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Potential_Part_3

# Potential_Part_3 - Potential cut-off(I The potential...

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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei The potential functions like L-J have an infinite range of interaction. In practice a cutoff radius R c is established and interactions between atoms separated by more than R c are ignored. There are two reasons for this: 1. The number of pair interactions grows as N 2 . Example: Consider system of 3000 atoms. There are N 2 /2 = 4.5 million pairs of atoms. Using a cutoff of 8-10 A we can reduce a number of interacting neighbors for each atom to ~50 and and we will have to evaluate force only ~50N = 150 thousand times. 2. The size of the system that can be simulated is finite, periodic boundary conditions are often used and we do not want an atom to interact with itself. Potential cut-off (I) ( ) ( ) ( ) c ij c ij c ij ij R r R r 0 R U r U r U > = A simple truncation of the potential creates a jump in the potential at the cutoff distance. This can spoil the energy conservation or lead to unphysical behavior in simulations of the effects where contribution of far-away molecules is important (surface tension, stacking faults, etc.). To avoid this potential can be shifted: For shifted potentials forces can have a jump at the cutoff. To avoid this, a smooth transition function that brings potential to zero can be added. In any case, physical quantities (cohesive energy, total pressure etc.) are affected by the truncation and most modern potentials for real materials are designed with a cutoff radius in mind, and go to zero at R c together with several first derivatives of the potential function.

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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei Potential cut-off (II) ( ) +
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