Practicing molecular simulations

Practicing molecular simulations.

Master Physique Informatique2011-2012

Lucyna Firlej

Laboratoire Charles CoulombUniversité Montpellier II

Lucyna FIRLEJMPI 2011

Provide you with the background and skills needed to:Provide you with the background and skills needed to:

Appreciate and understand the use of theory and Appreciate and understand the use of theory and simulation in research simulation in research Be able to read the simulation literature and evaluate Be able to read the simulation literature and evaluate

Goals of this courseGoals of this course

Be able to read the simulation literature and evaluate Be able to read the simulation literature and evaluate it criticallyit criticallyUnderstand the difference between quantumUnderstand the difference between quantum--based based and statistical thermodynamics based calculationsand statistical thermodynamics based calculationsBe able to start an atomistic simulation researchBe able to start an atomistic simulation research


OutlineOutline

Introduction Introduction –– molecular simulations in research molecular simulations in research Modeling of interactionsModeling of interactionsMC program MC program –– working case: adsorption in porous media.working case: adsorption in porous media.Calculation of thermodynamic propertiesCalculation of thermodynamic propertiesCalculation of thermodynamic propertiesCalculation of thermodynamic propertiesError analysisError analysis

:�No regular exam No regular exam –– project submissionproject submission


Modeling Modeling –– interdisciplinary scienceinterdisciplinary science

Numerical Modeling

Numerical simulations

[atomistic]

Quantum Chemistry (electrons)

[atomistic]

(Optimization,Monte Carlo, Molecular Dynamics)

Finite elements (objects > µµµµm)


What is molecular simulations ?What is molecular simulations ?

Molecular simulations is a computational “experiment” conducted on a molecular (atomic) level

up to 100.000, or more atoms are simulatedand real times up to 10-50 ns

(however, with current machines it is possible to(however, with current machines it is possible tostudy N up to several million, and times up to 1 μs)

Many configurations are generated,and averages taken to yield the “measurements.”

Molecular simulation has the character of both theory and experiment


Based on SDSC Blue Horizon (SP3)512-1024 processors1.728 Tflops peak performanceCPU time = 1 week / processor

10-6

10-3

100

(µµµµs)

(ms)

TIME/s

Mesoscale methods

Semi-empirical

Continuum

Lattice Monte CarloBrownian dynamicsDissipative particle dyn

Methods

Atomistic Simulation Methods

Theory and Simulation ScalesTheory and Simulation Scales

10-15

10-12

10-9

10-10 10-9 10-8 10-7 10-6 10-5 10-4(nm) (µµµµm)

(fs)

(ps)

(ns)

LENGTH/meters

Semi-empiricalmethods

Ab initiomethods

Monte Carlomolecular dynamics

tight-bindingMNDO, INDO/S

From: C. Alba-Simionesco et al., Effects of confinement on freezing and meltingJ.Phys.:Cond.Matter 18 (2006) 15-68


1. Discrete character of variables, ( ∆x, ∆t ) – defined by the problem

2. Constant number of independent variables

Limitations due to the speed and the memory capacity of computers

N – number of independent variables

(electrons, atoms or finite elements)

nmµµµµm –nm≥µ≥µ≥µ≥µm

N finite elements

N atoms N electrons

(electrons, atoms or finite elements)


Ab Initio Methods

Calculate properties from first principles, solving the Schrödinger (or Dirac) equation numerically.

Pros:• Can handle processes that involve bond breaking/formation, or electronic rearrangement (e.g. chemical reactions).• Methods offer ways to systematically improve on the

Electron localization function for (a) an isolated ammonium ion and (b) an ammonium ion with its first solvation shell, from ab

initio molecular dynamics. From Y. Liu, M.E. Tuckerman, J. Phys.

Chem. B 105, 6598 (2001)

• Methods offer ways to systematically improve on the results, making it easy to assess their quality.• Can (in principle) obtain essentially exact properties without any input but the atoms conforming the system.

Cons:• Can handle only small systems, about O(102) atoms.• Can only study fast processes, usually O(10) ps.• Approximations are usually necessary to solve the eqns.


Semi-empirical Methods

Use simplified versions of equations from ab initio methods, e.g. only treat valence electrons explicitly; include parameters fitted to experimental data.

Pros:• Can also handle processes that involve bond breaking/formation, or electronic rearrangement.• Can handle larger and more complex systems than ab

Structure of an oligomer of polyphenylene sulfide

phenyleneamine obtained with the semiempirical method. From R. Giro, D.S. Galvão, Int. J. Quant.

Chem. 95, 252 (2003)

• Can handle larger and more complex systems than ab initio methods, often of O(103) atoms.• Can be used to study processes on longer timescales than can be studied with ab initio methods, of about O(10) ns.

Cons:• Difficult to assess the quality of the results.• Need experimental input and large parameter sets.


Atomistic Simulation Methods

Use empirical or ab initio derived force fields, together with semi-classical statistical mechanics (SM), to determine thermodynamic (MC, MD) and transport (MD) properties of systems. SM solved ‘exactly’.

