for each RDF shown in Fig. 2. TABLE IV. Reference potentials used for initial input into EPSR fits to The total structure factor measurement for d6-DMSO diffraction data for acetone and DMSO ͑Refs. 10, 11, 27, and 40͒.

Acetone/FHMK ͑Ref. 27͒ ␧ −1 ␴ ͑ ͒ /kJmol Å qe

H 0.0 0.0 0.0

Cm 0.7605 3.88 −0.032 CC 0.439 3.75 0.566 O 0.878 2.96 −0.502

Acetone/WR ͑Ref. 40͒ ␧ −1 ␴ ͑ ͒ /kJmol Å qe

H 0.0 0.0 0.0

Cm 0.681 56 3.88 0.03 CC 0.415 59 3.78 0.48 O 0.706 5 3.01 −0.54

DMSO ͑Ref. 11͒ P1 P2 ␧ −1 ␴ ͑ ͒ /kJmol Å qe qe

H 0.0 0.0 0.0 0.0 C 1.23 3.20 0.0 0.160 S 0.997 41 3.40 0.54 0.129 FIG. 2. Site-site intermolecular pair-correlation functions for acetone gen- O 0.299 22 2.80 −0.54 −0.459 erated by EPSR ﬁts to the data using the FHMK and WR reference potentials ͑Refs. 27 and 40͒. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.172.48.58 On: Tue, 13 Oct 2015 15:21:27 074502-6 McLain, Soper, and Luzar J. Chem. Phys. 124, 074502 ͑2006͒

TABLE V. Coordination numbers for site-site radial distribution functions TABLE VI. Coordination number for site-site radial distribution functions from EPSR ﬁts to acetone using the FHMK reference potential ͑Ref. 27͒. from EPSR ﬁts to DMSO using the P1 reference potential ͑Refs. 10 and 11͒.

RDF r ͑Å͒ CN RDF r ͑Å͒ CN

CC –CC 7.14 12.1 H–H 2.09 0.5 O–CC 5.54 4.7 3.45 4.7 7.74 15.4 H–C 4.05 1.3

Cm –CC 6.46 8.8 H–S 6.67 9.8 H–CC 6.04 6.9 H–O 3.382 1.3 H–H 7.72 90.0 4.99 3.7

H–Cm 4.16 3.0 C–O 4.62 2.8 5.54 10.0 S–O 3.81 1.2 7.38 26.2 5.74 5.5 H–O 5.77 5.7 O–O 4.85 3.2

Cm –O 4.75 2.7 6.75 10.0 6.76 9.8 C–C 4.53 4.5 O–O 6.40 8.1 6.97 22.7 8.53 20.6 C–S 6.11 7.6

Cm –Cm 4.77 5.5 S–S 4.75 2.6 6.96 22.1 7.01 11.5

and the two subsequent EPSR fits to these data using P1 and tween light-atom correlations, which dominate the diffrac- P2 reference potentials are shown in Fig. 3 and the coordi- tion pattern, and the heavier-atom correlations, which are nation numbers are shown in Table VI. While both P1 and P2 much weaker in the data, the sensitivity of the simulation to reference potentials used for the EPSR models provide ad- heavy-atom correlations is therefore much greater than equate fits to the data over most of the Q range, there are would be suggested by a simple, “atomic” picture of the marked deviations between the data and EPSR fit when using fluid, where the Faber-Ziman coefficients alone would dic- the P2 potential in the low-Q region. Figure 4 shows the tate the sensitivity. corresponding RDF’s for DMSO from both EPSR models Comparing the RDF’s of the two measured fluids, the where the two potential models give somewhat different functions. The largest differences between the models are site-site radial distribution functions for both acetone models found in the g ͑r͒, g ͑r͒, and g ͑r͒ functions, indicating show similar trends to those seen in DMSO, but tend to be SS SO OO less structured in general. This is most notable in the g ͑r͒, differences in the dipole-dipole correlations, since the dipole CcO g ͑r͒, and g ͑r͒ functions ͑Fig. 2͒ which have similar moment axis is collinear with the S–O vector. Although the CcCc OO ͑ ͒ ͑ ͒ ͑ ͒ contribution of the heavier-atom RDF’s to the total DMSO shapes to the analogous gSS r , gSO r , and gOO r functions diffraction pattern is small ͑Table I͒ it is clear that the dif- extracted from the P1 reference potential EPSR fits for fraction data are apparently sensitive to these functions. This DMSO. Though all of these RDF’s are similar in shape to sensitivity can be understood because of the molecular na- each other, the DMSO RDF’s have more clearly defined peak ture of the fluid and the severely constrained intramolecular configuration space; light-atom and heavy-atom correlations are therefore not independent of each other and are, in fact, strongly correlated. Because of this close relationship be-

