Comparison of Ab Initio MP2/6-311+G(d,p) Predicted Carbon–Hydrogen Bond Distances with Experimentally Determined r 0 (C–H) Distances

Fifty different carbon–hydrogen distances have been predicted from ab initio MP2/6-311+G(d,p) calculations, which range from a short value of 1.0611 Å for HCNO to a long value of 1.1044 Å for H₂CO. The values include those predicted for a series of methyl (CH₃) moieties where the two different C–H distances vary by as much as 0.005 Å. These predicted values are compared to r ₀(C–H) distances obtained from the isolated carbon–hydrogen stretching frequencies, as well as to r ₀ or r _s parameters obtained from microwave data. Except for the very short C–H bonds, the ab initio values from the MP2/6–311+G(d,p) calculations can be used for the carbon–hydrogen distances with error limits of ± 0.003 Å. By utilizing the spectral data from CD₃CClO, it is shown that combination bands in the C–H stretching region could cause problems in the identification of the isolated C–H stretching frequency from the CD₂HCClO isotopomer. The value of the ab initio predicted C–H distances for checking unusually long or short r _s (C–H) or r ₀ values is demonstrated.     

A new direction in carbon-rich organometallic wires: diruthenium compounds bridged by E-hex-3-ene-1,5-diyn-diyl

New organometallic wires were obtained from two diruthenium units bridged by E-hex-3-ene-1,5-diyn-dyl.     

Loss-coupled distributed-feedback lasers with amplified optical feedback for optical microwave generation

Multisection semiconductor lasers for optical microwave generation have been fabricated that consist of a loss-coupled distributed feedback (LC-DFB), a phase control, and an amplifier section. High-frequency self-pulsations are generated according to the concept of a single-mode laser with short optical feedback. The effect of the optical feedback via the phase control and the amplifier section on the self-pulsation is apparently shown as a result of the superior single-mode characteristic of the LC-DFB section. Continuous frequency tuning is achieved in the range of 17-35 GHz.     

Absolute potassium cation affinities (PCAs) in the gas phase

The potassium cation affinities (PCAs) of 136 ligands (20 classes) in the gas phase were established by hybrid density functional theory calculations (B3-LYP with the 6-311+G(3df,2p) basis set). For these 136 ligands, 70 experimental values are available for comparison. Except for five specific PCA values-those of phenylalanine, cytosine, guanine, adenine (kinetic-method measurement), and Me(2)SO (by high-pressure mass spectrometric equilibrium measurement)-our theoretical estimates and the experimental affinities are in excellent agreement (mean absolute deviation (MAD) of 4.5 kJ mol(-1)). Comparisons with previously reported theoretical PCAs are also made. The effect of substituents on the modes of binding and the PCAs of unsubstituted parent ligands are discussed. Linear relations between Li+/Na+ and K+ affinities suggest that for the wide range of ligands studied here, the nature of binding between the cations and a given ligand is similar, and this allows the estimation of PCAs from known Li+ and/or Na+ affinities. Furthermore, empirical equations relating the PCAs of ligands with their dipole moments, polarizabilities (or molecular weights), and the number of binding sites were established. Such equations offer a simple method for estimating the PCAs of ligands not included in the present study.     

Synthesis of novel 2,6-disubstituted-3,4-dimethylidene tetrahydropyrans via Prins-type cyclization

Synthesis of novel substituted tetrahydropyrans with adjacent exo-methylene groups at the C3 and C4 positions via Prins-type cyclization has been described.     

Protonation and bromination of an osmabenzyne: reactions leading to the formation of new metallabenzynes

The reactivities of benzynes and metal-carbyne complexes are normally associated with the triple bond units. However, we have now found that electrophiles do not attack the formal osmium-carbon triple bond of osmabenzyne complex 1. Instead, 1 undergoes electrophilic substitution reactions-the typical reactions of aromatic systems.     

Templating and supersaturation-driven anti-templating: principles of biomineral architecture

The structural synergy between biominerals (CaCO(3), hydroxyapatite) and biosubstrates were examined for the first time. The templating effect of substrate and a newly identified supersaturation-driven interfacial structure mismatch effect were identified in the context of a new nucleation model. It follows that the heterogeneous nucleation which corresponds to a good structural match and synergy between biominerals and substrates will promote an ordered, compact, and tough complex biomineral structure, and occur only at low supersaturations, whereas at high supersaturations the heterogeneous nucleation associated with a poor structural match and synergy between biominerals and substrates will become dominant due to supersaturation-driven interfacial structural mismatch. The latter normally results in a disordered and porous structure. A phenomenon, so-called microgravity-driven homogeneous nucleation, was also examined. It turns out that microgravity will suppress convection and consequently promote homogeneous-like nucleation during biomineralization. This could be responsible for microgravity-induced osteoporousis.     

A new copper acetate-bis(oxazoline)-catalyzed, enantioselective Henry reaction

A highly enantioselective, nitroaldol reaction catalyzed by a chiral Cu(II) bis(oxazoline) complex has been developed. The reaction scope includes both aromatic and aliphatic aldehydes (15 examples) affording products in good yields and enantioselectivities (87-94% ee). An X-ray structure of the catalyst has been provided along with a rationalization of the sense of asymmetric induction.     

On Some Three-Color Ramsey Numbers

 In this paper we study three-color Ramsey numbers. Let K _i,j denote a complete i by j bipartite graph. We shall show that (i) for any connected graphs G ₁, G ₂ and G ₃, if r(G ₁, G ₂)≥s(G ₃), then r(G ₁, G ₂, G ₃)≥(r(G ₁, G ₂)−1)(χ(G ₃)−1)+s(G ₃), where s(G ₃) is the chromatic surplus of G ₃; (ii) (k+m−2)(n−1)+1≤r(K _1,k , K _1,m , K _n )≤ (k+m−1)(n−1)+1, and if k or m is odd, the second inequality becomes an equality; (iii) for any fixed m≥k≥2, there is a constant c such that r(K _k,m , K _k,m , K _n )≤c(n/logn), and r(C _2m , C _2m , K _n )≤c(n/logn) ^m/(m−1) for sufficiently large n. Received: July 25, 2000 Final version received: July 30, 2002 RID="*" ID="*" Partially supported by RGC, Hong Kong; FRG, Hong Kong Baptist University; and by NSFC, the scientific foundations of education ministry of China, and the foundations of Jiangsu Province Acknowledgments. The authors are grateful to the referee for his valuable comments. AMS 2000 MSC: 05C55     

On the Combinatorics of Lecture Hall Partitions

A lecture hall partition of length n is an integer sequence satisfying Bousquet-Mélou and Eriksson showed that the number of lecture hall partitions of length n of a positive integer N whose alternating sum is k equals the number of partitions of N into k odd parts less than 2n. We prove the fact by a natural combinatorial bijection. This bijection, though defined differently, is essentially the same as one of the bijections found by Bousquet-Mélou and Eriksson.