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Basing on the earlier works on the hierarchical equations of motion for quantum transport, we present in this paper a first principles scheme for time-dependent quantum transport by combining time-dependent density functional theory (TDDFT) and Keldysh's non-equilibrium Green's function formalism. This scheme is beyond the wide band limit approximation and is directly applicable to the case of non-orthogonal basis without the need of basis transformation. The overlap between the basis in the lead and the device region is treated properly by including it in the self-energy and it can be shown that this approach is equivalent to a lead-device orthogonalization. This scheme has been implemented at both TDDFT and density functional tight-binding level. Simulation results are presented to demonstrate our method and comparison with wide band limit approximation is made. Finally, the sparsity of the matrices and computational complexity of this method are analyzed. [ABSTRACT FROM AUTHOR]

A linear regression correction approach has been developed successfully to account for the electron correlation energy missing in Hartree–Fock calculation and to reduce the calculation errors of density functional theory. The numbers of lone-pair electrons, bonding electrons and inner layer electrons in molecules, and the number of unpaired electrons in the composing atoms in their ground states are chosen to be the most important physical descriptors to determine the correlation energy unaccounted by Hartree–Fock method or to improve the results calculated by B3LYP density functional theory method. As a demonstration, this proposed linear regression correction approach has been applied to evaluate the standard heats of formation ΔHf[variant_cap_theta] of 180 small-sized to medium-sized organic molecules at 298.15 K. Upon correction, the mean absolute deviation for the 150 molecules in the training set decreases from 351.0 to 4.6 kcal/mol and 360.9 to 4.6 kcal/mol for HF/6-31G(d) and HF/6-311+G(d,p) methods, respectively. For B3LYP method, the mean absolute deviations are reduced from 9.2 and 18.2 kcal/mol to 2.7 and 2.4 kcal/mol for 6-31G(d) and 6-311+G(d,p) basis sets, respectively. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]