Pros:• Can be used to determine the microscopic structure of more complex systems, O(105-6) atoms.

Structure of solid Lennard-Jones CCl4 molecules confined in a

model MCM-41 silica pore. From F.R. Hung, F.R. Siperstein, K.E.

Gubbins, in progress.

more complex systems, O(10 ) atoms.• Can study dynamical processes on longer timescales, up to O(1) ms

Cons:• Results depend on the quality of the force field used to represent the system.• Many physical processes happen on length- and timescales inaccessible by these methods, e.g. diffusion in solids, many chemical reactions, protein folding, micellization.


Mesoscale Methods

Introduce simplifications to atomistic methods to remove the faster degrees of freedom, and/or treat groups of atoms (‘blobs of matter’) as individual entities interacting through effective potentials.

Pros:• Can be used to study structural features of complex systems with O(108-9) atoms.• Can study dynamical processes on timescales inaccessible

Phase equilibrium between a lamellar surfactant-rich phase and a continuous surfactant-

poor phase in supercritical CO2, from a lattice MC simulation. From N. Chennamsetty, K.E.

Gubbins, in progress.

• Can study dynamical processes on timescales inaccessible to classical methods, even up to O(1) s.

Cons:• Can often describe only qualitative tendencies, the quality of quantitative results may be difficult to ascertain.• In many cases, the approximations introduced limit the ability to physically interpret the results.


Continuum Methods

Assume that matter is continuous and treat the properties of the system as field quantities. Numerically solve balance equations coupled with phenomenological equations to predict the properties of the systems.

Pros:• Can in principle handle systems of any (macroscopic) size and dynamic processes on longer timescales.

Temperature profile on a laser-heated surface obtained with the finite-element method. From S.M. Rajadhyaksha, P.

Michaleris, Int. J. Numer. Meth. Eng. 47, 1807 (2000)

size and dynamic processes on longer timescales.

Cons:• Require input (viscosities, diffusion coeffs., eqn of state, etc.) from experiment or from a lower-scale method that can be difficult to obtain.• Cannot explain results that depend on the electronic or molecular level of detail.

1990

2000

Evolution of Computational MethodsEvolution of Computational Methods

Combinationwith DFT

Molecular

Gradient corrections

Car-Parinello

Multiscale methodslink to macroscopic models

Quantum Monte Carlo

2010 Mesoscale modeling

Ab initio molecular dynamics

1960

1980

1970

Solid State Physics Quantum ChemistryStatistical Mechanics

Molecular dynamics andMonte Carlo

Molecular Mechanics

Force fieldsSemi-empirical

parameters

Total energies

Analytical forcesgeometry optimization

Analytical frequencies

SCF

Hartree-Fock

Total energies

ForcesCar-Parinello

Density functional

Tight-binding

Energy band structures

ewolucja od indywiduum do wiekszej ilosci: les methodes disponibles

Simulationsnumériques

Expérience

Real systems(nature)

Theories(analytical solution)

Model (parameters, interaction, ...)

Numerical experiments

experiment

Why simulations ?Why simulations ?

1. Fundamental studies, e.g. to determine range of validity of :Fick’s law of diffusion, Newton’s law of viscosity,

Exact solution(trajectories of all particles)

Tests of model Tests of theories

data (spectra)experimental

Approximate solutions

viscosity, etc.

2. Test theories by comparing theory and simulation

3. Test model by comparing simulated and experimental properties. Then use model in further simulations to carry out “experiments” not possible in the laboratory, e.g. critical points for molecules that decompose below Tc, properties of molten salts, long-chain hydrocarbon properties at very high pressures, properties of confined nano-phases, etc.


Construction of model

Method

Model of interaction

Numerical simulations: how ?Numerical simulations: how ?

Real systems

Pores structure and adsorbed atoms (neutral system)

Van der Waals and repulsive, no

Numerical Simulationsin statistical ensemble

Generation of states

Trajectory analysis

interaction

Interaction with

environment

Equation of motion

T = const.N variable

and repulsive, no electrostatics

Stochastic (Monte Carlo)

Grand CanonicalMonte Carlo algorithm

Mean values and fluctuations of:

EnergiesNumber of atoms


Working case: MC simulation of adsorption in a poreWorking case: MC simulation of adsorption in a pore

Interface – starting point of adsorption problems.Special case – materials with large surface:

cfd

b a : corrugationb : bottle neckc : opening

porous materials: specific surface between 0.1 and 2600 m2g-1 (or more)

� mesopores (nano-pores):2 – 50 nm in diameter

a

dc : openingd : interconnectione : close-endedf : closed (isolated)

2 – 50 nm in diameter

� “nanomaterials” of technological interestswith 1, 2 or 3 dimensions ≤ 100 nm



(Examples of porous systems)


Some (evident) applications of porous materials:Some (evident) applications of porous materials:(only those related to adsorption phenomenon)(only those related to adsorption phenomenon)(only those related to adsorption phenomenon)(only those related to adsorption phenomenon)