͑ ͒ ͑ ͒ FIG. 3. F Q data circles for d6-DMSO at T=298 K and subsequent fits to the data using the P1 and P2 potentials ͑solid lines͒͑Refs. 10 and 11͒,as FIG. 4. Site-site intermolecular pair-correlation functions for DMSO gener- reference potentials in the EPSR simulation. The P2 potential fit and data ated by the EPSR fit to the data using the P1 potential ͑solid͒ and P2 have been displaced by 0.5 for clarity. potential ͑circles͒͑Refs. 10 and 11͒. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.172.48.58 On: Tue, 13 Oct 2015 15:21:27 074502-7 Orientational correlations in acetone and dimethyl sulfoxide J. Chem. Phys. 124, 074502 ͑2006͒

FIG. 5. Spatial density functions for acetone generated by the EPSR ﬁt to FIG. 6. Spatial density functions for DMSO generated by the EPSR ﬁt to the the data using the FHMK reference potential. ͑a͒ shows the neighboring data using the P1 reference potential. ͑a͒ shows the neighboring molecules molecules in the distance range of 2–5 Å where the contour level has been in the distance range of 2–5 Å where the contour level has been chosen so chosen so that the surface shown encloses 70% of the neighboring mol- that the plotted surface encloses 70% of the neighboring molecules and ͑b͒ ecules and ͑b͒ shows the neighboring molecules at the distance range of shows the neighboring molecules at the distance range of 5–7 Å where the 5–7 Å where the contour level has been chosen so that the surface chosen contour level has been chosen so that the plotted surface encloses 15% of encloses 15% of the molecules. In both pictures the size of the plotting box the molecules. In both pictures the size of the plotting box is 16 Å. is 16 Å.

