Modeling Charge Resonance in Cationic Molecular Clusters: Combining DFT-Tight Binding with Configuration Interaction

International audienceIn order to investigate charge resonance situations in molecular complexes, Wu et al. (J. Chem. Phys. 2007, 127, 164119) recently proposed a configuration interaction method with a valence bond-like multiconfigurational basis obtained from constrained DFT calculations. We adapt this method to the Self-Consistent Charge Density-Functional-based Tight Binding (SCC-DFTB) approach and provide expressions for the gradients of the energy with respect to the nuclear coordinates. It is shown that the method corrects the wrong SCC-DFTB behavior of the potential energy surface in the dissociation regions. This scheme is applied to determine the structural and stability properties of positively charged molecular dimers with full structural optimization, namely, the benzene dimer cation and the water dimer cation. The method yields binding energies in good agreement with experimental data and high-level reference calculations

Derivative Discontinuity in the Strong-Interaction Limit of Density-Functional Theory

We generalize the exact strong-interaction limit of the exchange-correlation energy of Kohn-Sham density functional theory to open systems with fluctuating particle numbers. When used in the self-consistent Kohn-Sham procedure on strongly interacting systems, this functional yields exact features crucial for important applications such as quantum transport. In particular, the steplike structure of the highest-occupied Kohn-Sham eigenvalue is very well captured, with accurate quantitative agreement with exact many-body chemical potentials. While it can be shown that a sharp derivative discontinuity is present only in the infinitely strongly correlated limit, at finite correlation regimes we observe a slightly smoothened discontinuity, with qualitative and quantitative features that improve with increasing correlation. From the fundamental point of view, our results obtain the derivative discontinuity without making the assumptions used in its standard derivation, offering independent support for its existence. © 2013 American Physical Society

Energy Density Functionals From the Strong-Coupling Limit Applied to the Anions of the He Isoelectronic Series

Anions and radicals are important for many applications including environmental chemistry, semiconductors, and charge transfer, but are poorly described by the available approximate energy density functionals. Here we test an approximate exchange-correlation functional based on the exact strong-coupling limit of the Hohenberg-Kohn functional on the prototypical case of the He isoelectronic series with varying nuclear charge $Z<2$, which includes weakly bound negative ions and a quantum phase transition at a critical value of $Z$, representing a big challenge for density functional theory. We use accurate wavefunction calculations to validate our results, comparing energies and Kohn-Sham potentials, thus also providing useful reference data close to and at the quantum phase transition. We show that our functional is able to bind H$^-$ and to capture in general the physics of loosely bound anions, with a tendency to strongly overbind that can be proven mathematically. We also include corrections based on the uniform electron gas which improve the results.Comment: Accepted for the JCP Special Topic Issue "Advances in DFT Methodology

Kohn-Sham density functional theory for quantum wires in arbitrary correlation regimes

We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to construct an approximation for the exchange-correlation term of the Kohn-Sham approach. The resulting exchange-correlation potential is able to capture the features of the strongly correlated regime without breaking the spin or any other symmetry. In particular, it shows “bumps” (or barriers) that give rise to charge localization at low densities and that are a well-known key feature of the exact Kohn-Sham potential for strongly correlated systems. Here, we illustrate this approach for the study of both weakly and strongly correlated model quantum wires, comparing our results with those obtained with the configuration interaction method and with the usual Kohn-Sham local density approximation

Energy densities in the strong-interaction limit of density functional theory

We discuss energy densities in the strong-interaction limit of density functional theory, deriving an exact expression within the definition (gauge) of the electrostatic potential of the exchange-correlation hole. Exact results for small atoms and small model quantum dots are compared with available approximations defined in the same gauge. The idea of a local interpolation along the adiabatic connection is discussed, comparing the energy densities of the Kohn-Sham, the physical, and the strong-interacting systems. We also use our results to analyze the local version of the Lieb-Oxford bound, widely used in the construction of approximate exchange-correlation functionals.Comment: 12 page

Hydrogen Molecule Dissociation Curve with Functionals Based on the Strictly Correlated Regime

Using the dual Kantorovich formulation, we compute the strictly correlated electrons (SCE) functional (corresponding to the exact strong-interaction limit of density functional theory) for the hydrogen molecule along the dissociation curve. We use an exact relation between the Kantorovich potential and the optimal map to compute the comotion function, exploring corrections based on it. In particular, we analyze how the SCE functional transforms in an exact way the electron-electron distance into a one-body quantity, a feature that can be exploited to build new approximate functionals. We also show that the dual Kantorovich formulation provides in a natural way the constant in the Kohn-Sham potential recently introduced by Levy and Zahariev [Phys. Rev. Lett. 2014, 113, 113002] for finite systems

PAH-related Very Small Grains in photodissociation regions: implications from molecular simulations

International audienceThe analysis of mid-IR emission suggests that a population of PAH-related very small grains containing a few hundreds of atoms are present in the deep regions of molecular clouds, although no specific species has been identified yet. In this review, we discuss several candidates for these grains: neutral and ionised PAH clusters and complexes of PAHs with Si atoms. The theoretical modelling of the properties of such molecular complexes or nanograins is a challenging task. We first present an overview of quantum chemistry derived models which can be efficiently used on-the-fly in extensive sampling of the potential energy surfaces, as required by structural optimization, classical molecular dynamics or Monte Carlo algorithms. From the simulations, various observables can be determined, such as the binding energies, finite temperature IR spectra, nucleation and evaporation rates. We discuss the relevance of those candidates in the molecular clouds photodissociation regions and propose constrains and perspectives for the nature and size of those very small grains