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1330 Journal of Chemical Education • Vol. 81 No. 9 September 2004 • www.JCE.DivCHED.org

Computer simulations are now used to study complexchemical events ranging from the folding of proteins (1) tothe high energy desorption of organic molecules from metalsurfaces (2). Simulations not only offer an alternative methodfor performing costly experiments, but they also provide anadded molecular-level insight into the chemistry that is notalways available via experiment. In the past, computationaltechniques were introduced to the undergraduate student asan aid in the visualization of molecular structures or as amethod of determining reaction energetics. These applica-tions failed to demonstrate the power of the computationalmethods. Students were left unaware of which computationalmethod is most appropriate for the problem at hand or ofthe abundance of problems that could be examined via com-putational techniques. Even worse, the theory behind thesetechniques was often deemed too demanding for studentcomprehension, and left unmentioned. Recently, however,many examples of how the theories behind computer simu-lations can be showcased in the undergraduate classroom havebeen presented in this Journal (3–9). Students are introducedto the theories behind these computational techniques in thephysical chemistry lecture. Consequently, the physical chem-istry laboratory is a natural place for students to use thesetechniques.

This laboratory experiment utilizes the technique of mo-lecular dynamics (MD) computer simulation to investigatethe microscopic structure of simple liquids. In the spirit ofthe inquiry-based approach, students are encouraged to ex-plore how varying simulation parameters affects the structureand physical properties of a specific liquid. Students utilizethe Amber suite (10) of programs to simulate the behavior ofone or more liquids under varying environmental conditions.Amber is commonly utilized in both academia and industryto simulate condensed phase systems involving small moleculesor large biomolecules. Although its interface is not graphical,our students have quickly mastered its use. The advantage ofAmber over more graphical-based programs is that many sta-tistical mechanical analysis programs exist within the Ambersuite. These analysis programs facilitate the calculation of avariety of statistical mechanical properties, such as radial dis-tribution functions, from the simulated data.

Liquids are particularly interesting because, even thoughthey do not exhibit the macroscopic order of solids, they pos-sess a definite molecular-level structure. The long-range or-ganizational structure that emerges from this molecular-levelstructure is not readily apparent with even today’s most so-phisticated molecular visualization packages. However, it canbe determined from a liquid’s atom–atom radial distributionfunction. The atom–atom radial distribution function, gαβ(r)is defined as (11–13),

bg r

r( ) = ( )

αββ

β

ρ

ρ uulk (1)

where ρβ(r) is the density of β-type atoms, averaged over thelength of the simulation, at a distance r from a central α-type atom and ρβbulk is the average density for β-type atomsin the bulk of the liquid. Thus, gαβ(r) is a measure of thelocal structure of the β-type atoms in the liquid as you moveradially away from the central α-type atom. For a randomdistribution of molecules, gαβ(r) would equal one. In addi-tion, the individual peaks in the radial distribution functioncan be integrated to determine the coordination number, orthe average number of nearest neighbors within each neigh-bor shell, nc (11, 13):

bulk dn g r r rc 4 2πρβ αβ= ( )∫ (2)

For a molecular liquid, such as water, there are three differentatomic radial distribution functions that define the structureof the liquid: gOO(r), gHO(r), and gHH(r). Each function high-lights a different aspect of the overall structure of the waterand the functions taken together form a complete picture ofthe local environment experienced by each water molecule.Discussions of the radial distribution function and its rela-tionship to the long-range organizational structure of a liq-uid can be found in many modern physical chemistrytextbooks (14–16).

Most physical chemistry students realize that liquids haveshort-range organization—that is, more molecular-level struc-ture than gases and less than solid crystals—but they havelittle idea of how to make this observation quantitative. Ra-dial distribution functions provide them with visual proofthat what they have been taught is, in fact, the case. Manystudents are excited to merely explore how changing the tem-perature affects the radial distribution function. Other stu-dents wonder how the different macroscopic properties oftwo liquids will be reflected in their microscopic structure.Finally, a few students become quite ambitious and attemptto observe specific types of intermolecular structure such asthe appearance of the π–π stacking in benzene or the dipole–dipole interactions in acetonitrile.

