Atomic multipoles and perpendicular electrostatic forces in diatomic and planar molecules

Current methods for assigning atomic multipoles focus on reproduction of the molecular electrostatic potential. Another aspect of electrostatic interaction, which is usually overlooked, is the forces that an external electric field exerts on the nuclei of a molecule. In a self-consistent theory, both the electrostatic potential and force should be accounted for. However, in general it is not easy to meet this requirement for the force. For planar molecules, though, a formal solution is available in terms of atomic multipoles that are extracted from the molecular multipolar tensors. These Force-Related (FR) atomic multipoles are discussed in detail for some typical diatomics and planar polyatomics, and are shown to provide a solid uniform framework for treating both aspects of the electrostatics. In contrast, the commonly used potential-derived charges (i.e., the atomic charges obtained by fitting the electrostatic potential) can yield large deviations with respect to electrostatic forces on the nuclei, even when the electrostatic potential is very well reproduced.     

Krein's strings,the symmetric moment problem,and extending a real positive definite function

The symmetric moment problem is to find a possibly unique, positive symmetric measure that will produce a given sequence of moments {M_n}. Let us assume that the (Hankel) condition for existence of a solution is satisfied, and let σ_n be the unique measure, supported on n points, whose first 2n moments agree with M₀,…,M_2n−1. It is known that σ_2n ⇒ σ₀ (weak convergence) and σ_2n+1 ⇒ σ_∞, where σ₀ and σ_∞ are solutions to the full moment problem. Moreover, σ₀ = σ_∞ if and only if the problem has a unique solution. In this paper we present an analogue of this theorem for Krein's problem of extending to ℝ a real, even positive definite function originally defined on [−T,T] where T < ∞. Our proof relies on the machinery of Krein's strings. As we show, these strings help explain the connection between the moment and the extension problems. © 1999 John Wiley & Sons, Inc.     

The realization graph of a degree sequence with majorization gap 1 is Hamiltonian

It is known that the degree sequences of threshold graphs are characterized by the property that they are not majorized strictly by any degree sequence. Consequently every degree sequence d can be transformed into a threshold sequence by repeated operations consisting of subtracting I from a degree and adding 1 to a larger or equal degree. The minimum number of these operations required to transform d into a threshold sequence is called the majorization gap of d. A realization of a degree sequence d of length n is a graph on the vertices 1, …, n, where the degree of vertex i is d_i. The realization graph %plane1D;4A2;(d) of a degree sequence d has as vertices the realizations of d, and two realizations are neighbors in %plane1D;4A2;(d) if one can be obtained from the other by deleting two existing edges [a, b], [c, d] and adding two new edges [a, d]; [b, c] for some distinct vertices a, b, c, d. It is known that %plane1D;4A2;(d) is connected. We show that if d has a majorization gap of 1, then %plane1D;4A2;(d) is Hamiltonian.     

Self-deflection and all-optical beam steering in CdZnTe

We report on the experimental observation of very large self-deflection of optical beams, along with all-optical steering, and electro-optic beam deflection. We observe as many as 27 resolvable spots of deflection at 1-W/cm2 intensity. These deflections arise from enhanced photorefractive effects in CdZnTe:V, giving rise to optically induced index changes in excess of 0.08, which is to our knowledge the strongest nonlinearity ever reported for any bulk semiconductor.     

Correlation effects in the excited states of polydiacetylene models

Correlation effects in the π-electron system of models for diacetylenic systems have been investigated. Although doubly excited configuratons are important, the correlation correction is smaller than in the corresponding polyenes: the ¹A_g-like excited state is above the ¹B_u-like state. In-plane double-bonding orbitals mix significantly with the π excitations.     

An assessment of interfuel substitution by electric utilities

This paper applies a translog model to a pooled sample in order to measure the extent of regional interfuel substitution effects in the electric power industry. The results obtained indicate that relative changes in fuel prices both regionally and nationally have significant effects on fossil fuel consumption. This, in turn, has important implications for public policy. In particular, the market system appears better able to deal with exogenous shifts in energy supplies than has frequently been assumed in the formulation of public policies toward the energy crisis.Further, compared to aggregate United States time series estimates, a more elastic fuel price response is found thus questioning whether full long-run adjustment is being measured in the pure time series estimates. Given the importance of the latter in energy tax policy analysis for example, the question is indeed more than academic.