Efficient grid-based method in nonequilibrium Green's function calculations: Application to model atoms and molecules

The finite-element discrete variable representation is proposed to express the nonequilibrium Green's function for strongly inhomogeneous quantum systems. This method is highly favorable against a general basis approach with regard to numerical complexity, memory resources, and computation time. Its flexibility also allows for an accurate representation of spatially extended Hamiltonians and thus opens the way toward a direct solution of the two-time Schwinger-Keldysh-Kadanoff-Baym equations on spatial grids, including, for example, the description of highly excited states in atoms. As benchmarks, we compute and characterize, in Hartree-Fock and second Born approximations, the ground states of the He atom, the H2 molecule, and the LiH molecule in one spatial dimension. Thereby, the ground-state and binding energies, densities, and bond lengths are compared with the direct solution of the time-dependent Schroedinger equation.