Correlation5

# Correlation5 - Structure function S(Q 2 N N sin(Qrij S(Q =...

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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei Structure function S(Q) This equation can be used to calculate the structure function from an atomic configuration. ∑∑ =< + = N j N j i ij ij Qr Qr N Q S 1 ) sin( 2 1 ) ( The calculations, however, involve the summation over all pairs of atoms in the system, leading to the quadratic dependence of the computational cost on the number of atoms and making the calculations expensive for large systems. => = N j N j i ρ π Nr 1 ij 0 2 ) r δ (r 2 1 g(r) An alternative approach to calculation of S(Q) is to substitute the double summation over atomic positions by integration over pair distribution function [2] The expression for the structure function can be now reduced to the integration over r (equivalent to Fourier of g(r) ): The calculation of g(r) still involves N 2 /2 evaluations of interatomic distances r ij , but it can be done much more efficiently than the direct calculation of S(Q) , which requires evaluation of the sine function and

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Correlation5 - Structure function S(Q 2 N N sin(Qrij S(Q =...

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