Microtech2010 2010

A density matrix based electronic structure method applied to nanoparticles: treatment of the idempotency problem

M.J.H. Hoffman
University of the Free State, ZA

Keywords: density matrix, idempotency, electronic structure, nano particles


During the last 15 years there has been considerable interest in density matrix based methods for electronic structure calculations. The “difficult” problem of ensuring idempotency conservation of the density matrix through an appropriate purification scheme as well as the use of the “nearsightedness” and associated sparsity of the density matrix to achieve linear scaling with system size has been discussed by various authors. In this study a density matrix based fictitious electron dynamics method for calculating electronic structure has been applied to nanoparticles. This method uses an equation of motion that implicitly ensures the idempotency constraint on the density matrix. The effectiveness of this method compared to conventional purification schemes is discussed. Important properties of the density matrix and its sub matrices, including its sparsity and conditions for effective linear independence of a column sub matrix of the density matrix are discussed and illustrated within the context of nanoparticles. The density matrix is calculated using alternatively semi-empirical quantum chemistry or DFT methods. It is shown how the full density matrix can be reconstructed through a fast QR factorization of a column sub matrix using a Choleski factorization of its principal sub matrix.
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