Purification of gases (closed atmosphere)or liquids (edible fluids)or solids (cleaning of the sol)

Storage of gas (natural, responsible for greenhouse effect, hydrogen)

Catalysis (carried out in confined geometry)


Catalysis (carried out in confined geometry)

Separation of molecules (molecular sieves)

Storage of energy (adsorption is exothermic)Potable water production (elimination of humid acids, detergents,

insecticides… by adsorption on carbons) Purification of edible liquids and of effluents from industrial plantsRetention by soil (especially by clays) of fertilizers, water, insecticides,

radioactive waste...Detergency and cleaning in liquid medium (adsorption of surfactants, softening of water by adsorption, dissolution of stains and re-adsorption on porous powders…)


Adsorption – a phenomenon general which involves the preferentialpartitioning of substances from the gaseous or liquid phase onto thesurface of a solid substrate

Gaz adsorbable«adsorbable»


Adsorbant

«adsorbable»

Phase adsorbée, «adsorbat»

Physical adsorption is caused mainly by van der Waals forces and electrostatic forces between adsorbate molecules and the atoms which compose the adsorbent surface. Thus adsorbents are characterized first by surface properties such as surface area, structure (roughness) and polarity.


Fundamental questions :1. Mechanism of adsorption – influence of

the geometry and pore structure2. Influence of confined geometry

(interaction with walls) on structural transformations

3. Capillary condensation4. Hysteresis and metastability

nσ/ms

B

B

I II III

IV V VI

nσ/ms

B

B

I II III

IV V VI


Numerical challenge:1. Simulations of equilibrium between gas and adsorbed phase

2. Modeling of interaction between pore walls and adsorbed particles

4. Hysteresis and metastability

p/p0p/p0

p/p°

nσ/ms


Pathways and difficulties for H2 use in transportationPathways and difficulties for H2 use in transportation

• Hydrogen production– Hopefully from renewable sources (wind, solar), or non-CO2 producing

(nuclear)• Fuel cells

– Serious cost problem, alternatives to Pt necessary• Storage (in particular in a vehicle)

– Weight & volume– Temperature– Vibrations– Safety, etc

• “Chicken and the egg”– No vehicles ⇔ No infrastructure


Gas storage (past & present)Gas storage (past & present)

First NG vehicle 1910 (USA) ~1930 (France)

Current NG vehicle with high-pressure tank in trunk

Problem: Trunk space is gone!

~200 bar (~3000 psi)


”Magic numbers” for: 2010 2015 UltimateEnergetic capacity

(kWh kg−1) (specific energy) 1.5 1.8 2.5

Gravimetric capacity(g H2 / kg) 45 (4.5 wt%) 55 (5.5 wt%) 75 (7.5 wt%)

DOE targets for hydrogen storage systemDOE targets for hydrogen storage system

Volumetric capacity (energy density) (kWh l−1) 0.9 1.3 2.3

Volumetric capacity(g H2 / l) 28 40 70


23

31

71

� ��

��

in g/L

pressure

Gas

den

sity

Basic definitionsBasic definitions

23

��

��

VHmvsc )( 2= [kgH2/m3]

)( )()(

2

2CmHm

Hmgsc += [%wt]

� ��

� ��

� ��

)( )( )()( )(

22

22

CmHmHmHmHmExcess o

o

+−−= [%wt]


Activated carbons.Activated carbons.

R.E.Franklin, Proc.Roy.Soc.London 209. 1951

more or less locally parallel graphite-like structures

N.A.Seaton. Carbon 27, 1989

J.Romanos,APS 2010 F.Rodriguez Reinoso, 2007


Adsorbent modelAdsorbent model

��ø < 2 nm – nanopores

2nm< ø < 50 nm - mezoporesø > 50 nm – macropores

��

5 10 15 20 25 30 35 40 45 500.00

0.05

0.10

0.15

0.20

Differential Pore Volume (cm3 /(g·Å))

Pore Width (Å)

Batch 5.1 S-33/k

Nanptechnology 20, 2009

H2H2H2 H2

~ 100 Ǻ~ 90 Ǻ

szerokość6-20 Ǻ


2

4

6

8

10

T = 298 KE = 4.5 kJ/molw

eigh

t %

298 K

DOE 2010

DOE 2015

Result : Adsorption limits vs. DOE requirements.

6 8 10 12 140

2

DOE 2010

DOE 2015

77 K

6 8 10 12 1402468

10121416

wei

ght %

pore width (Å)

T = 77 KE = 4.5 kJ/mol


Problem: Fluid adsorption in cylindrical pores.Problem: Fluid adsorption in cylindrical pores.Problem: Fluid adsorption in cylindrical pores.Problem: Fluid adsorption in cylindrical pores.

µVT- constant

Grand Canonical Monte Carlo


µ(gas) = µ(adsorbate)

µ(gas, ideal) = µ0(gas) + kBT ln(P)

µVT PVT - constant

External ideal gas pressure P


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Practicing molecular simulations