Abstract: By means of density functional theory based first-principles calculations, the structural, vibrational, and electronic properties of 1H- and 1T-phases of single-layer CaX2 (X = F, Cl, Br, or I) structures are investigated. Our results reveal that both the 1H- and 1T-phases are dynamically stable in terms of their phonon band dispersions with the latter being the energetically favorable phase for all single-layers. In both phases of single-layer CaX2 structures, significant phonon softening occurs as the atomic radius increases. In addition, each structural phase exhibits distinctive Raman active modes that enable one to characterize either the phase or the structure via Raman spectroscopy. The electronic band dispersions of single-layer CaX2 structures reveal that all structures are indirect bandgap insulators with a decrease in bandgaps from fluorite to iodide crystals. Furthermore, the calculated linear elastic constants, in-plane stiffness, and Poisson ratio indicate the ultra-soft nature of CaX2 single-layers, which is quite important for their nanoelastic applications. Overall, our study reveals that with their dynamically stable 1T- and 1H-phases, single-layers of CaX2 crystals can be alternative ultra-thin insulators.

Abstract: Atomistic simulation methods for the quantification of free energies are in wide use. These methods operate by sampling the probability density of a system along a small set of suitable collective variables (CVs), which is, in turn, expressed in the form of a free energy surface (FES). This definition of the FES can capture the relative stability of metastable states but not that of the transition state because the barrier height is not invariant to the choice of CVs. Free energy barriers therefore cannot be consistently computed from the FES. Here, we present a simple approach to calculate the gauge correction necessary to eliminate this inconsistency. Using our procedure, the standard FES as well as its gauge-corrected counterpart can be obtained by reweighing the same simulated trajectory at little additional cost. We apply the method to a number of systems—a particle solvated in a Lennard-Jones fluid, a Diels–Alder reaction, and crystallization of liquid sodium—to demonstrate its ability to produce consistent free energy barriers that correctly capture the kinetics of chemical or physical transformations, and discuss the additional demands it puts on the chosen CVs. Because the FES can be converged at relatively short (sub-ns) time scales, a free energy-based description of reaction kinetics is a particularly attractive option to study chemical processes at more expensive quantum mechanical levels of theory.

Abstract: In order to increase the accuracy of the linearized augmented plane wave (LAPW) method, we present a new approach where the plane wave basis function is augmented by two different atomic radial components constructed at two different linearization energies corresponding to two different electron bands (or energy windows). We demonstrate that this case can be reduced to the standard treatment within the LAPW paradigm where the usual basis set is enriched by the basis functions of the tight binding type, which go to zero with zero derivative at the sphere boundary. We show that the task is closely related with the problem of extended core states which is currently solved by applying the LAPW method with local orbitals (LAPW+LO). In comparison with LAPW+LO, the number of supplemented basis functions in our approach is doubled, which opens up a new channel for the extension of the LAPW and LAPW+LO basis sets. The appearance of new supplemented basis functions absent in the LAPW+LO treatment is closely related with the existence of the ul-component in the canonical LAPW method. We discuss properties of additional tight binding basis functions and apply the extended basis set for computation of electron energy bands of lanthanum (face and body centered structures) and hexagonal close packed lattice of cadmium. We demonstrate that the new treatment gives lower total energies in comparison with both canonical LAPW and LAPW+LO, with the energy difference more pronounced for intermediate and poor LAPW basis sets.