Self-consistent DFT+U method for real-space time-dependent density functional theory calculations

We implemented various DFT+U schemes, including the ACBN0 self-consistent density-functional version of the DFT+U method [Phys. Rev. X 5, 011006 (2015)] within the massively parallel real-space time-dependent density functional theory (TDDFT) code Octopus. We further extended the method to the case of the calculation of response functions with real-time TDDFT+U and to the description of non-collinear spin systems. The implementation is tested by investigating the ground-state and optical properties of various transition metal oxides, bulk topological insulators, and molecules. Our results are found to be in good agreement with previously published results for both the electronic band structure and structural properties. The self consistent calculated values of U and J are also in good agreement with the values commonly used in the literature. We found that the time-dependent extension of the self-consistent DFT+U method yields improved optical properties when compared to the empirical TDDFT+U scheme. This work thus opens a different theoretical framework to address the non equilibrium properties of correlated systems

On the use of Neumann's principle for the calculation of the polarizability tensor of nanostructures

The polarizability measures how the system responds to an applied electrical field. Computationally, there are many different ways to evaluate this tensorial quantity, some of which rely on the explicit use of the external perturbation and require several individual calculations to obtain the full tensor. In this work, we present some considerations about symmetry that allow us to take full advantage of Neumann's principle and decrease the number of calculations required by these methods. We illustrate the approach with two examples, the use of the symmetries in real space and in spin space in the calculation of the electrical or the spin response.Comment: 7 pages, 5 figures, accepted for publication in the Journal of Nanoscience and Nanotechnolog

Generating relativistic pseudo-potentials with explicit incorporation of semi-core states using APE, the Atomic Pseudo-potentials Engine

We present a computer package designed to generate and test norm-conserving pseudo-potentials within Density Functional Theory. The generated pseudo-potentials can be either non-relativistic, scalar relativistic or fully relativistic and can explicitly include semi-core states. A wide range of exchange-correlation functionals is included.Program summaryhttp://www.sciencedirect.com/science/article/B6TJ5-4R7J89B-3/1/539d407a3f8f5790a3d31b2c8baa5ff

Density-based mixing parameter for hybrid functionals

A very popular ab-initio scheme to calculate electronic properties in solids is the use of hybrid functionals in density functional theory (DFT) that mixes a portion of Fock exchange with DFT functionals. In spite of their success, a major problem still remains, related to the use of one single mixing parameter for all materials. Guided by physical arguments that connect the mixing parameter to the dielectric properties of the solid, and ultimately to its band gap, we propose a method to calculate this parameter from the electronic density alone. This method is able to cut significantly the error of traditional hybrid functionals for large and small gap materials, while retaining a good description of structural properties. Moreover, its implementation is simple and leads to a negligible increase of the computational time.Comment: submitte

Accuracy of generalized gradient approximation functionals for density functional perturbation theory calculations

We assess the validity of various exchange-correlation functionals for computing the structural, vibrational, dielectric, and thermodynamical properties of materials in the framework of density-functional perturbation theory (DFPT). We consider five generalized-gradient approximation (GGA) functionals (PBE, PBEsol, WC, AM05, and HTBS) as well as the local density approximation (LDA) functional. We investigate a wide variety of materials including a semiconductor (silicon), a metal (copper), and various insulators (SiO$_2$ $\alpha$-quartz and stishovite, ZrSiO$_4$ zircon, and MgO periclase). For the structural properties, we find that PBEsol and WC are the closest to the experiments and AM05 performs only slightly worse. All three functionals actually improve over LDA and PBE in contrast with HTBS, which is shown to fail dramatically for $\alpha$-quartz. For the vibrational and thermodynamical properties, LDA performs surprisingly very good. In the majority of the test cases, it outperforms PBE significantly and also the WC, PBEsol and AM05 functionals though by a smaller margin (and to the detriment of structural parameters). On the other hand, HTBS performs also poorly for vibrational quantities. For the dielectric properties, none of the functionals can be put forward. They all (i) fail to reproduce the electronic dielectric constant due to the well-known band gap problem and (ii) tend to overestimate the oscillator strengths (and hence the static dielectric constant)

Band widths and gaps from the Tran-Blaha functional : Comparison with many-body perturbation theory

For a set of ten crystalline materials (oxides and semiconductors), we compute the electronic band structures using the Tran-Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TB09) functional. The band widths and gaps are compared with those from the local-density approximation (LDA) functional, many-body perturbation theory (MBPT), and experiments. At the density-functional theory (DFT) level, TB09 leads to band gaps in much better agreement with experiments than LDA. However, we observe that it globally underestimates, often strongly, the valence (and conduction) band widths (more than LDA). MBPT corrections are calculated starting from both LDA and TB09 eigenenergies and wavefunctions. They lead to a much better agreement with experimental data for band widths. The band gaps obtained starting from TB09 are close to those from quasi-particle self-consistent GW calculations, at a much reduced cost. Finally, we explore the possibility to tune one of the semi-empirical parameters of the TB09 functional in order to obtain simultaneously better band gaps and widths. We find that these requirements are conflicting.Comment: 18 pages, 16 figure

Hybrid adaptive control of a dragonfly model

Dragonflies show unique and superior flight performances than most of other insect species and birds. They are equipped with two pairs of independently controlled wings granting an unmatchable flying performance and robustness. In this paper, it is presented an adaptive scheme controlling a nonlinear model inspired in a dragonfly-like robot. It is proposed a hybrid adaptive (HA) law for adjusting the parameters analyzing the tracking error. At the current stage of the project it is considered essential the development of computational simulation models based in the dynamics to test whether strategies or algorithms of control, parts of the system (such as different wing configurations, tail) as well as the complete system. The performance analysis proves the superiority of the HA law over the direct adaptive (DA) method in terms of faster and improved tracking and parameter convergence

Some Bryozoa species recently introduced into the Azores: reproductive strategies as a proxy for further spread

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