Assessment of density matrix methods for electronic structure calculations ∗

Purification and minimization methods for computation of the one-particle density matrix are compared. This is done by considering the work needed by each method to achieve a given accuracy in terms of the difference to the exact solution. Simulations employing orthogonal as well as non-orthogonal versions of the methods are performed using both element magnitude and cutoff radius based truncation approaches. The results indicate that purification is considerably more efficient than the studied minimization methods even when a good starting guess for minimization is available. The computational cost of the studied minimization methods is observed to be significantly more sensitive to small band gaps than purification. An O( √ 1/ξ) dependence on the band gap ξ is observed for minimization which can be compared to the O(ln (1/ξ)) dependence for purification. Minimization is found to perform at its best at 50% occupancy. Error control and stopping criteria are also discussed.