EFFICIENT SCALING OF CALCULATIONS INVOLVING SEPARABLE NONLOCAL POTENTIALS

We examine the system-size scaling behavior for performing nonlocal op erations in first-principles total-energy and force computations. A pr ocedure is derived and demonstrated for computing the nonlocal part of the total energy and its derivatives in O(N(a)(2)log(2)N(a)) operatio ns (where N-a is the number of atoms) for calculations involving separ able, nonlocal pseudopotentials. This procedure is performed in recipr ocal space and is equivalent to the conventional approach, which scale s as O(N-a(3)). Thus no approximations or new sources of error are int roduced.