“pyramid” above the central S atom. Also there is no density ͑ ͒ positions than the acetone fits; the peaks are sharper in these present below the CH3 2SO pyramid, signifying a low prob- heavy-atom RDF’s for DMSO, compared with the analogous ability of locating nearest-neighbor molecules in this region functions for acetone. of the first shell. As was the case with the acetone SDF’s, the As both the FHMK and WR EPSR models of acetone coordination in the second nearest-neighbor shell from show virtually identical RDF’s, the remainder of this paper 5 to 7 Å with the surface contour enclosing 15% of the mol- shows only functions ͑SDF’s and OCF’s͒ extracted with the ecules in this shell in Fig. 6͑b͒ shows the inverse of the first FHMK reference potential. Figure 5 shows two SDF’s for shell with the density being located in front of the central acetone from this EPSR fit to the data. In both Figs. 5͑a͒ and DMSO molecule as well as perpendicular to the zx plane. ͑ ͒ ͑ ͒ ͑ ͒ 5 b , the central carbon CC of the acetone molecule, mol- Only the SDF’s and OCF’s discussion below generated us- ecule 1 ͑described in Sec. III A 2͒, is located at the origin of ing the P1 reference potential are shown as this model ͑Fig. the central axes. In keeping with the measured data, the ac- 2͒ provides the best fit to the measured diffraction data. A selection of the OCF’s generated from the FHMK etone molecule retains its planar C2␯ symmetry as the carbonyl bond is located along the z axis while the methyl-methyl EPSR fit to the acetone data is shown in Fig. 7. The OCF’s vector lies in the yz plane ͑the methyl hydrogens have been were extracted, as described in Sec. III A 2, as a function of omitted for clarity͒. Figure 5͑a͒ shows the SDF where the surface contour encloses 70% of the molecules in the distance range of 2–5 Å. At this distance the majority of the nearest-neighbor molecules in liquid acetone are located either in a ring above the oxygen atom or along the plane of the molecule on both sides. Figure 5͑b͒ shows the SDF for acetone in the second coordination shell at a distance of 5–7 Å where the surface contour encloses 15% of the molecules. Here the second shell shows the inverse of the first coordination shell with the highest density occurring perpendicular to the xz plane of the central molecule as well as below the xy plane. Figure 6 shows the SDF’s for DMSO from the EPSR fit using the P1 reference potential, where the sulfur atom on the central DMSO molecule is placed at the origin of the reference coordinate axes. As is the case with the carbonyl bond in acetone ͑Fig. 5͒, the sulfonyl bond is located along the z axis; however, the methyl carbons are canted away from the yz plane and lie below the xy plane in order to give the correct pyramidal symmetry of the molecule, Cs. DMSO, in addition to retaining a different molecular geometry to acetone, shows a very different configuration both in the first and second coordination shells. In the first coordination shell, Fig. 6͑a͒, from 2 to 5 Å where again the surface contour encloses 70% of the molecules in this shell, the nearest- FIG. 7. Orientational correlations for acetone from the EPSR fits to the data using the FMHK potentials ͑Ref. 28͒. The contour level has been chosen so neighbor molecules are found in a concave semicircular ring that the surface shown encloses 15% of the neighboring molecules in the behind the central molecule at the apex of the intramolecular distance range of 2–5 Å. In each case the size of the plotting box is 16 Å. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.172.48.58 On: Tue, 13 Oct 2015 15:21:27 074502-8 McLain, Soper, and Luzar J. Chem. Phys. 124, 074502 ͑2006͒

