Carine Clavagu era Laboratoire de Chimie Physique, CNRS ... · Force elds and molecular modelling...
Transcript of Carine Clavagu era Laboratoire de Chimie Physique, CNRS ... · Force elds and molecular modelling...
Force fields and molecular modelling
Carine Clavaguera
Laboratoire de Chimie Physique, CNRS & Universite Paris Sud,Universite Paris Saclay
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Outline
Class I and class II force fields
Class III force fields
Solvent modelling
Applications
Reactive force fields
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Multiscale modelling
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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 2000I More and more publications about classical molecular dynamics simulationsI Wide availability of codesI New generation force fields
Carine Clavaguera Force fields and molecular modelling 4 / 76
Potential energy
rN : 3N coordinates{x,y,z} for N particules (atoms)
Force field = mathematical equations to compute the potential energy + parameters
U (rN ) = Us + Ub + Uφ︸ ︷︷ ︸intramolecular interactions
+ Uvdw + Uelec + Upol︸ ︷︷ ︸intermolecular interactions
1-4 long-range interaction terms = interactions between 2 rigid spheres
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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 atomiccharges
V (r) =∑s
ks(r − ro)2 +∑b
kb(θ − θo)2 +∑
torsion
Vn [1 + cos((nφ)− δ)]
+∑i<j
qiqjεrij
+ 4ε
[( r0
r
)12
−( r0
r
)6]
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Bond stretching / bond angle
Harmonic approximation
Taylor series expansion aroundboUbond =
∑b Kb(b − b0)2
Chemical Kbond b0
type (kcal/mol/A2) (A)C−C 100 1.5C−−C 200 1.3C−−−C 400 1.2
Bond energy versus bond length
Taylor series expansion aroundθo
Uangle =∑a
Ka(θ − θo)2
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Torsion
May be treated by direct 1-4 interaction termsMuch more efficient to use a periodic form
Utorsion =∑
torsion
Vn [1 + cos((nφ)− δ)]
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Improper torsion
To describe out-of-plane movements
Mandatory to control planar structures
Example : peptidic bonds, benzene
Uimproper =∑φKφ(φ− φo)2
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van der Waals interactions
London dispersion forces in 1/R6 and repulsive wall at short distances
Lennard-Jones 6-12 potential
ELJ (R) = 4ε
[(Ro
R
)12
−(Ro
R
)6]
Diatomic parameters
RABo =
1
2(RA
o + RBo )
εAB =√εA + εB
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Electrostatic interaction
Interactions between punctual atomic charges Eelec =∑i<j
qiqjεrij
Quantum chemical calculation of atomiccharges
1- Quantum chemical calculations ofmolecular models.
2- Electrostatic potential on a grid ofpoints surrounding a molecule.
3- Atomic charges derived from theelectrostatic potential.
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Electrostatic potential fit
Electrostatic potential (ESP) from the wave function (QM calculations)
φesp(r)) =
nuc∑A
ZA
|RA − r | −∫
Ψ∗(r′)Ψ(r′)
|r′ − r| dr′
Basic idea : fit this quantity with point charges
Minimize error function
ErrF (Q) =
Npoints∑r
(φesp(r)−
Natoms∑a
QA(Ra)
|Ra − r|
)
An example : Restrained ElectrostaticPotential (RESP) charges → potential isfitted just outside of the vdW radius
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Class I force fields
CHARMM, AMBER, OPLS, GROMOS...
