LAMMPS MD: Equation of State (pressure vs. density) - SPC/E Water

Additional simulation details are in the sample input file, see below.

Results

2. Pressure-density-energy equation of state

The following graphics show the pressure-density equations of state and the internal energy per molecule versus density in the form of a phase diagram for select temperatures (300, 400, and 500 K). In both graphics, the solid lines are the corresponding equation of state and energy as calculated from Grand Canonical-Transition Matrix Monte Carlo Simulations (GC-TMMC, see results elsewhere in the NIST SRSW). Solid symbols indicate the results from LAMMPS simulations, with the standard error shown by error bars. There is relatively good agreement between the two sets of results, except for the isotherm at 500K, which is approaching the critical temperature, where system-size effects are expected to lead to disagreement between different techniques.

 

 

 

 

Reproducing output

The LAMMPS MD results in the preceding table and graphics may be reproduced using example LAMMPS runs described as follows.

1. LAMMPS Installation

The data shown above were generated using a generic installation of LAMMPS, the executables of which may be reproduced as described here. This tutorial assumes some level of familiarity with POSIX-compliant operating systems (e.g., Unix, Linux, or Mac OSX) at the command-prompt level and access to a system with the GCC compiler, OpenMPI parallelization suite, Python, and the git version control system. This tutorial uses ">" to indicate the shell command prompt and $LAMMPS_DIR to identify the directory where LAMMPS is downloaded and later compiled. First, LAMMPS can be obtained using the instructions at http://lammps.sandia.gov/download.html#git via:

   >git clone https://github.com/lammps/lammps.git

Second, LAMMPS executables may be compiled via:

   >cd $LAMMPS_DIR
   >git checkout stable_31Mar2017
   >cd src
   >make purge
   >make package-update
   >make yes-user-misc yes-molecule yes-rigid yes-kspace
   >make -j8 mpi

The installation sequence 1) switches to the "stable_31Mar2017" commit of LAMMPS (to ensure that a user is using the same code used to generate the data shown above), 2) removes any existing installation of LAMMPS, 3) updates any out of date packages, 4) installs the "USER-MISC", "MOLECULE", "RIGID", and "KSPACE" packages to enable the simulation of a rigid molecule using Ewald-type long-range electrostatics, and 5) builds an MPI-enabled executable using eight processor cores for parallel compilation. The end result is an executable named "lmp_mpi" located in the $LAMMPS_DIR/src directory.

Finally, we used the following operating system, compiler, and MPI libraries to build the LAMMPS executable:
   Linux OS: CentOS 7; 3.10.0-514.21.1.el7.x86_64 kernel
   GCC: v4.8.5 (2015-06-23, listed as Red Hat 4.8.5-11)
   OpenMPI: v1.10.3 (2016-06-14)
   LAMMPS: Git Checkout Tag stable_31Mar2017 (2017-03-31)

2. Example LAMMPS Scripts

Example LAMMPS scripts and initial configurations that will yield the data shown above may be obtained from a git repository at: https://github.com/dwsideriusNIST/LAMMPS_Examples, e.g. via:

   >git clone git [at] github.com:dwsideriusNIST/LAMMPS_Examples.git

This tutorial assumes that the git repository resides in $EXAMPLES_DIR. The relevant inner directories are:

3. Example LAMMPS Run

A short example LAMMPS run is available in $EXAMPLES_DIR/SPCE_example, which may be run to confirm that LAMMPS is operating properly. This simulation is executed via:

   >cd $EXAMPLES_DIR/SPCE_example
   >sh example.sh

In the "example.sh" script, one can see that this script runs an SPC/E simulation at ρ=1000 kg/m³ and T=300 K for 60000 time steps (all LAMMPS settings are as shown previously, using the Particle-particle Particle-mesh k-space option) then analyzes the MD trajectory to report the average temperature, pressure, and potential energy. The final output, from the block analysis script, will report the following ensemble averages and uncertainty:

4. SPC/E Reference Energy Calculations using LAMMPS

NIST provides reference energy calculations for SPC/E configuration elsewhere in the Standard Reference Simulation Website (9 Å cutoff and 10 Å cutoff); those calculations were made using a custom implementation of the Ewald summation. Here we provide a script that can recreate those reference calculations using LAMMPS, with some modifications. The git repository referenced earlier contains the four SPC/E configurations from the SPC/E reference calculations in LAMMPS format, as files spce_sample_config_periodic_cubicN.LAMMPS, with "N" replaced with 1, 2, 3, or 4. The energy of one of these configurations, using the 9 Å cutoff, may be computed via:
 

5. Production LAMMPS Runs