␸ ␪ ␹ three variables, r, M, and M, by averaging over the M ␹ angular coordinates where M corresponds to the rotation of the methyl positions relative to the CvO axis. In this figure the central panel shows an acetone molecule superimposed on the laboratory axes again without the hydrogen atoms. The surrounding panels show the OCF’s plotted for a particular position relative to the central acetone molecule. As was described in detail in Sec. III A 2, the OCF can be extracted from the nearest-neighbor shell by probing the relative position of the second molecule ͑those located in the nearest-neighbor shell͒ to molecule 1 set at the origin of the ϵ͑ ␻ ͒ϵ͑ ␪ ␸ ͒ laboratory axes where r r, L r, L L defines the position of the molecules in the nearest-neighbor shell. Each panel shows the OCF at a particular location in the first co- ␻ ordination shell where each position shows a different L value relative to the central axis and in each case r=2–5 Å. For example, the panel in the top right-hand corner of Fig. 7 shows the most probable orientation of the next-nearest- ␻ ϵ␪ ␸ neighbor shell in liquid acetone at a position of L L L =45°0° where at this position the nearest-neighbor CvO orientation is antiparallel to the central molecule. Because each of these orientational correlation functions has been averaged over rotations of the methyl positions about the central C O bond ͑␹ ͒ only the orientation of the C O bond FIG. 8. Orientational correlations from the EPSR fits to the data using the v M v ͑ ͒ relative to the central molecule is shown in each surrounding P1 reference potential for DMSO Ref. 10 . The contour level has been chosen so that the surface shown encloses 15% of the neighboring mol- panel with the methyl groups omitted. Similar to the SDF’s ecules in the distance range of 2–5 Å. In each case the size of the plotting each OCF has a shell showing the most likely location of the box is 16 Å. nearest neighbor here relative to the central molecule at the ␻ ϵ␪ ␸ coordinates indicated in the panel, L L L. Where the ͑Fig. 2͒ each show a broad distribution of distances with the SDF’s show the density of the most probable location of exception of the g ͑r͒ function which shows a prominent HCc molecules in the nearest-neighbor shell, the OCF shows the peak at around 4 Å. Though this peak is clear evidence of an most probable orientation of nearest-neighbor molecules at a intermolecular H¯CC contact, the distance is not suffi- particular location in this shell. To show this pictorially, each ciently short to signify a hydrogen bond. Moreover, the pres- panel in Fig. 7 surrounding the central molecule has the oxy- ence of a H¯O intermolecular contact is not discernable in gen in the C O bond pointed toward the portion of the ͑ ͒ v the gOH r function, indicating that there is no methyl hydro- shell which shows the most probable orientation. gen oxygen, Cm –H¯O, hydrogen bonding present in the In the same manner as acetone, a selection of the liquid. It has been suggested that weak C –H O contacts ␹ m ¯ OCF’s—extracted by averaging over M to give a three- may “stabilize” the liquid structure,7 and these contacts have ͑ ␸ ␪ ͒ variable r, M, and M OCF—from the EPSR fit to DMSO been linked to the anomalous heat-capacity behavior seen in data using the P1 reference potential is shown in Fig. 8. solid-state acetone.9 Our simulations do not support this sug- Again the surrounding panels show the OCF’s plotted for a gestion for the structure of acetone in the liquid state. particular position relative to the central DMSO molecule DMSO on the other hand shows more “structured” hy- ͑␻ ϵ␪ ␸ ͒ L L L where in each case r=2–5 Å. The most prob- drogen RDF’s irrespective of the reference potential used able orientation in the nearest-neighbor shell is again shown ͑Fig. 4͒. While this does not indicate hydrogen bonding per by the S–O bond of the surrounding molecules pointing to- ͑ ͒ se it is indicative of preferred H¯X X=C or O intermo- ward the portion of the probability shell which shows the lecular contacts in liquid DMSO, reminiscent of crystalline highest density. Only the S–O bond is shown in each panel as DMSO which contains intermolecular O¯H distances of each OCF function has been averaged over all methyl rota- 2.40, 2.51, and 2.70 Å.64 This is also supported by a recent tions, as described above. x-ray diffraction and molecular dynamics ͑MD͒ study of liquid DMSO which showed that the three nearest-neighbor- 12 V. DISCUSSION atoms to the oxygen atom were hydrogen. In a previous neutron diffraction study, these contacts were attributed to A. RDF’s intramolecular distances; however, in that study it was not Given that the diffraction patterns in all cases are domi- possible to distinguish between intra- and intermolecular nated by scattering from the hydrogen-containing partial contributions to the diffraction pattern.10 These contacts have structure factors ͑Table I͒, the hydrogen-containing RDF’s previously been attributed to weak hydrogen bonds to the for each liquid provide a reasonable picture of nearest- oxygen atoms in DMSO;34,35 though given the molecular na- neighbor contacts with respect to the methyl groups. The ture of the system these contacts most likely arise from the RDF’s for intermolecular hydrogen contacts in acetone dipole-dipole alignment of DMSO molecules in the fluid. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. 