We use the asymptotic expansions of the semiclassical neutral atom as a reference system in density functional theory to construct accurate generalized gradient approximations (GGAs) for the exchange-correlation and kinetic energies without any empiricism. These asymptotic functionals are among the most accurate GGAs for molecular systems, perform well for solid state, and overcome current GGA state of the art in frozen density embedding calculations. Our results also provide evidence for the conjointness conjecture between exchange and kinetic energies of atomic systems.
We present a new class of noninteracting kinetic energy (KE) functionals, derived from the semiclassical-atom theory. These functionals are constructed using the link between exchange and kinetic energies and employ a generalized gradient approximation (GGA) for the enhancement factor, namely, the Perdew-Burke-Ernzerhof (PBE) one. Two of them, named APBEK and revAPBEK, recover in the slowly varying density limit the modified second-order gradient (MGE2) expansion of the KE, which is valid for a neutral atom with a large number of electrons. APBEK contains no empirical parameters, while revAPBEK has one empirical parameter derived from exchange energies, which leads to a higher degree of nonlocality. The other two functionals, APBEKint and revAPBEKint, modify the APBEK and revAPBEK enhancement factors, respectively, to recover the second-order gradient expansion (GE2) of the homogeneous electron gas. We first benchmarked the total KE of atoms/ions and jellium spheres/surfaces: we found that functionals based on the MGE2 are as accurate as the current state-of-the-art KE functionals, containing several empirical parameters. Then, we verified the accuracy of these new functionals in the context of the frozen density embedding (FDE) theory. We benchmarked 20 systems with nonbonded interactions, and we considered embedding errors in the energy and density. We found that all of the PBE-like functionals give accurate and similar embedded densities, but the revAPBEK and revAPBEKint functionals have a significant superior accuracy for the embedded energy, outperforming the current state-of-the-art GGA approaches. While the revAPBEK functional is more accurate than revAPBEKint, APBEKint is better than APBEK. To rationalize this performance, we introduce the reduced-gradient decomposition of the nonadditive kinetic energy, and we discuss how systems with different interactions can be described with the same functional form.
We tested Laplacian-level meta-generalized gradient approximation (meta-GGA) noninteracting kinetic energy functionals based on the fourth-order gradient expansion (GE4). We considered several well-known Laplacian-level meta-GGAs from the literature (bare GE4, modified GE4, and the MGGA functional of Perdew and Constantin (Phys. Rev. B 2007,75, 155109)), as well as two newly designed Laplacian-level kinetic energy functionals (L0.4 and L0.6). First, a general assessment of the different functionals is performed to test them for model systems (one-electron densities, Hooke's atom, and different jellium systems) and atomic and molecular kinetic energies as well as for their behavior with respect to density-scaling transformations. Finally, we assessed, for the first time, the performance of the different functionals for subsystem density functional theory (DFT) calculations on noncovalently interacting systems. We found that the different Laplacian-level meta-GGA kinetic functionals may improve the description of different properties of electronic systems, but no clear overall advantage is found over the best GGA functionals. Concerning the subsystem DFT calculations, the here-proposed L0.4 and L0.6 kinetic energy functionals are competitive with state-of-the-art GGAs, whereas all other Laplacian-level functionals fail badly. The performance of the Laplacian-level functionals is rationalized thanks to a two-dimensional reduced-gradient and reduced-Laplacian decomposition of the nonadditive kinetic energy density.
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.
In order to remedy some of the shortcomings of the Random Phase Approximation (RPA) within Adiabatic Connection Fluctuation-Dissipation (ACFD) Density Functional Theory we introduce a short-ranged, exchange-like kernel that is one-electron self-correlation free and exact for two-electron systems in the high density limit. By tuning a free parameter in our model to recover an exact limit of the homogeneous electron gas correlation energy we obtain a non-local, energy-optimized kernel that reduces the errors of RPA for both homogeneous and inhomogeneous solids. Using wavevector symmetrization for the kernel, we also implement RPA renormalized perturbation theory for extended systems, and demonstrate its capability to describe the dominant correlation effects with a low-order expansion in both metallic and non-metallic systems. The comparison of ACFD structural properties with experiment is also shown to be limited by the choice of norm conserving pseudopotential.
Enhanced thermoelectric performance of Cu3SbS4 with fine microstructure and optimized carrier concentration by Sn-doping.
Atomic clusters of TiO(2) are modeled by means of state-of-the-art techniques to characterize their structural, electronic and optical properties. We combine ab initio molecular dynamics, static density functional theory, time-dependent density functional theory, and many body techniques, to provide a deep and comprehensive characterization of these systems. TiO(2) clusters can be considered as the starting seeds for the synthesis of larger nanostructures, which are of technological interest in photocatalysis and photovoltaics. In this work, we prove that clusters with anatase symmetry are energetically stable and can be considered as the starting seeds to growth much larger and complex nanostructures. The electronic gap of these inorganic molecules is investigated, and shown to be larger than the optical gap by almost 4 eV. Therefore, strong excitonic effects appear in these systems, much more than in the corresponding bulk phase. Moreover, the use of various levels of theory demonstrates that charge transfer effects play an important role under photon absorption, and therefore the use of adiabatic functionals in time dependent density functional theory has to be carefully evaluated.
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.
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