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We have performed a systematic and broad study of the performance of the ab initio OEP2-sc functional for spin-polarized systems, including the computation of ionization potentials and atomization and reaction energies of closed- and open-shell molecules. The results have revealed that, in line with other second-order methods, OEP2-sc can provide accurate results, being competitive to the orbital-optimized MP2 method. Moreover, the analysis of total and relative energies has shown that, unlike the case of double-hybrid functionals, this relatively good performance is not based on an error cancellation effect.

We show that the leading term in the strong-interaction limit of the adiabatic connection that has as weak-interaction expansion the Møller-Plesset perturbation theory can be fully determined from a functional of the Hartree-Fock density. We analyze this functional and highlight similarities and differences with the strong-interaction limit of the density-fixed adiabatic connection case of Kohn-Sham density functional theory.

The performance of functionals based on the idea of interpolating between the weak- and the strong-interaction limits the global adiabatic-connection integrand is carefully studied for the challenging case of noble-metal clusters. Different interpolation formulas are considered and various features of this approach are analyzed. It is found that these functionals, when used as a correlation correction to Hartree-Fock, are quite robust for the description of atomization energies, while performing less well for ionization potentials. Future directions that can be envisaged from this study and a previous one on main group chemistry are discussed.

The development of semilocal models for the kinetic energy density (KED) is an important topic in density functional theory (DFT). This is especially true for subsystem DFT, where these models are necessary to construct the required non-additive embedding contributions. In particular, these models can also be efficiently employed to replace the exact KED in meta-Generalized Gradient Approximation (meta-GGA) exchange-correlation functionals allowing to extend the subsystem DFT applicability to the meta-GGA level of theory. Here, we present a two-dimensional scan of semilocal KED models as linear functionals of the reduced gradient and of the reduced Laplacian, for atoms and weakly bound molecular systems. We find that several models can perform well but in any case the Laplacian contribution is extremely important to model the local features of the KED. Indeed a simple model constructed as the sum of Thomas-Fermi KED and 1/6 of the Laplacian of the density yields the best accuracy for atoms and weakly bound molecular systems. These KED models are tested within subsystem DFT with various meta-GGA exchange-correlation functionals for non-bonded systems, showing a good accuracy of the method.

We introduce a novel non-local ingredient for the construction of exchange density functionals: the reduced Hartree parameter, which is invariant under the uniform scaling of the density and represents the exact exchange enhancement factor for one- and two-electron systems. The reduced Hartree parameter is used together with the conventional meta-generalized gradient approximation (meta-GGA) semilocal ingredients (i.e., the electron density, its gradient, and the kinetic energy density) to construct a new generation exchange functional, termed u-meta-GGA. This u-meta-GGA functional is exact for the exchange of any one- and two-electron systems, is size-consistent and non-empirical, satisfies the uniform density scaling relation, and recovers the modified gradient expansion derived from the semiclassical atom theory. For atoms, ions, jellium spheres, and molecules, it shows a good accuracy, being often better than meta-GGA exchange functionals. Our construction validates the use of the reduced Hartree ingredient in exchange-correlation functional development, opening the way to an additional rung in the Jacob's ladder classification of non-empirical density functionals.

We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded molecular systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level approximation to the KED which overcomes this limitation and provides a simple and accurate way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the approximations in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method.

The performance of correlated optimized effective potential (OEP) functionals based on the spin-resolved second-order correlation energy is analysed. The relative importance of singly- and doubly- excited contributions as well as the effect of scaling the same- and opposite- spin components is investigated in detail comparing OEP results with Kohn-Sham (KS) quantities determined via an inversion procedure using accurate ab initio electronic densities. Special attention is dedicated in particular to the recently proposed scaled-opposite-spin OEP functional [I. Grabowski, E. Fabiano, and F. Della Sala, Phys. Rev. B 87, 075103 (2013)] which is the most advantageous from a computational point of view. We find that for high accuracy, a careful, system dependent, selection of the scaling coefficient is required. We analyse several size-extensive approaches for this selection. Finally, we find that a composite approach, named OEP2-SOSh, based on a post-SCF rescaling of the correlation energy can yield high accuracy for many properties, being comparable with the most accurate OEP procedures previously reported in the literature but at substantially reduced computational effort.

We extend the frozen density embedding theory to non-integer subsystems' particles numbers. Different features of this formulation are discussed, with special concern for approximate embedding calculations. In particular, we highlight the relation between the non-integer particle-number partition scheme and the resulting embedding errors. Finally, we provide a discussion of the implications of the present theory for the derivative discontinuity issue and the calculation of chemical reactivity descriptors.

We apply the frozen density embedding method, using a full relaxation of embedded densities through a freeze-and-thaw procedure, to study the electronic structure of several benchmark ground-state charge-transfer complexes, in order to assess the merits and limitations of the approach for this class of systems. The calculations are performed using both semilocal and hybrid exchange-correlation (XC) functionals. The results show that embedding calculations using semilocal XC functionals yield rather large deviations with respect to the corresponding supermolecular calculations. Due to a large error cancellation effect, however, they can often provide a relatively good description of the electronic structure of charge-transfer complexes, in contrast to supermolecular calculations performed at the same level of theory. On the contrary, when hybrid XC functionals are employed, both embedding and supermolecular calculations agree very well with each other and with the reference benchmark results. In conclusion, for the study of ground-state charge-transfer complexes via embedding calculations hybrid XC functionals are the method of choice due to their higher reliability and superior performance.