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The differences between the two models of DMSO, P1 neighbors which passes between the two methyl head and P2, are expected in the heavy atom RDF’s given that the groups, and a shell of neighbors around each individual me- P1 potential does not have charge associated with the methyl thyl head group. groups while the P2 potential does include methyl charges ͑Table IV͒. Whereas the RDF’s for acetone are virtually C. Orientational correlation functions identical for each reference potential, the non-hydrogen- containing RDF’s in DMSO provide a distinguishing differ- A direct picture of the dipole-dipole interactions present ence between the two starting reference potentials. Specifi- in the first coordination sphere of liquid acetone and DMSO cally, in the P2 potential the methyl carbon has a charge of can be seen by the orientational plots shown in Figs. 7 and 8, respectively. qe =0.160 while the P1 potential eliminates this charge and assumes the dipole moment in DMSO to be associated with only the sulfur and oxygen atoms. The EPSR fit to the data 1. Acetone OCF’s using the P1 potential provides a much better fit and as such In acetone, Fig. 7, the dipole orientation in the nearest- the RDF’s generated with this potential provide a better rep- neighbor shell directly in front and behind the zy plane of the resentation of the local order in the data measured. ␪ ␸ ␪ ␸ 10 central molecule at L L =45°0° and L L =45°180° shows In the previous analysis of DMSO, the agreement be- an antiparallel alignment ͑with the oxygen atom pointing tween neutron diffraction data and MD simulations was de- downwards͒ relative to the central molecule. This dipole in- termined by visual comparison to an extracted composite teraction “flips” to a parallel alignment at ␪ ␸ =135°0° and ͑ ͒ ͑ ͒ L L Sxx Q function X=S, O, and C from the neutron diffraction ␪ ␸ at L L =135°180° again on both sides of the central mol- data. Both P1 and P2 showed a good agreement with the 10,11 ecule, with the oxygen atom pointing upwards towards the measured HH and XH functions while P2 showed a central acetone molecule at these locations in the first coor- slightly worse agreement with the neutron-derived XX func- ␪ ␸ dination sphere. Between these two locations at L L tion compared to P1, but was more accurate with regard to ␪ ␸ =90°0° and L L =90°180° there is a transition between the thermodynamics of liquid DMSO. In the present study antiparallel and parallel alignments. At each position in the ͑ ͒ the diffraction data Fig. 3 are, in fact, fit better by the EPSR first coordination shell in front or behind the plane of the method using the P1 reference potential, again showing as central molecule, the oxygen atom is pointed toward this before that this model reproduces the structure more accu- 10 central molecule. rately than with the P1 potential. The preferred orientation in the first coordination sphere ͑␪ ␸ ͒ directly above L L =0°0° the central acetone molecule is with the C O bond pointed away from the central molecule B. Spatial density functions v with the second nearest neighbor canted either to the right or ͑␪ ␸ ͒ The SDF’s for acetone ͑Fig. 5͒ and DMSO ͑Fig. 6͒ show left while below the central molecule L L =180°0° the different distributions in the first coordination sphere. In ac- orientation of the dipole is parallel with a “ring” of different etone there is an equal probability of the next nearest neigh- distributions all with the CvO pointed toward the central bor being located on either each side of the xy plane or above molecule. Upon inspection of the first coordination shell the central molecule. DMSO, on the other hand, shows SDF for acetone ͑Fig. 5͒ it is evident that there is a low nearest-neighbor density located in a concave semicircle probability of finding nearest-neighbor molecules directly around the apex of the pyramid where the S atom is located. below the central molecule. The differences in the SDF’s of these two liquids can be Figure 7 shows evidence of preferred orientation in the attributed largely to the difference in molecular geometries first coordination shell of liquid acetone. The symmetric ori- of the two molecules. The pyramidal molecular geometry of entations seen on both sides of the central acetone molecule DMSO prevents molecules from approaching each other un- are expected, given that acetone is symmetric with respect to derneath the pyramid very easily while in acetone, which is both the xz and yz planes. Additionally, this behavior in the planar, there is an equal probability of finding other mol- first coordination shell is observed in a comparative simula- ecules on each side of the central molecule in the yz plane. tion and integral equation study by Richardi et al.31 It is also Although the two molecules show vastly different densities of note that early diffraction measurements of the liquid, in the yz and xy planes of the extracted SDF’s, the liquids are where orientational correlations were not directly similar in the respect that there is a high probability of determined,7 predicted predominantly perpendicular dipole nearest-neighbor molecules being located directly above the interactions in the first coordination shell of acetone. Here, oxygen atom of the central molecule: in each liquid there is given that the most likely location of molecules in the clear density in both Figs. 5 and 6 above the z axis. nearest-neighbor shell is around the oxygen atom of the cen- We also note that the arrangement of neighbors around tral molecule, the average would more likely show an anti- the methyl groups in both molecules is qualitatively similar: parallel configuration. This is similar to the crystalline struc- the only real difference is that in acetone this arrangement ture where the nearest-neighbor molecules are aligned as lies symmetric about the yz plane, while in DMSO it is ro- dimers in an antiparallel configuration.9 The top panel in Fig. tated about the molecular y axis to around 45° along the 7 shows the most probable location of dipole-dipole align- positive x axis, corresponding to the rotated positions of the ment with the CvO bond diagonal to the central molecule methyl groups in DMSO compared to acetone. In both cases and the oxygen atom pointing away from the center around the methyl group coordination consists of a central band of the ring shown in this figure. Though the exact methyl ori- This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.172.48.58 On: Tue, 13 Oct 2015 15:21:27 074502-10 McLain, Soper, and Luzar J. Chem. Phys. 124, 074502 ͑2006͒

