lssc2011 optimization of intermolecular interaction potential energy parameters for monte-carlo and...

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


Skopje, Macedonia

Anasas [email protected]

Institute of Informatics, Faculty of Natural Sciences


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.



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.



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).



Computational Details and Algorithms

• Introduction• Monte Carlo simulations. • The Optimization Problem• Representation of the Solution• The Optimization Procedure • Results• Conclusion



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.



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



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).



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




• The following combination rules were used to generate two-site Lennard-Jones parameters ij and ij from the single-site ones:

jiij jiij




• 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



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.



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



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



The Optimization Problem

C

Cl

C

Cl

q ε σ



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



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



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



Pick a random position and swap allsubsequent genes in the two parents

Crossover

qCl εCl σCl εC σC qCl εCl σCl εC σC




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



qClεCl

σClεC

σC

qClεCl

σClεC

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



The Optimization Procedure on GRID

• http://jgap.sourceforge.net



The Optimization Procedure on GRID



The standard LJ parameters.

• Table 1. Lennard-Jones interaction potential parameters used initially in Monte-Carlo simulations


CClClClCl

0.248-0.062-0.062-0.062-0.062

0.0500.2660.2660.2660.266

3.8003.4703.4703.4703.470



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



The optimized LJ parameters.

Table 3. The optimized Lennard-Jones for CCl4 parameters by the genetic algorithm


CClClClCl

0.412-0.103-0.103-0.103-0.103

0.0250.3740.3740.3740.374

3.3280.1490.1490.1490.149



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



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.

lssc2011 optimization of intermolecular interaction potential energy parameters for monte-carlo and...

Technology

optimization problem

constant pressure c

parents q

fittest q

monte carlo program

series of monte

monte carlosimulations

liquid ccl