The use of a divide-and-conquer strategy for diagonalizing the Fock matrix in molecular orbital theory. Application to the calculation of the ground state energy of biomolecules

Abstract:

Originally developed for the density functional theory, the divide-and-conquer procedure is one of the most promising in a growing list of techniques that exhibit linear scaling with respect to the number of basis functions in quantum mechanical systems. The key to linear scaling consits in replacing the calculation of the full quantum system with a set of calculations performed on subsystems obtained by partinioning the Fock matrix for the whole quantum system into smaller Fock matrices for overlapping subsystems. The subsystems do not sum up to the original quantum system. The subsystems contain buffering regions which allow them to exchange electronic information with the neighboring subsystems, and increase convergence rate. For the systems tested (e.g. polyglycine) linear scaling is achieved and the accuracy of the calculation can be controlled by the partitioning and buffering schemes.

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