Force fields and molecular modelling
Carine Clavagu´era
Laboratoire de Chimie Physique, CNRS & Universit´eParis Sud, Universit´eParis Saclay
Carine Clavagu´era Force fields and molecular modelling 1 / 76 Outline
Class I and class II force fields
Class III force fields
Solvent modelling
Applications
Reactive force fields
Carine Clavagu´era Force fields and molecular modelling 2 / 76 Multiscale modelling
Carine Clavagu´era Force fields and molecular modelling 3 / 76 History
1930 : Origin of molecular mecanics : Andrews, spectroscopist
1960 : Pioneers of force fields : Wiberg, Hendrickson, Westheimer
1970 : Proof of concept : Allinger
1980 : Basis of force fields for classical molecular dynamics : Scheraga, Karplus, Kollman, Allinger
1990 : Commercial distribution of program packages
Since 2000 I More and more publications about classical molecular dynamics simulations I Wide availability of codes I New generation force fields
Carine Clavagu´era Force fields and molecular modelling 4 / 76 Potential energy r N : 3N coordinates{x,y,z} for N particules (atoms)
Force field = mathematical equations to compute the potential energy + parameters
N U (r ) = Us + Ub + Uφ + Uvdw + Uelec + Upol | {z } | {z } intramolecular interactions intermolecular interactions
1-4 long-range interaction terms = interactions between 2 rigid spheres
Carine Clavagu´era Force fields and molecular modelling 5 / 76 Class I force fields
CHARMM, AMBER, OPLS, GROMOS. . .
I Intramolecular interactions : harmonic terms only I Intermolecular interactions : Lennard-Jones 6-12 and Coulomb term based on atomic charges
X 2 X 2 X V (r) = ks (r − ro ) + kb (θ − θo ) + Vn [1 + cos((nφ) − δ)] s b torsion 12 6 X qi qj r0 r0 + + 4ε − εrij r r i Carine Clavagu´era Force fields and molecular modelling 6 / 76 Bond stretching / bond angle Harmonic approximation Taylor series expansion around Bond energy versus bond length bo P 2 Ubond = b Kb (b − b0) Chemical Kbond b0 type (kcal/mol/A˚2)(A)˚ C−C 100 1.5 C−C 200 1.3 C−C 400 1.2 Taylor series expansion around θo X 2 Uangle = Ka (θ − θo ) a Carine Clavagu´era Force fields and molecular modelling 7 / 76 Torsion May be treated by direct 1-4 interaction terms Much more efficient to use a periodic form X Utorsion = Vn [1 + cos((nφ) − δ)] torsion Carine Clavagu´era Force fields and molecular modelling 8 / 76 Improper torsion To describe out-of-plane movements Mandatory to control planar structures Example : peptidic bonds, benzene P 2 Uimproper = φ Kφ(φ − φo ) Carine Clavagu´era Force fields and molecular modelling 9 / 76 van der Waals interactions London dispersion forces in 1/R6 and repulsive wall at short distances Lennard-Jones 6-12 potential " # R 12 R 6 E (R) = 4ε o − o LJ R R Diatomic parameters 1 RAB = (RA + RB ) o 2 o o p εAB = εA + εB Carine Clavagu´era Force fields and molecular modelling 10 / 76 Electrostatic interaction X qi qj Interactions between punctual atomic charges Eelec = εrij i Quantum chemical calculation of atomic charges 1- Quantum chemical calculations of molecular models. 2- Electrostatic potential on a grid of points surrounding a molecule. 3- Atomic charges derived from the electrostatic potential. Carine Clavagu´era Force fields and molecular modelling 11 / 76 Electrostatic potential fit Electrostatic potential (ESP) from the wave function (QM calculations) nuc Z ∗ 0 0 X ZA Ψ (r )Ψ(r ) 0 φesp (r)) = − 0 dr |RA − r| |r − r| A Basic idea : fit this quantity with point charges Minimize error function Npoints Natoms ! X X QA(Ra ) ErrF (Q) = φesp (r) − |Ra − r| r a An example : Restrained Electrostatic Potential (RESP) charges → potential is fitted just outside of the vdW radius Carine Clavagu´era Force fields and molecular modelling 12 / 76 Class I force fields