V (r) =∑s
ks(r − ro)2 +∑b
kb(θ − θo)2 +∑
torsion
Vn [1 + cos((nφ)− δ)]
+∑i<j
qiqjεrij
+ 4ε
[( r0
r
)12
−( r0
r
)6]
Force field bond and angle vdw Elec Cross MoleculesAMBER P2 12-6 and 12-10 charge none proteins, nucleic acids
CHARMM P2 12-6 charge none proteinsOPLS P2 12-6 charge none proteins, nucleic acids
GROMOS P2 12-6 charge none proteins, nucleic acids
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Class I force fields : differences
AMBER (Assisted Model Building with Energy Refinement)I Few atoms available, some calculations are impossibleI Experimental data + quantum chemical calculationsI Possible explicit terms for hydrogen bonds and treatment of lone pairs
CHARMM (Chemistry at HARvard Molecular Mechanics)I Slightly better for simulations in solutionI Charges parameterized from soluted-solvent interaction energiesI 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 solvationI No lone pair, no hydrogen bond term
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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
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Class II force fields
MMFF94, MM3, UFFI Anharmonic terms (Morse, higher orders,...)I Coupling terms (bonds/angles, . . .)I Alternative forms for non-bonded interactions
MM2/MM3I Successful for organic molecules and hydrocarbons
MMFF (Merck Molecular Force Field)I Based on MM3, parameters extracted on ab initio data onlyI Good structures for organic moleculesI Problem : condensed phase properties
ImprovementsI Conformational energiesI Vibrational spectra
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Bond stretching
Morse potential → Taylor series expansion around ro
Beyond harmonic approximation :
Ubond =∑
K2(b − b0)2 + K3(b − b0)3 + K4(b − b0)4 + ...
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Bond angle
Harmonic approximation :
Uangle =∑a
Ka(θ − θo)2
Taylor series expansion around θo
MM3 : beyond a quadratic expressionθ3 term mandatory for deformation larger than 10-15◦.
Uangle =∑a
Ka(θ − θo)2[1− 0.014(θ − θo) + 5.6.10−5(θ − θo)2
− 7.0.10−7(θ − θo)3 + 2.2.10−8(θ − θo)4]
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Couplings
Coupling terms between at least 2 springs
Stretch-bend coupling
Esb =∑l,l′
Klθ
[(l − l0) +
(l − l ′0
)](θ − θ0)
Other couplings : stretch-torsion, angle-torsion, ...
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Interactions de van de Waals
Alternative to Lennard-Jones potential : Buckingham potential
Evdw (R) = ε
e−aRo
R −(Ro
R
)6
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 MoleculesMM2 P3 Exp-6 dipole sb generalMM3 P4 Exp-6 dipole sb, bb, st general
MMFF P4 14-7 charge sb generalUFF P2 or Morse 12-6 charge none all elements
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Comparison of conformational energies for organic molecules
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Comparison of conformational energies for organic molecules
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Comparison of conformational energies for organic molecules
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Biological force fields
M.R. Shirts, J.W. Pitera, W.C. Swope, V.S. Pande, J. Chem. Phys. 119, 5740 (2003)
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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
TransferabilityI 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 andmagnetic properties)
→ Impossible to have breaking or formation of chemical bonds
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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 onF Induced dipolesF Drude modelF Fluctuating charges
X-Pol, SIBFA, AMOEBA, NEMO, evolution of AMBER, CHARMM
I Able to reproduce physical terms derived from QM : total electrostatic energy, chargetransfer, ...
I Optimized for hybrid methods (QM/MM)
I To account for the electronegativity and for hyperconjugation
I Reactive force fields
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Accurate description of electrostatic effects
H2O H2O + q
Cisneros et al. Chem. Rev. 2014
Multipole expansion
Dipole-Dipole interaction : (µ1 µ2)/R3
Dipole-Quadrupole interaction : (µ1 Q2)/R4
Quadrupole-Quadrupole interaction :(Q1 Q2)/R5
Errors (V) for electrostatic potential on a
surface around N-methyl propanamide
Point charges vs. multipole expansion
Stone Science, 2008
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Multipolar distributions
Distributed multipole analysis (DMA) : multipole moments extracted from thequantum 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
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Solvent induced dipoles
• The matter is polarized proportionally to the strength of an applied external electricfield.
• The constant of proportionality α is called the polarizability with µinduit = αE
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Induced dipole polarization model
Induced dipole on each site i
µindi,α = αiEi,α (α ∈ {x , y, z}) αi : atomic polarizability, Ei,α : electric field
Mutual polarization by self-consistent iteration (all atoms included) : sum of thefields generated by both permanent multipoles and induced dipoles
µindi,α = αi
∑{j}
TijαMj
︸ ︷︷ ︸induced dipole on site i by the
permanent multipoles of the
other molecules
+ αi
∑{j ′}
Ti,j ′α,βµ
indj ′,β
︸ ︷︷ ︸interaction dipole on site i by
the other induced dipole
T : interaction matrix
Implemented in the several force fields : AMOEBA, SIBFA, NEMO, etc.
