Hydrogen bond symmetrization and elastic constants under pressure of δ-AlOOH.

The elastic constants of δ-AlOOH have been calculated for applied pressures in the range 0-40 GPa using three exchange-correlation functionals, i.e. PBEsol, TCAsol and PBE. PBEsol and TCAsol, which describe the geometry of this system very well, give similar results, while the PBE values are smaller, a consequence of the fact that the PBE lattice parameters are too large. In agreement with the experiments, the calculations show that at low pressure the axial compressibility is greater in the b direction and smaller in the c direction, while the opposite is true at high pressure. This change takes place 5 GPa before the calculated hydrogen bond symmetrization transition. Combining this result with those reported in the experimental papers, one obtains a strong indication that symmetrization takes place at about 15 GPa, in excellent agreement with the PBEsol and TCAsol predictions.

Stability of the different AlOOH phases under pressure.

The pressure effects on three different AlOOH structures (α, γ, and δ phases) are systematically analyzed by density functional theory with different exchange and correlation energy functional approximations, namely two local, two generalized-gradient approximation (GGA), and two GGA for solids (GGAsol). Phase stability, compressibility and hydrogen bond evolution are studied in a range of pressures from 0 to 30 GPa. In general, the use of GGAsol functionals is mandatory in order to have the correct phase stability order, a good description of the hydrogen bonds, and a close agreement with the experimental lattice parameters at the various pressures. Pressure-induced hydrogen-bond symmetrization is found in γ and δ phases at high compression, while the hydrogen bonds in the α phase remain asymmetric. A detailed analysis of the uncertainties on the values of the bulk moduli and their pressure derivative at zero pressure deduced by fitting calculated or experimental (P,V) data is also presented.

Global hybrids from the semiclassical atom theory satisfying the local density linear response.

We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 2011, 106, 186406] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetic and structural testing, including thermochemistry and geometry, transition metal complexes, noncovalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semiempirical dispersion corrections are also provided.

Classical to quantum transition of heat transfer between two silica clusters.

Heat transfer between two silica clusters is investigated by using the nonequilibrium Green's function method. In the gap range between 4 Å and 3 times the cluster size, the thermal conductance decreases as predicted by the surface charge-charge interaction. Above 5 times the cluster size, the volume dipole-dipole interaction predominates. Finally, when the distance becomes smaller than 4 Å, a quantum interaction where the electrons of both clusters are shared takes place. This quantum interaction leads to the dramatic increase of the thermal coupling between neighbor clusters due to strong interactions. This study finally provides a description of the transition between radiation and heat conduction in gaps smaller than a few nanometers.

Effective electron displacements: a tool for time-dependent density functional theory computational spectroscopy.

We extend our previous definition of the metric Δr for electronic excitations in the framework of the time-dependent density functional theory [C. A. Guido, P. Cortona, B. Mennucci, and C. Adamo, J. Chem. Theory Comput. 9, 3118 (2013)], by including a measure of the difference of electronic position variances in passing from occupied to virtual orbitals. This new definition, called Γ, permits applications in those situations where the Δr-index is not helpful: transitions in centrosymmetric systems and Rydberg excitations. The Γ-metric is then extended by using the Natural Transition Orbitals, thus providing an intuitive picture of how locally the electron density changes during the electronic transitions. Furthermore, the Γ values give insight about the functional performances in reproducing different type of transitions, and allow one to define a "confidence radius" for GGA and hybrid functionals.

Communication: one third: a new recipe for the PBE0 paradigm.

We analyze the performances of the parameter-free hybrid density functional PBE0-1/3 obtained combining the PBE generalized-gradient functional with a predefined amount of exact exchange of 1/3, as recently discussed by Cortona [J. Chem. Phys. 136, 086101 (2012)]. The numerical results that we have obtained for various properties, such as atomization energies (G2-148 dataset), weak interactions (NCB31 dataset), hydrogen-bond length optimizations, and dissociation energies (HB10 dataset), and vertical excitation energies, show an increased performance of PBE0-1/3 with respect to the widely used PBE0. We therefore propose to use one third as the mixing coefficient for the PBE-based hybrid functional.

On the Metric of Charge Transfer Molecular Excitations: A Simple Chemical Descriptor.

A new index is defined with the aim of further exploring the metric of excited electronic states in the framework of the time-dependent density functional theory. This descriptor, called Δr, is based on the charge centroids of the orbitals involved in the excitations and can be interpreted in term of the hole-electron distance. The tests carried out on a set of molecules characterized by a significant number of charge-transfer excitations well illustrate its ability in discriminating between short (Δr ≤ 1.5 Å) and long-range (Δr ≥ 2.0 Å) excitations. On the basis of the well-known pitfalls of TD-DFT, its values can be then associated to the functional performances in reproducing different type of transitions and allow for the definition of a "trust radius" for GGA and hybrid functionals. The study of other systems, including some well-known difficult cases for other metric descriptors, gives further evidence of the high discrimination power of the proposed index. The combined use with other density or orbital-based descriptors is finally suggested to have a reliable diagnostic test of TD-DFT transitions.