CHARMM, AMBER, OPLS, GROMOS... X 2 X 2 X V (r) = ks (r − ro ) + kb (θ − θo ) + Vn [1 + cos((nφ) − δ)] s b torsion 12 6 X qi qj r0 r0 + + 4ε − εrij r r i Force field bond and angle vdw Elec Cross Molecules AMBER P2 12-6 and 12-10 charge none proteins, nucleic acids CHARMM P2 12-6 charge none proteins OPLS P2 12-6 charge none proteins, nucleic acids GROMOS P2 12-6 charge none proteins, nucleic acids Carine Clavagu´era Force fields and molecular modelling 13 / 76 Class I force fields : differences AMBER (Assisted Model Building with Energy Refinement) I Few atoms available, some calculations are impossible I Experimental data + quantum chemical calculations I Possible explicit terms for hydrogen bonds and treatment of lone pairs CHARMM (Chemistry at HARvard Molecular Mechanics) I Slightly better for simulations in solution I Charges parameterized from soluted-solvent interaction energies I No lone pair, no hydrogen bond term OPLS (Optimized Potentials for Liquid Simulations) I Derived from AMBER (intramolecular) I Non-bonded terms optimized for small molecule solvation I No lone pair, no hydrogen bond term Carine Clavagu´era Force fields and molecular modelling 14 / 76 How to obtain intramolecular parameters ? Quantum chemistry and experimental data → Force constants in bonded terms : vibrational frequencies, conformational energies → Geometries : computations or experiments (ex. X-ray) Example : potential energy surfaces of molecules with several rotations Carine Clavagu´era Force fields and molecular modelling 15 / 76 Class II force fields MMFF94, MM3, UFF I Anharmonic terms (Morse, higher orders,...) I Coupling terms (bonds/angles, . . .) I Alternative forms for non-bonded interactions MM2/MM3 I Successful for organic molecules and hydrocarbons MMFF (Merck Molecular Force Field) I Based on MM3, parameters extracted on ab initio data only I Good structures for organic molecules I Problem : condensed phase properties Improvements I Conformational energies I Vibrational spectra Carine Clavagu´era Force fields and molecular modelling 16 / 76 Bond stretching Morse potential → Taylor series expansion around ro Beyond harmonic approximation : X 2 3 4 Ubond = K2(b − b0) + K3(b − b0) + K4(b − b0) + ... Carine Clavagu´era Force fields and molecular modelling 17 / 76 Bond angle Harmonic approximation : X 2 Uangle = Ka (θ − θo ) a Taylor series expansion around θo MM3 : beyond a quadratic expression θ3 term mandatory for deformation larger than 10-15◦. X 2 −5 2 Uangle = Ka (θ − θo ) [1 − 0.014(θ − θo ) + 5.6.10 (θ − θo ) a −7 3 4 − 7.0.10 (θ − θo ) + 2.2.10−8(θ − θo ) ] Carine Clavagu´era Force fields and molecular modelling 18 / 76 Couplings Coupling terms between at least 2 springs Stretch-bend coupling X 0 Esb = Klθ (l − l0) + l − l0 (θ − θ0) l,l0 Other couplings : stretch-torsion, angle-torsion, ... Carine Clavagu´era Force fields and molecular modelling 19 / 76 Interactions de van de Waals Alternative to Lennard-Jones potential : Buckingham potential aRo 6 − R E (R) = ε e R − o vdw R Used in the MM2/MM3 force fields However, LJ potential is usually preferred in biological force fields → Computational cost of the exponential form in comparison with R−12 Force field bond and angle vdw Elec Cross Molecules MM2 P3 Exp-6 dipole sb general MM3 P4 Exp-6 dipole sb, bb, st general MMFF P4 14-7 charge sb general UFF P2 or Morse 12-6 charge none all elements Carine Clavagu´era Force fields and molecular modelling 20 / 76 Comparison of conformational energies for organic molecules Carine Clavagu´era Force fields and molecular modelling 21 / 76 Comparison of conformational energies for organic molecules Carine Clavagu´era Force fields and molecular modelling 22 / 76 Comparison of conformational energies for organic molecules Carine Clavagu´era Force fields and molecular modelling 23 / 76 Biological force fields M.R. Shirts, J.W. Pitera, W.C. Swope, V.S. Pande, J. Chem. Phys. 119, 5740 (2003) Carine Clavagu´era Force fields and molecular modelling 24 / 76 Limitations ”Additive force fields” I No full physical meaning of the individual terms of the potential energy I No inclusion of the electric field modulations I No change of the charge distribution induced by the environment → No many-body effects Transferability I Better accuracy for the same class of compounds used for parameterization I No transferability between force fields Properties from electronic structure unavailable (electric conductivity, optical and magnetic properties) → Impossible to have breaking or formation of chemical bonds Carine Clavagu´era Force fields and molecular modelling 25 / 76 Class III force field class Next Generation Force Fields → To overcome the limitation of additive empirical force fields I Polarizable force fields : 3 models based on F Induced dipoles F Drude model F Fluctuating charges X-Pol, SIBFA, AMOEBA, NEMO, evolution of AMBER, CHARMM I Able to reproduce physical terms derived from QM : total electrostatic energy, charge transfer, ... I Optimized for hybrid methods (QM/MM) I To account for the electronegativity and for hyperconjugation I Reactive force fields Carine Clavagu´era Force fields and molecular modelling 26 / 76 Accurate description of electrostatic effects H2OH2O + q Cisneros et al. Chem. Rev. 2014 Errors (V) for electrostatic potential on a surface around N-methyl propanamide Multipole expansion 3 Dipole-Dipole interaction : (µ1 µ2)/R 4 Dipole-Quadrupole interaction : (µ1 Q2)/R Quadrupole-Quadrupole interaction : 5 (Q1 Q2)/R Point charges vs. multipole expansion Stone Science, 2008 Carine Clavagu´era Force fields and molecular modelling 27 / 76 Multipolar distributions Distributed multipole analysis (DMA) : multipole moments extracted from the quantum wave function Multipoles are fitted to reproduce the electrostatic potential A. J. Stone, Chem. Phys. Lett. 1981, 83, 233 Acrolein : molecular electrostatic potential (a) QM (reference) (b) DMA (c) Fitted multipoles Difference between ab initio ESP and (d) DMA (e) Fitted multipoles C. Kramer, P. Gedeck, M. Meuwly, J. Comput. Chem. 2012, 33, 1673 Carine Clavagu´era Force fields and molecular modelling 28 / 76 Solvent induced dipoles • The matter is polarized proportionally to the strength of an applied external electric field. • The constant of proportionality α is called the polarizability with µinduit = αE Carine Clavagu´era Force fields and molecular modelling 29 / 76 Induced dipole polarization model Induced dipole on each site i ind µi,α = αi Ei,α (α ∈ {x, y, z}) αi : atomic polarizability, Ei,α : electric field Mutual polarization by self-consistent iteration (all atoms included) : sum of the fields generated by both permanent multipoles and induced dipoles ind X ij X i,j 0 ind µi,α = αi Tα Mj + αi Tα,β µj 0,β T : interaction matrix {j } {j 0} | {z } | {z } induced dipole on site i by the interaction dipole on site i by permanent multipoles of the the other induced dipole other molecules Implemented in the several force fields : AMOEBA, SIBFA, NEMO, etc. Carine Clavagu´era Force fields and molecular modelling 30 / 76 Polarizable Atomic Multipole-Based AMOEBA Force Field for Proteins Comparison of Ramachandran potential of mean force maps for GPGG peptide Proline-2 : (a) AMOEBA (b) PDB Glycine-3 : (c) AMOEBA (d) PDB Y. Shi, Z. Xia, J. Zhang, R. Best, C. Wu, J.W. Ponder, P. Ren, J. Chem. Theo. Comput., 9, 4046 (2013) Carine Clavagu´era Force fields and molecular modelling 31 / 76 Polarizable Atomic Multipole-Based AMOEBA Force Field