Lucian A. Constantin

Restoring the density-gradient expansion for exchange in solids and surfaces.

Popular modern generalized gradient approximations are biased toward the description of free-atom energies. Restoration of the first-principles gradient expansion for exchange over a wide range of density gradients eliminates this bias. We introduce a revised Perdew-Burke-Ernzerhof generalized gradient approximation that improves equilibrium properties of densely packed solids and their surfaces.Successful modern generalized gradient approximations (GGAs) are biased toward atomic energies. Restoration of the first-principles gradient expansion for the exchange energy over a wide range of density gradients eliminates this bias. With many collaborators, I introduce PBEsol, a revised Perdew-Burke-Ernzerhof GGA that improves equilibrium properties of densely-packed solids and their surfaces.

Relevance of the slowly varying electron gas to atoms, molecules, and solids.

We present a Thomas-Fermi-inspired density scaling under which electron densities of atomic, molecular, or condensed matter become both large and slowly varying, so that semiclassical approximations and second-order density gradient expansions are asymptotically exact for the kinetic and exchange energies. Thus, even for atoms and molecules, density-functional approximations should recover the universal second-order gradient expansions in this limit. We also explain why common generalized gradient approximations for exchange do not.

Meta-GGA Exchange-Correlation Functional with a Balanced Treatment of Nonlocality

We construct a meta-generalized-gradient approximation which properly balances the nonlocality contributions to the exchange and correlation at the semilocal level. This nonempirical functional shows good accuracy for a broad palette of properties (thermochemistry, structural properties) and systems (molecules, metal clusters, surfaces, and bulk solids). The accuracy for several well-known problems in electronic structure calculations, such as the bending potential of the silver trimer and the dimensional crossover of anionic gold clusters, is also demonstrated. The inclusion of empirical dispersion corrections is finally discussed and analyzed.

Generalized Gradient Approximations of the Noninteracting Kinetic Energy from the Semiclassical Atom Theory: Rationalization of the Accuracy of the Frozen Density Embedding Theory for Nonbonded Interactions.

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.

Condition on the Kohn-Sham kinetic energy and modern parametrization of the Thomas-Fermi density.

We study the asymptotic expansion of the neutral-atom energy as the atomic number Z-->infinity, presenting a new method to extract the coefficients from oscillating numerical data. Recovery of the correct expansion yields a condition on the Kohn-Sham kinetic energy that is important for the accuracy of approximate kinetic energy functionals for atoms, molecules, and solids. For example, this determines the small gradient limit of any generalized gradient approximation and conflicts somewhat with the standard gradient expansion. Tests are performed on atoms, molecules, and jellium clusters using densities constructed from Kohn-Sham orbitals. We also give a modern, highly accurate parametrization of the Thomas-Fermi density of neutral atoms.

Two-Dimensional Scan of the Performance of Generalized Gradient Approximations with Perdew-Burke-Ernzerhof-Like Enhancement Factor.

We assess the performance of the whole class of functionals defined by the Perdew-Burke-Ernzerhof (PBE) exchange-correlation enhancement factor, by performing a two-dimensional scan of the μ and κ parameters (keeping β fixed by the recovery of the local density approximation linear response). We consider molecular (atomization energies, bond lengths, and vibrational frequencies), intermolecular (hydrogen-bond and dipole interactions), and solid-state (lattice constant and cohesive energies) properties. We find, for the energetical properties, a whole family of functionals (with μ and κ interrelated) giving very similar results and the best accuracy. Overall, we find that the original PBE and the recently proposed APBE functional [Phys. Rev. Lett.2011, 106, 186406], based on the asymptotic expansion of the semiclassical neutral atom, give the highest global accuracy, with a definite superior performance of the latter for all of the molecular properties.

High-Level Correlated Approach to the Jellium Surface Energy, without Uniform-Gas Input

We resolve the long-standing controversy over the metal surface energy: Density-functional methods that require uniform-electron-gas input agree with each other, but not with high-level correlated calculations such as Fermi hypernetted chain and diffusion Monte Carlo calculations that predict the uniform-gas correlation energy. Here we apply the inhomogeneous Singwi-Tosi-Land-Sjölander method, and find that the density functionals are indeed reliable (because the surface energy is bulklike). Our work also vindicates the use of uniform-gas-based nonlocal kernels in time-dependent density-functional theory.

Laplacian-Level Kinetic Energy Approximations Based on the Fourth-Order Gradient Expansion: Global Assessment and Application to the Subsystem Formulation of Density Functional Theory

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, Hookes 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.

Exchange-correlation generalized gradient approximation for gold nanostructures

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.

Optical Spectra of Solids Obtained by Time-Dependent Density-Functional Theory with the Jellium-with-Gap-Model Exchange-Correlation Kernel

Within the framework of ab initio Time Dependent-Density Functional Theory (TD-DFT), we propose a static approximation to the exchange-correlation kernel based on the jellium-with-gap model. This kernel accounts for electron-hole interactions and it is able to address both strongly bound excitons and weak excitonic effects. TD-DFT absorption spectra of several bulk materials (both semiconductor and insulators) are reproduced in very good agreement with the experiments and with a low computational cost. The theoretical description of the optical properties of materials by first principles calculations is one of the classical issues in solid state physics. After photon absorption, the excitonic effects, driven by the electron and hole (e-h) interactions, are principal actors, rendering the ab initio computational description demanding. The most successful approach is, so far, based on ManyBody Perturbation theory: the GW self energy accounts for electron-electron (e-e) many-body effects in the band structure calculations, whereas the Bethe-Salpeter Equation is solved to introduce e-h interactions [1]. This accu