Site symmetry dependence of repulsive interactions between chemisorbed oxygen atoms on Pt{100}-(1×1)

[[abstract]]Ab initio total energy calculations using density functional theory with the generalized gradient approximation have been performed for the chemisorption of oxygen atoms on a Pt$100%-~131! slab. Binding energies for the adsorption of oxygen on different high-symmetry sites are presented. The bridge site is the most stable at a coverage of 0.5 ML, followed by the fourfold hollow site. The atop site is the least stable. This finding is rationalized by analyzing the ‘‘local structures’’ formed upon oxygen chemisorption. The binding energies and heats of adsorption at different oxygen coverages show that pairwise repulsive interactions are considerably stronger between oxygen atoms occupying fourfold sites than those occupying bridge sites. Analysis of the partial charge densities associated with Bloch states demonstrates that the O–Pt bond is considerably more localized at the bridge site. These effects cause a sharp drop in the heats of adsorption for oxygen on hollow sites when the coverage is increased from 0.25 to 0.5 ML. Mixing between oxygen p orbitals and Pt d orbitals can be observed over the whole metal d-band energy range.[[notice]]補正完畢[[journaltype]]國內[[booktype]]紙

Variational formulas of higher order mean curvatures

In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total $2p$-th mean curvature functional $\mathcal {M}_{2p}$ of a submanifold $M^n$ in a general Riemannian manifold $N^{n+m}$ for $p=0,1,...,[\frac{n}{2}]$. As an example, we prove that closed complex submanifolds in complex projective spaces are critical points of the functional $\mathcal {M}_{2p}$, called relatively $2p$-minimal submanifolds, for all $p$. At last, we discuss the relations between relatively $2p$-minimal submanifolds and austere submanifolds in real space forms, as well as a special variational problem.Comment: 13 pages, to appear in SCIENCE CHINA Mathematics 201

Application of Instantons: Quenching of Macroscopic Quantum Coherence and Macroscopic Fermi-Particle Configurations

Starting from the coherent state representation of the evolution operator with the help of the path-integral, we derive a formula for the low-lying levels $E = \epsilon_0 - 2\triangle\epsilon cos (s+\xi)\pi$ of a quantum spin system. The quenching of macroscopic quantum coherence is understood as the vanishing of $cos (s+\xi)\pi$ in disagreement with the suppression of tunneling (i.e. $\triangle\epsilon = 0$) as claimed in the literature. A new configuration called the macroscopic Fermi-particle is suggested by the character of its wave function. The tunneling rate ($(2\triangle\epsilon)/(\pi)$) does not vanish, not for integer spin s nor for a half-integer value of s, and is calculated explicitly (for the position dependent mass) up to the one-loop approximation.Comment: 13 pages, LaTex, no figure