The use of semiempirical energy partitioning terms in the study of through space (homoaromatic) interactions

MNDO and AMI calculations, including configuration interactions, were performed on cycloheptatriene (2), 1,6-methano[10]annulene (3), and the tautomeric elassovalenes (4), (5), and (6). The goal of this study is to examine these systems and assess indicators of the importance of through space (homoaromatic) interactions. It is established that the two-center energy partitioning terms are capable of detecting favorable (negative two-center term) through space interactions. In cases of cyclic conjugation (homoconjugation), it is also shown that the inclusion of CI is necessary.     

Sparse direct factorizations through unassembled hyper-matrices

We set out to efficiently compute the solution of a sequence of linear systems A_ix_i = b_i, where the matrix A_i is tightly related to matrix A_{i –1}. In the setting of an hp -adaptive Finite Element Method, the sequence of matrices A_i results from successive local refinements of the problem domain. At any step i > 1, a factorization already exists and it is the updated linear system relative to the refined mesh for which a factorization must be computed in the least amount of time. This observation holds the promise of a tremendous reduction in the cost of an individual refinement step. We argue that traditional matrix storage schemes, whether dense or sparse, are a bottleneck, limiting the potential efficiency of the solvers. We propose a new hierarchical data structure, the Unassembled Hyper-Matrix (UHM), which allows the matrix to be stored as a tree of unassembled element matrices, hierarchically ordered to mirror the refinement history of the physical domain. The factorization of such an UHM proceeds in terms of element matrices, only assembling nodes when they need to be eliminated. Efficiency comes in terms of both performance and space requirements. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Macroscopic limits for stochastic partial differential equations of McKean–Vlasov type

A class of quasilinear stochastic partial differential equations (SPDEs), driven by spatially correlated Brownian noise, is shown to become macroscopic (i.e., deterministic), as the length of the correlations tends to 0. The limit is the solution of a quasilinear partial differential equation. The quasilinear SPDEs are obtained as a continuum limit from the empirical distribution of a large number of stochastic ordinary differential equations (SODEs), coupled though a mean-field interaction and driven by correlated Brownian noise. The limit theorems are obtained by application of a general result on the convergence of exchangeable systems of processes. We also compare our approach to SODEs with the one introduced by Kunita.     

Modeling intermolecular effects on nonlinear optical properties of transition-metal complexes. An effective core potential study

An initial effort to study the nonlinear optical (NLO) properties of interacting transition-metal-oxo complexes is presented and studied by effective core potential approaches. Osmium tetroxide is used for this study. Favorable intermolecular interaction effects, even within this weak interaction regime, that yield enhancements in NLO properties have been found. Interaction effects increase alpha (polarizability) up to 6% and gamma (second hyperpolarizability) up to 100% relative to the isolated monomer result for OsO4. The magnitude of the interaction (hyper)polarizabilities, and indeed even the sign, is found to be quite sensitive to the relative orientation of the osmium tetroxide monomers.