Team:EPF-Lausanne/Theory

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*The ''Lennard-Jones potential'' is the most commonly used form, with two parameters: σ, the diameter, and ε, the well depth. It takes into account the Van der Waals forces. It represents the non-bonded forces and the total potential energy can be calculated from the sum of energy contributions between pairs of atoms.  
*The ''Lennard-Jones potential'' is the most commonly used form, with two parameters: σ, the diameter, and ε, the well depth. It takes into account the Van der Waals forces. It represents the non-bonded forces and the total potential energy can be calculated from the sum of energy contributions between pairs of atoms.  
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[[Image:lennard_jones_vdw_forces.jpg]] [[Image:Lennard_jones.jpg|300px|thumb|Lennard-Jones pair potential showing the r<sup>−12</sup> and r<sup>−6</sup> contributions]]
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[[Image:lennard_jones_vdw_forces.jpg]] [[Image:Lennard_jones.jpg|300px|center|thumb|Lennard-Jones pair potential showing the r<sup>−12</sup> and r<sup>−6</sup> contributions]]
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*when electrostatic charges are present, we add the ''Coulomb force'', where Q1, Q2 are the  charges and ϵ0 is the permittivity of free space
*when electrostatic charges are present, we add the ''Coulomb force'', where Q1, Q2 are the  charges and ϵ0 is the permittivity of free space
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==the bonded interactions:==  
==the bonded interactions:==  
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angles, bonds and dihedral angles have to be taken into account
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Angles, bonds and dihedral angles have to be taken into account
[[Image:bonded.jpg‎|400px|center]]
[[Image:bonded.jpg‎|400px|center]]

Latest revision as of 12:23, 8 September 2009

Contents


Molecular dynamics theory



Molecular dynamics simulation consists of the numerical, step-by-step, solution of the classical equations of motion. For this purpose we need to be able to calculate the forces acting on the atoms, and these are usually derived from a potential energy. This potential energy can be divided into:

the non-bonded interactions:

  • The Lennard-Jones potential is the most commonly used form, with two parameters: σ, the diameter, and ε, the well depth. It takes into account the Van der Waals forces. It represents the non-bonded forces and the total potential energy can be calculated from the sum of energy contributions between pairs of atoms.
Lennard jones vdw forces.jpg
Lennard-Jones pair potential showing the r−12 and r−6 contributions
  • when electrostatic charges are present, we add the Coulomb force, where Q1, Q2 are the charges and ϵ0 is the permittivity of free space
Coulomb.jpg

the bonded interactions:

Angles, bonds and dihedral angles have to be taken into account

Bonded.jpg


To understand a bit more, you can see the following article: Introduction to Molecular Dynamics Simulation - Michael P. Allen


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