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

carine.clavaguera@u-psud.fr

Carine Clavaguera 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

Multiscale modelling

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

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

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

−( r0

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

Torsion

May be treated by direct 1-4 interaction termsMuch more efficient to use a periodic form

Utorsion =∑

torsion

Vn [1 + cos((nφ)− δ)]

Improper torsion

To describe out-of-plane movements

Mandatory to control planar structures

Example : peptidic bonds, benzene

Uimproper =∑φKφ(φ− φo)2

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

Diatomic parameters

RABo =

o + RBo )

εAB =√εA + εB

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.

Electrostatic potential fit

Electrostatic potential (ESP) from the wave function (QM calculations)

φesp(r)) =

nuc∑A

|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

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

−( r0

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

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

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

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

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 + ...

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]

Couplings

Coupling terms between at least 2 springs

Stretch-bend coupling

Esb =∑l,l′

[(l − l0) +

(l − l ′0

)](θ − θ0)

Other couplings : stretch-torsion, angle-torsion, ...

Interactions de van de Waals

Alternative to Lennard-Jones potential : Buckingham potential

Evdw (R) = ε

e−aRo

R −(Ro

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

Comparison of conformational energies for organic molecules

Biological force fields

M.R. Shirts, J.W. Pitera, W.C. Swope, V.S. Pande, J. Chem. Phys. 119, 5740 (2003)

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

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

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

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,

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

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

∑{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.

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)

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

→ 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)

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

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

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

∂N 2︸︷︷︸∂2E∂N2 =η

( ∆N︸︷︷︸∆N=−Q

2 parameters per chemical element :electronegativity (χ) and hardness (η)

Sum over sites (atomic centers)

Eelec = E0 +∑A

χAQA +1

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.

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

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)

Basin-hopping : global minima for C60 − (H2O)n clusters

Role of the C60−H2O polarizable potential

Hydrophobic water-fullerene interactionhighlighted

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 !

Solvation role

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

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

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 ?

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

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

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

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

Water as a solvent

Water models with 3 to 5 interaction sites

(a) 3 sites : TIP3P (b) 4 sites : TIP4P (c) 5 sites : TIP5P

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

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)

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.

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 ?

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

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

Molecular dynamics

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

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

Coordination number CN

CN : number of atoms or ligands

CN (r) = 4πρ

∫ r1

g(r ′)r ′2dr

Example : solvation of K+, Na+

and Cl− ions

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

Micro-solvation of the K+ ion

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→∞

∫ τ

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

Example : transport coefficients

Diffusion coefficient D directly related to the time integral of the velocity autocorrelationfunction

∫ ∞0

〈vi(0) · vi(t)〉dt

Example : Diffusion coefficient forK+, Na+ and Cl− ions in water

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

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

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

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 ?

Results

Hydrophobic complex

Cs+/L activity at the interfaceIon transfer easier in IL than inCLF

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

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)

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

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)

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

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)

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

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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