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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)
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Polarizable Atomic Multipole-Based AMOEBA Force Field for Proteins
Superimposition of the final structures fromAMOEBA simulations (green) and theexperimental 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 simulatedprotein structures) = 1.33 ASeven 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 Clavaguera 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 harmonicspring with a force constant kD
qD =√kD · α
→ Response to the local electrostatic field E via aninduced dipole µ
µ =q2DE
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, andDrude-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)
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A polarizable force field for monosaccharides
Application of the Drude model derived from CHARMM
Drude particles (blue, ‘D’) attached tonon-H atoms
Oxygen lone pairs (green, ‘LP’)connected with bond, angle and torsionterms
Hydrogen non polarizable
8 diastereomer
Polarization necessary to accuratelymodel the cooperative hydrogenbonding effects
Parameter optimization on quantumchemistry calculations in gas phase
Transferability of the model to othermonosaccharides
D.S. Patel , X. He, A.D. MacKerell Jr, J. Phys. Chem. B 2015, 119, 637
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A polarizable force field for monosaccharides
Drude vs. CHARMM comparison
43 conformers : dipole moments andrelative conformational energies
Validation of the model oncondensed phase properties
I Subtil soluted-water and water-waterequilibrium
I Role of concentration and temperature
Error on densities ' 1%
Agreement of the polarizable FF withNMR experiments
→ Population of conformers with oneexocyclique torsion for D-glucose andD-galactose
D.S. Patel , X. He, A.D. MacKerell Jr, J. Phys. Chem. B 2015,
119, 637
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The fluctuating charge model
Polarization is introduced via the ”movement” of the charges
Expand energy at 2nd order as a function of thenumber of electrons N
E = E0 +∂E
∂N︸︷︷︸∂E∂N
=−χ
∆N +1
2
∂2E
∂N 2︸ ︷︷ ︸∂2E∂N2 =η
( ∆N︸︷︷︸∆N=−Q
)2
2 parameters per chemical element :electronegativity (χ) and hardness (η)
Sum over sites (atomic centers)
Eelec = E0 +∑A
χAQA +1
2
∑AB
ηABQAQB
Minimizing the electrostatic energy
→ Explicitly account for polarization and charge transfer
Main application : cooperative polarization in water
A. M. Rappe and 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.
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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
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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
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Basin-hopping : global minima for C60 − (H2O)n clusters
Role of the C60−H2O polarizable potential
Hydrophobic water-fullerene interactionhighlighted
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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. CostPairwise fixed charges implicit implicitInduced dipoles
√implicit
Drude oscillator√
implicitFluctuating charges
√ √
Lack of reactivity but important for chemists !
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Solvation role
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Implicit solvent vs. explicit solvent
Explicit : each solvent molecule isconsidered
Implicit : the solvent is treated as a conti-nuum descriptionNeed to define a cavity that contains thesolute
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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
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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 ?
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Periodic boundary conditions
Explicit solvation schemes
The fully solvated central cell is simulated, in theenvironment produced by the repetition of thiscell in all directions just like in a crystal
→ Infinite system with small number of particles
Introducing a periodicity level frequently absentin reality
Applications : liquids, solids
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Periodic boundary conditions
When an atom moves off the cell, it reappearson the other side (number of atoms in the cellconserved)
Ideally, every atom should interact with everyother atom
Problem : the number of non-bonded interactionsgrows as N 2 where N is the number of particles→ limitation of the system size
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Cutoff Methods
Some interatomic forces decrease strongly withdistance (van der Waals, covalent interactionsetc.) : short-range interactions
→ Ignore atoms at large distances without toomuch loss of accuracy
→ Introduce a cutoff radius for pairwiseinteractions and calculate the potential only forthose 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 thelong-range interactions without cutoffs
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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 ofthe 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
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Water as a solvent
Water models with 3 to 5 interaction sites
(a) 3 sites : TIP3P (b) 4 sites : TIP4P (c) 5 sites : TIP5P
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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 of3 3 3point
chargesµgaz (D) 2.27 2.35 2.18 1.85
µliq. (D) 2.27 2.35 2.182.85
(at 25 C)ε0 65 82 53 78.4
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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∆Hvap. 10.77 10.45 10.66 10.51
(kcal.mol−1)Cp 23.4 16.8 19.3 17.99
(cal.mol−1.deg−1)
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Water phase diagram
In the solid phase, water exhibits one of the most complex phase diagrams, having13 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.