2. DMSO OCF’s

The pyramidal geometry ensures that, distinct from acetone, DMSO is only symmetric with respect to the xz plane and as such the dipole-dipole orientations in the first coordination shell ͑Fig. 8͒ vary at different positions in front and behind the plane of the central molecule. Behind the central molecule in the zy plane, DMSO molecules in the first coordination shell show a head-to-tail dipole S–O¯S–O align- ͑␪ ␸ ␪ ␸ ment at all positions L L =45°180°, L L =90°180°, and ␪ ␸ ͒ L L =135°180° where in each case the oxygen atom in these nearest-neighbor molecules points toward the sulfur atom in the central DMSO molecule, analogous to what hap- pens in acetone. Directly in front of the central DMSO pyra- ͑␪ ␸ ␪ ␸ ␪ ␸ mid, in the zy plane L L =45°0°, L L =90°0°, and L L =135°0°͒ the orientation of molecules in the surrounding shell all shows the S–O bond pointing away from the S–O bond in the central molecule. It should be noted that at ␪ ␸ ␪ ␸ L L =90°0° and L L =135°0° the likelihood of nearest- neighbor molecules being present here is quite low given the absence of density seen in the SDF ͑Fig. 6͒ at these loca- FIG. 9. ͑a͒ g͑000;00;r͒+0.5 and g͑110;00;r͒−1 functions for acetone. For tions. ͑ ͒ ͑ ͒ clarity, the coefficients are shown as g 110;00;r −1 and g 110;00;r Above the central DMSO molecule ͑␪ ␸ =0°0°͒ the +1.0. ͑b͒ The ratio −͑1/3ͱ3͓͒g͑110;00;r͒/g͑000;00;r͔͒, which represents L L the average cosine between dipoles in acetone as a function of molecular orientation of nearest-neighbor molecules shows a preference separation. for the S–O bond to point away from the oxygen atom in the ͑␪ ␸ ͒ central molecule while below the molecule L L =180°0° the S–O bonds of the nearest-neighbor molecule point to- ͑ entations are unspecified in the present plots because the ward the central sulfur atom at the origin of the central mol- correlation functions shown in this figure have been aver- ecule. aged over rotations about the CvO bond for ease of presen- In the first coordination sphere, it is evident at each lo- ͒ tation , this implies that there is an interaction between the cation that the most probable alignment of the S–O bonds of methyl groups and the oxygen atom at this location. This the surrounding molecules is in a head-to-tail fashion with interaction is probably weak and does not show formal hy- the S–O bond of the central molecule. From Fig. 9, it is clear drogen bonding, given the absence of any obvious structure that there is a S–O/S–O alignment between the central mol- ͑ ͒ in the hydrogen-containing RDF’s for acetone Fig. 3 ; how- ecule and the surrounding molecules in the shell. ever, it does resemble the solid-state structure of acetone It has been asserted in the literature that the crystalline where Cm –H¯O contacts are thought to stabilize the structure is partially retained in liquid DMSO, which shows 9 structure. antiparallel interactions between DMSO molecules.6,12,64 Given that the graphs of Fig. 7 show only the orienta- Here the only antiparallel configuration is behind the S–O tions of the top 15% molecules in the distance range speci- ␪ ␸ bond of the central molecule at L L =45°180°. The antipar- fied, it might be concluded that the orientational correlations allel configuration of DMSO molecules from the crystal in acetone are weak. In order to assess the strength of the structure is not retained in the liquid. As stated above at all orientation correlations in acetone, Fig. 9͑a͒ shows the positions in the first coordination shell the molecular align- g͑000;00;r͒ and g͑110;00;r͒ coefficients obtained from the ment shows “head-to-tail” S–O/S–O interactions. This type spherical harmonic expansion of the orientational pair- of dipole-dipole preference in liquid DMSO is predicted by correlation function ͑Sec. III A 2͒. The former function rep- simulation34,35 and is found to have a local minima in density resents the center-center radial distribution function between functional theory ͑DFT͒ calculations on DMSO-DMSO molecules, and the latter, when multiplied by C͑110:00͒/3 12,38 ͱ dimers. =−1/3 3, represents the distribution of the cosine of the Though the dipole-dipole orientations in liquid DMSO angle between dipole moment vectors on pairs of molecules, and acetone are different in many respects they also show ͗⍀ ⍀ ͉⍀ ͉͉⍀ ͉͘ 62 1 · 2 / 1 2 , as a function of separation. The ratio certain similarities, the dipole orientations directly above ͑ ͱ ͓͒ ͑ ͒ ͑ ͔͒ ͑ ͒ ͑ ͒ − 1/3 3 g 110;00;r /g 000;00;r , Fig. 9 b , therefore both molecules both show the X–O X=S or CC bond point- represents the mean value of this cosine for a pair molecules ing away from the central molecule. In acetone there is a separated by a distance r. The values of this function in the broad distribution of CvO orientations above the molecule region of the first neighbor peak are not those of weakly while in DMSO the S–O bond is in a more specific location. correlated orientations. Indeed the orientations are strongly In both cases this implies some Cm –H¯O interactions correlated in the first neighbor shell, and flip from being where this interaction is more structured in DMSO, as evi- strongly antiparallel at short distances to more parallel denced by a comparison of the hydrogen-containing RDF’s. slightly further out. Although neither of these liquids show an intermediate range This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.172.48.58 On: Tue, 13 Oct 2015 15:21:27 074502-11 Orientational correlations in acetone and dimethyl sulfoxide J. Chem. Phys. 124, 074502 ͑2006͒

