where the second equality requires the equivalence of particles 1 , … … , N − − 1 . The formula above is useful for relating g ( r ) to the static structure factor S ( q ) , defined by S ( q ) = ⟨ ⟨ ∑ ∑ i j e − − i q ( r i − − r j ) ⟩ ⟩ / N , since we have: