Elimination of the diagonalization bottleneck in parallel Direct-SCF methods

Summary

It is shown that the matrix diagonalization bottleneck associated with thesequential O(N ³_BFN ) diagonalization of the fock matrix within each iteration of the Direct-SCF procedure may be eliminated, and replaced instead with a combination ofparallel O(N ^<4_BFN ) andsequential O(N ³_Sub ) steps. For large basis sets, the relation N_Sub

N_BFN between the dimension of the expansion subspace and the number of basis functions leads to a method of wave-function optimization in which the sequential bottleneck is eliminated. As a side benefit, the second-order iterative procedure on which this method is based displays superior convergence properties, and provides greater insight into the behavior of the energy with respect to orbital variations, than the traditional first-order, fixed-point, iterative approaches. The implementation of this method may be incorporated into essentially any existing Direct-SCF program with only minimal, and localized, changes.