Team:EPF-Lausanne/Theory
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- | ==Molecular dynamics theory | + | |
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+ | <font size="6" color="#007CBC"><i>Molecular dynamics theory</i></font> | ||
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+ | <br> | ||
+ | ---- | ||
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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: | 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. | |
- | + | <center> | |
- | [[Image: | + | [[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]] |
+ | </center> | ||
+ | *when electrostatic charges are present, we add the ''Coulomb force'', where Q1, Q2 are the charges and ϵ0 is the permittivity of free space | ||
+ | [[Image:Coulomb.jpg|200px|center]] | ||
- | + | ==the bonded interactions:== | |
- | [[Image:bonded.jpg|400px | + | Angles, bonds and dihedral angles have to be taken into account |
+ | [[Image:bonded.jpg|400px|center]] | ||
- | + | To understand a bit more, you can see the following article: | |
[[Media:Introduction_to_molecular_Dynamics_Simulation.pdf | Introduction to Molecular Dynamics Simulation - Michael P. Allen]] | [[Media:Introduction_to_molecular_Dynamics_Simulation.pdf | Introduction to Molecular Dynamics Simulation - Michael P. Allen]] | ||
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Latest revision as of 12:23, 8 September 2009
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.
- when electrostatic charges are present, we add the Coulomb force, where Q1, Q2 are the charges and ϵ0 is the permittivity of free space
the bonded interactions:
Angles, bonds and dihedral angles have to be taken into account
To understand a bit more, you can see the following article:
Introduction to Molecular Dynamics Simulation - Michael P. Allen