for Proteins Superimposition of the final structures from AMOEBA simulations (green) and the experimental X-ray crystal structures (gray) (a) Crambin (b) Trp cage (c) villin headpiece (d) ubiquitin (e) GB3 domain (f) RD1 antifreeze protein (g) SUMO-2 domain (h) BPTI (i) FK binding protein (j) lysozyme Overall average RMSD (ten simulated protein structures) = 1.33 A˚ Seven of them are close to 1.0 A˚ Y. Shi, Z. Xia, J. Zhang, R. Best, C. Wu, J.W. Ponder, P. Ren, J. Chem. Theo. Comput., 9, 4046 (2013) Carine Clavagu´era Force fields and molecular modelling 32 / 76 The Drude oscillator model Classical Drude Oscillator Virtual sites carrying a partial electric charge qD (the Drude charge) Attached to individual atoms via a harmonic spring with a force constant kD √ qD = kD · α → Response to the local electrostatic field E via an induced dipole µ q 2 E µ = D kD → Changes in the electrostatic term in force fields and in the potential energy I Uelec represents all Coulombic electrostatic interactions (atom-atom, atom-Drude, and Drude-Drude) I Adding a UDrude term that represents the atom-Drude harmonic bonds A popular implementation : polarizable CHARMM force field H. Yu, WF van Gunsteren, Comput. Phys. Commun. 172, 69-85 (2005) Carine Clavagu´era Force fields and molecular modelling 33 / 76 A polarizable force field for monosaccharides Application of the Drude model derived from CHARMM 8 diastereomer Drude particles (blue, ‘D’) attached to Polarization necessary to accurately non-H atoms model the cooperative hydrogen Oxygen lone pairs (green, ‘LP’) bonding effects connected with bond, angle and torsion Parameter optimization on quantum terms chemistry calculations in gas phase Hydrogen non polarizable Transferability of the model to other monosaccharides D.S. Patel , X. He, A.D. MacKerell Jr, J. Phys. Chem. B 2015, 119, 637 Carine Clavagu´era Force fields and molecular modelling 34 / 76 A polarizable force field for monosaccharides Validation of the model on condensed phase properties I Subtil soluted-water and water-water equilibrium I Role of concentration and temperature Error on densities ' 1% Agreement of the polarizable FF with NMR experiments → Population of conformers with one exocyclique torsion for D-glucose and D-galactose Drude vs. CHARMM comparison 43 conformers : dipole moments and D.S. Patel , X. He, A.D. MacKerell Jr, J. Phys. Chem. B 2015, relative conformational energies 119, 637 Carine Clavagu´era Force fields and molecular modelling 35 / 76 The fluctuating charge model Polarization is introduced via the ”movement” of the charges Expand energy at 2nd order as a function of the number of electrons N 2 ∂E 1 ∂ E 2 E = E0 + ∆N + ( ∆N ) ∂N 2 ∂N 2 |{z} |{z} | {z } ∆N =−Q ∂E 2 =−χ ∂ E =η ∂N ∂N 2 2 parameters per chemical element : electronegativity (χ) and hardness (η) Sum over sites (atomic centers) X 1 X E = E + χ Q + η Q Q elec 0 A A 2 AB A B A AB Minimizing the electrostatic energy → Explicitly account for polarization and charge transfer Main application : cooperative polarization in water A. M. Rapp´eand W. A. Goddard III, J. Phys. Chem. 1991, 95, 3358. S. W. Rick, S. J. Stuart, B. J. Berne, J. Chem. Phys. 1994, 101, 6141. Carine Clavagu´era Force fields and molecular modelling 36 / 76 Basin-hopping : C60 − (H2O)n clusters Interaction energies ∆E C60 + nH2O −→ C60 − (H2O)n Potential energy of C60 − (H2O)n with 2 contributions H2O − H2O interaction : TIP4P model, class I and rigid, developed for bulk water C60 − H2O interaction : repulsion-dispersion (Lennard-Jones) + polarization For n = 1, ∆Ea = ∆Eb (1/3 from polarization) D.J. Wales et al., J. Phys. Chem. B 110 (2006) 13357 Carine Clavagu´era Force fields and molecular modelling 37 / 76 Basin-hopping : global minima for