Effective Hamiltonian for femtosecond vibrational dynamics

Time propagation of zero-order states of an effective spectroscopic Hamiltonian is tested against femtosecond time dependent dynamics of adiabatic wavepackets evolving on a model potential energy surface for two coupled modes of the radical HO(2) with multiple potential wells and above barrier motion. A generalized Hamiltonian which breaks the usual conserved polyad action by including extra resonance couplings (V(2:1) and V(3:1)) successfully describes the time evolution after the further addition of two "ultrafast" couplings. These new couplings are a nonresonant coupling a(1)a(2)+a(1)(?)a(2)(?) and a resonant coupling V(1:1) that functions as an ultrafast term because the system is far from 1:1 frequency resonance.     

Correlation diagram for rigid and nonrigid three-body systems

We consider the relation between energy level patterns of rigid structures and those of systems in which the particle motions are uncorrelated. Defining an ideal model system of the non-rigid limit for N identical particles, we exhibit the correlation diagram connecting this limit to an ideal rigid system for N = 3. States of the two limits are related in a simple manner. Vibration-rotation levels for three identical spin-0 and spin-1/2 particles are classified explicitly, according to their quantum numbers in both limits.     

Visualizing the zero order basis of the spectroscopic Hamiltonian

Recent works have shown that a generalization of the spectroscopic effective Hamiltonian can describe spectra in surprising regions, such as isomerization barriers. In this work, we seek to explain why the effective Hamiltonian is successful where there was reason to doubt that it would work at all. All spectroscopic Hamiltonians have an underlying abstract zero-order basis (ZOB) which is the "ideal" basis for a given form and parameterization of the Hamiltonian. Without a physical model there is no way to transform this abstract basis into a coordinate representation. To this end, we present a method of obtaining the coordinate space representation of the abstract ZOB of a spectroscopic effective Hamiltonian. This method works equally well for generalized effective Hamiltonians that encompass above-barrier multiwell behavior, and standard effective Hamiltonians for the vicinity of a single potential minimum. Our approach relies on a set of converged eigenfunctions obtained from a variational calculation on a potential surface. By making a one-to-one correspondence between the energy eigenstates of the effective Hamiltonian and those of the coordinate space Hamiltonian, a physical representation of the abstract ZOB is calculated. We find that the ZOB basis naturally adjusts its complexity depending on the underlying nature of phase space, which allows spectroscopic Hamiltonians to succeed for systems sampling multiple stationary points.     

Spatial correlation of atomic electrons: He

For any two-electron wavefunction whose angular dependence is given in terms of the spherical harmonics of the individual electrons and/or o₁₂, where o₁₂ is the interelectronic angle. a transformation is generated which reduces |ψ(r₁, r₂, o₂, o₁, o₁₂ )|² to |ψ(r₁, r₂, o₁₂)|². Geometric aspects of electron correlation are analyzed in terms of this resulting three-coordinate function, with specific application to a number of wave functions for doubly-excited helium. Angular correlation has been studied by integrating |ψ(r₁, r₂, o₁₂)|² over its radial dependence to yield p(o₁₂), the probability density function for the interelectronic angle. Trends of p(o₁₂) for doubly-excited states of the helium atom are related to a number of quantities including energies and autoionization widths. These trends can be rationalized in terms of a simple classical model. The full spatial correlation involving |ψ(r₁, r₂, o₁₂)|² is explored by the use of three-dimensional graphs for some of these states.     

Low-molecular-weight polybenzimidazoles from aromatic dinitriles and aromatic diamines

Three oligomeric benzimidazoles have been prepared by the oxidative cyclization of the corresponding polyamidines. These materials are high melting and are soluble in solvents like dimethylformamide. They exhibit inherent viscosities of 0.20–0.25 in DMF at 0.5g/100 ml. Several model compounds have also been prepared to show the feasibility and scope of the oxidative cyclization reaction.     

Polymers with a graphitic-type structure. II

Further work has been done on the synthesis of a polymer from 1,4,5,8-tetraaminoanthraquinone on 1,3,6,8-tetraketo-1,2,3,6,7,8-hexahydropyrene which has a graphitic-type structure. Improved purity of the starting materials, particularly of the tetraketone, has given a final product of better quality. The reaction conditions have been improved by lowering the temperature and increasing the time of the reaction.     

Moment of inertia, backbending, and molecular bifurcation

We predict an anomaly in highly excited bending spectra of acetylene with high vibrational angular momentum. We interpret this in terms of a vibrational shape effect with moment of inertia backbending, induced by a sequence of bifurcations with a transition from "local" to "orthogonal" modes.     

Characterisation of spatial variability and patterns in tree and soil δ13C at forested sites in eastern Canada

Wholistic isotopic studies provide a necessary foundation on which to build conceptual understanding of ecosystem development processes and provide the basis for further isotopic studies at a site or within an ecophysiological region. This study seeks to broadly characterise δ¹³C spatial variability and spatial patterns within soils and canopy tissues at five forest research sites in eastern Canada. We observe consistent and predictable patterns of leaf δ¹³C variation within trees and a consistent offset between woody and leafy tree tissues. Patterns are similar for both hardwoods and softwoods, but overall hardwoods had canopies that were more depleted in ¹³C. Soil carbon δ¹³C enrichment occurred with depth and appeared to vary according to site soil texture. Upper soil δ¹³C was intermediate between leaves and woody tissues, whereas deeper soil values suggested important contributions from more enriched tree tissues, such as persistent woody debris and possibly roots. The relationship between aboveground and belowground signatures suggests functional or developmental differences between study sites.     

Perceptual learning and human expertise

We consider perceptual learning: experience-induced changes in the way perceivers extract information. Often neglected in scientific accounts of learning and in instruction, perceptual learning is a fundamental contributor to human expertise and is crucial in domains where humans show remarkable levels of attainment, such as language, chess, music, and mathematics. In Section 2, we give a brief history and discuss the relation of perceptual learning to other forms of learning. We consider in Section 3 several specific phenomena, illustrating the scope and characteristics of perceptual learning, including both discovery and fluency effects. We describe abstract perceptual learning, in which structural relationships are discovered and recognized in novel instances that do not share constituent elements or basic features. In Section 4, we consider primary concepts that have been used to explain and model perceptual learning, including receptive field change, selection, and relational recoding. In Section 5, we consider the scope of perceptual learning, contrasting recent research, focused on simple sensory discriminations, with earlier work that emphasized extraction of invariance from varied instances in more complex tasks. Contrary to some recent views, we argue that perceptual learning should not be confined to changes in early sensory analyzers. Phenomena at various levels, we suggest, can be unified by models that emphasize discovery and selection of relevant information. In a final section, we consider the potential role of perceptual learning in educational settings. Most instruction emphasizes facts and procedures that can be verbalized, whereas expertise depends heavily on implicit pattern recognition and selective extraction skills acquired through perceptual learning. We consider reasons why perceptual learning has not been systematically addressed in traditional instruction, and we describe recent successful efforts to create a technology of perceptual learning in areas such as aviation, mathematics, and medicine. Research in perceptual learning promises to advance scientific accounts of learning, and perceptual learning technology may offer similar promise in improving education.