Molecular dynamics Some random notes on molecular dynamics simulations Seminar based on work by Bert de Groot and many anonymous Googelable colleagues

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Molecular dynamicsSome random notes on
molecular dynamics simulationsSeminar based
on work by Bert de Groot and many anonymous
Googelable colleagues
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Most material in this seminar has been produced
by Bert de Groot at the MPI in Göttingen.
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Schrödinger equation
Born-Oppenheimer approximation
Nucleic motion described classically
Empirical force field
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Inter-atomic interactions
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Motions of nuclei are described classically
Non-bonded interactions
Covalent bonds
Eibond
approximated
exact
KBT
?0
R
Potential function Eel describes the electronic
influence on motions of the nuclei and is
approximated empirically ? classical MD
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Force-Field
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Non-bonded interactions
Coulomb potential
Lennard-Jones potential
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Now we need to give all atoms some initial speed,
and then, evolve that speed over time using the
forces we now know. The average speed of nitrogen
in air of 300K is about 520 m/s. The ensemble of
speeds is best described by a Maxwell
distribution.
Back of the enveloppe calculation 500 m/s 5.10
Å/s Lets assume that we can have things fly
0.1 A in a straight line before we calculate
forces again, then we need to recalculate forces
every 20 femtosecond one femtosecond is 10
sec. In practice 1 fsec integration steps are
being used.
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-15
http//en.wikipedia.org/wiki/Verlet_integration ht
tp//en.wikipedia.org/wiki/Maxwell_speed_distribut
ion
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Knowing the forces (and some randomized Maxwell
distributed initial velocities) we can evolve the
forces over time and get a trajectory. Simple
Euler integration wont work as this figure
explains. You can imagine that if you know where
you came from, you can over-compensate a bit.
These overcompensation algorithms are called
Verlet-algorithm, or Leapfrog algorithm.
If you take bigger time steps you overshoot your
goal. The Shake algorithm can fix that. Shake
allows you larger time steps at the cost of
little imperfection so that longer simulations
can be made in the same (CPU) time.
http//en.wikipedia.org/wiki/Verlet_integration
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Molecule (classical) N-particle
system Newtonian equations of motion
Integrate numerically via the leapfrog scheme
with ?t ? 1fs!
(equivalent to the Verlet algorithm)
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BPTI Molecular Dynamics (300K)
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Solve the Newtonian equations of motion
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Molecular dynamics is very expensive ...
Example A one nanosecond Molecular Dynamics
simulation of F1-ATPase in water (total 183 674
atoms) needs 106 integration steps, which boils
down to 8.4 1017 floating point operations.
on a 100 Mflop/s workstation ca 250
years ...but performance has been improved by use
of multiple time stepping ca. 25
years structure adapted multipole
methods ca. 6 years FAMUSAMM ca.
2 years parallel computers ca. 55
days
Whatever that is
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MD-Experiments with Argon Gas
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Role of environment - solvent
Explicit or implicit?
Box or droplet?
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periodic boundary conditions
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H. Frauenfelder et al., Science 229 (1985) 337
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Limits of MD-Simulations classical description
chemical reactions not describedpoor
description of H-atoms (proton-transfer)poor
description of low-T (quantum) effectssimplified
electrostatic modelsimplified force
fieldincomplete force field only small systems
accessible (104 ... 106 atoms)only short time
spans accessible (ps ... µs)