C60 − (H2O)n clusters Method proposed by D. J. Wales → Potential energy surface converted into the set of basins of attraction of all the local minima D.J. Wales and J.P.K. Doye, J. Phys. Chem. A 101 (1997) 5111 Carine Clavagu´era Force fields and molecular modelling 38 / 76 Basin-hopping : global minima for C60 − (H2O)n clusters Role of the C60 − H2O polarizable potential Hydrophobic water-fullerene interaction highlighted Carine Clavagu´era Force fields and molecular modelling 39 / 76 Summary : electrostatic effects Class III force fields → To overcome the limitation of additive empirical force fields → To reproduce accurately electrostatic and polarization contributions Model Polarization Charge Transfer Comput. Cost Pairwise fixed charges implicit√ implicit Induced dipoles √ implicit Drude oscillator √ implicit√ Fluctuating charges Lack of reactivity but important for chemists ! Carine Clavagu´era Force fields and molecular modelling 40 / 76 Solvation role Carine Clavagu´era Force fields and molecular modelling 41 / 76 Implicit solvent vs. explicit solvent Implicit : the solvent is treated as a conti- Explicit : each solvent molecule is nuum description considered Need to define a cavity that contains the solute Carine Clavagu´era Force fields and molecular modelling 42 / 76 Implicit vs. explicit Computational efficiency for alanine dipeptide Solvent ∆G (kcal/mol) CPU Time (s) Explicit -13.40 3.4x105 Implicit -13.38 1.0x10−1 Are implicit solvents sufficient ? Structure of DNA Explicit solvent Experimental Implicit solvent Carine Clavagu´era Force fields and molecular modelling 43 / 76 Implicit vs. explicit Computational efficiency for alanine dipeptide Solvent ∆G (kcal/mol) CPU Time (s) Explicit -13.40 3.4x105 Implicit -13.38 1.0x10−1 Are implicit solvents sufficient ? Carine Clavagu´era Force fields and molecular modelling 44 / 76 Periodic boundary conditions Explicit solvation schemes The fully solvated central cell is simulated, in the environment produced by the repetition of this cell in all directions just like in a crystal → Infinite system with small number of particles Introducing a periodicity level frequently absent in reality Applications : liquids, solids Carine Clavagu´era Force fields and molecular modelling 45 / 76 Periodic boundary conditions When an atom moves off the cell, it reappears on the other side (number of atoms in the cell conserved) Ideally, every atom should interact with every other atom Problem : the number of non-bonded interactions grows as N 2 where N is the number of particles → limitation of the system size Carine Clavagu´era Force fields and molecular modelling 46 / 76 Cutoff Methods Some interatomic forces decrease strongly with distance (van der Waals, covalent interactions etc.) : short-range interactions → Ignore atoms at large distances without too much loss of accuracy → Introduce a cutoff radius for pairwise interactions and calculate the potential only for those within the cutoff sphere Computing time dependence reduced to N Electrostatic interaction is very strong and falls very slowly : long-range interactions → The use of a cutoff is problematic and should be avoided Several algorithms exist (Ewald summation, Particle Mesh Ewald, ....) to treat the long-range interactions without cutoffs Carine Clavagu´era Force fields and molecular modelling 47 / 76 Setting up a simulation Optimize the solute geometry in vacuum (no more constraint) Add counter-ions if necessary Choose the good cell shape (cubic, hexagonal prism, etc.) depending on the shape of the system Add solvent molecules around the solute (water for example) Delete the solvent molecules which are too close to the solute Create the periodic boundary conditions ”Equilibration” of