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Water dimer properties
POL5 TIP4P/FQ TIP5P ab initio expU (kcal/mol) -4.96 -4.50 -6.78 -4.96 -5.4±0.7
r (A) 2.896 2.924 2.676 2.896 2.98θ (degrees) 4.7 0.2 -1.6 4.8 0±6φ (degrees) 62.6 27.2 50.2 57.3 58±6µ (D) 2.435 3.430 2.920 2.683 2.643〈µ〉 (D) 2.063 2.055 2.292 2.100 ?
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Bulk water properties
POL5 TIP4P/FQ TIP5P expU (kcal/mol) -9.92±0.01 -9.89±0.02 -9.87±0.01 -9.92ρ (g/cm3) 0.997±0.001 0.998±0.001 0.999±0.001 0.997µ (D) 2.712±0.002 2.6 2.29 ? (2.5-3.2)ε0 98±8 79±8 82±2 78.3D (10−9 m2/s) 1.81±0.06 1.9±0.1 2.62±0.04 2.3τNMR (ps) 2.6±0.1 2.1±0.1 1.4±0.1 2.1
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From the single water molecule to the liquid phase
H2O µ(D) αxx (A3) αyy (A3) αzz (A3)AMOEBA 1.853 1.660 1.221 1.332QM 1.84 1.47 1.38 1.42Exp. 1.855 1.528 1.415 1.468
(H2O)2 De (kcal/mol) rO−O (A) µtot. (D)AMOEBA 4.96 2.892 2.54QM 4.98/5.02 2.907/2.912 2.76Exp. 5.44 ± 0.7 2.976 2.643
Liquid ρ (g/cm3) ∆Hv ε0AMOEBA 1.0004 ± 0.0009 10.48 ± 0.08 81 ± 13Exp. 0.9970 ± 0.7 10.51 78.3
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Molecular dynamics
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Trajectory analysis
Along the trajectory, atomic coordinates and velocities can be stored for furtherprocessing
A number of properties, e.g. structural, can then be computed and averaged overtime
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The radial distribution function
g(r) : probability of finding aparticle at a distance r fromanother particle, relative to thesame probability for an ideal gas
g(r) : can be determinedexperimentally, from X-ray andneutron diffraction patterns
g(r) : can be computed from MDsimulations
Example : solvation of the K+ ionI Simulation time : 2 nsI Time step : 0.1 fsI T = 298 KI 216 water molecules d’eau or 100
formamide molecules
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Coordination number CN
CN : number of atoms or ligands
CN (r) = 4πρ
∫ r1
r
g(r ′)r ′2dr
Example : solvation of K+, Na+
and Cl− ions
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Micro-solvation of the K+ ion
Cluster of 34 water moleculesaround the cation
Simulation time : 10 ns
Timestep : 1 fs
Force field : AMOEBA polarizableforce field
T = 200 K
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Micro-solvation of the K+ ion
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Time Correlation Functions C(t)
A(t) and B(t) : two time dependent signals
A correlation function C(t) can be defined
C (t) = 〈A(t0) · B(t0 + t)〉 = limτ→∞
1
τ
∫ τ
0
A(t0)B(t0 + t)dt0
If A and B represent the same quantity (A ≡ B), then C(t) is called ”autocorrelationfunction”
→ The autocorrelation function shows how a value of A at t=t0 + t is correlated to itsvalue at t0
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Example : transport coefficients
Diffusion coefficient D directly related to the time integral of the velocity autocorrelationfunction
D =1
3
∫ ∞0
〈vi(0) · vi(t)〉dt
Example : Diffusion coefficient forK+, Na+ and Cl− ions in water
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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
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Conditions of the simulations
AMBER force field and corresponding codeI TIP3P water modelI OPLS chloroform modelI Extraction of new parameters for ILI Cs+ parameters : QM micro-hydration
SolventsI Adjacent cubic boxes of IL and water for the interface representationI System size
F IL (219 molecules)/water (2657 molecules)F CLF (722 molecules)/water (2657 molecules)
I Energy minimization of the systems mandatory !