order in molecular fluids. In particular, the orientational information contained in Figs. 7–10 will be proven highly in- formative in more complex systems for identifying the local molecular order. Through a detailed study of the orientational correlations found from EPSR fits to measured neutron diffraction data it is found that DMSO and acetone show some similarities but also marked differences between their nearest-neighbor dipole alignment in the liquid. The structure of the first shell is strongly influenced by the shape of the molecule, with a predominance of close contacts around the oxygen atom of both molecules, and much weaker correlations at a larger distance around the methyl head groups. This distribution follows the underlying symmetry of the central molecule, with a symmetric distribution of neighbors found around the acetone molecule, and a strongly asymmetric distribution found around the pyramidal DMSO molecule, Figs. 5 and 6. There is also a high degree of preferred orientation shown in the first coordination shell in each liquid, Figs. 7 and 8. Both liquids show a predominance of antiparallel alignments of molecular dipole moments at short distances inside the main FIG. 10. ͑a͒ g͑000;00;r͒ and g͑110;00;r͒ functions for DMSO. For clarity, the coefficients are shown as g͑000;00;r͒−1 and g͑110;00;r͒+1.0. ͑b͒ The nearest-neighbor peak, while at larger distances they become ratio −͑1/3ͱ3͓͒g͑110;00;r͒/g͑000;00;r͔͒, which represents the average more parallel, adopting a range of orientations. In acetone cosine between dipoles in DMSO as a function of molecular separation. these arrangements are symmetric about the central plane of the acetone molecule, but in DMSO the antiparallel arrange- order, it is apparent that there is some ordering of dipoles in ment is found only behind the molecule, with a more parallel the first coordination shell as a proportion of the molecules or tangential orientation in front of the molecule, a region show dipole-induced alignments. which, however, is only sparsely populated in the first shell. As for acetone, the mean dipole-dipole cosine for A general rule for both molecules is that outside the antipar- DMSO is shown in Fig. 10. Here it is seen that the orienta- allel arrangement seen at short distances, the molecules tional correlations are even stronger in the first shell than for adopt more of a head-to-tail configuration, reminiscent of acetone. Again a strong antiparallel alignment is seen at dis- what might occur due to dipole ordering over longer-distance tances shorter than the main near-neighbor peak. Beyond that scales. This ordering is, however, tempered by the underly- the alignment becomes more parallel, as discussed with re- ing symmetry of the molecule. The alignment seen in ac- spect to Fig. 9, but the size of the mean cosine indicates that etone would not be possible in DMSO given its pyramidical these orientational correlations are strong, even if complex in molecular geometry. Additionally there is evidence for weak nature. intermolecular Cm –H¯O contacts in both fluids.

