We present a model for the exchange-correlation hole and the exchange-correlation energy in the strong-correlation (SC) limit of density functional theory. The SC limit is useful in the construction of exchange-correlation functionals through interpolation of the adiabatic connection. The new approximation (referred to as shell model) is an improvement of the non-local radius (NLR) model recently proposed by Wagner and Gori-Giorgi [Phys. Rev. A 90, 052512 (2014)]. The NLR model does not correctly reproduce the limit of the strongly correlated homogeneous electron gas and this shortcoming is remedied by the shell model. As in the case of the NLR model, the spherically averaged electron density ρ(r,u)=∫dΩ4πρ(r+u) is the starting point for the construction of the shell model and it is also its computational bottleneck. We show how ρ(r, u), the NLR, and the shell model can be implemented efficiently. For this purpose, analytical integrals for the normalization and the energy density of the underlying holes are provided. Employing the shell model, we illustrate how improved adiabatic connection interpolations can be constructed.

Among other applications, complex absorbing potentials (CAPs) have proven to be useful tools in the theory of metastable states. They facilitate the conversion of unbound states of a finite lifetime into normalized bound states with a complex energy. Adding CAPs to a conventional Hamiltonian turns it into a non-Hermitian operator. Recently, we introduced a complex density functional theory (CODFT) that extends the Kohn-Sham method to the realm of non-Hermitian systems. Here, we combine CAPs with CODFT and present the first application of CODFT to metastable systems. In particular, we consider the negative ions of the beryllium atom and the nitrogen molecule. Using conventional exchange-correlation functionals as functionals of a complex density, the resonance positions and the resonance lifetimes are obtained, and they are in line with the findings of other studies.

Drawing on the adiabatic connection of density functional theory, exchange-correlation functionals of Kohn-Sham density functional theory are constructed which interpolate between the extreme limits of the electron-electron interaction strength. The first limit is the non-interacting one, where there is only exchange. The second limit is the strong correlated one, characterized as the minimum of the electron-electron repulsion energy. The exchange-correlation energy in the strong-correlation limit is approximated through a model for the exchange-correlation hole that is referred to as nonlocal-radius model [L. O. Wagner and P. Gori-Giorgi, Phys. Rev. A 90, 052512 (2014)]. Using the non-interacting and strong-correlated extremes, various interpolation schemes are presented that yield new approximations to the adiabatic connection and thus to the exchange-correlation energy. Some of them rely on empiricism while others do not. Several of the proposed approximations yield the exact exchange-correlation energy for one-electron systems where local and semi-local approximations often fail badly. Other proposed approximations generalize existing global hybrids by using a fraction of the exchange-correlation energy in the strong-correlation limit to replace an equal fraction of the semi-local approximation to the exchange-correlation energy in the strong-correlation limit. The performance of the proposed approximations is evaluated for molecular atomization energies, total atomic energies, and ionization potentials.

A simple model for electron transport through molecules is provided by the source-sink potential (SSP) method [F. Goyer, M. Ernzerhof, and M. Zhuang, J. Chem. Phys. 126, 144104 (2007)]. In SSP, the boundary conditions of having an incoming and outgoing electron current are enforced through complex potentials that are added to the Hamiltonian. Depending on the sign of the imaginary part of the potentials, current density is generated or absorbed. In this way, a finite system can be used to model infinite molecular electronic devices. The SSP has originally been developed for the Hückel method and subsequently it has been extended [F. Goyer and M. Ernzerhof, J. Chem. Phys. 134, 174101 (2011)] to the Hubbard model. Here we present a step towards its generalization for first-principles electronic structure theory methods. In particular, drawing on our earlier work, we discuss a new generalized density functional theory for complex non-Hermitian Hamiltonians. This theory enables us to combine SSP and Kohn-Sham theory to obtain a method for the description of open systems that exchange current density with their environment. Similarly, the Hartree-Fock method is extended to the realm of non-Hermitian, SSP containing Hamiltonians. As a proof of principle, we present the first applications of complex-density functional theory (CODFT) as well as non-Hermitian Hartree-Fock theory to electron transport through molecules.

International audienceZero-dimensional graphenes, also called nanographenes (NGs), consist of fragments of graphene with a finite number of hexagons. NGs can be viewed as a subset of the polycyclic aromatic hydrocarbons (PAHs) that continue to attract chemists' attention. We developed a simple theory for the ballistic electron transport through NGs which combines elements of the electronic structure theory of graphene, intuitive methods for the calculation of the molecular conductance, and chemical concepts such as Kekule structures. This theory enables one to analyze the relation between the structure of NGs and their conductance. General formulas and rules for the zero-voltage conductance as a function of the contact positions are derived. These formulas and rules require at most simple paper and pencil calculations in applications to systems containing several tens of carbon atoms