Assessing modern GGA functionals for solids.

We present periodic calculations carried out with Gaussian-type basis sets on a test set of 21 solids with nine exchange-correlation functionals, extending previous works performed with two parameter-free correlation functionals (TCA and revTCA) which showed promising results for molecules in terms of key structural and energetic properties. Two LDAs and seven GGAs were considered for the prediction of equilibrium lattice constants, bulk moduli, and cohesive energies, using the same test set for all properties when possible. The effect of combining the TCA correlation with exchange potentials other than the PBE form originally used is also addressed. We find that the previously noted good accuracy of the parameter-free TCA functional for molecules also holds for solids, as long as a modified form of the exchange potential that is more biased towards solids than PBE is taken into account. In particular, the PBEsolTCA functional performs well overall for the three key structural and energetic properties considered here.

Density-functional calculations for large systems: can GGA functionals be competitive with hybrid functionals?

Two recently proposed correlation functionals, TCA and RevTCA, belonging to the generalized-gradient approximation (GGA) class, are briefly presented and their performances are discussed. The emphasis is put on the comparison with hybrid functionals, which are often the preferred ones for applications to molecular (but not to solid-state) systems. We show that the TCA and RevTCA performances are not far from those of hybrid functionals such as B3LYP or PBE0 when standard tests are performed and can be even better when less standard systems are considered. This is particularly interesting in view of applications to nano-scale systems or systems of biological interest, and, in general, in all the cases where the computer time requirements become an important constraint.

Toward a combined DFT/QTAIM description of agostic bonds: the critical case of a Nb(III) complex.

A detailed analysis concerning the effect of the exchange-correlation functional on a prototypical agostic niobium complex has been carried out, with particular attention to a fundamental property of the functional, namely, the recovering of the uniform electron gas limit. The obtained results allow for revisiting the role of this limit for a proper description of the beta-H agostic interaction. Starting from these results, a new criterion for the bond analysis based on the electron density behavior is proposed. Indeed, the density homogeneity between the metal and the involved hydrogen has been evaluated at the bond critical point, as defined in the framework of Bader's atoms in molecules theory, by calculating the average variation rates of the (reduced) density gradients. Such descriptors not only provide useful insights on the nature of such an interaction but also could be used as a starting point for a deep (and new) analysis of the chemical bond.

A new parameter-free correlation functional based on an average atomic reduced density gradient analysis.

A new parameter-free correlation functional based on the local Ragot-Cortona approach [J. Chem. Phys. 121, 7671 (2004)] is presented. This functional rests on a single ansatz for the gradient correction enhancement factor: it is assumed to be given by a simple analytic expression satisfying some exact conditions and containing two coefficients. These coefficients are determined without implementing the functional and without using a fitting procedure to experimental data. Their values are determined by requiring that the functional gives a correct average reduced density gradient for atoms, which, to some extent, can be considered an intrinsic atomic property. The correlation functional is then coupled with the Perdew-Burke-Erzernhof (PBE) exchange and compared with the original PBE approach as well as with some other pure density or hybrid approaches. Standard tests for atomic and molecular systems show that our new functional significantly improves on PBE, showing very interesting properties.

Correlation energy of many-electron systems: a modified Colle-Salvetti approach.

The Colle and Salvetti approach [Theo. Chim. Acta 37, 329 (1975)] to the calculation of the correlation energy of a system is modified in order to explicitly include into the theory the kinetic contribution to the correlation energy. This is achieved by deducing from a many electrons wave function, including the correlation effects via a Jastrow factor, an approximate expression of the one-electron reduced density matrix. Applying the latter to the homogeneous electron gas, an analytic expression of the correlation kinetic energy is derived. The total correlation energy of such a system is then deduced from its kinetic contribution inverting a standard procedure. At variance of the original Colle-Salvetti theory, the parameters entering in both the kinetic correlation and the total correlation energies are determined analytically, leading to a satisfactory agreement with the results of Perdew and Wang [Phys. Rev. B 45, 13244 (1992)]. The resulting (parameter-free) expressions give rise to a modified-local-density approximation that can be used in self-consistent density-functional calculations. We have performed such calculations for a large set of atoms and ions and we have found results for the correlation energies and for the ionization potentials which improve those of the standard local-density approximation.