Radial Distribution Function The purpose of this exercise is to explore the role of MD simulation in

Radial Distribution Function The purpose of this exercise is to explore the role of MD simulation in determin-ing the properties of liquids, argon in this case. You may use any MD programyou like, there are many open source codes available. Your task is to determinethe density as a function of temperature and pressure, and then the radial dis-tribution function. You will use the RDF to calculate the internal energy usingEq. (9.11). You will compare how two force fields, Lennard–Jones and Bucking-ham potential, affect behavior. (a) An experimental paper by Itterbeek and Verbeke [43] reports

View complete question »Radial Distribution Function The purpose of this exercise is to explore the role of MD simulation in determin-ing the properties of liquids, argon in this case. You may use any MD programyou like, there are many open source codes available. Your task is to determinethe density as a function of temperature and pressure, and then the radial dis-tribution function. You will use the RDF to calculate the internal energy usingEq. (9.11). You will compare how two force fields, Lennard–Jones and Bucking-ham potential, affect behavior. (a) An experimental paper by Itterbeek and Verbeke [43] reports measure-ments of the density of liquid nitrogen and argon as a function of temper-ature and pressure. The data are for the “compressed liquid” domain. Youwill see that for a given temperature, the pressure is a very strong functionof the density. If you use an NPT ensemble, the density becomes a depen-dent variable and an output of the simulation. Select 89.13 K in Table II ofItterbeek and Verbeke and then vary the pressure over the values in the table(use seven equally spaced values from the table). Set the temperature andpressure using a thermostat and a barostat. For each pressure, determinethe density from the simulation.You will notice that the density fluctuates, so calculate the standard devi-ation too. One question in MD simulations is when to start averaging andhow many time steps to average over. If you start too soon, then the resultmay be biased by the transient startup. One way to decide when you havewaited long enough to start averaging is to plot both the average and thestandard deviation as a function of time. Once the numbers have settleddown, then start averaging. If you don’t average over enough time stepsthen the variance, or standard deviation, will be too large. Once you havedecided that you have good numbers, then plot the density along with thedata in Table II. (b) After you have run eachT–Psimulation, calculate the radial distributionfunction. Then write a script in your favorite programming environment(Matlab, Mathematica, etc.) to perform the integration in Eq. (9.11). Com-pare the results with the energy output by the MD program.

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