Electronic currents and Born-Oppenheimer molecular dynamics

Born-Oppenheimer variable separation is the mainstay of studies of chemical reactivity and dynamics. A long-standing problem of this ansatz is the absence of electronic currents in a system undergoing dynamics. I analyze the physical origin of the "missing" electronic currents in Born-Oppenheimer wavefunctions. By examining the problem within the multi-state Born-Huang ansatz, I demonstrate that electronic currents arise from the first-order non-adiabatic coupling to electronically excited states. I derive two expressions for the electronic currents induced by nuclear motion. The sum-over-the-states formula, identical to the result of "complete adiabatic" treatment of Nafie [J. Chem. Phys. 79, 4950 (1983)] leads to a transparent and intuitive physical picture of the induced currents, but is unsuitable for practical implementation in all but the simplest systems. The equivalent expression in terms of the electronic energy derivatives is straightforward to implement numerically. I present first applications of this approach to small systems of potential chemical interest.     

Radical Impurity Mechanisms for Helium Incorporation into Buckminsterfullerene

Radical impurity mechanisms for incorporating He into C₆₀ have been examined by semiempirical (MNDO) and density functional (BLYP/3-21G) calculations. The key step in these mechanisms is the insertion of He into C₆₀X or C₆₀X₂ intermediates generated by adding the impurity X to C₆₀ (X = H, Me in our model study). Contrary to C_60. several window-type structures with one broken C,C bond exist as local minima on the MNDO potential surfaces of C₆₀X and C₆₀X₂, but they are mechanistically irrelevant due to extremely facile ring closure. Effective activation barriers for the penetration of He through intact hexagons and various windows are reported for 65 different pathways in C₆₀X and C₆₀X₂. Window-type transition states are stabilized significantly when there is a C? X bond involving a C-atom from the broken C,C bond. The corresponding barriers in C₆₀X and C₆₀X₂ are much lower than in C₆₀, This provides some theoretical support for the suggested impurity mechanisms even though the computed barriers for X = H, Me are still higher than indicated by the experiment (X unknown).     

One‐level Newton–Krylov–Schwarz algorithm for unsteady non‐linear radiation diffusion problem

In this paper, we present a parallel Newton–Krylov–Schwarz (NKS)‐based non‐linearly implicit algorithm for the numerical solution of the unsteady non‐linear multimaterial radiation diffusion problem in two‐dimensional space. A robust solver technology is required for handling the high non‐linearity and large jumps in material coefficients typically associated with simulations of radiation diffusion phenomena. We show numerically that NKS converges well even with rather large inflow flux boundary conditions. We observe that the approach is non‐linearly scalable, but not linearly scalable in terms of iteration numbers. However, CPU time is more important than the iteration numbers, and our numerical experiments show that the algorithm is CPU‐time‐scalable even without a coarse space given that the mesh is fine enough. This makes the algorithm potentially more attractive than multilevel methods, especially on unstructured grids, where course grids are often not easy to construct. Copyright © 2004 John Wiley & Sons, Ltd.     

Modeling of dynamics of field-induced transformations in charge density waves

We present a modeling of stationary states and their transient dynamic for charge density waves in restricted geometries of realistic junctions under the applied voltage or the passing current. The model takes into account multiple fields in mutual nonlinear interactions: the amplitude and the phase of the charge density wave complex order parameter, distributions of the electric field, the density and the current of normal carriers. The results show that stationary states with dislocations are formed after an initial turbulent multi-vortex process. Static dislocations multiply stepwise when the voltage across or the current through the junction exceed a threshold. The dislocation core forms a charge dipole which concentrates a steep drop of the voltage, thus working as a self-tuned microscopic tunnelling junction. That can gives rise to features observed in experiments on the inter-layer tunneling in mesa-junctions.     

Photoemission and near-edge X-ray absorption fine structure studies of the bacterial surface protein layer of Bacillus sphaericus NCTC 9602

The electronic structure of the regular, two-dimensional bacterial surface protein layer of Bacillus sphaericus NCTC 9602 has been examined by photoemission (PE) and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy. Both the O 1s and the N 1s core-level PE spectra show a single structure, whereas the C 1s core-level spectrum appears manifold, suggesting similar chemical states for each oxygen atom and also for each nitrogen atom, while carbon atoms exhibit a range of chemical environments in the different functional groups of the amino acids. This result is supported by the element-specific NEXAFS spectra of the unoccupied valence electronic states, which exhibit a series of characteristic NEXAFS peaks that can be assigned to particular molecular orbitals of the amino acids by applying a phenomenological building-block model. The relative contributions of the C-O, C-N, and C-C bond originating signals into the C 1s PE spectrum are in good agreement with the number ratios of the corresponding bonds calculated from the known primary structure of the bacterial surface protein. First interpretation of the PE spectrum of the occupied valence states is achieved on the basis of electronic density-of-states calculations performed for small peptides. It was found that mainly the pi clouds of the aromatic rings contribute to both the lowest unoccupied and the highest occupied molecular orbitals.     

Exchange interactions in the three phases of vanadyl pyrophosphate (VO)(2)P(2)O(7)

The magnetic exchange constants of vanadyl pyrophosphate (VO)(2)P(2)O(7) have been calculated on the basis of a combined DFT/broken symmetry approach. The three reported phases, ambient-pressure orthorhombic, ambient-pressure monoclinic, and high-pressure orthorhombic, have been explicitly considered. Calculations have been performed on four types of model clusters extracted from the crystal lattices. The singularity of each phase is clearly reflected through the number and values of exchange parameters. Our results show that the exchange interactions can be described in first approximation within the alternating antiferromagnetic chain model. The largest exchange coupling along the chain occurs through O-P-O bridges. The interchain interactions are much weaker and are of ferromagnetic nature.     

Harmonization and homogenization on fractals

This paper suggests a direct approach to define the Laplacian, the spectral dimension of nested fractals and the pre-Sierpinski carpet conductivity. We find a geometric construction of the harmonic functions on the gasket and therefore can describe effectively the dense set of functions having finite energy. The paper is mostly aimed at the homogenization on the pre-Sierpinski gasket, whose horizontal and nonhorizontal bonds have different conductivities:a andb respectively. We prove the -convergence of the rescaled energies on the pre-Sierpinski gasket to (a, b), where is the standard energy on the gasket with uniform conductivities. We also find an explicit expression for the effective conductivity (a, b) and deduce that its set of singularities turns out to be the Julia set of a certain rational function. A special section is devoted to the problem of the pre-Sierpinski carpet conductivity asymptotic behavior; for this problem a new proof of Barlow-Bass inequalities with sharper constants is given.     

On two questions about circular choosability

We answer two questions of Zhu on circular choosability of graphs. We show that the circular list chromatic number of an even cycle is equal to 2 and give an example of a graph for which the infimum in the definition of the circular list chromatic number is not attained. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:261‐269, 2008