lssc2011 optimization of intermolecular interaction potential energy parameters for monte-carlo and...
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Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations using Genetic Algorithms (GA)TRANSCRIPT
Ljupvo Pejov [email protected] 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 [email protected]
Institute of Informatics, Faculty of Natural Sciences
University “Ss. Cyril and Methodius”
Skopje, Macedonia
Ljupco [email protected]
Institute of Chemistry, Faculty of Natural Sciences
University “Ss. Cyril and Methodius”
Skopje, Macedonia
Anasas [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
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 2Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
Introduction
• Condensed-phase systems are of substantial importance in both fundamental natural sciences and technology.
• Theoretical modeling of such systems has been shown to be of crucial importance for a thorough understanding of their properties.
• It has been often demonstrated that theoretical model can be complementary to the experimental studies of condensed phases.
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 3Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
Introduction
• 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
07.06.2011 4Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
Introduction
• 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
07.06.2011 5Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
Computational Details and Algorithms
• Introduction• Monte Carlo simulations. • The Optimization Problem• Representation of the Solution• The Optimization Procedure • Results• Conclusion
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 6Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
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
07.06.2011 7Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
Monte Carlo simulations• We have also carried out a Monte Carlo
simulation of pyrrole solution in CCl4:
– is important for modeling the solvent effects on the vibrational N-H stretching band of pyrrole in liquid carbon tetrachloride
– 1 pyrrole molecule solvated by 412 carbon tetrachloride molecules
– relatively accurate experimental data are available
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 8Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
Monte Carlo simulations• DICE
– FORTRAN– NOT Parallel – K. Coutinho and S. Canuto, DICE: A Monte Carlo program for
molecular liquid simulation, University of São Paulo, Brazil, version 2.9 (2003).
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 9Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
Monte Carlo 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
rrU
0
2612
44
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 10Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
Monte Carlo simulations
• The following combination rules were used to generate two-site Lennard-Jones parameters ij and ij from the single-site ones:
jiij jiij
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 11Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
Monte Carlo simulations
• Table 1. Lennard-Jones interaction potential parameters used initially in Monte-Carlo simulations
Atom q/e ε/(kcal mol-1) σ/Å
CClClClCl
0.248-0.062-0.062-0.062-0.062
0.0500.2660.2660.2660.266
3.8003.4703.4703.4703.470
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 12Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
Results with the standard LJ parameters
• 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
07.06.2011 13Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
Results with the standard LJ parameters
VPUNkTv
H
2
3
2
2
2
3
kT
HNkv
T
HC
c
PP
222ccc HHH
2
11
kTV
HV
TT
V
Vc
P
P
ccc HVVHHV
kTV
V
P
V
VT
T
21
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 14Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
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.
)()()()()( ,4321 mptp CrelerrcrelerrcrelerrcrelerrcSCost
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 15Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
The Optimization Problem
C
Cl
C
Cl
q ε σ
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 16Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
Outline of a Genetic Algorithm (GA)
Create a random starting population of chromosomes
Calculate the fitness of each chromosome
Select the next generation
Crossover
Mutation
?>= N generations?YES
END
NO
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 17Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
Representation of the Solution
• Chromosome S = {qCl, εCl, σCl, qC, εC, σC},
qCl εCl σCl εC σC
1 0 0 . . . 0 1 1
GENE
CHROMOSOME
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 18Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
Mutation
1 0 . . 0 1 0 . .
GENE
1 1
1 0 . . 0 0 0 . . 1 1
MUTATED GENEMUTATED GENE
FLIP a BIT in a Random positionwith a certain probability
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 19Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
Pick a random position and swap allsubsequent genes in the two parents
Crossover
qCl εCl σCl εC σC qCl εCl σCl εC σC
qCl εCl σCl εC σC
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 20Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
Select the best individuals with higher probability:
*Always select the fittest
Selection
qCl εCl σCl εCσC
qCl εCl σCl εC σCqCl ε
Cl σCl ε
C σC
qCl ε
Cl σCl ε
C σC
qCl εCl σCl εC σC
qCl εCl σCl εC σC
qClεCl
σClεC
σC
qClεCl
σClεC
σC
qCl εCl σCl εC σC
qCl εCl σCl εC σC
qClεCl
σClεC
σC
qClεCl
σClεC
σC
qCl εCl σCl εCσC
qCl εCl σCl εC σCqCl ε
Cl σCl ε
C σC
qCl ε
Cl σCl ε
C σC
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 21Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
The Optimization Procedure on GRID
• http://jgap.sourceforge.net
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 22Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
The Optimization Procedure on GRID
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 23Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
The standard LJ parameters.
• Table 1. Lennard-Jones interaction potential parameters used initially in Monte-Carlo simulations
Atom q/e ε/(kcal mol-1) σ/Å
CClClClCl
0.248-0.062-0.062-0.062-0.062
0.0500.2660.2660.2660.266
3.8003.4703.4703.4703.470
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 24Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
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
07.06.2011 25Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
The optimized LJ parameters.
Table 3. The optimized Lennard-Jones for CCl4 parameters by the genetic algorithm
Atom q/e ε/(kcal mol-1) σ/Å
CClClClCl
0.412-0.103-0.103-0.103-0.103
0.0250.3740.3740.3740.374
3.3280.1490.1490.1490.149
Optimization of intermolecular interaction potential energy parameters for Monte-Carlo and Molecular dynamics simulations
07.06.2011 26Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
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
07.06.2011 27Ljupvo Pejov [email protected] Sahpaski [email protected] Anastas Misev [email protected]
Conclusions and Directions for Future work
• 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.