Electrostatics in Periodic Slab Geometries I

We propose a new method to sum up electrostatic interactions in 2D slab geometries. It consists of a combination of two recently proposed methods, the 3D Ewald variant of Yeh and Berkowitz, J. Chem. Phys. 111 (1999) 3155, and the purely 2D method MMM2D by Arnold and Holm, to appear in Chem. Phys. Lett. 2002. The basic idea involves two steps. First we use a three dimensional summation method whose summation order is changed to sum up the interactions in a slab-wise fashion. Second we subtract the unwanted interactions with the replicated layers analytically. The resulting method has full control over the introduced errors. The time to evaluate the layer correction term scales linearly with the number of charges, so that the full method scales like an ordinary 3D Ewald method, with an almost linear scaling in a mesh based implementation. In this paper we will introduce the basic ideas, derive the layer correction term and numerically verify our analytical results.Comment: 10 pages, 7 figure

Electrostatics in Periodic Slab Geometries II

In a previous paper a method was developed to subtract the interactions due to periodically replicated charges (or other long-range entities) in one spatial dimension. The method constitutes a generalized "electrostatic layer correction" (ELC) which adapts any standard 3D summation method to slab-like conditions. Here the implementation of the layer correction is considered in detail for the standard Ewald (EW3DLC) and the PPPM mesh Ewald (PPPMLC) methods. In particular this method offers a strong control on the accuracy and an improved computational complexity of O(N log N) for mesh-based implementations. We derive anisotropic Ewald error formulas and give some fundamental guidelines for optimization. A demonstration of the accuracy, error formulas and computation times for typical systems is also presented.Comment: 14 pages, 7 figure

Bilayer Edge and Curvature Effects on Partitioning of Lipids by Tail Length: Atomistic Simulations

The partitioning of lipids among different microenvironments in a bilayer is of considerable relevance to characterization of composition variations in biomembranes. Atomistic simulation has been ill-suited to model equilibrated lipid mixtures because the time required for diffusive exchange of lipids among microenvironments exceeds typical submicrosecond molecular dynamics trajectories. A method to facilitate local composition fluctuations, using Monte Carlo mutations to change lipid structures within the semigrand-canonical ensemble (at a fixed difference in component chemical potentials, Δμ), was recently implemented to address this challenge. This technique was applied here to mixtures of dimyristoylphosphatidylcholine and a shorter-tail lipid, either symmetric (didecanoylphosphatidylcholine (DDPC)) or asymmetric (hexanoyl-myristoylphosphatidylcholine), arranged in two types of structure: bilayer ribbons and buckled bilayers. In ribbons, the shorter-tail component showed a clear enrichment at the highly curved rim, more so for hexanoyl-myristoylphosphatidylcholine than for DDPC. Results on buckled bilayers were variable. Overall, the DDPC content of buckled bilayers tended to exceed by several percent the DDPC content of flat ones simulated at the same Δμ, but only for mixtures with low overall DDPC content. Within the buckled bilayer structure, no correlation could be resolved between the sign or magnitude of the local curvature of a leaflet and the mean local lipid composition. Results are discussed in terms of packing constraints, surface area/volume ratios, and curvature elasticity

Structure of Mo₂C_<i>x</i> and Mo₄C_<i>x</i> Molybdenum Carbide Nanoparticles and Their Anchoring Sites on ZSM‑5 Zeolites

Mo carbide nanoparticles supported on ZSM-5 zeolites are promising catalysts for methane dehydroaromatization. For this and other applications, it is important to identify the structure and anchoring sites of Mo carbide nanoparticles. In this work, structures of Mo₂C_<i>x</i> (<i>x</i> = 1, 2, 3, 4, and 6) and Mo₄C_<i>x</i> (<i>x</i> = 2, 4, 6, and 8) nanoparticles are identified using a genetic algorithm with density functional theory (DFT) calculations. The ZSM-5 anchoring sites are determined by evaluating infrared vibrational spectra for surface OH groups before and after Mo deposition. The spectroscopic results demonstrate that initial Mo oxide species preferentially anchors on framework Al sites and partially on Si sites on the external surface of the zeolite. In addition, Mo oxide deposition causes some dealumination, and a small fraction of Mo oxide species anchor on extraframework Al sites. Anchoring modes of Mo carbide nanoparticles are evaluated with DFT cluster calculations and with hybrid quantum mechanical and molecular mechanical (QM/MM) periodic structure calculations. Calculation results suggest that binding through two Mo atoms is energetically preferable for all Mo carbide nanoparticles on double Al-atom framework sites and external Si sites. On single Al-atom framework sites, the preferential binding mode depends on the particle composition. The calculations also suggest that Mo carbide nanoparticles with a C/Mo ratio greater than 1.5 are more stable on external Si sites and, thus, likely to migrate from zeolite pores onto the external surface of the zeolite. Therefore, in order to minimize such migration, the C/Mo ratio for zeolite-supported Mo carbide nanoparticles under hydrocarbon reaction conditions should be maintained below 1.5