the global system at constant pressure and temperature Carine Clavagu´era Force fields and molecular modelling 48 / 76 Water as a solvent Water models with 3 to 5 interaction sites (a) 3 sites : TIP3P (b) 4 sites : TIP4P (c) 5 sites : TIP5P Carine Clavagu´era Force fields and molecular modelling 49 / 76 Force field comparison for water The most used : 3 interaction sites such as SPC and TIP3P SPC TIP3P TIP4P Exp. Autors Berendsen Jorgensen Jorgensen Number of point 3 3 3 charges µgaz (D) 2.27 2.35 2.18 1.85 2.85 µ (D) 2.27 2.35 2.18 liq. (at 25˚C) 0 65 82 53 78.4 Carine Clavagu´era Force fields and molecular modelling 50 / 76 Experimental and computed thermodynamic data 25◦C, 1 atm SPC TIP3P TIP4P Exp. ρ (kg.dm−3) 0.971 0.982 0.999 0.997 E (kcal.mol−1) -10.18 -9.86 -10.07 -9.92 ∆H vap. 10.77 10.45 10.66 10.51 (kcal.mol−1) C p 23.4 16.8 19.3 17.99 (cal.mol−1.deg−1) Carine Clavagu´era Force fields and molecular modelling 51 / 76 Water phase diagram In the solid phase, water exhibits one of the most complex phase diagrams, having 13 different (known) solid structures. → Can simple models describe the phase diagram ? TIP4P Experiment SPC or TIP3P Only TIP4P provides a qualitatively correct phase diagram for water. Carine Clavagu´era Force fields and molecular modelling 52 / 76 Water dimer properties POL5 TIP4P/FQ TIP5P ab initio exp U (kcal/mol) -4.96 -4.50 -6.78 -4.96 -5.40.7 r (A)˚ 2.896 2.924 2.676 2.896 2.98 θ (degrees) 4.7 0.2 -1.6 4.8 06 φ (degrees) 62.6 27.2 50.2 57.3 586 µ (D) 2.435 3.430 2.920 2.683 2.643 hµi (D) 2.063 2.055 2.292 2.100 ? Carine Clavagu´era Force fields and molecular modelling 53 / 76 Bulk water properties POL5 TIP4P/FQ TIP5P exp U (kcal/mol) -9.920.01 -9.890.02 -9.870.01 -9.92 ρ (g/cm3) 0.9970.001 0.9980.001 0.9990.001 0.997 µ (D) 2.7120.002 2.6 2.29 ? (2.5-3.2) 0 988 798 822 78.3 D(10−9 m2/s) 1.810.06 1.90.1 2.620.04 2.3 τNMR (ps) 2.60.1 2.10.1 1.40.1 2.1 Carine Clavagu´era Force fields and molecular modelling 54 / 76 From the single water molecule to the liquid phase 3 3 3 H2O µ(D) αxx (A˚ ) αyy (A˚ ) αzz (A˚ ) AMOEBA 1.853 1.660 1.221 1.332 QM 1.84 1.47 1.38 1.42 Exp. 1.855 1.528 1.415 1.468 (H2O)2 De (kcal/mol) rO−O (A)˚ µtot. (D) AMOEBA 4.96 2.892 2.54 QM 4.98/5.02 2.907/2.912 2.76 Exp. 5.44 0.7 2.976 2.643 3 Liquid ρ (g/cm ) ∆Hv 0 AMOEBA 1.0004 0.0009 10.48 0.08 81 13 Exp. 0.9970 0.7 10.51 78.3 Carine Clavagu´era Force fields and molecular modelling 55 / 76 Molecular dynamics Carine Clavagu´era Force fields and molecular modelling 56 / 76 Trajectory analysis Along the trajectory, atomic coordinates and velocities can be stored for further processing A number of properties, e.g. structural, can then be computed and averaged over time Carine Clavagu´era Force fields and molecular modelling 57 / 76 The radial distribution function g(r) : probability of finding a particle at a distance r from another particle, relative to the same probability for an ideal gas g(r) : can be determined experimentally, from X-ray and neutron diffraction patterns g(r) : can be computed from MD simulations Example : solvation of the K+ ion I Simulation time : 2 ns I Time step : 0.1 fs I T = 298 K I 216 water molecules d’eau or 100 formamide molecules Carine Clavagu´era Force fields and molecular modelling 58 / 76 Coordination number CN CN : number of atoms or ligands Z r1 CN (r) = 4πρ g(r 0)r 02dr r Example : solvation of K+, Na+ and Cl− ions Carine Clavagu´era Force fields and molecular modelling 59 / 76 Micro-solvation of the K+ ion Cluster of 34 water molecules around the cation Simulation time : 10 ns Timestep : 1 fs Force field : AMOEBA polarizable force field T = 200 K Carine Clavagu´era Force fields and molecular modelling 60 / 76 Micro-solvation of the K+ ion Carine