Introduction To Molecular Simulation 고려대 화공생명공학과 강정원
Introduction To Molecular Simulation
고려대 화공생명공학과
강정원
Computer Simulation …
Computer experiments (simulation ) become a general research tool.
Motivation of computer …– Development of Nuclear Weapons– Code breaking
MANIAC, 1952 – Metreopolis was interested in solving broad spectrum of
problems on this machine.
ScientificCalculation
Metropolis Monte-CarloSimulation Method
Method before computer simulation
Approximate TheoriesMechanical Simulation – Plastic foam balls– Metal bearings
Tedious, laborious Quite realistic
Molecular SimulationA study of state of matter using computer. – Gas state– Liquid State– Solid State– Other specialized state : nano-space, structured polymers ,…
Why computer ? – We cannot solve many-body problems even using simple
Newtonian mechanics. (What about quantum mechanics ?)– There is no hope to get answer to many-body problem using pencil
and paper….Before computer simulation …– Approximate theories
Van der Waals equation for non-polar fluidsDebye-Huckel for electrolytes
Use of Molecular Simulation
RealProblem
Model
Experimental Result
Exact Resultfor Model
TheoreticalPredictions
Test ofModel
Test of Theories
Perform Experiments
Carry outComputer Simulation
ConstructApproximate
Theories
Compare Compare
Liquid StateGas StatePolymerNano space
Lennard-Jones potentialHard Sphere potentialSquare-well potential
Van der WaalsDebye-Huckel
Use of Molecular SimulationTest of model– Test of model potential, model structure– Comparison with experimental data
Test of approximate theories– Comparison with theoretical prediction– Computer-generated exact result
Prediction of properties– Replacement of experimental data– Computer does not care about the condition….
Simulation at 10,000 K (?) Discovery of new fact – Alder and Wainwright (1950s) : predicted 1st order freezing
transition for harsh short range repulsive molecules.
Procedure to perform molecular simulation
ModelStatisticalAveraging
Method
ComputerImplementation
SimulationResult
Interaction Energy model
StructuralModel
StatisticalMechanics
Ensemble Average
Random NumberGeneration
RandomWalk
Test of Model
Test of Theory
Property Prediction
New Discovery
Statistical Treatment
Method of Integration
Need to study molecular simulation…
Computer simulations (computer experiments) become general research tool. Understanding the “Black box” greatly improve the efficiency of using it. The techniques can be applied to various field of science and engineering. – Polymer science– Nano technology– Biological materials– Special structures : Zeolites, Supercritical fluid,
Aerogels,….
Recent Research Topics2001-2003
Molecular Simulation of Diblock copolymer filmsAdsorption of materials in a single-wall carbon nano-tube ZeolitesDrug delivery devicesViscosity in nano spacingNanoscale heat transfer Supercritical behavior Aerogels
Prerequisite for the course
Programming skill (FORTRAN or C/C++) Statistical Mechanics – Will be covered shortly in 2 week lecture.
Basic Thermodynamics
Statistical Thermodynamics
Link between microscopic properties and bulk properties
Microscopic Properties
T,PU,H,A,G,S
μ,Cp,…
Microscopic Properties
Statistical Thermodynamics
Molecular Properties Thermodynamic Properties
uij
r
)1( += JhcBJEJvhcvE ~)
21( +=ν
2
22
8mXhnEn =
Potential Energy
Kinetic Energy
Crash course in statistical mechanics
Mechanics
ClassicalMechanics
Quantum Mechanics
Statistical Thermodynamics
MolecularPartition Functions
EnsembleAveraging
Method
Phase Space Integration
−
−>=<
NN
NNN
dU
dUAA
rr
rrr
))(exp(
))(exp()(
β
β
Classical Mechanics …
Hamiltonian : Total Energy of System– r : position vectors (N)– p: momentum vectors (N)
Using Legendre Transformation Technique,
),...,,(2
),(
energy) alPE(potenti energy) KE(kinetic),(
21 Ni i
iNN
NN
Um
H
H
rrrppr
pr
+=
+=
ii
ii
H
H
rp
pr
=
∂∂
−=
∂∂
CanonicalRelationship
Ex) if N= 1.E24 then
6.E24 initial values6.E24 set of 1st order differential equations
Can you solve it ?
Quantum Mechanics …
Failure of classic mechanics– Blackbody – radiation– The Planck distribution– Heat capacities at low T– Atomic and molecular spectra
Wave-particle duality – Waves have characteristics of particles– Particles have characteristics of waves
Conclusion of Quantum Mechanics
Particles can only have discrete values of energiesThe energy values can be calculated using Schrodinger equation
Ψ=Ψ+Ψ∇−i
ii
EUm
h 22
2
8π
Second order differential equationEigen value problem : series of allowed solutions
Available energy values
Examples of solution to Schrodinger Equation
Translational motion of a free particle
Vibrational Motion (harmonic motion)
Rotational motion of a linear rotor...3,2,1,0),1( =+= JJhcBJEr
...3,2,1,0,,)21(
2/1
=
=+= v
mkvEv ωω
...3,2,1,0,2
cossin)(22
==
+=
km
kE
kxDkxCx
k
k
ψ