We study the edge magnetization and the local density of states of chiral graphene nanoribbons using a π-orbital Hubbard model in the mean-field approximation. We show that the inclusion of a realistic next-nearest hopping term in the tight-binding Hamiltonian changes the graphene nanoribbons band structure significantly and affects its magnetic properties. We study the behavior of the edge magnetization upon departing from half filling as a function of the nanoribbon chirality and width. We find that the edge magnetization depends very weakly in the nanoribbon width, regardless of chirality as long as the ribbon is sufficiently wide. We compare our results to recent scanning tunneling microscopy experiments reporting signatures of magnetic ordering in chiral nanoribbons and provide an interpretation for the observed peaks in the local density of states, that does not depend on the antiferromagnetic interedge interaction.

Understanding the molecular stability is important for predicting the relative reactivity of chemical agents and the relative yields of desirable products. However, over decades, a consistent estimate of a particular chemical equilibrium (proton-tautomerism) has proven challenging. We revisit the molecular orbital analysis in the classic tautomeric oxo-hydroxy case, i.e., 2-pyridone/2-hydroxypyridine in gas-phase and solution, (Wong et al. 1992). Our results indicate the possibility of tuning the tautomeric equilibrium through directing groups. Our findings also reveal the lack of <a></a>reproducibility of orbital energies as responsible for the remarkable contrast between the results of the wavefunction and density functional methods. Our proposal leads the correction in the estimation of relative stability in excellent agreement with experiments in gas-phase and solution. The analogous approach for different compounds corroborates the reliability of our description on the molecular stability and its potential application, e.g., a guide to estimate the relative stability of molecules, to measure the confidence of the proposed reaction mechanisms by different theoretical methods, development of the molecular switches and computer-aided drug design. A software tool for Gaussian 09 package, in the support information, is available on the author's ORCiD page.<br>

The comprehension of the molecular stability is important to predict the relative reactivity of the chemical agents and the relative yields of desirable products. However, for decades, the prediction on the proton tautomeric equilibrium by wavefunction (WF) and density functional (DFT) methods show that a quantitative agreement with the relative energy is a challenge. We revise the molecular orbital analysis in the classic tautomeric 2-pyridone/2-hydroxypyridine case, (Wong et al. 1992). Our findings reveal the unsatisfactory level of reproducibility of orbital energies as responsible<br>for the remarkable contrast between the WF and DFT results. The correction leads the estimation of the relative stability in excellent agreement with experiments. The<br>analogous approach for other tautomeric compounds corroborates the reliability of our description and its potential application, e.g., on the development of the molecular<br>switches, computer-aided drug design, and new DFT functionals. A software tool for Gaussian 09 package, in the support information, is available on the author's ORCiD page.<br>

We analyze the energy spectrum of graphene in the presence of spin-orbit coupling and a unidirectionally periodic Zeeman field, focusing on the stability and location of Dirac points it may support. It is found that the Dirac points at the K and K points are generically moved to other locations in the Brillouin zone, but that they remain present when the Zeeman field ∆(x) integrates to zero within a unit cell. A large variety of locations for the Dirac points is shown to be possible: when ∆ ẑ they are shifted from their original locations along the direction perpendicular to the superlattice axis, while realizations of ∆(x) that rotate periodically move the Dirac points to locations that can reflect the orbit of the rotating electron spin as it moves through a unit cell. When a uniform Zeeman field is applied in addition to a periodic ∆ ẑ integrating to zero, the system can be brought into a metallic, Dirac semimetal, or insulating state, depending on the direction of the uniform field. The latter is shown to be an anomalous quantum Hall insulator.

Understanding the molecular stability is important for predicting the relative reactivity of chemical agents and the relative yields of desirable products. However, over decades, a consistent estimate of a particular chemical equilibrium (proton-tautomerism) has proven challenging. We revisit the molecular orbital analysis in the classic tautomeric oxo-hydroxy case, i.e., 2-pyridone/2-hydroxypyridine in gas-phase and solution, (Wong et al. 1992). Our results indicate the possibility of tuning the tautomeric equilibrium through directing groups. Our findings also reveal the lack of <a></a>reproducibility of orbital energies as responsible for the remarkable contrast between the results of the wavefunction and density functional methods. Our proposal leads the correction in the estimation of relative stability in excellent agreement with experiments in gas-phase and solution. The analogous approach for different compounds corroborates the reliability of our description on the molecular stability and its potential application, e.g., a guide to estimate the relative stability of molecules, to measure the confidence of the proposed reaction mechanisms by different theoretical methods, development of the molecular switches and computer-aided drug design. A software tool for Gaussian 09 package, in the support information, is available on the author's ORCiD page.<br>