Analytical force constant calculation as a minimization problem

In this letter we show that the calculation of analytic second derivatives of variational potential energy surfaces with respect to nuclear coordinates is a minimization problem.     

Some Parity Results for 16-Cores

Kolitsch and Sellers showed recently that a₈(n), the number of 8-core partitions of n, is even when n belongs to certain arithmetic progressions. We prove a similar result for 16-cores. In doing so, we prove the surprising result that the a₁₆(n), given by

The small molecule tool (S)-(-)-blebbistatin: novel insights of relevance to myosin inhibitor design

The small molecule blebbistatin is now a front line tool in the study of myosin function. Chemical modification of the tricyclic core of blebbistatin could deliver the next generation of myosin inhibitors and to help address this we report here on the impact of structural changes in the methyl-substituted aromatic ring of blebbistatin on its biological activity. Chemical methods for the preparation of isomeric methyl-containing analogues are reported and a series of co-crystal structures are used to rationalise the observed variations in their biological activity. These studies further support the view that the previously identified binding mode of blebbistatin to Dictyostelium discoideum myosin II is of relevance to its mode of action. A discussion of the role that these observations have on planning the synthesis of focused libraries of blebbistatin analogues is also provided including an assessment of possibilities by computational methods. These studies are ultimately directed at the development of novel myosin inhibitors with improved affinity and different selectivity profiles from blebbistatin itself.     

Tiling Proofs of Recent Sum Identities Involving Pell Numbers

In a recent note, Santana and Diaz-Barrero proved a number of sum identities involving the well-known Pell numbers. Their proofs relied heavily on the Binet formula for the Pell numbers. Our goal in this note is to reconsider these identities from a purely combinatorial viewpoint. We provide bijective proofs for each of the results by interpreting the Pell numbers as enumerators of certain types of tilings. In turn, our proofs provide helpful insight for straightforward generalizations of a number of the identities. Received July 20, 2006     

Theory for Atomic Diffusion on Fixed and Deformable Crystal Lattices

We develop a theoretical framework, for the diffusion of a single unconstrained species of atoms on a crystal lattice, that provides a generalization of the classical theories of atomic diffusion and diffusion-induced phase separation to account for constitutive nonlinearities, external forces, and the deformation of the lattice. In this framework, we regard atomic diffusion as a microscopic process described by two independent kinematic variables: (i) the atomic flux, which reckons the local motion of atoms relative to the motion of the underlying lattice, and (ii) the time-rate of the atomic density, which encompasses nonlocal interactions between migrating atoms and characterizes the kinematics of phase separation. We introduce generalized forces power-conjugate to each of these rates and require that these forces satisfy ancillary microbalances distinct from the conventional balance involving the forces that expend power over the rate at which the lattice deforms. A mechanical version of the second law, which takes the form of an energy imbalance accounting for all power expenditures (including those due to atomic diffusion and phase separation), is used to derive restrictions on constitutive equations. With these restrictions, the microbalance involving the forces conjugate to the atomic flux provides a generalization of the usual constitutive relation between the atomic flux and the gradient of the diffusion potential, a relation that in conjunction with the atomic balance yields a generalized Cahn–Hilliard equation.     

The thermal rearrangements of 1,1,2,2,4,4-hexafluorospiropentane and perfluorospiropentane

The title compounds were synthesized $\text{via}$ CF₂: addition to the respective methylenecyclopropanes. The hexafluorospiropentane thermally rearranges to 2,2,4,4-tetrafluoro-1-(difluoromethylene)cyclobutane in competition with CF₂: extrusion, whereas perfluorospiropentane decomposes exclusively by CF₂: extrusion.     

Vibrational analyses employing cartesian coordinates

Geometry-optimised ab initio (STO-3G minimal basis set) calculations have been carried out for S-trans and orthogonal forms of 1,3-butadiene. The central C-C bond is shorter (1.482 Å) in the S-trans form than the orthogonal form (1.504 Å). Calculations on the orthogonal form indicate that the additional bond length decrease destabilizes the σ bond. the stabilization of the S-trans form being associated with conjugative (or π delocalization) effects.