Other dataI T = 300 K (Berendsen thermostat)I Leapfrog Algorithme, 2 fs time stepI Long equilibration ! Can be until 600 psI Long simulations
F From 20 to 60 ns for IL/waterF From 0.4 to 2 ns for CLF/water
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Simulations with the Cs+/NO−3 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
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Simulations with the Cs+L/NO−3 complex
From previous conclusion : the Cs+/NO−3 pair behaviour is different in IL and CLF
A complexe is made with Cs+ and the ligand L, NO−3 as counterion
Starting point : 3 complexesI 1 in waterI 1 at the interfaceI 1 in IL
Same simulation with chloroform
QuestionsI 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 ?
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Results
Hydrophobic complex
Cs+/L activity at the interfaceIon transfer easier in IL than inCLF
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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, AIREBOI To get a smooth transition from non-bonded to single, double and triple bonded
systemsI Use of bond length/bond order relationships updated along the simulation
BUTI Very large number of parameters, expensive computational costI The validation step is crucial
ReaxFF is 10-50 times slower thannon-reactive force fields
Better behaviour than quantummethodsNlogN for ReaxFF vs >N3 for QM
Carine Clavaguera 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 aremade bond-order dependent→ Ensure that energy contributionsdisappear upon bond dissociation
Over- and under-coordination of atomsmust be avoided
→ Energy penalty when an atom has morebonds than its valence allows
→ e.g. Carbon no more than 4 bonds,Hydrogen no more than 1
Electrostatic term = fluctuating chargesto 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)
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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 Clavaguera Force fields and molecular modelling 71 / 76
Oxidation of aluminum nanoparticles
ANPs : a solid propellant in theapplication of solid-fuel rockets
I high combustion enthalpyI result of an oxidation process
Growth of the oxide layer on ANPs :combined effects
I inward diffusion of oxygen atomsI role of temperature, pressure of
oxygen gas, induced electric fieldthrough the oxide layer
ReaxFF reactive force field to assess thefull dynamics of the oxidation processof ANPs
Aluminum/oxygen interactions from anatomistic-scale view
Growth of an oxide film with temperature
Starting point 473 K, 573 K, 673 K
S. Hong, A.C.T. van Duin, J. Phys. Chem. C, 119, 17876 (2015)
Carine Clavaguera Force fields and molecular modelling 72 / 76
Oxidation of aluminum nanoparticles
Mecanism of oxidation
1 adsorption of the oxygen molecules→ highly exothermic reaction
2 formation of hot-spot regions on thesurfaces of the ANPs
3 void space created in these regions→ reduction of reaction barrier for O2
diffusion
4 growth of the oxide layer
Temperature and pressure of oxygengas
I Role on the number of void spacesI Density of the oxide layer
Role of the pressure of the oxygen gas
Growth of the oxide layer with temperature
300 K 500 K 900 K
Carine Clavaguera 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 energyI C-CI Ni/Ni-CI 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)
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Nanotube formation with the aid of Ni-catalysis
T = 2500 K
Without Ni catalyst, 5 C60 in thenanotube
At 16 ps, coalescence only atT = 2500 K
In agreement with the energy barrier forthe formation of the C60 dimer
T = 1800 K
With Ni catalyst : 5 C60 + 2 Nibetween 2 C60
Lower coalescence temperature :T = 1800 K
Carine Clavaguera Force fields and molecular modelling 75 / 76
References
Molecular modelling : principles and applications, A. R. Leach, Addison WesleyLongman, 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
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