Density functional theory of molecular conductivity

This thesis is about current-density functional theory. Current plays a role in three important types of physical systems: molecular electronic devices (MED), broken current-symmetry states of atoms and molecules, and states of atoms and molecules in external magnetic fields. Developments in these three areas of current-density functional theory are presented in this thesis. First, the thesis proposes an extension of conventional density functional theory that accounts for the direct current flow through a MED under a voltage bias. The irreversible current flow in a MED is introduced by coupling the MED to a pair of reservoirs at two distinct local equilibria. This coupling defines a model non-Hermitian Hamiltonian whose eigenfunctions correspond to the coherent current carrying modes of the MED. A stationarity principle for the irreversible state of MED is constructed that resembles the variational principle of conventional quantum mechanics. As an application of the stationarity principle, a generalization of Kohn-Sham density functional theory suitable for MEDs is derived. The developed current density functional theory is applied to a di-thiol benzene molecule under a voltage bias. The new approach agrees with the established non-equilibrium Green's functions method. Second, this thesis develops an approximate functional that accounts for the current dependence of the exchange-correlation energy in systems with broken current symmetry. Starting from the Perdew-Burke-Ernzerhof generalized gradient approximation, first principle conditions are employed to built a non-empirical exchange functional. Matching the correlation functional to that for exchange yields a current-dependent approximation for correlation. The resulting functional is given in a simple closed form. The benchmark of this functional against the broken current symmetry ground-states of open shell atoms indicates an improvement, as compared to the current-independent generalized gradient approximations. Third, this thesis presents a current-dependent approach to magnetic response properties of atoms and molecules. The NMR shielding tensors computed for a benchmark set of molecules indicate a superiority of the novel approach over the common generalized gradient approximations and hybrid functionals for strongly deshielded nuclei.

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