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Chemical Physics Letters

Reply to Comment on ‘On the optimal symmetric purification scheme of the one-particle density matrix’

Jaehoon Kim, Yousung Jung

Published Jan 17, 2012• 1 citation
Publisher
DOI
10.1016/j.cplett.2012.01.015

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Recently we proposed an information entropy based method for electronic structure calculations within the density-matrix functional theory(DMFT) (Phys. Rev. Lett. 128, 013001), dubbed as iii-DMFT. Comments have been raised regarding the accuracy of the one-particle density-matrix compared to that from the wave function, and the universality of the functional. We address these questions and the problematic case of HeH+^++.
An implicit purification scheme is proposed for calculation of the temperature-dependent, grand canonical single-particle density matrix, given as a Fermi-Dirac operator expansion in terms of the Hamiltonian. The computational complexity is shown to scale with the logarithm of the polynomial order of the expansion, or equivalently, with the logarithm of the inverse temperature. The system of linear equations that arise in each implicit purification iteration is solved efficiently by a conjugate gradient solver. The scheme is particularly useful in connection with linear scaling electronic structure theory based on sparse matrix algebra. The efficiency of the implicit temperature expansion technique is analyzed and compared to some explicit purification methods for the zero temperature density matrix.