Correlation3

Correlation3 - Density-density correlation function I Pair...

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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei Let’s define g( r ), density – density correlation function that gives us the probability to find a particle in the volume element d r located at r if at r = 0 there is another particle. () = N j j r r δ ) r ρ ( r r r Density-density correlation function I Pair correlation function, g(r) ∑∑ = = N i N j ij 2 0 r r δ N V ρ ) r C( ) r c( r r r r At atomic level the density distribution in a system of N particles can be described as Then, by definition, the density – density autocorrelation function is ()( ) i i i r r ρ r ρ ) r C( r r r r + = 1 r r δ ) r ρ ( N j j i i = = r r r where ( ) = + = + N j ij N j j i i r r δ r r r δ ) r r ρ ( r r r r r r r and ()( ) = = + = N i N j ij i N j ij i i i r r δ N 1 r r δ r r ρ r ρ ) r C( r r r r r r r r Therefore To relate the probability to find a particle at r to what is expected for a uniform random distribution of particles of the same density, we can
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Correlation3 - Density-density correlation function I Pair...

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