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.     

Synthesis of febrifugine derivatives and a solution to the puzzle of the structural determination of febrifugine

The stereo-structure of piperidine lactone (3), a synthetic intermediate of the antimalarial agent febrifugine ((+)-1) with a piperidine ring in the trans relative configuration, was re-revised to the cis-form. We determined that isomerization to the trans-form from the cis-form occurred in the stage (6 from 5) of deprotection in Baker's synthesis.     

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.     

Approximate formulas for the characteristics of interelectronic angle densities

The accuracies of approximate formulas are examined for several characteristics of the interelectronic angle density A(₁₂), where ₁₂ (0₁₂) is the angle subtended by the position vectors r₁ and r₂ of two electrons. Numerical results for 102 atoms show that simple approximations have sufficient accuracies for the moments with n=1–4, the central moments _n with n=2, 4, and the kurtosis, when measured by the absolute and relative errors. For heavy atoms, however, the relative errors for the third central moment ₃ and the skewness are large.     

Interatomic interactions in momentum space. Momentum density and kinetic energy in chemical bonding

On the basis of the virial theorem for a uniform scaling process of a polyatomic system, the total energy and its gradient are quantitatively related with the behavior of the electron density in momentum space through the kinetic energy of the system. For attractive and repulsive interactions, the behavior of the momentum density distribution and its effect on the stabilization energy and the interatomic force are examined. Some guiding principles are deduced for their interrelation. The results are used to clarify the role of kinetic energy in chemical bonding. Possible energy partitioning in this approach is also mentioned.     

Dynamics of unidirectional exciton migration to the molecular periphery in a photoexcited compact dendrimer

We have studied dynamical natures of electronic excited states in a compact series of phenylacetylene dendrimers. So as to clarify the mechanism of unidirectional migration of a photogenerated exciton in a compact dendrimer, we theoretically investigated the temporal behavior of the photogenerated exciton in the molecule by numerically solving the time-dependent Schrodinger equation for the electronic excited states. The structure of the dendrimers is optimized in the ground state, and it is fixed during the calculation of the exciton dynamics. The calculated results show that the exciton generated in the dendrimeric framework tends to migrate toward the outside of the molecule rather than the inside, and to itinerate around the periphery via the through-space interaction between the outer crowding benzene units. This is one of the intrinsic properties that originates from a highly branched treelike structure of the compact dendrimers.     

Note on the electron–electron counterbalance hole

The electron–electron counterbalance hole implies that two parallel spin electrons cannot be at opposite positions with respect to the spatial inversion center, if it exists. The hole is known to appear for any approximate and exact wave functions with an even inversion parity. We point out that for particular cases, the counterbalance hole also appears when wave functions have an odd inversion parity and two electrons with anti-parallel spins are involved.     

A novel polymeric electrolyte based on a copolymer containing self-assembled stearylate moiety for lithium-ion batteries

A novel polymeric electrolyte based on a self-assembled copolymer moiety has been prepared by a simple method of photo-induced radical polymerization of a mixture consisting of stearylmethacrylate (SMA) and poly(ethylene glycol)-monomethacrylate (PEM) that dissolves LiBF₄ as the electrolytic salt. The SMA moiety work as mechanically stable backbone and the PEM unit dissolving the salts serves as ion-conducting path in the polymeric composite. Solid-state NMR measurements indicated that the resulting polymer composite consists of PEM-rich and SMA-rich phases, each of which exists within several nanometers apart. The ionic conductivity of the polymer electrolyte with the composition of PEM/SMA = 7/3 (by mass ratio) was 2.8 × 10^?5 S cm^?1 at 50 °C, which was significantly higher than that of the polymer electrolyte based on cross-linked PEM copolymer without SMA.