Perturbative Approximations to Avoid Matrix Diagonalization
With the aim of developing linear-scaling methods, we discuss perturbative approaches designed to avoid diagonalization of large matrices. Approximate molecular orbitals can be corrected by perturbation theory, in course of which the Laplace transformation technique proposed originally by Almløf facilitates linear scaling. The first order density matrix P corresponding to a one-electron problem can be obtained from an iterative formula which preserves the trace and the idempotency of P so that no purification procedures are needed. For systems where P is sparse, the procedure leads to a linear scaling method. The algorithm is useful in course of geometry optimization or self-consistent procedures, since matrix P of the previous step can be used to initialize the density matrix iteration at the next step. Electron correlation methods based on the Hartree-Fock density matrix, without making reference to molecular orbitals are commented on.
KeywordsLinear scaling Density matrix Laplace-transform Idempotency conserving iteration
This work has been supported by the Hungarian National Research Fund (OTKA), grant numbers NI-67702, K-81588 and K-81590. The European Union and the European Social Fund have also provided financial support to the project under the grant agreement no. TÁMOP 4.2.1./B-09/1/KMR-2010-0003.
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