Abstract:
It is demonstrated that the commonly applied self interaction correction (SIC) used in density functional theory does not remove all self interaction. We present as an alternative a novel method which, by construction, is totally free from self interaction. The method has the correct asymptotic 1/r dependence. We apply the new theory to localized $f$-electrons in praseodymium and compare with the old version of SIC, the local density approximation (LDA) and with an atomic Hartree-Fock calculation. The results show a lowering of the $f$ level, a contraction of the $f$ electron cloud and a lowering of the total energy by 13 eV per 4\f electron compared to LDA. The equilibrium volume of the new SIC method is close to the ones given by LDA and the older SIC method, and is in good agreement with experiment. The experimental cohesive energy is in better agreement using the new SIC method, both compared to LDA and another SIC method.

Abstract:
In this paper we review, and elaborate on, the literature on a regression artifact related to Lord’s paradox in a continuous setting. Specifically, the question is whether a continuous property of individuals predicts improvement from training between a pretest and a posttest. If the pretest score is included as a covariate, regression to the mean will lead to biased results if two critical conditions are satisfied: (1) the property is correlated with pretest scores and (2) pretest scores include random errors. We discuss how these conditions apply to the analysis in a published experimental study, the authors of which concluded that linearity of children’s estimations of numerical magnitudes predicts arithmetic learning from a training program. However, the two critical conditions were clearly met in that study. In a reanalysis we find that the bias in the method can fully account for the effect found in the original study. In other words, data are consistent with the null hypothesis that numerical magnitude estimations are unrelated to arithmetic learning.

Abstract:
First-principles electronic structure calculations have been performed for the double perovskite Bi$_2$CoMnO$_6$ in its non-centrosymmetric polar state using generalized gradient approximation plus Hubbard U approach. We find that while Co is in a high spin state, Mn is in an intermediate spin state. The calculated dynamical charge tensors are anisotropic reflecting a low-symmetry structure of the compound. Magnetic structure dependent phonon frequencies indicate the presence of spin-phonon coupling. Using Berry phase method, we obtain a spontaneous electronic polarization of 5.88 ${\mu}C/cm^2$ which is close to the experimental value observed for a similar compound, Bi$_2$NiMnO$_6$.

Abstract:
The theory of correlated electron systems is formulated in a form which allows to use as a reference point an ab initio band structure theory (AIBST). The theory is constructed in two steps. As a first step the total Hamiltonian is transformed into a correlated form. In order to elucidate the microscopical origin of the parameters of the periodical Hubbard-Anderson model (PHAM) the terms of the full Hamiltonian which have the operator structure of PHAM are separated. It is found that the matrix element of mixing interaction includes ion-configuration and number-of-particles dependent contributions from the Coulomb interaction. In a second step the diagram technique (DT) is developed by means of generalization of the Baym-Kadanoff method for correlated systems.

Abstract:
A monolayer of graphene irradiated with circularly polarized light suggests a unique platform for surface electromagnetic wave (plasmon-polariton) manipulation. In fact, the time periodicity of the Hamiltonian leads to a geometric Aharonov-Anandan phase and results in a photovoltaic Hall effect in graphene, creating off-diagonal components of the conductivity tensor. The latter drastically changes the dispersion relation of surface plasmon-polaritons, leading to hybrid wave generation. In this paper we present a systematic and self-contained analysis of the hybrid surface waves obtained from Maxwell equations based on a microscopic formula for the conductivity. We consider a practical example of graphene sandwiched between two dielectric media and show that in the one-photon approximation there is formation of propagating hybrid surface waves. From this analysis emerges the possibility of a reliable experimental realization to study Zitterbewegung of charge carriers of graphene.

Abstract:
We have investigated theoretically the adsorption of molecules onto graphene with divacancy defects. Using ab-initio density functional calculations, we have found that O2, CO, N2, B2 and H2O molecules all interact strongly with a divacancy in a graphene layer. Along with a complex geometry of the molecule-graphene bonding, metallic behavior of the graphene layer in presence of CO and N2 molecules have been found with a large density of states in the vicinity of the Fermi level suggesting an increase in the conductivity. The adsorption of N2 is particularly interesting since the N atoms dissociate in the vicinity of the defects, and take the place where the missing C atoms of the divacancy used to sit. In this way, the defected graphene structure is healed geometrically, and at the same time doped with electron states.

Abstract:
Lattice dynamical methods used to predict phase-transformations in crystals typically evaluate the harmonic phonon spectra and therefore do not work in frequent and important situations where the crystal structure is unstable in the harmonic approximation, such as the $\beta$ structure when it appears as a high-temperature phase of the shape memory alloy (SMA) NiTi. Here it is shown by self consistent {\it ab initio} lattice dynamical calculations (SCAILD) that the critical temperature for the pre-martensitic $R$ to $\beta$ phase-transformation in NiTi can be effectively calculated with good accuracy, and that the $\beta$-phase is a result primarily of the stabilizing interaction between different lattice vibrations.

Abstract:
We have performed density functional calculations as well as employed a tight-binding theory, to study the effect of passivation of zigzag graphene nanoribbons (ZGNR) by Hydrogen. We show that each edge C atom bonded with 2 H atoms open up a gap and destroys magnetism for small widths of the nanoribbon. However, a re-entrant magnetism accompanied by a metallic electronic structure is observed from 8 rows and thicker nanoribbons. The electronic structure and magnetic state are quite complex for this type of termination, with sp$^3$ bonded edge atoms being non-magnetic, whereas the nearest neighboring atoms are metallic and magnetic. We have also evaluated the phase stability of several thicknesses of ZGNR, and demonstrate that sp$^3$ bonded edge atoms, with 2 H atoms at the edge, should be stable at temperatures and pressures which are reachable in a laboratory environment.

Abstract:
Tailor-made magnetic nanostructures offer a variety of functionalities useful for technological applications. In this work, we explore the possibilities of realizing Fe nanostructures at the interfaces of 2D graphene and h-BN by ab initio density functional calculations. With the aid of ab initio Born-Oppenheimer molecular dynamics simulations and diffusion barriers calculated by nudged elastic band method, we find that (i) diffusion barriers of Fe on BN are much smaller than those on graphene, (ii) the Fe adatoms form clusters within a short time interval (~2.1 ps) and (iii) Fe clusters diffuse easily across the C-N interface but become immobile at the C-B interface. The calculated magnetic exchange coupling between Fe clusters at C-B interfaces varies non-monotonically as a function of the width of BN separating the graphene parts. One may envisage design of magnetic nanostructures at the C-B interface of 2D graphene/h-BN hybrids to realize interesting applications related to spintronics.

Abstract:
Lattice dynamical methods used to predict phase transformations in crystals typically deal with harmonic phonon spectra and are therefore not applicable in important situations where one of the competing crystal structures is unstable in the harmonic approximation, such as the bcc structure involved in the hcp to bcc martensitic phase transformation in Ti, Zr and Hf. Here we present an expression for the free energy that does not suffer from such shortcomings, and we show by self consistent {\it ab initio} lattice dynamical calculations (SCAILD), that the critical temperature for the hcp to bcc phase transformation in Ti, Zr and Hf, can be effectively calculated from the free energy difference between the two phases. This opens up the possibility to study quantitatively, from first principles theory, temperature induced phase transitions.