Molecular Dynamics and Molecular Modeling CHEM 388

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Molecular Modeling, Simulation and Design
Principles and Applications CHEM 388
http//sdixit.web.wesleyan.edu/wescourses/2006s/ch
em388/01/mdcourse/
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Choice of Molecular Model
Process of Interest
Modeling Technique Force Field, Solvent, Sampling
Required Accuracy
Size / Computing Power
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Parallel Processing

• Why ? Limitations Memory, Time
• How ?

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Pittsburgh Supercomputing Center

• SCALE
• 3000 processors
• SIZE
• 1 basketball court
• COMPUTING POWER
• 6 TeraFlops (6 trillion floating point
  operations per second)
• Will do in 3 hours what a PC will do in a year

The Terascale Computing System (TCS) at the
Pittsburgh Supercomputing Center
Upon entering production in October 2001, the TCS
was the most powerful computer in the world for
unclassified research
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Pittsburgh Supercomputing Center

• HEAT GENERATED
• 2.5 million BTUs
• (169 lbs of coal per hour)
• AIR CONDITIONING
• 900 gallons of water per minute
• (375 room air conditioners)
• BOOT TIME
• 3 hours

The Terascale Computing System (TCS) at the
Pittsburgh Supercomputing Center
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NCSA National Center for Super-computing
Applications

• SCALE
• 1774 processors
• ARCHITECHTURE
• Intel Itanium2
• COMPUTING POWER
• 10 TeraFlops

The TeraGrid cluster at NCSA
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TACCTexas Advanced Computing Center

• SCALE
• 1024 processors
• ARCHITECHTURE
• Intel Xeon
• COMPUTING POWER
• 6 TeraFlops

LoneStar at TACC
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The worlds largest collection of supercomputers
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Teragrid Resource Scale

• 40 teraflops (1012) compute
• Desktop CPU 2GHz
• 1 petabyte (1015) online storage
• Desktop Machine hard Disk Storage 80GB
• 10-40Gbps networking
• Modem a few Kbps
• LAN a few Mbps

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TeraGrid Resources
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Before the TeraGridSupercomputing The Old
Fashioned way

• Each supercomputer center was its own
  independent entity.
• Users applied for time at a specific
  supercomputer center
• Each center supplied its own
• compute resources
• archival resources
• accounting
• user support

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The TeraGrid Strategy

• Creating a unified user environment
• Single user support resources.
• Single authentication point
• Common software functionality
• Common job management infrastructure
• Globally-accessible data storage
• across heterogeneous resources
• 7 computing architectures
• 5 visualization resources
• diverse storage technologies

• Create a unified national HPC infrastructure that
  is both heterogeneous and extensible

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Molecular Modeling, Simulation and Design
Principles and Applications CHEM 388
http//sdixit.web.wesleyan.edu/wescourses/2006s/ch
em388/01/mdcourse/
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What is a system?

• A system is
• A portion of the world on which to focus
  attention
• A subset of the universe (System Surrounding)
• Composed of any number of similar or dissimilar
  parts (i.e. be homogeneous or heterogeneous)

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• What is a state of the system?
• A specific conditions of all the parts
• What are the Observables of a system?
• Numerical values referring to a state or function
  which are, in principle, measurable
  experimentally
• Eg. PV NkBT
• How is a N-particle molecular system defined?
• In terms of the position and momentum
• Eg. A(pN(t),rN(t))?A(p1x,p1y,p1z,p2x, .
  x1,y1,z1,x2, . t)

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State Variables
Extensive variable Scales linearly with system
size Intensive variable Conjugate field,
size-independent
Ensembles
EVN Microcanonical TPN Isothermal-isobaric TVN
Canonical TV? Grand-canonical
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Connection Between Experiment, Theory and
Computer Simulations
Model System
Real System
Make Models
Construct Approximate Theories
Carry out Computer Simulations
Perform Experiments
Experimental Results
Results For Model
Theoretical Predictions
Compare
Compare
Test of Models
Test of Theories
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Modeling vs. Simulation

• A model is a representation of the system,
  conceptual or mathematical, which
• Behaves like the system
• But involves fewer states
• i.e. some interactions of lesser importance are
  neglected
• A simulation is a numerical calculation of
  properties of a model based on sampling multiple
  states of the system.
• Decompose interactions
• More constraints

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Models for Molecular Simulation
Molecular Interactions

Simulated Model
Boundary Conditions
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Steps in Simulation (Virtual Laboratory)

• Model building
• Calculation of a trajectory (sampling states)
• Analysis of the trajectory

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Assessment of a Simulation

• What are the possible sources of error or
  uncertainty?
• Are sampled populations representative?
• Are the results reproducible?
• Are the results internally consistent?
• Do the results confirm results from elsewhere?

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Relation to Statistical Mechanics
The Time Average
The Ensemble Average
Ergodic Hypothesis Ensemble average ? Time
Average
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Monte Carlo Method
Sum over states form of the phase space integral
If
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Metropolis Monte Carlo

• The algorithm
• Select a particle at random, and calculate its
  energy
• Give the particle a random displacement, rrD
  and calculate its new energy E(r)
• If DE E(r)-E(r) ? 0 accept move to r
• Else, accept the move from r to r if exp(-b DE)
  gt ran, else reject

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Difference Between MD and MD Methods

• Monte Carlo
• Stochastic
• Each move depends only its immediate predecessor
• Ensemble Average (M configurations)
• Easier to implement for discontinuous potential
  functions

• Molecular Dynamics
• Deterministic
• Each move can be predicted from any of its
  preceding moves
• Time Average (M time steps)
• Easier to estimate heat capacity,
  compressibility, transport properties, time
  correlation function
• Length of simulation is a good measure for
  comparison to relaxation time

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Simulation Deterministic vs. Stochastic
Deterministic
Stochastic
Metropolis Monte Carlo
Force-Biased Monte Carlo
Brownian Dynamics
Langevin Dynamics
Molecular Dynamics
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Newtonian Dynamics

• First Law
• A system will be at rest or moving at a specific
  velocity until a force acts on it.
• Second Law
• F ma
• Third Law
• Any force exerted by molecule 1 on molecule 2
  must be balanced by a force exerted by 2 on 1

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Hamiltonian Dynamics
Hamiltonian
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Difference Between Newtonian and Hamiltonian
Dynamics

• Newtonian Dynamics considers forces explicitly
• Hamiltonian Dynamics conserves Hamiltonian