Procedure

This laboratory has been performed successfully in ourjunior-level physical chemistry laboratory course. As prepa-ration, the Lennard-Jones potential is introduced in an ear-lier physical chemistry lecture. Both the elementary basis ofclassical dynamics simulations and how one would actuallyperform a MD simulation are then discussed in the prelabo-ratory lecture. A thorough overview of this material is pro-vided in the Supplemental Material.W

This experiment is conducted over two, four-hour labo-ratory periods. In the first week, the students are taught howto use Amber (10) to perform a MD simulation for a bulkliquid, such as water, and how to view snapshots of their

Molecular Dynamics Simulations of Simple Liquids WOwen F. Speer, Brian C. Wengerter, and Ramona S. Taylor*Department of Chemistry, College of the Holy Cross, Worcester, MA 01610; *rtaylor@holycross.edu

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www.JCE.DivCHED.org • Vol. 81 No. 9 September 2004 • Journal of Chemical Education 1331

simulations (17). At the end of the first week, the studentsare asked to design a set of MD simulations to investigatesome aspect of how modifying the simulation parameters in-fluences the microscopic structures of their liquids. Studentsmay choose either to model two very different liquids, suchas H2O and benzene, or to examine the effect varying an en-vironmental parameter, such as temperature, has on the struc-ture of a liquid.

Along with deciding on which chemical question to ex-plore, each group of students is asked to formulate a viablehypothesis for what they expect to happen and to constructa tentative schedule of when the simulations will be per-formed and who will be responsible for starting the varioussimulation runs so that all of the data can be collected andanalyzed before the end of week two.

A typical group consists of two to three students. Eachgroup has one SGI Octane 2 workstation at its disposal forthe two-week period allocated to do this experiment. Thus,this experiment would require a two-week commitment offour workstations for a laboratory section of 12 students. Al-ternatively, a single workstation can be used if this experi-ment is but one of the experiments that the students rotatethrough during the course of the semester. This latter round-robin format has worked well in our physical chemistry labo-ratory course at Holy Cross.

Students are given an initial set of equilibrated coordi-nates (at 25 �C) and a topology file for each of the liquidsavailable for analysis. Each topology file contains the bond-ing and potential model information for its specific liquid.The liquids available for analysis include water (756 mol-ecules) (18), benzene (288 molecules) (19), ethanol (267molecules) (20), and acetonitrile (216 molecules) (21). Stu-dents perform an equilibration run of 200 ps and a produc-tion run of 50 ps, which is adequate to calculate statisticallymeaningful radial distribution functions for each of their pro-posed systems. At 25 �C, the size of the equilibrated peri-odic boxes range from 25.0 Å × 25.0 Å × 25.0 Å for 756water molecules to 35.0 Å × 35.0 Å × 35.0 Å for 288 ben-zene molecules.

The two observables that students measure are the den-sity and the average microscopic structure of the liquid. Thedensity of a liquid depends both on the mass of the particlesthat comprise the liquid and the intermolecular spacing be-tween these particles. Thus, one needs to be careful whencomparing densities of dissimilar liquids. To this end, stu-dents are re-introduced to the concept of number density asopposed to mass density. In a constant pressure simulation(a NPT ensemble where N is the number of molecules andT is the temperature), density can be calculated by dividingthe number of particles by the volume of the simulation box.Amber reports this as mass density in the output file (10)and the students convert it to number density. As describedabove, the structure of the liquid can be derived from its ra-dial distribution function, gαβ(r). It is relatively straightfor-ward to calculate the atomic radial distribution functions fora bulk liquid using the analysis programs that are availablewithin the Amber 6.0 (or higher) suite of programs (10).Detailed instructions on how to calculate radial distributionfunctions using Amber 6.0 are included in the Supplemen-tal Material.W

Hazards

No significant hazards exist.

Examples of Student Results

One of the most common questions posed by the stu-dents is how does temperature affect the microscopic struc-ture of the liquid. The oxygen–oxygen radial distributionfunctions calculated in one such investigation are shown inFigure 1. Here, the students chose to model ethanol at fourdifferent temperatures: 200 K, 298 K, 313 K, and 343 K. At200 K, the O�O distribution function is sharply peaked.As the temperature is increased, the peaks begin to broadenand lessen in intensity. Yet, the appearance of liquid-like struc-ture is retained. At 200 K, the probability of finding an etha-nol molecule between the first and second neighbor shell isapproximately zero. However, upon increased temperaturethis changes and the likelihood of finding an ethanol mol-ecule between the first and second coordination shells in-creases. Beyond 6 Å from the central ethanol molecule, nostructure is apparent in the liquid.