Clavagu´era Force fields and molecular modelling 61 / 76 Time Correlation Functions C(t) A(t) and B(t) : two time dependent signals A correlation function C(t) can be defined 1 Z τ C (t) = hA(t0) · B(t0 + t)i = lim A(t0)B(t0 + t)dt0 τ→∞ τ 0 If A and B represent the same quantity (A ≡ B), then C(t) is called ”autocorrelation function” → The autocorrelation function shows how a value of A at t=t0 + t is correlated to its value at t0 Carine Clavagu´era Force fields and molecular modelling 62 / 76 Example : transport coefficients Diffusion coefficient D directly related to the time integral of the velocity autocorrelation function 1 Z ∞ D = hvi (0) · vi (t)idt 3 0 Example : Diffusion coefficient for K+, Na+ and Cl− ions in water Carine Clavagu´era Force fields and molecular modelling 63 / 76 Molecular Dynamics Study of the Liquid-Liquid Interface N. Sieffert and G. Wipff, J. Phys. Chem. B 2006, 110, 19497 I + − (BMI /Tf2N ) ionic liquid/water biphasic system I Influence of the solvent of the Cs+ extraction by the ligand ”L” (calix[4]arene-crown-6) I Comparison with chloroform Carine Clavagu´era Force fields and molecular modelling 64 / 76 Conditions of the simulations AMBER force field and corresponding code I TIP3P water model I OPLS chloroform model I Extraction of new parameters for IL I Cs+ parameters : QM micro-hydration Solvents I Adjacent cubic boxes of IL and water for the interface representation I System size F IL (219 molecules)/water (2657 molecules) F CLF (722 molecules)/water (2657 molecules) I Energy minimization of the systems mandatory ! Other data I T = 300 K (Berendsen thermostat) I Leapfrog Algorithme, 2 fs time step I Long equilibration ! Can be until 600 ps I Long simulations F From 20 to 60 ns for IL/water F From 0.4 to 2 ns for CLF/water Carine Clavagu´era Force fields and molecular modelling 65 / 76 + − Simulations with the Cs /NO3 ion pair Position of the interface defined by the intersection of the density curves 3 distinct domains including a 12 A˚ interface Starting point : 12 ion pairs in water Carine Clavagu´era Force fields and molecular modelling 66 / 76 + − Simulations with the Cs L/NO3 complex + − From previous conclusion : the Cs /NO3 pair behaviour is different in IL and CLF + − A complexe is made with Cs and the ligand L, NO3 as counterion Starting point : 3 complexes I 1 in water I 1 at the interface I 1 in IL Same simulation with chloroform Questions I Where will the complexes go ? I Will Cs+ remain as a complex ? I Which differences will be observed in the 3 domains ? I What will be the differences between IL and CLF ? Carine Clavagu´era Force fields and molecular modelling 67 / 76 Results Hydrophobic complex Ion transfer easier in IL than in Cs+/L activity at the interface CLF Carine Clavagu´era Force fields and molecular modelling 68 / 76 Reactive force fields How to bridge the gap between quantum chemistry and empirical force fields ? How to deal with chemical reactivity with a force field ? REAXFF, REBO, AIREBO I To get a smooth transition from non-bonded to single, double and triple bonded systems I Use of bond length/bond order relationships updated along the simulation BUT I Very large number of parameters, expensive computational cost I The validation step is crucial ReaxFF is 10-50 times slower than non-reactive force fields Better behaviour than quantum methods NlogN for ReaxFF vs >N3 for QM Carine Clavagu´era Force fields and molecular modelling 69 / 76 REAXFF Epotential = (Ebond + Eover + Eunder ) + (Eangle + Epenalty ) + Etorsion +Elone−pair + Econjugaison + EH −bond + EvdW + Eelec All connectivity-dependent interactions are made bond-order dependent Over- and under-coordination of atoms → Ensure that energy contributions must be avoided