Multicriteria optimization of force field models for molecular - PowerPoint PPT Presentation

Multicriteria optimization of force field models for molecular simulation of interfacial and bulk properties Martin Thomas Horsch, 1, 2 Stephan Werth, 1 Katrin Stöbener, 1, 3 Peter Klein, 3 Karl-Heinz Küfer, 3 and Hans Hasse 1 1 Laboratory of Engineering Thermodynamics, University of Kaiserslautern, Germany, 2 Department of Chemical Engineering, Indian Institute of Technology Kanpur, 3 Fraunhofer Institute for Industrial Mathematics, Kaiserslautern, Germany Indo-German MSO Conference Bankura, West Bengal, February 23, 2017

Molecular simulation software development homogeneous systems heterogeneous systems T ms2 ℓ s1 ρ http://www.ms–2.de/ http://www.ls1–mardyn.de/ Feb 23, 2017 M. T. Horsch, S. Werth, K. Stöbener, P. Klein, K.-H. Küfer, and H. Hasse 2

Molecular simulation of bulk fluid systems Self-diffusion coefficient Shear viscosity 20 Thermal conductivity Second virial coefficient 3.5 N2 5 3.0 O2 CO2 -1 s -1 B / cm 3 mol -1 CO2 10 2 λ / W m -1 K -1 C2H4 15 4 10 4 η s / Pa s 2.5 10 4 D ρ / mol m 10 2 λ / Wm -1 K -1 C2H6 2.0 3 10 1.5 2 1.0 5 1 0.5 0 0.0 0 T / K 20 25 30 35 5 10 15 20 25 20 22 24 26 28 30 10 -3 ρ / mol m -3 10 -3 ρ / mol m -3 10-3 ρ / mol m-3 10 -3 ρ / mol m - 3 10 -3 ρ / mol m -3 10 -3 ρ / mol m -3 ms2 is freely available for academic use: register at www.ms-2.de Vapour-liquid equilibira: Saturated densities and vapour pressures log P * T / K ρ / mol l -1 T -1 / K -1 Feb 23, 2017 M. T. Horsch, S. Werth, K. Stöbener, P. Klein, K.-H. Küfer, and H. Hasse 3

Scalable molecular dynamics simulation Spatial domain decomposition Dynamic load balancing Communication (almost) only with neighbour processes Linked-cell data structure near-field pair potentials Summation techniques, (non-blocking, over- lapping MPI send/ e.g. Janeček and FMM receive operations) l arge s ystems “ 1 ”: m olecul ar dyn amics http://www.ls1-mardyn.de/ Feb 23, 2017 M. T. Horsch, S. Werth, K. Stöbener, P. Klein, K.-H. Küfer, and H. Hasse 4

Long range correction at planar interfaces short range long range Long-range correction from the (explicit) (correction) density profile, following Janeček. 1–3 cutoff radius Angle-averaging expression for multi-site models, following Cook and Rowlinson 4, 5 as well as Lustig. 3, 6 1 Janeček, J. Phys. Chem. B, 110, 6264, 2006 ; 2 Goujon et al. , J. Chem. Theory Comput. 11, 4573, 2015 ; 3 Werth et al. , Mol. Phys. 112, 2227, 2014 ; 4 Cook and Rowlinson, Proc. Roy. Soc. A 219, 405, 1953 ; 5 Werth et al. , Mol. Phys. 113, 3750, 2015; 6 Lustig, Mol. Phys. 65, 175, 1988 . Feb 23, 2017 M. T. Horsch, S. Werth, K. Stöbener, P. Klein, K.-H. Küfer, and H. Hasse 5

Computational Molecular Engineering Engineering Physics (quantitative reliability) (qualitative accuracy) • Physically realistic modelling of • No blind fitting, but parameters of intermolecular interactions effective pair potentials are adjusted to experimental data • Separate contributions due to repulsive and dispersive as well as • Physical realism facilitates reliable electrostatic interactions interpolation and extrapolation Feb 23, 2017 M. T. Horsch, S. Werth, K. Stöbener, P. Klein, K.-H. Küfer, and H. Hasse 6

Molecular model validation simulation density 2CLJQ models: [mol/l] DIPPR correlation • 2 LJ centres • 1 quadrupole vapour pressure (logarithmic) Fit of parameters σ , ε , L , Q to VLE data of 29 fluids by Stoll et al. No interfacial properties were Deviation: considered for the • δρ ' ≈ 1 % parameterization. • δP sat ≈ 5 % inverse temperature [1/K] Feb 23, 2017 M. T. Horsch, S. Werth, K. Stöbener, P. Klein, K.-H. Küfer, and H. Hasse 7