The C�C radial distribution function for the same foursystems where the C�C distance is calculated from the cen-ter-of-mass between the two carbon atoms in ethanol’s tail isshown in Figure 2. Notice that the peaks are much less in-tense for the C�C interactions than for the O�O interac-tions. This signifies that the hydrogen bonding interactionsare the driving force in determining the local structure inethanol at all four temperatures. Besides this decrease in peakintensities, two additional items are worth noticing in Fig-ure 2. First, the C�C interactions show a much longer-rangestructure than the O�O interactions. This occurs becausethe carbon tails of ethanol extend approximately 4 Å beyondthe O atoms. Second, the nearest-neighbor C�C peak at 200K is split into two distinct peaks. Upon careful analysis, stu-

Figure 1. O–O radial distribution function for ethanol as a functionof temperature.

0

1

2

3

4

5

6

32 4 5 6 7

rOO / Å

g OO

(r)

200 K298 K313 K343 K

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1332 Journal of Chemical Education • Vol. 81 No. 9 September 2004 • www.JCE.DivCHED.org

dents can show that the two C�C nearest neighbor geom-etries originate from the hydrogen-donating and hydrogen-accepting abilities of each ethanol molecule involved in ahydrogen bond.

In agreement with the experimental results (22), the den-sity of ethanol decreases from 0.88 g�cm3 at 200 K to 0.73g�cm3 at 343 K. Using the calculated density values, theO�O radial distribution function and eq 2, one finds thatthe number of nearest neighbors in the first coordination shellof ethanol decreases from 2.0 at 200 K to 1.9 at 343 K.

Summary

Students are given the opportunity to perform molecu-lar dynamics simulations on a series of molecular liquids us-ing the Amber suite of programs. They are introduced bothto the physical theories underlying classical mechanics simu-lations and to the atom–atom pair distribution function. Us-ing this distribution function, they can graphically “see” thatliquids do in fact posses some sort of long-range microscopicstructure and that the extent of this structure differs fromliquid to liquid and from one temperature to another. In thespirit of the guided-inquiry approach, each group of studentsis asked to design a set of simulations to answer their self-determined question. This allows the students a chance todevelop their own scientific creativity.

Acknowledgments

We would like to thank the Camille and Henry Drey-fus Foundation (Grant # SU-99-076) and the College of HolyCross for their support of this project. Also RST would liketo thank the students in her spring 2001 and fall 2002 Physi-cal Chemistry Laboratory courses for their help and patiencein the development of this laboratory.

WSupplemental Material

Instructor’s notes, which include an equipment list, a de-tailed description of how to obtain radial distribution func-tions using Amber 6, and CPU times for completing a 50,000

step simulation for each liquid; a complete laboratory writeupfor use by the students; and comments on possible modifi-cations to this laboratory are available in this issue of JCEOnline.

Literature Cited

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10. Case, D. A; Pearlman, D. A.; Caldwell, J. W.; Cheatham, T.E., III; Ross, W. S.; Simmerling, C. L.; Darden, T. A.; Merz,K. M.; Stanton, R. V.; Cheng, A. L.; Vincent, J. J.; Crowley,M.; Tsui, V.; Radmer, R. J.; Duan, Y.; Pitera, J.; Massova, I.;Seibel, G. L.; Singh, U. C.; Weiner, P. K.; Kollman, P. A.AMBER 6.0, University of California, San Francisco, 1999.

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17. Utilities exist within Amber to transform the xyz-formattedcoordinate files into the PDB (protein database) format. Thus,any graphics program that will allow students to depict PDBfiles as ball-and-stick representations will work. At Holy Cross,we are currently using Spartan ’02 for UNIX (Wavefunction,Inc., Irvine, CA). However, programs such as VMD [http://www.ks.uiuc.edu/Research/vmd (accessed May 2004)] orCHIME [http://www.mdl.com/chime (accessed May 2004)],which are available free of cost for the Windows environment,will also work.

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20. Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. J. Am. Chem.Soc. 1996, 118, 11225.

21. Bohm, H. J.; McDonald, I. R.; Madden, P. A. Molec. Phys.1983, 49, 347.

22. CRC Handbook of Chemistry and Physics; Linde, D. R., Ed.;CRC Press: Boca Raton, FL, 1999; pp 6–136.

Figure 2. C–C radial distribution function for ethanol as a functionof temperature.

0.0

0.5

1.0

1.5

2.0

2 3 4 5 6 7 8 9 10

rCC / Å

g CC(r

)

200 K298 K313 K343 K