Cloud-resolving model simulations with one- and two-way couplings via the weak temperature gradient approximation

A cloud-resolving model is modified to implement the weak temperature gradient approximation in order to simulate the interactions between tropical convection and the large-scale tropical circulation. The instantaneous domain-mean potential temperature is relaxed toward a reference profile obtained from a radiative–convective equilibrium simulation of the cloud-resolving model. For homogeneous surface conditions, the model state at equilibrium is a large-scale circulation with its descending branch in the simulated column. This is similar to the equilibrium state found in some other studies, but not all. For this model, the development of such a circulation is insensitive to the relaxation profile and the initial conditions. Two columns of the cloud-resolving model are fully coupled by relaxing the instantaneous domain-mean potential temperature in both columns toward each other. This configuration is energetically closed in contrast to the reference-column configuration. No mean large-scale circulation develops over homogeneous surface conditions, regardless of the relative area of the two columns. The sensitivity to nonuniform surface conditions is similar to that obtained in the reference-column configuration if the two simulated columns have very different areas, but it is markedly weaker for columns of comparable area. The weaker sensitivity can be understood as being a consequence of a formulation for which the energy budget is closed. The reference-column configuration has been used to study the convection in a local region under the influence of a large-scale circulation. The extension to a two-column configuration is proposed as a methodology for studying the influence on local convection of changes in remote convection.

LDA or GGA? A combined experimental inelastic neutron scattering and ab initio lattice dynamics study of alkali metal hydrides

In a previous work, we carried out inelastic neutron scattering (INS) spectroscopy experiments and preliminary first principles calculations on alkali metal hydrides. The complete series of alkali metal hydrides, LiH, NaH, KH, RbH and CsH was measured in the high-resolution TOSCA INS spectrometer at ISIS. Here, we present the results of ab initio electronic structure calculations of the properties of the alkali metal hydrides using both the local density approximation (LDA) and the generalized gradient approximation (GGA), using the Perdew–Burke–Ernzerhof (PBE) parameterization. Properties calculated were lattice parameters, bulk moduli, dielectric constants, effective charges, electronic densities and inelastic neutron scattering (INS) spectra. We took advantage of the currently available computer power to use full lattice dynamics theory to calculate thermodynamic properties for these materials. For the alkali metal hydrides (LiH, NaH, KH, RbH and CsH) using lattice dynamics, we found that the INS spectra calculated using LDA agreed better with the experimental data than the spectra calculated using GGA. Both zero-point effects and thermal contributions to free energies had an important effect on INS and several thermodynamic properties.

The vibrational spectrum and ultimate modulus of polyethylene

We have performed the first completely ab initio lattice dynamics calculation of the full orthorhombic cell of polyethylene using periodic density functional theory in the local density approximation (LDA) and the generalized gradient approximation (GGA). Contrary to current perceptions, we show that LDA accurately describes the structure whereas GGA fails. We emphasize that there is no parametrization of the results. We then rigorously tested our calculation by computing the phonon dispersion curves across the entire Brillouin zone and comparing them to the vibrational spectra, in particular the inelastic neutron scattering (INS) spectra, of polyethylene (both polycrystalline and aligned) and perdeuteriopolyethylene. The F-point frequencies (where the infrared and Raman active modes occur) are in good agreement with the latest low temperature data. The near-perfect reproduction of the INS spectra, gives confidence in the results and allows Lis to deduce a number of physical properties including the elastic moduli, parallel and perpendicular to the chain. We find that the Young's modulus for an infinitely long, perfectly crystalline polyethylene is 360.2 GPa at 0 K. The highest experimental value is 324 GPa, indicating that current high modulus fibers are similar to 90% of their maximum possible strength.

Adsorption of organic molecules at the TiO2(110) surface: the effect of van der Waals interactions

Understanding the interaction of organic molecules with TiO2 surfaces is important for a wide range of technological applications. While density functional theory (DFT) calculations can provide valuable insight about these interactions, traditional DFT approaches with local exchange-correlation functionals suffer from a poor description of non-bonding van der Waals (vdW) interactions. We examine here the contribution of vdW forces to the interaction of small organic molecules (methane, methanol, formic acid and glycine) with the TiO2 (110) surface, based on DFT calculations with the optB88-vdW functional. The adsorption geometries and energies at different configurations were also obtained in the standard generalized gradient approximation (GGA-PBE) for comparison. We find that the optB88-vdW consistently gives shorter surface adsorbate-to-surface distances and slightly stronger interactions than PBE for the weak (physisorbed) modes of adsorption. In the case of strongly adsorbed (chemisorbed) molecules both functionals give similar results for the adsorption geometries, and also similar values of the relative energies between different chemisorption modes for each molecule. In particular both functionals predict that dissociative adsorption is more favourable than molecular adsorption for methanol, formic acid and glycine, in general agreement with experiment. The dissociation energies obtained from both functionals are also very similar, indicating that vdW interactions do not affect the thermodynamics of surface deprotonation. However, the optB88-vdW always predicts stronger adsorption than PBE. The comparison of the methanol adsorption energies with values obtained from a Redhead analysis of temperature programmed desorption data suggests that optB88-vdW significantly overestimates the adsorption strength, although we warn about the uncertainties involved in such comparisons.

The importance of anisotropic Coulomb interaction in LaMnO3

In low-temperature anti-ferromagnetic LaMnO3, strong and localized electronic interactions among Mn 3d electrons prevent a satisfactory description from standard local density and generalized gradient approximations in density functional theory calculations. Here we show that the strong on-site electronic interactions are described well only by using direct and exchange corrections to the intra-orbital Coulomb potential. Only DFT+U calculations with explicit exchange corrections produce a balanced picture of electronic, magnetic and structural observables in agreement with experiment. To understand the reason, a rewriting of the functional form of the +U corrections is presented that leads to a more physical and transparent understanding of the effect of these correction terms. The approach highlights the importance of Hund’s coupling (intra-orbital exchange) in providing anisotropy across the occupation and energy eigenvalues of the Mn d states. This intra-orbital exchange is the key to fully activating the Jahn-Teller distortion, reproducing the experimental band gap and stabilizing the correct magnetic ground state in LaMnO3. The best parameter values for LaMnO3 within the DFT(PBEsol)+U framework are determined to be U = 8 eV and J = 1.9 eV.

Plane wave approximation of homogeneous Helmholtz solutions

In this paper, we study the approximation of solutions of the homogeneous Helmholtz equation Δu + ω 2 u = 0 by linear combinations of plane waves with different directions. We combine approximation estimates for homogeneous Helmholtz solutions by generalized harmonic polynomials, obtained from Vekua’s theory, with estimates for the approximation of generalized harmonic polynomials by plane waves. The latter is the focus of this paper. We establish best approximation error estimates in Sobolev norms, which are explicit in terms of the degree of the generalized polynomial to be approximated, the domain size, and the number of plane waves used in the approximations.