Ljupvo Pejov [email protected]Dragan Sahpaski [email protected]Anastas Misev [email protected]Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations using Genetic Algorithms (GA) Dragan Sahpaski [email protected]Institute of Informatics, Faculty of Natural Sciences University “Ss. Cyril and Methodius” Skopje, Macedonia Ljupco Pejov [email protected]. ukim.edu.mk Institute of Chemistry, Faculty of Natural Sciences University “Ss. Cyril and Methodius” Skopje, Macedonia Anasas Misev [email protected]Institute of Informatics, Faculty of Natural Sciences University “Ss. Cyril and Methodius” Skopje, Macedonia *This work is supported by the FP7 project HP- SEE
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LSSC2011 Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations using Genetic Algorithms (GA)
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations using Genetic Algorithms (GA)
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• Theory can sometimes predict certain properties or systems’ behavior which hasn’t been observed yet (or, in certain cases, is not even observable with the current experimental techniques).
• The most widely used theoretical methods for modeling of condensed phases are Monte Carlo and molecular dynamics techniques.
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
• We aim to propose a general methodology (approach) for optimization of the interaction potentials, using genetic algorithms
• We analyze the performances and drawbacks of non-optimized potentials and emphasize the need for a very careful construction of general-purpose potentials.
• As a particular example, we focus our attention on liquid carbon tetrachloride (CCl4).
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
Monte Carlo simulations• Chosen system: liquid CCl4 (of broad interest for
chemistry and technology as one of the most frequently used organic solvents).
• To generate the structure of liquid, first a series of Monte-Carlo (MC) simulations were performed, using the statistical mechanics code DICE.– MC simulations of 500 carbon tetrachloride molecules
placed in a cubic box with side length of 43.36 Å, imposing periodic boundary conditions.
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
• Intermolecular interactions were described by a sum of Lennard-Jones 12-6 site-site interaction energies plus Coulomb terms:
• where i and j are sites in interacting molecular systems a and b, rij is the interatomic distance between sites i and j, while e is the elementary charge.
ij
ji
ij
ij
ij
ija
i
b
jijab r
eqq
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0
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Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
• We have chosen the following physical quantities as representative to test the quality of the used LJ potential energy parameters:– the average density of the liquid (ρ), – the thermal expansion coefficient (αP),
– isothermal compressibility (βT)
– molar heat capacity at constant pressure (CP,m) of the liquid.
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
The Optimization Problem • Find a set of values for S = {qCl, εCl, σCl, qC, εC, σC}, such that the cost function
is minimal. The function relerr gives the relative error of the parameter computed by the simulation procedure and the experimental value for the parameters ρ, αP, βT and CP,m. c1, c2, c3 and c4 are integer constants defining the weights in which each relative error affects the cost function.
Results with the standard LJ parameters Table 2. Comparison of the density, thermal expansion coefficient, molar heat capacity at constant pressure and isothermal compressibility of liquid carbon tetrachloride computed from the MC simulation with the standard (non-optimized) LJ potential parameters with the available experimental data.
Parameter MC Experimental Rel. error %
ρ / (g cm-3) 1.5697 1.5867 10.7
CP,m / (J K-1 mol-1) 80.65 129.35 37.6
βT / Pa-1 1.126·10-9 1.034·10-9 8.9
αP / K-1 4.6199·10-3 1.236·10-3 273.8
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
Results with the optimized LJ parameters Table 4. Comparison of the density, thermal expansion coefficient, molar heat capacity at constant pressure and isothermal compressibility of liquid carbon tetrachloride computed from the MC simulation with the standard (non-optimized) LJ potential parameters with the available experimental data.
Parameter MC - GA Experimental Rel. error %
ρ / (g cm-3) 1.5884 1.5867 0.10
CP,m / (J K-1 mol-1) 122.13 129.35 5.6
βT / Pa-1 3.459·10-12 1.034·10-9 99.6
αP / K-1 3.3522·10-3 1.236·10-3 171.2
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
• We have efficiently implemented a genetic algorithm to optimize the interaction potential energy parameters of liquid CCl4 to be used in statistical physics simulations of the pure liquid, as well as of various solutions thereof.
• We have demonstrated that it is possible to improve the values of certain parameters characterizing the static and dynamical properties of the liquid by the approach that we have adopted.
• It is also tempting to apply such novel approach to the problem of construction and optimization of intermolecular interaction energy parameters for various types of simulations of a number of molecular liquid systems.