Coumarins with an unprecedented tetracyclic skeleton and coumarin dimers from chemically engineered extracts of a marine-derived fungus

The unprecedented tetracyclic coumarin derivatives 1 and 2 and the coumarin dimers 3–5 were isolated from chemically engineered extracts (coumarin dimerization of natural extract) of the marine-derived fungus Eurotium rubrum. The structures of these compounds were established using NMR, MS and IR methods. The absolute configuration of 1 was determined by ECD calculations. The unprecedented tetracyclic coumarin skeleton was generated by domino-Knoevenagel-Diels-Alder reactions. Compounds 1–5 showed tyrosinase inhibitory activity (IC₅₀?=?1.7, 1.2, 4.9, 1.8 and 2.9?μM, respectively). The isolated coumarin derivatives 1–5 were not observed by HPLC analysis in crude extracts of E. rubrum, suggesting that chemically engineered extract generated these new coumarin derivatives with tyrosinase inhibitory activity.     

Subshell-pair correlation coefficients of atoms in momentum space

Angular correlation coefficients τ ^{nl,n^′ l^′} [p] between linear momenta of an electron in a subshell nl and another electron in a subshell n′ l′ are studied for the 102 neutral atoms He through Lr in their ground states, where n and l are the principal and azimuthal quantum numbers, respectively. We theoretically find that electron momenta are negatively correlated or uncorrelated; τ ^{nl,n^′ l^′} [p] < 0 when |l − l′|=1, while τ ^{nl,n^′ l^′} [p]=0 when |l − l′| ≠ 1. Numerical examinations of the atoms show that except for the He–B atoms, negative correlations are largest between 1s and 2p subshells, which have the most diffuse electron distributions in momentum space.     

Chemo-enzymatic short-step total synthesis of symbioramide

A concise synthesis of symbioramide, a marine-origin ceramide from a common starting material, methyl (±)-trans-2,3-epoxyoctadecanoate, in a convergent manner was achieved. The key step is the direct lipase-catalyzed coupling reaction between methyl (2R,3E)-2-hydroxy-3-octadecenoate and non-protected (±)-erythro-dihydrosphingosine, giving natural (2S,3R,2′R)-symbioramide and its (2R,3S,2′R)-isomer in 38% and 37% yield, respectively. The optically active β,γ-unsaturated α-hydroxyester was prepared by Mg(ClO₄)₂-mediated isomerization of epoxide and the subsequent lipase PS-catalyzed kinetic resolution.     

Double even tempering of orbital exponents: Application to Roothaan-Hartree-Fock calculations for He through Xe in Slater-type basis sets

Summary Double even tempering (DET) of orbital exponents is proposed as a useful generalization of even tempering (ET). The DET scheme uses two sets of basis functions for each angular momentum. The two sets have different principal quantum numbers and their exponents are generated by two different geometric sequences. Roothaan-Hartree-Fock (RHF) calculations on the atoms from He through Xe using both ET and DET Slater-type basis sets of the same size are carried out to demonstrate the substantial improvement offered by the DET scheme. The DET scheme reduces the maximum deviation of the RHF energies relative to the Hartree-Fock limit from 1.4 to 0.3 millihartrees.     

Average inner product sums of electron linear momenta for atoms and ions

From the second moments of the electron-pair densities in momentum space, accurate Hartree–Fock values of the average inner product sum 〈∑ _i<j p _i ·p _j 〉 of electron linear momenta are evaluated for the 102 neutral atoms from He to Lr, the 53 singly charged cations from Li⁺ to Cs⁺, and the 43 stable anions from H⁻ to I⁻ in their experimental ground states. The present results are new for 38 species and improve the literature values for 68 species. Received: 18 July 2002 / Accepted: 4 September 2002 / Published online: 8 November 2002 Acknowledgement. This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan. Correspondence to: H. Matsuyama e-mail: hisashi@mmm.muroran-it.ac.jp     

Variational calculations for helium-like ions using generalized Kinoshita-type expansions

 Variational calculations are reported for the ground states of the helium atom and its isoelectronic ions H⁻, Li⁺, …, Ne⁸⁺. The calculations use generalized Kinoshita expansions with freely optimized, noninteger powers of the Hylleraas coordinates s and u. One hundred-term expansions of this type lead to better energies than any other expansions in the literature with comparable numbers of terms. Received: 4 September 2002 / Accepted: 14 October 2002 / Published online: 21 January 2003 Correspondence to: T. Koga e-mail: koga@mmm.muroran−it.ac.jp Acknowledgements. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada, and in part by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan. The final 100-term computations with real powers were performed at the Advanced Computational Research Laboratory of the University of New Brunswick.     

Energy-density relations in momentum space

The integrated Hellmann-Feynman theorem is used to derive a rigorous relation between the energy and the electron density in momentum space. Choosing the electron mass as a differential parameter, we obtain a formula corresponding to the Wilson-Frost formula in coordinate space. Analysing the mass-dependence of momentum density, we then show that the present formula is equivalent to one of the previous results deduced from the virial theorem. Use of the integral Hellmann-Feynman theorem is also discussed. Several illustrative examples are given for the calculation of energy from momentum density.