Molecular model validation: Surface tension 2CLJQ: Two LJ centres + quadrupole 1 2CLJD: Two LJ + dipole 2 1 S. Werth , K. Stöbener, P. Klein, K.-H. Küfer, M. Horsch, H. Hasse, Chem. Eng. Sci. 121, 110–117, 2015 2 S. Werth, M. Horsch, H. Hasse, J. Chem. Phys. 144, 054702, 2016 Feb 23, 2017 M. T. Horsch, S. Werth, K. Stöbener, P. Klein, K.-H. Küfer, and H. Hasse 8

Molecular model validation: Surface tension Quadrupolar: 2CLJQ Non-polar: 1CLJ Propylene (CH 3 -CH=CH 2 ) Neon (Ne) Fluorine (F 2 ) Oxygen (O 2 ) Argon (Ar) Chlorine (Cl 2 ) R846 (SF 6 ) Carbon dioxide (CO 2 ) Literature Krypton (Kr) Bromine (Br 2 ) Carbon sulfide (CS 2 ) R14 (CF 4 ) + 20 % Xenon (Xe) Iodine (I 2 ) R10 (CCl 4 ) models by J. Ethane (C 2 H 6 ) Methane (CH 4 ) Nitrogen (N 2 ) R113 (CFCl 2 -CF 2 Cl) Ethylene (C 2 H 4 ) Stoll, H. Hasse, R114 (CF 2 Cl-CF 2 Cl) Acetylene (C 2 H 2 ) Dipolar: 2CLJD R115 (CF 3 -CF 2 Cl) R116 (C 2 F 6 ) J. Vrabec et al. , R1114 (C 2 F 4 ) R134 (CHF 2 -CHF 2 ) Carbon monoxide (CO) R32 (CH 2 F 2 ) R150B2 (CH 2 Br-CH 2 Br) 2001 – 2016 R1110 (C 2 Cl 4 ) R11 (CFCl 3 ) R30 (CH 2 Cl 2 ) Propadiene (CH 2 =C=CH 2 ) R114B2 (CBrF 2 -CBrF 2 ) R12 (CF 2 Cl 2 ) R30B2 (CH 2 Br 2 ) R1120 (CHCl=CCl 2 ) Propyne (CH 3 -C≡CH) R13 (CF 3 Cl) CH 2 I 2 R13B1 (CBrF 3 ) R12B2 (CBr 2 F 2 ) + 12 % Multicentric United Atom Models R22 (CHF 2 Cl) R12B1 (CBrClF 2 ) R23 (CHF 3 ) R10B1 (CBrCl 3 ) R41 (CH 3 F) R161 (CH 2 F-CH 3 ) Isobutane (C 4 H 10 ) Dimethyl sulfide (CH 3 -S-CH 3 ) Cyanogen (C 2 N 2 ) R123 (CHCl 2 -CF 3 ) R150a (CHCl 2 -CH 3 ) Cyclohexane (C 6 H 12 ) Cyanogen chloride (CClN ) Hydrogen cyanide (HCN) R124 (CHFCl-CF 3 ) R140 (CHCl 2 -CH 2 Cl) Acetonitrile (NC 2 H 3 ) Formic acid (CH 2 O 2 ) Methanol (CH 3 OH) R125 (CHF 2 -CF 3 ) R140a (CCl 3 -CH 3 ) Ethylene glycol (C 2 H 6 O 2 ) Ethanol (C 2 H 5 OH) Thiophene (SC 4 H 4 ) R134a (CH 2 F-CF 3 ) R130a (CH 2 Cl-CCl 3 ) Nitromethane (CH 3 NO 2 ) TIP4P/2012 water (H 2 O) Formaldehyde (CH 2 =O) R141b (CH 3 -CFCl 2 ) R160B1 (CH 2 Br-CH 3 ) Hydrazine (N 2 H 4 ) Dimethyl ether (CH 3 -O-CH 3 ) Phosgene (COCl 2 ) R142b (CH 3 -CF 2 Cl) R150B2 (CHBr 2 -CH 3 ) Monomethylhydrazine (CH 6 N 2 ) Acetone (C 3 H 6 O) Benzene (C 6 H 6 ) R143a (CH 3 -CF 3 ) R131b (CH 2 F-CCl 3 ) Toluene (C 7 H 8 ) Dimethylhydrazine (C 2 H 8 N 2 ) Ammonia (NH 3 ) R152a (CH 3 -CHF 2 ) R123B1 (CHClBr-CF 3 ) Perfluorobutane (C 4 F 10 ) Methylamine (NH 2 -CH 3 ) Chlorobenzene (C 6 H 5 Cl) R40 (CH 3 Cl) R112a (CCl 3 -CF 2 Cl) Dichlorobenzene (C 6 H 4 Cl 2 ) Ethyl acetate (C 4 H 8 O 2 ) Dimethylamine (CH 3 -NH-CH 3 ) R40B1 (CH 3 Br) R1141 (CHF=CH 2 ) HMDSO (C 6 H 12 OSi 2 ) R227ea (CF 3 -CHF-CF 3 ) Cyclohexanol (C 6 H 11 OH) CH 3 I R1132a (CF 2 =CH 2 ) D4 (C 8 H 24 O 4 Si 4 ) Sulfur dioxide (SO 2 ) Cyclohexanone (C 6 H 10 O) R30B1 (CH 2 BrCl) R1140 (CHCl=CH 2 ) Ethylene oxide (C 2 H 4 O) R20 (CHCl 3 ) R1122 (CHCl=CF 2 ) + 22 % R20B3 (CHBr 3 ) R1113 (CFCl=CF 2 ) R21 (CHFCl 2 ) R1113B1 (CFBr=CF 2 ) Feb 23, 2017 M. T. Horsch, S. Werth, K. Stöbener, P. Klein, K.-H. Küfer, and H. Hasse 9

