Superconducting properties of MgB2 from first principles

Solid MgB(2) has rather interesting and technologically important properties, such as a very high superconducting transition temperature. Focusing on this compound, we report the first nontrivial application of a novel density-functional-type theory for superconductors, recently proposed by the authors. Without invoking any adjustable parameters, we obtain the transition temperature, the gaps, and the specific heat of MgB(2) in very good agreement with experiment. Moreover, our calculations show how the Coulomb interaction acts differently on sigma and pi states, thereby stabilizing the observed superconducting phase.     

Benchmark calculations for reduced density-matrix functional theory

Reduced density-matrix functional theory (RDMFT) is a promising alternative approach to the problem of electron correlation. Like standard density functional theory, it contains an unknown exchange-correlation functional, for which several approximations have been proposed in the last years. In this article, we benchmark some of these functionals in an extended set of molecules with respect to total and atomization energies. Our results show that the most recent RDMFT functionals give very satisfactory results compared to standard quantum chemistry and density functional approaches.     

A torsional potential for graphene derived from fitting to DFT results

We present a simple torsional potential for graphene to accurately describe its out-of-plane deformations. The parameters of the potential are derived through appropriate fitting with suitable DFT calculations regarding the deformation energy of graphene sheets folded around two different folding axes, along an armchair or along a zig-zag direction. Removing the energetic contribution of bending angles, using a previously introduced angle bending potential, we isolate the purely torsional deformation energy, which is then fitted to simple torsional force fields. The presented out-of-plane torsional potential can accurately fit the deformation energy for relatively large torsional angles up to 0.5 rad. To test our proposed potential, we apply it to the problem of the vertical displacement of a single carbon atom out of the graphene plane and compare the obtained deformation energy with corresponding DFT calculations. The dependence of the deformation energy on the vertical displacement of the pulled carbon atom is indistinguishable in these two cases, for displacements up to about 0.5 Å. The presented potential is applicable to other sp² carbon structures.     

Superconductivity in lithium, potassium, and aluminum under extreme pressure: a first-principles study

Extreme pressure strongly affects the superconducting properties of "simple" elemental metals, such as Li, K, and Al. Pressure induces superconductivity in Li (as high as 17 K) while suppressing it in Al. We report first-principles investigations of the superconducting properties of dense Li, K, and Al based on a recently proposed, parameter-free, method. Our results show an unprecedented agreement with experiments, assess the predictive power of the method over a wide range of densities and electron-phonon couplings, and provide predictions for K, where no experiments exist so far. More importantly, our results help uncover the physics of the different behaviors of Li and Al in terms of phonon softening and Fermi surface nesting in Li.     

Performance of the constrained minimization of the total energy in density functional approximations: the electron repulsion density and potential

In the constrained minimization method of Gidopoulos and Lathiotakis [N.I. Gidopoulos, N.N. Lathiotakis, J. Chem. Phys. 136, 224109 (2012)], the Hartree exchange and correlation Kohn-Sham potential of a finite N-electron system is replaced by the electrostatic potential of an effective charge density that is everywhere positive and integrates to a charge of N ? 1 electrons. The optimal effective charge density (electron repulsion density, ρ_rep) and the corresponding optimal effective potential (electron repulsion potential v_rep) are obtained by minimizing the electronic total energy in any density functional approximation. The two constraints are sufficient to remove the self-interaction errors from v_rep, correcting its asymptotic behavior at large distances from the system. In the present work, we describe, in complete detail, the constrained minimization method, including recent refinements. We also assess its performance in removing the self-interaction errors for three popular density functional approximations, namely LDA, PBE and B3LYP, by comparing the obtained ionization energies to their experimental values for an extended set of molecules. We show that the results of the constrained minimizations are almost independent of the specific approximation with average percentage errors 15%, 14%, 13% for the above DFAs respectively. These errors are substantially smaller than the corresponding errors of the plain (unconstrained) Kohn-Sham calculations at 38%, 39% and 27% respectively. Finally, we showed that this method correctly predicts negative values for the HOMO energies of several anions.     

Fractional spin in reduced density-matrix functional theory

We study the behavior of different functionals of the one-body reduced density matrix (1RDM) for systems with fractional z-component of the total spin. We define these systems as ensembles of integer spin states. It is shown that, similarly to density functional theory, the error in the dissociation of diatomic molecules is directly related to the deviation from constancy of the atomic total energies as functions of the fractional spin. However, several functionals of the 1RDM show a size inconsistency which leads to additional errors. We also investigate the difference between a direct evaluation of the energy of an ensemble of integer-spin systems and a direct minimization of the energy of a fractional-spin system.     

Constraining density functional approximations to yield self-interaction free potentials

Self-interactions (SIs) are a major problem in density functional approximations and the source of serious divergence from experimental results. Here, we propose to optimize density functional total energies in terms of the effective local potential, under constraints for the effective potential that guarantee it is free from SI errors and consequently asymptotically correct. More specifically, we constrain the Hartree, exchange and correlation potential to be the electrostatic potential of a non-negative effective repulsive density of N - 1 electrons. In this way, the optimal effective potentials exhibit the correct asymptotic decay, resulting in significantly improved one-electron properties.