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Controlling the accuracy of the density matrix renormalization group method The Dynamical B.pdf

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Controlling the accuracy of the density matrix renormalization group method The Dynamical B

Controlling the accuracy of the density matrix renormalization group method: The Dynamical Block State Selection approach ∗ ¨ O. Legeza, J. R¨oder and B. A. Hess Chair of Theoretical Chemistry, Friedrich–Alexander University Erlangen–Nuremberg. D-91058 Erlangen, Egerlandstr. 3, Germany (February 1, 2008) 2 We have applied the momentum space version of the Density Matrix Renormalization Group 0 method (k-DMRG) in quantum chemistry in order to study the accuracy of the algorithm in the 0 new context. We have shown numerically that it is possible to determine the desired accuracy of 2 the method in advance of the calculations by dynamically controlling the truncation error and the r number of block states using a novel protocol which we dubbed Dynamical Block State Selection p (DBSS). The relationship between the real error and truncation error has been studied as a function A of the number of orbitals and the fraction of ﬁlled orbitals. We have calculated the ground state of the molecules CH , H O, and F as well as the ﬁrst excited state of CH . Our largest calculations 9 2 2 2 2 2 were carried out with 57 orbitals, the largest number of block states was 1500–2000, and the largest dimensions of the Hilbert space of the superblock conﬁguration was 800.000–1.200.000. ] l e - r t s . t a m - d n o c [ 1 v