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We present a self-consistent ab initio simulation method to calculate coherent quantum transport through a molecule connected to metal electrodes in the linear-response regime. Density-functional theory (DFT) is applied to the metal-molecule-metal system. The molecule and the metal electrodes are treated on the same footing as one extended molecule. The Full Approximation Scheme (FAS) nonlinear multigrid technique is used to accelerate convergence in a nonorthogonal localized orbital basis. The Landauer formula is employed to calculate the current with the transmission function obtained from a Green's function calculation. The current-voltage characteristics of a benzene-1,4-dithiolate (BDT) extended molecule are studied as an example, and our results are compared to other theoretical calculations. We also show that a recently formulated constrained-current formalism is invariant to a reversal in the imposed current. Hence, the predicted voltage drop must be zero. This suggests the theory must be modified to properly treat possible nonlinearities in the nonzero current case [ABSTRACT FROM PUBLISHER]