disappear upon bond dissociation → Energy penalty when an atom has more bonds than its valence allows → e.g. Carbon no more than 4 bonds, Hydrogen no more than 1 Electrostatic term = fluctuating charges to account for polarization effects van Duin, Dasgupta, Lorant, Goddard, J. Phys. Chem. A, 105, 9396 (2001) Strachan, Kober, van Duin, Oxgaard, Goddard, J. Chem. Phys., 122, 054502 (2005) Carine Clavagu´era Force fields and molecular modelling 70 / 76 Electrostatic interactions Fluctuating charge model = electrostatic and polarization effets Good reproduction of Mulliken charges Largest part of the computational cost in the reactive force field Must be computed at each step of the simulation Carine Clavagu´era Force fields and molecular modelling 71 / 76 Oxidation of aluminum nanoparticles ANPs : a solid propellant in the application of solid-fuel rockets Growth of an oxide film with temperature I high combustion enthalpy I result of an oxidation process Growth of the oxide layer on ANPs : combined effects I inward diffusion of oxygen atoms I role of temperature, pressure of oxygen gas, induced electric field through the oxide layer ReaxFF reactive force field to assess the full dynamics of the oxidation process of ANPs Aluminum/oxygen interactions from an atomistic-scale view Starting point 473 K, 573 K, 673 K S. Hong, A.C.T. van Duin, J. Phys. Chem. C, 119, 17876 (2015) Carine Clavagu´era Force fields and molecular modelling 72 / 76 Oxidation of aluminum nanoparticles Mecanism of oxidation Role of the pressure of the oxygen gas 1 adsorption of the oxygen molecules → highly exothermic reaction 2 formation of hot-spot regions on the surfaces of the ANPs 3 void space created in these regions → reduction of reaction barrier for O2 diffusion 4 growth of the oxide layer Growth of the oxide layer with temperature Temperature and pressure of oxygen gas I Role on the number of void spaces I Density of the oxide layer 300 K 500 K 900 K Carine Clavagu´era Force fields and molecular modelling 73 / 76 Nanotube formation with the aid of Ni-catalysis Synthesis of chains of C60 molecules inside single-wall carbon nanotubes → REAX-FF : various levels for the potential energy I C-C I Ni/Ni-C I Ni cluster Understand the first stage of the nanotube growth I 5 C60 in a (10,10) nanotube I van der Waals interactions I ∼ 3.5 eV / C60 Validation with quantum chemistry calculations : geometries, binding energies, reaction barrier height, heat capacity, etc. Simulations at 1800, 2000, 2400 and 2500 K H. Su, R.J. Nielsen, A.C.T. van Duin, W.A. Goddard III, Phys. Rev. B, 75, 134107 (2007) Carine Clavagu´era Force fields and molecular modelling 74 / 76 Nanotube formation with the aid of Ni-catalysis T = 2500 K T = 1800 K Without Ni catalyst, 5 C in the 60 With Ni catalyst : 5 C + 2 Ni nanotube 60 between 2 C60 At 16 ps, coalescence only at T = 2500 K Lower coalescence temperature : In agreement with the energy barrier for T = 1800 K the formation of the C60 dimer Carine Clavagu´era Force fields and molecular modelling 75 / 76 References Molecular modelling : principles and applications, A. R. Leach, Addison Wesley Longman, 2001 (2nd edition) Understanding molecular simulation : from algorithmes to applications, D. Frenkel & B. Smit, Computational Science Series, vol. 1, 2002 (2nd edition) Molecular Dynamics : survey of methods for simulating the activity of proteins, S. A. Adcock and J. A. McCammon, Chem. Rev. 2006, 105, 1589 Classical Electrostatics for Biomolecular Simulations, G. A. Cisneros, M. Karttunen, P. Ren and C. Sagui, Chem. Rev. 2004, 114, 779 Force Fields for Protein Simulation, J. W. Ponder and D. A. Case, Adv. Prot. Chem. 2003, 66, 27 Carine Clavagu´era Force fields and molecular modelling 76 / 76