LAMC - Linear alkanes Monte Carlo

This repository centralizes the code implemented for research during my Master's of Science in Chemical Engineering at Unicamp.

“Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics.” - D.L. Goodstein, States of Matter (1975).

Objective

The program implemented here utilizes Configurational Bias Monte Carlo for simulating linear alkanes in different ensembles: $NVT$, $NPT$ and $\mu VT$. Confinement evaluated using an implicit potential (Steele 10-4-3) and perturbation terms can be calculated. Simulation potentials are: Hard-sphere and Mie.

Structure

This code is divided into folders:

1. src: source code files, main components for running the program, implementation of Monte Carlo algorithms as well as properties calculations and input/output routines;
2. scripts: python files used for post-processing data, running multiple simulations on parallel and other routines;
3. data: results used in the dissertation;
4. notebooks: additional jupyter-notebook files used for analyzing, post-processing the data and creating input files.

Code compilation and utilization

The main program is written in C and requires an adequate compiler (such as gcc). It can be compiled with the MakeFile available inside src folder:

$ cd src
$ make

This will generate several .o files and an executable LAMC.exe. For running the program it is necessary to parse the input file with extension .inp.

Input files

An input file is a text file specifying the simulation parameters, with the following structure:

SIMULATION_ENSEMBLE NVT
EQUILIBRATION_ENSEMBLE NVT
NUBMER_OF_MOLECULES 1000
CHAIN_SIZE 1
TEMPERATURE 600.0
BOX_X_SIZE 133.24475446068766
BOX_Y_SIZE 133.24475446068766
BOX_Z_SIZE 30.0
NUMBER_TOTAL_CYCLES 60000
NUMBER_EQUILIBRATION_CYCLES 30000
ACCEPTANCE_RATIO 0.4
CYCLES_TO_CALCULATE_PROPERTIES 3
CYCLES_TO_RECORD_CONFIGURAITON 3000
CYCLES_TO_GET_PROFILES 3000
CLOSED_BOX 1
DISPLACEMENT_PROBABILITY 0.33
INSERTION_PROBABILITY 0.33
DELETION_PROBABILITY 0.33
FUGACITY 1000000.0
PRESSURE 5000000.0
REFERENCE_POTENTIAL LENNARD_JONES
PERTURBED_POTENTIAL LENNARD_JONES

Each field is described below:

• SIMULATION_ENSEMBLE - ensemble for running the production steps, must be one of NVT, muVT or NPT;
• EQUILIBRATION_ENSEMBLE - ensemble for running the equilibration steps, must be one of NVT, muVT or NPT. More specifically, if EQUILIBRATION_ENSEMBLE and SIMULATION_ENSEMBLE different then the first half the equilibration steps are run in the equilibration ensemble and the latter half on the simulation ensemble;
• NUBMER_OF_MOLECULES - number of molecules for the simulation, must be an integer. Fixed number for NVT or NPT simulations or initial number for muVT;
• CHAIN_SIZE - integer specifying the size of the alkane chain;
• TEMPERATURE - simulation temperature in Kelvin;
• BOX_X_SIZE - float with the size of the X axis of the box;
• BOX_Y_SIZE - float with the size of the Y axis of the box;
• BOX_Z_SIZE - float with the size of the Z axis of the box;
• NUMBER_TOTAL_CYCLES - integer with the number of cycles for the total simulation, during each cycle each molecule is submitted to one movement attempt (on average);
• NUMBER_EQUILIBRATION_CYCLES - integer with the number of cycles for the equilibration part, same definition of cycle as before;
• ACCEPTANCE_RATIO - target acceptance ratio for displacement attempts;
• CYCLES_TO_CALCULATE_PROPERTIES - integer with the number of cycles to update properties calculation;
• CYCLES_TO_RECORD_CONFIGURAITON - integer with the number of cycles to record configuration;
• CYCLES_TO_GET_PROFILES - integer with the number of cycles to record raw profile data, only used for closed box simulations;
• CLOSED_BOX: either 1 for closed box or 0 for open;
• DISPLACEMENT_PROBABILITY - probability for performing a displacement attempt on muVT simulation;
• INSERTION_PROBABILITY - probability for performing a molecule insertion attempt on muVT simulation;
• DELETION_PROBABILITY - probability for performing a molecule deletion attempt on muVT simulation;
• FUGACITY - fugacity in Pa for muVT simulation;
• PRESSURE - pressure in Pa for NPT simulation;
• REFERENCE_POTENTIAL - reference potential, either one or two values: LENNARD_JONES or HARD_SPHERE;
• PERTURBED_POTENTIAL - perturbation potential, either one or two values: LENNARD_JONES or HARD_SPHERE;

Finally, the program can be run with:

$ LAMC.exe <input_file>.inp

Output files

Once the code is executed and the simulation is complete four files will be generated for analysis. Each file name is constructed from the original filename of the input file, considering for instance an input file with name <input_filename>.inp the generated files will be:

• <input_filename>_properties_data.out.dat: a file containing the sampled properties every CYCLES_TO_CALCULATE_PROPERTIES cycles;
• <input_filename>_configurations.out.xyz: a file containing the configuration sampled every CYCLES_TO_RECORD_CONFIGURAITON;
• <input_filename>.out.log: a file containing the simulation summary;
• <input_filename>_properties_data.out.dat: a file containing the raw profiles data id est the center of mass position on the z axis of each molecule and the corresponding orientation parameter (evaluated as the second Legendre polynomial). This file is only generated for closed box simulations and the orientation parameter is only calculated if CHAIN_SIZE is bigger than or equal to 2.

Post-processing

The files generated during the simulation can be processed to generate relevant statistics and other results for analysis. Inside the folder scripts there are pre-implemented codes for these tasks alongside a README.md with a detailed explanation on each .py file.

Multiprocessing

Monte Carlo algorithms are intrinsically serial structures, however multiple independent simulations can be executed in parallel. For such cases the script run_multiprocessing.py in the folder scripts can be used. Further details at the README.md file on the corresponding folder.

References

The development of this code has been made possible by several research materials mainly, but not restricted, to:

1. Frenkel, Daan, and Berend Smit. Understanding molecular simulation: from algorithms to applications. Vol. 1. Elsevier, 2001.
2. Allen, Michael P., and Dominic J. Tildesley. Computer simulation of liquids. Oxford university press, 2017.

Additional references are enumerated on the dissertation associated with this work.