We discuss, simplify, and improve the spin-dependent correction of Constantin et al. [Phys. Rev. B 84, 233103 (2011)] for atomization energies, and develop a density parameter of the form v ∝ |∇n|/n(10/9), found from the statistical ensemble of one-electron densities. The here constructed exchange-correlation generalized gradient approximations (GGAs), named zvPBEsol and zvPBEint, show a broad applicability, and a good accuracy for many applications, because these corrected functionals significantly improve the atomization and binding energies of molecular systems, without worsening the behavior of the original functionals (PBEsol and PBEint) for other properties. This spin-dependent correction is also applied to meta-GGA dynamical correlation functionals combined with exact-exchange; in this case a significant (about 30%) improvement in atomization energies of small molecules is found.

We present an extension of the charge-dipole model for the description of periodic systems. This periodic charge-dipole electrostatic model (PCDEM) allows one to describe the linear response of periodic structures in terms of charge- and dipole-type gaussian basis functions. The long-range electrostatic interaction is efficiently described by means of the continuous fast multipole method. As a first application, the PCDEM method is applied to describe the polarizability of silver slabs. We find that for a correct description of the polarizability of the slabs both charges and dipoles are required. However a continuum set of parametrizations, i.e., different values of the width of charge- and dipole-type gaussians, leads to an equivalent and accurate description of the slabs polarizability but a completely unphysical description of induced charge-density inside the slab. We introduced the integral squared density measure which allows one to obtain a unique parametrization which accurately describes both the polarizability and the induced density profile inside the slab. Finally the limits of the electrostatic approximations are also pointed out.

We analyze the accuracy of the frozen density embedding (FDE) method, with hybrid and orbital-dependent exchange-correlation functionals, for the calculation of the total interaction energies of weakly interacting systems. Our investigation is motivated by the fact that these approaches require, in addition to the non-additive kinetic energy approximation, also approximate non-additive exact-exchange energies. Despite this further approximation, we find that the hybrid/orbital-dependent FDE approaches can reproduce the total energies with the same accuracy (about 1 mHa) as the one of conventional semi-local functionals. In many cases, thanks to error cancellation effects, hybrid/orbital-dependent approaches yield even the smallest error. A detailed energy-decomposition investigation is presented. Finally, the Becke-exchange functional is found to reproduce accurately the non-additive exact-exchange energies also for non-equilibrium geometries. These performances are rationalized in terms of a reduced-gradient decomposition of the non-additive exchange energy.

We compare the performance of different exchange-correlation functionals, based on the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation, for the structural and electronic properties of gold nanostructures. In particular we consider PBEsol (constructed to correctly describe solid-state systems) and PBEint [Phys. Rev. B 82, 113104 (2010)] which was recently introduced for hybrid interfaces and preserves the correct second-order gradient expansion of exchange energy (as in PBEsol) providing as well a significant nonlocality for higher density variation (as in PBE). We find that the PBEint functional gives a well balanced description of atomization energies, structural properties, energy differences between isomers, and bulk properties. Results indicate that PBEint is expected to be the most accurate functional for medium and large size gold clusters of different shapes., (© 2011 American Institute of Physics.)

The Kohn-Sham equations with constrained electron density are extended to hybrid exchange-correlation (XC) functionals. We derive the frozen density embedding generalized Kohn-Sham (FDE-GKS) scheme which allows to treat the nonlocal exact-exchange in the subsystems. For practical calculations we propose an approximated version of the FDE-GKS in which the nonadditive exchange potential is computed at a semilocal level. The proposed method is applied to compute the ground-state electronic properties of small test systems and selected DNA base pairs. The results of calculations employing the hierarchy of XC functionals BLYP/B3LYP/BHLYP and PBE/PBE0 are presented, in order to analyze the effect of nonlocal exchange contributions, and compared with reference coupled-cluster singles and doubles results. We find that the use of hybrid functionals leads to a significant improvement in the description of ground-state electronic properties of the investigated systems. The semilocal version of the FDE-GKS correctly reproduces the dipole and the electron density distribution of the exact GKS supramolecular system, with errors smaller than the ones obtained using conventional semilocal XC functionals.

We investigate the role of the exact exchange in describing the biphenylthiol/gold interface. The study is performed by simulating the electronic properties of mercaptobiphenylthiol and aminobiphenylthiol molecules adsorbed on a Au(23) cluster, using local, semilocal and hybrid functionals and an effective exact exchange method, namely, the localized Hartree-Fock (LHF). We find that the local/semilocal functionals strongly underestimate the charge transfer and the bond dipole at the interface due to the self-interaction-error (SIE), which alters the correct level alignment. On the other hand the LHF method is SIE free and predicts a larger charge transfer and bond dipole. We also found that LHF results can be reproduced using hybrid functionals and that conventional local/semilocal correlation functionals are unable to improve over the exchange-only description.

A local Kohn-Sham (KS) exchange-correlation potential is derived by localizing the second-order self-energy operator, using approximations to the linear response Sham-Schlüter equation. Thanks to the use of the resolution-of-identity technique for the calculation of the self-energy matrix elements, the method is very efficient and can be applied to large systems. The authors investigate the KS energy gaps and lowest excitation energies of atoms and small- and medium-size molecules. Reference KS energy gaps (from accurate densities) of atoms and small molecules can be reproduced with great accuracy. For larger systems they found that the KS energy gap is smaller than the one obtained from the local-density approximation, showing the importance of an ab initio correlation in the Kohn-Sham potential.