ACKNOWLEDGMENTS VI. CONCLUSIONS The authors would like to thank U.S. National Science The problem of extracting reliable structural information Foundation for financial support for one of the authors about molecular arrangement and orientation in relatively ͑S.E.M.͒ under Award No. OISE-0404938 and for another simple molecular fluids such as the present examples is well author ͑A.L.͒ under Award Nos. CHE-0211626 and CHE- known.63 Unlike the case of water of HF,50,52 where the dif- 0512131. fraction data can be separated into the complete set of partial structure factors, this is not possible to achieve in most cases 1 J. March and M. B. Smith, March’s Advanced Organic Chemistry: Reac- likely to be of chemical or biological interest. The present tions, Mechanisms and Structure, 5th ed. ͑Wiley, New York, 2000͒. experiment and analysis have relied heavily on EPSR to fill 2 Handbook of Chemistry and Physics,83rded.͑CRC, New York, 2002͒. 3 in the gaps of missing structural information by imposing H. Dreizler and G. Dendl, Z. Naturforsch. A 19A,512͑1964͒. 4 F. A. Cotton and R. Francis, J. Am. Chem. Soc. 82, 1986 ͑1960͒. reasonable constraints on atomic overlap and on the likely 5 R. J. Gillespie and E. A. Robinson, Angew. Chem., Int. Ed. Engl. 35,495 molecular geometries. By comparing the model and data di- ͑1996͒. rectly in the reciprocal space of the measurements, one has 6 H. Bertagnolli and P. Chieux, Phys. Chem. 93,88͑1989͒. 7 the best chance of avoiding the spurious structures and con- H. Bertagnolli, M. Hoffman, and M. Ostheimer, Z. Phys. Chem. 165,165 ͑1989͒. clusions that might be generated by systematic effects in the 8 H. Bertagnolli, M. Hoffman, and P. Chieux, Z. Phys. Chem. 159,185 data ͑such as inelasticity effects with neutron scattering or ͑1988͒. Compton scattering with x rays͒. We believe the present 9 D. R. Allan, S. J. Clark, R. M. Ibberson, S. Parsons, C. R. Pulham, and L. ͑ ͒ comparison in Q space using the total differential scattering Sawyer, Chem. Commun. Cambridge 1999, 751. 10 A. Luzar, A. K. Soper, and D. Chandler, J. Chem. Phys. 99, 6836 ͑1993͒. cross sections as measured, rather than the derived functions, 11 A. Luzar and D. Chandler, J. Chem. Phys. 98, 8160 ͑1993͒. is likely to give a more accurate representation of the local 12 U. Onthong, T. Megyes, I. Bako, T. Radnai, T. Grosz, K. Hermansson, This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.172.48.58 On: Tue, 13 Oct 2015 15:21:27 074502-12 McLain, Soper, and Luzar J. Chem. Phys. 124, 074502 ͑2006͒

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