Multicriteria molecular model optimization Pareto optimality criterion Multiple objectives (2CLJQ for carbon dioxide) Multicriteria optimization requires massively parallel molecular modelling. Feb 23, 2017 M. T. Horsch, S. Werth, K. Stöbener, P. Klein, K.-H. Küfer, and H. Hasse 10

Computation of the Pareto set p model parameters q optimization criteria (here, p = 4) (here, q = 3) ● LJ size parameter σ ● Saturated liquid density ρ ' ● LJ energy parameter ε ● Saturated vapour pressure p s ● Model elongation L ● Vapour-liquid surface tension γ ● Multipole moment µ or Q Dimension of the Pareto set cannot be greater than q – 1. Dimension of Pareto set d ≤ p . d = min( p , q – 1 ). (here, d = 2) Feb 23, 2017 M. T. Horsch, S. Werth, K. Stöbener, P. Klein, K.-H. Küfer, and H. Hasse 11

Computation of the Pareto set 1, 2 Multicriteria optimization problem Simultaneously minimized objective functions f ξ with ξ ∊ { ρ ', p s , γ } given by ( 1 − ξ exp ( T ) ) T / T c = 0.55 + 0.4i / N 2 N sim ( T ) 1 N + 1 ∑ 2 〉 0.55 T c f ξ =〈δξ exp = lim (here: N = 9). exp < T < 0.95 T c ξ N →∞ i = 0 Sandwiching Alternating construction of inner (reachable) and outer (unreachable) approximations, assuming local convexity of the Pareto set. Hyperboxing In non-convex regions (hyperboxes), Pascoletti-Serafini scalarization is employed to obtain a suitable local single-criterion optimization problem. 1 M. Bortz et al. , Comput. Chem. Eng. 60, 354, 2014 ; 2 Stöbener et al. , Fluid Phase Equilib. 411, 33, 2016 . Feb 23, 2017 M. T. Horsch, S. Werth, K. Stöbener, P. Klein, K.-H. Küfer, and H. Hasse 12

Multicriteria molecular model optimization 1, 2 Representation of objective and parameter spaces by patch plots : Pareto-optimal 2CLJQ models of molecular oxygen 1 Stöbener et al. , Fluid Phase Equilib. 373, 100, 2014 ; 2 Stöbener et al. , Fluid Phase Equilib. 408, 141, 2016 . Feb 23, 2017 M. T. Horsch, S. Werth, K. Stöbener, P. Klein, K.-H. Küfer, and H. Hasse 13

Multicriteria molecular model optimization 1, 2 Requirements for the criteria follow the priorities of the target application: Restrictions imposed on 2CLJ models of molecular oxygen 1 Stöbener et al. , Fluid Phase Equilib. 373, 100, 2014 ; 2 Stöbener et al. , Fluid Phase Equilib. 408, 141, 2016 . Feb 23, 2017 M. T. Horsch, S. Werth, K. Stöbener, P. Klein, K.-H. Küfer, and H. Hasse 14

Multicriteria molecular model optimization 1, 2 Requirements for the criteria follow the priorities of the target application: 2CLJ models of molecular oxygen fulfilling all requirements 1 Stöbener et al. , Fluid Phase Equilib. 373, 100, 2014 ; 2 Stöbener et al. , Fluid Phase Equilib. 408, 141, 2016 . Feb 23, 2017 M. T. Horsch, S. Werth, K. Stöbener, P. Klein, K.-H. Küfer, and H. Hasse 15