The Ups and Downs of Percent (and Some Interesting Connections)

Percent is a standardized ratio comparison that is often used to describe relative amounts of increase and decrease. In this paper, the nonsymmetric relationship between percent of increase and percent of decrease is explored in several ways. Beginning with a simple graphical representation of the relationship, the functional relationship is developed, with relative decrease expressed as a function of relative increase. Once expressed in the form f(x) = 100x/(100 + x), an immediate connection is made to two other topics commonly found within the study of rates—the work problem and the harmonic mean. Finally, successive percents of increase or decrease are shown to be everyday applications of the geometric mean. This deeper look at a common mathematical concept has uncovered rich structural relationships between topics that are often isolated in the curriculum.     

Quantum size effects in the attractive hubbard model

We investigate superconducting pair correlations in the attractive Hubbard model on a finite square lattice. Our aim is to understand the pronounced size dependence which they display in the weak and intermediate coupling regimes. These size effects originate from the electronic shell structure of finite systems and severely complicate a reliable extrapolation of numerical simulation data from small systems to the thermodynamic limit. To analyze the size effects in detail, we use the BCS approximation, as well as a particle number conserving modification of it and compare the results with those of quantum Monte Carlo simulations. As an application, we explore the possibility of reducing the shell effects in simulation data by changing the shape of the system and the imposed boundary conditions and by making use of the size dependence of corresponding BCS data.     

Projector Quantum Monte Carlo without minus-sign problem

Quantum Monte Carlo techniques often suffer from the so-called minus-sign problem. This paper explores a possibility to circumvent this fundamental problem by combining the Projector Quantum Monte Carlo method with the variational principle. Results are presented for the two-dimensional Hubbard model.     

Boson peak and fast relaxation process near the glass transition in polystyrene

Atactic polystyrene, both side group and main chain deuterated, was investigated by inelastic neutron scattering in a wide temperature range around the glass transition from 2 to 450 K. In the glass the Boson peak position is only very weakly influenced by the deuteration of the phenyl group. In the neighborhood of the glass transition temperatureT _g we find a fast relaxation process similar to other glasses. The onset of the fast relaxation in polystyrene, however, is observed already at temperaturesT _g — 200 K. Results from partially deuterated polystyrene suggest a change of the phenyl ring dynamics already far belowT _g.     

On the choice of active space orbitals in MCSCF calculations

We describe a procedure which may be used to aid selection of the active space in multiconfigurational self-consistent field (MCSCF) calculations for general chemical systems. Starting from a restricted Hartree-Fock calculation, we define a hierarchy of interacting virtual orbitals for every occupied orbital. The most strongly interacting orbitals are then taken to constitute the active space in a configuration interaction (CI) calculation. The natural orbital occupation numbers obtained from the CI calculation are then used to choose the active space to be used in a subsequent MCSCF calculation. We illustrate our method on a number of systems (Li₂, B₂, C₂, carbonyl oxide and the transition state for oxidation of H₂S by dioxirane). In all these cases, ‘intuitive’ active spaces are inadequate, as are active spaces derived from the natural orbitals of unrestricted Hartree-Fock calculations.     

Germacrene A is a product of the aristolochene synthase-mediated conversion of farnesylpyrophosphate to aristolochene

The biosynthesis of several sesquiterpenes has been proposed to proceed via germacrene A. However, to date, the production of germacrene A has not been proven directly for any of the sesquiterpene synthases for which it was postulated as an intermediate. We demonstrate here for the first time that significant amounts of germacrene A (7.5% of the total amount of products) are indeed released from wild-type aristolochene synthase (AS) from Penicillium roqueforti. Germacrene A was identified through direct GC-MS comparison to an authentic sample and through production of beta-elemene in a thermal Cope rearrangement. AS also produced a small amount of valencene through deprotonation of C6 rather than C8 in the final step of the reaction. On the basis of the X-ray structure of AS, Tyr 92 was postulated to be the active-site acid responsible for protonation of germacrene A (Caruthers, J. M.; Kang, I.; Rynkiewicz, M. J.; Cane, D. E.; Christianson, D. W. J. Biol. Chem. 2000, 275, 25533-25539). The CD spectra of a mutant protein, ASY92F, in which Tyr 92 was replaced by Phe, and of AS were very similar. ASY92F was approximately 0.1% as active as nonmutated recombinant AS. The steady-state kinetic parameters were measured as 0.138 min(-1) and 0.189 mM for k(cat) and K(M), respectively. Similar to a mutant protein of 5-epi-aristolochene (Rising, K. A.; Starks, C. M.; Noel, J. P.; Chappell, J. J. Am. Chem. Soc. 2000, 122, 1861-1866), the mutant released significant amounts of germacrene A (approximately 29%). ASY92F also produced various amounts of a further five hydrocarbons of molecular weight 204, valencene, beta-(E)-farnesene, alpha- and beta-selinene, and selina-4,11-diene.     

Comment: 2004's fastest organic and biomolecular chemistry!

In January 2003, the Royal Society of Chemistry launched Organic & Biomolecular Chemistry (OBC)--a journal promising to provide high quality research from all aspects of synthetic, physical and biomolecular organic chemistry. The journal was set to build upon the foundations laid down by its predecessor publications (J. Chem. Soc., Perkin Trans. 1 and J. Chem. Soc., Perkin Trans. 2) as well as complement the subject coverage already published in prestigious general chemistry journals such as Chemical Communications and Chemical Society Reviews. Nearly two years on, just how is the programme developing and what can the community expect to see from the Royal Society of Chemistry (RSC)?     

Facile synthesis of novel functionalized bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) derivatives

An improved and efficient synthetic route to four functionalized bis(ethylenedithio)-tetrathiafulvalene (BEDT-TTF) derivatives 2-5 is reported. Tetrathiolate 1 was readily prepared from 2,2'-bis(1,3,4,6-tetrathiapentalen-5-one) under carefully controlled conditions. Subsequent reaction of 1 with selected primary alkyl halides affords new functionalized BEDT-TTF derivatives in good yields.     

Comment: 2004's fastest organic and biomolecular chemistry!

In January 2004, the Royal Society of Chemistry launched Organic & Biomolecular Chemistry (OBC) - a journal promising to provide high quality research from all aspects of synthetic, physical and biomolecular organic chemistry. The journal was set to build upon the foundations laid down by its predecessor publications (J. Chem. Soc., Perkin Trans. 1 and J. Chem. Soc., Perkin Trans. 2) as well as complement the subject coverage already published in prestigious general chemistry journals such as Chemical Communications and Chemical Society Reviews. Nearly two years on, just how is the programme developing and what can the community expect to see from the Royal Society of Chemistry (RSC)?