Modulation of Stacking Interactions by Transition‐Metal Coordination: Ab Initio Benchmark Studies

A series of ab initio calculations are used to determine the C? H???π and π???π‐stacking interactions of aromatic rings coordinated to transition‐metal centres. Two model complexes have been employed, namely, ferrocene and chromium benzene tricarbonyl. Benchmark data obtained from extrapolation of MP2 energies to the basis set limit, coupled with CCSD(T) correction, indicate that coordinated aromatic rings are slightly weaker hydrogen‐bond acceptors but are significantly stronger hydrogen‐bond donors than uncomplexed rings. It is found that π???π stacking to a second benzene is stronger than in the free benzene dimer, especially in the chromium case. This is assigned, by use of energy partitioning in the local correlation method, to dispersion interactions between metal d and benzene π orbitals. The benchmark data is also used to test the performance of more efficient theoretical methods, indicating that spin‐component scaling of MP2 energies performs well in all cases, whereas various density functionals describe some complexes well, but others with errors of more than 1 kcal mol^?1.     

A Dimeric Magnesium(I) Compound as a Facile Two‐Center/Two‐Electron Reductant

The odd couple : A dimeric magnesium(I) complex acts as a facile and selective two‐center/two‐electron reductant towards a series of unsaturated substrates (see scheme; Ar=2,6‐iPr₂C₆H₃, Ad=1‐adamantyl). The novel reduced or reductively coupled products obtained from these reductions suggest that magnesium(I) compounds may find wide use in organic and organometallic syntheses.

     

On Ramanujan’s function k(q)=r(q)r 2(q 2)

In both his second and lost notebooks, Ramanujan introduced a function, related to the Rogers–Ramanujan continued fraction and its quadratic transformation, and listed several of its properties. We extend these results and develop a systematic theory.     

Synthetic, structural and theoretical studies of amidinate and guanidinate stabilised germanium(I) dimers

The neutral germanium(i) dimers, [{Ge(Piso)}(2)] and [{Ge(Giso)}(2)], Piso = [(ArN)(2)CBu(t)](-), Giso = [(ArN)(2)CNPr(i)(2)](-), Ar = C(6)H(3)Pr(i)(2)-2,6, which are stabilised by bulky amidinate and guanidinate ligands respectively, have been prepared by reduction of the corresponding germanium(ii) chlorides, [Ge(Piso)Cl] and [Ge(Giso)Cl]; theoretical studies suggest that the Ge-Ge bonds of [{Ge(Piso)}(2)] and [{Ge(Giso)}(2)] are associated with their HOMOs, whilst their LUMOs have substantial Ge-Ge pi-bonding character.     

Synthesis of the mycolactone core by ring-closing metathesis

The undecenolide core of mycolactone was synthesized by ring-closing metathesis and the structure confirmed using single-crystal X-ray diffraction techniques.     

Incompatible strains associated with defects in nematic elastomers

In a nematic elastomer the deformation of the polymer network chains is coupled to the orientational order of the mesogenic groups. Statistical arguments have derived the so-called neoclassical free energy that models this coupling. Here we show that the neoclassical model supplemented by the usual Frank energy predicts incompatible network strains associated with the formation of standard nematic textures. The incompatibility is measured by the Riemann curvature tensor, which we find to be nonzero for both radial hedgehog defects and escaped disclinations of strength +1 in circular cylinders. Analogous problems for conventional nonlinearly elastic solids do not possess solutions with such incompatibilities. Compatibility in nematic elastomers would require either more complicated nematic textures in elastomers than in conventional (polymeric and low molecular weight) liquid crystals or a free-energy density more complicated than the neoclassical expression.     

Polyenylpyrroles and polyenylfurans from an Australian Isolate of the soil ascomycete Gymnoascus reessii

[structure: see text] An Australian isolate of the soil ascomycete Gymnoascus reessii yielded a series of cytotoxic metabolites, including the known polyenylpyrroles rumbrin (1) and auxarconjugatin A (2), and the new rumbrin stereoisomer 12E-isorumbrin (3), as well as an unprecedented class of polyenylfurans exemplified by gymnoconjugatins A (4) and B (5). Structures were assigned with detailed spectroscopic analysis.     

Is the Home Equity Conversion Mortgage in the United States sustainable? Evidence from pricing mortgage insurance premiums and non-recourse provisions using the conditional Esscher transform

The purpose of this paper is to build a modeling and pricing framework to investigate the sustainability of the Home Equity Conversion Mortgage (HECM) program in the United States under realistic economic scenarios, i.e., whether the premium payments cover the fair premiums for the inherent risks in the HECM program. We note that earlier HECM models use static mortality tables, neglecting the dynamics of mortality rates and extreme mortality jumps. The earlier models also assume housing prices follow a geometric Brownian motion, which contradicts the fact that housing prices exhibit strong autocorrelation and varying volatility over time. To solve these problems, we propose a generalized Lee-Carter model with asymmetric jump effects to fit the mortality data, and model the house price index via an ARIMA-GARCH process. We then employ the conditional Esscher transform to price the non-recourse provision of reverse mortgages and compare it with the calculated mortgage insurance premiums. The HECM program turns out to be sustainable based on our model setup and parameter settings.     

Arithmetic properties of partitions with odd parts distinct

In this work, we consider the function pod(n), the number of partitions of an integer n wherein the odd parts are distinct (and the even parts are unrestricted), a function which has arisen in recent work of Alladi. Our goal is to consider this function from an arithmetic point of view in the spirit of Ramanujan’s congruences for the unrestricted partition function p(n). We prove a number of results for pod(n) including the following infinite family of congruences: for all α≥0 and n≥0,