Relationships between charge density response functions, exchange holes and localized orbitals

The charge density response function and the exchange hole are closely related to each other via the fundamental fluctuation-dissipation theorem of physics. A simple approximate model of the static response function is visually compared on several examples in order to demonstrate this relationship. This study is completed by illustrating the well-known isomorphism between the exchange hole and the square of the dominant localized orbital lying in the space region of the reference point of the exchange hole function. The implications of these relationships for the interpretation of common chemical concepts, such as delocalization, are discussed.Comment: 10 two-columns pages, including 3 figure

Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation

An adiabatic-connection fluctuation-dissipation theorem approach based on a range separation of electron-electron interactions is proposed. It involves a rigorous combination of short-range density functional and long-range random phase approximations. This method corrects several shortcomings of the standard random phase approximation and it is particularly well suited for describing weakly-bound van der Waals systems, as demonstrated on the challenging cases of the dimers Be$_2$ and Ne$_2$.Comment: 4 pages, 2 figure

Range-separated density-functional theory with random phase approximation: detailed formalism and illustrative applications

Using Green-function many-body theory, we present the details of a formally exact adiabatic-connection fluctuation-dissipation density-functional theory based on range separation, which was sketched in Toulouse, Gerber, Jansen, Savin and Angyan, Phys. Rev. Lett. 102, 096404 (2009). Range-separated density-functional theory approaches combining short-range density functional approximations with long-range random phase approximations (RPA) are then obtained as well-identified approximations on the long-range Green-function self-energy. Range-separated RPA-type schemes with or without long-range Hartree-Fock exchange response kernel are assessed on rare-gas and alkaline-earth dimers, and compared to range-separated second-order perturbation theory and range-separated coupled-cluster theory.Comment: 15 pages, 3 figures, 2 table

Van der Waals forces in density functional theory: perturbational long-range electron interaction corrections

Long-range exchange and correlation effects, responsible for the failure of currently used approximate density functionals in describing van der Waals forces, are taken into account explicitly after a separation of the electron-electron interaction in the Hamiltonian into short- and long-range components. We propose a "range-separated hybrid" functional based on a local density approximation for the short-range exchange-correlation energy, combined with a long-range exact exchange energy. Long-range correlation effects are added by a second-order perturbational treatment. The resulting scheme is general and is particularly well-adapted to describe van der Waals complexes, like rare gas dimers.Comment: 8 pages, 1 figure, submitted to Phys. Rev.

Assessing the Performance of Recent Density Functionals for Bulk Solids

We assess the performance of recent density functionals for the exchange-correlation energy of a nonmolecular solid, by applying accurate calculations with the GAUSSIAN, BAND, and VASP codes to a test set of 24 solid metals and non-metals. The functionals tested are the modified Perdew-Burke-Ernzerhof generalized gradient approximation (PBEsol GGA), the second-order GGA (SOGGA), and the Armiento-Mattsson 2005 (AM05) GGA. For completeness, we also test more-standard functionals: the local density approximation, the original PBE GGA, and the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA. We find that the recent density functionals for solids reach a high accuracy for bulk properties (lattice constant and bulk modulus). For the cohesive energy, PBE is better than PBEsol overall, as expected, but PBEsol is actually better for the alkali metals and alkali halides. For fair comparison of calculated and experimental results, we consider the zero-point phonon and finite-temperature effects ignored by many workers. We show how Gaussian basis sets and inaccurate experimental reference data may affect the rating of the quality of the functionals. The results show that PBEsol and AM05 perform somewhat differently from each other for alkali metal, alkaline earth metal and alkali halide crystals (where the maximum value of the reduced density gradient is about 2), but perform very similarly for most of the other solids (where it is often about 1). Our explanation for this is consistent with the importance of exchange-correlation nonlocality in regions of core-valence overlap.Comment: 32 pages, single pdf fil

Blind test of density-functional-based methods on intermolecular interaction energies

In the past decade, a number of approaches have been developed to fix the failure of (semi) local density-functional theory (DFT) in describing intermolecular interactions. The performance of several such approaches with respect to highly accurate benchmarks is compared here on a set of separation-dependent interaction energies for ten dimers. Since the benchmarks were unknown before the DFT-based results were collected, this comparison constitutes a blind test of these methods

Alkane adsorption in Na-exchanged chabazite: The influence of dispersion forces

Structure and properties of metal-exchanged zeolites studied using gradient-corrected and hybrid functionals. III. Energetics and vibrational spectroscopy of adsorbates J. Chem. Phys. 136, 06450