Molecular dynamics
This presentation is the property of its rightful owner.
Sponsored Links
1 / 18

Most material in this seminar has been produced by Bert de Groot at the MPI in G ö ttingen. PowerPoint PPT Presentation


  • 95 Views
  • Uploaded on
  • Presentation posted in: General

Molecular dynamics Some random notes on molecular dynamics simulations Seminar based on work by Bert de Groot and many anonymous Googelable colleagues. Most material in this seminar has been produced by Bert de Groot at the MPI in G ö ttingen. Schrödinger equation.

Download Presentation

Most material in this seminar has been produced by Bert de Groot at the MPI in G ö ttingen.

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Most material in this seminar has been produced by bert de groot at the mpi in g ttingen

Molecular dynamicsSome random notes on molecular dynamics simulationsSeminar based on work by Bert de Groot and many anonymous Googelable colleagues


Most material in this seminar has been produced by bert de groot at the mpi in g ttingen

Most material in this seminar has been produced by Bert de Groot at the MPI in Göttingen.


Most material in this seminar has been produced by bert de groot at the mpi in g ttingen

Schrödinger equation

Born-Oppenheimer approximation

Nucleic motion described classically

Empirical force field


Most material in this seminar has been produced by bert de groot at the mpi in g ttingen

Inter-atomic interactions


Most material in this seminar has been produced by bert de groot at the mpi in g ttingen

=

=

R

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“:


Most material in this seminar has been produced by bert de groot at the mpi in g ttingen

„Force-Field“


Non bonded interactions

Non-bonded interactions

Coulomb potential

Lennard-Jones potential


Most material in this seminar has been produced by bert de groot at the mpi in g ttingen

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

Let’s 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.

12

-15

http://en.wikipedia.org/wiki/Verlet_integration

http://en.wikipedia.org/wiki/Maxwell_speed_distribution


Most material in this seminar has been produced by bert de groot at the mpi in g ttingen

Knowing the forces (and some randomized Maxwell distributed initial velocities) we can evolve the forces over time and get a trajectory. Simple Euler integration won’t 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


Most material in this seminar has been produced by bert de groot at the mpi in g ttingen

Molecule: (classical) N-particle system

Newtonian equations of motion:

Integrate numerically via the „leapfrog“ scheme:

with

Δt  1fs!

(equivalent to the Verlet algorithm)


Most material in this seminar has been produced by bert de groot at the mpi in g ttingen

BPTI: Molecular Dynamics (300K)


Most material in this seminar has been produced by bert de groot at the mpi in g ttingen

Solve the Newtonian equations of motion:


Most material in this seminar has been produced by bert de groot at the mpi in g ttingen

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 steppingca. 25 years

+ structure adapted multipole methods*ca. 6 years

+ FAMUSAMM*ca. 2 years

+ parallel computers ca. 55 days

* Whatever that is


Most material in this seminar has been produced by bert de groot at the mpi in g ttingen

MD-Experiments with Argon Gas


Role of environment solvent

Role of environment - solvent

Explicit or implicit?

Box or droplet?


Most material in this seminar has been produced by bert de groot at the mpi in g ttingen

periodic boundary conditions


Most material in this seminar has been produced by bert de groot at the mpi in g ttingen

H. Frauenfelder et al., Science229 (1985) 337


Most material in this seminar has been produced by bert de groot at the mpi in g ttingen

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)


  • Login