Bounds to average interelectronic angles in Hartree-Fock theory of atoms

The average interelectronic is the expectation value of the angle thetaij (0 < or = thetaij < or = pi) subtended by the position vectors ri and rj of a pair of electrons i and j. In the Hartree-Fock theory of atoms, we point out that the angle and its subshell-pair components nl,n'l' are bounded from above and below, where n and l are the principal and azimuthal quantum numbers. The upper bounds for nl,n'l' with 0 < or = l, l' < or = 3 are 9pi/16 (=101.25 degrees), 135pi/256 (approximately 94.922 degrees), 265pi/512 (approximately 93.164 degrees), and 129pi/256 (approximately 90.703 degrees) for sp, pd, df, and sf pairs, respectively, while they are pi/2 (=90 degrees ) for the other ll' pairs, independent of n and n'. A weighted sum of these subshell-pair bounds gives an upper bound to . The lower bounds are pi/2 in all the cases.     

Regioselectivity in palladium-indium iodide-mediated allylation reaction of glyoxylic oxime ether and N-sulfonylimine

Allylation reaction of electron-deficient imines with allylic alcohol derivatives in the presence of a catalytic amount of palladium(0) complex and indium(I) iodide was studied. The reversibility of allylation was observed in the reaction of glyoxylic oxime ether having camphorsultam. As the important effect of water on regioselectivity, the gamma-adducts were kinetically formed from monosubstituted allylic reagents in the presence of water. The selective formation of thermodynamically stable alpha-adducts was observed in anhydrous THF. In contrast, the allylation of N-sulfonylimine gave the gamma-adducts with high regioselectivities even under anhydrous reaction conditions.     

Asymmetric synthesis of alpha-amino acids: indium-mediated reactions of glyoxylic oxime ether in aqueous media

The indium-mediated allylation and alkylation reactions of the Oppolzer camphorsultam derivative of glyoxylic oxime ether proceeded with excellent diastereoselectivity in aqueous media, providing a variety of enantiomerically pure alpha-amino acids.     

Stannyl radical addition-cyclization of oxime ethers connected with olefins

Stannyl radical addition-cyclization of oxime ethers connected with olefin moieties was studied. The radical reactions proceeded effectively by the use of triethylborane as a radical initiator to provide the functionalized pyrrolidines via a carbon-carbon bond-forming process.     

Enantioselectively catalyzed oxidation of 3,4-dihydroxy-l-phenylalanine by N-lauroyl L or D-histidine-Cu(II) complex in CTABr micelles.

In order to investigate the enzyme model reaction the oxidation of 3,4-dihydihydroxy-L-phenylalanine(L-DOPA) was carried out using optically active catalyst, N-lauroyl L or D-histidine-Cu(II) complex(L or D-LauHis-Cu(II)), showing appreciable enantioselectivity in the presence of the mixed micelles with CTABr.     

Atomic one- and two-electron subshell moments in position and momentum spaces

For 357 subshells of the 53 neutral atoms He through Xe in their ground states, the two-electron intracule (relative motion) <u ^k > _nl and extracule (center-of-mass motion) <R ^k > _nl subshell moments in position space are examined as well as their counterparts <v ^k > _nl and <P ^k > _nl in momentum space, where n and l are the principal and azimuthal quantum numbers of the atomic subshell, respectively. It is clarified that between the intracule and extracule moments the “2 ^k -rule” is strictly valid, which means <u ^k > _nl = 2 ^k <R ^k > _nl and <v ^k > _nl = 2 ^k <P ^k > _nl for any nl subshell. Theoretical analysis also proves that for a particular case of k = +2, two relations <u ²> _nl = (N _nl −1)<r ²> _nl and <v ²> _nl = (N _nl −1)<p ²> _nl hold exactly, where N _nl (≥2) is the number of electrons in the subshell nl, and <r ^k > _nl and <p ^k > _nl are the familiar one-electron subshell moments in position and momentum spaces, respectively. The latter equality establishes a new and rigorous relation between the second electron-pair moments in momentum space and the total energy of an atom through the virial theorem. For k=+1, −1, and −2, the numerical Hartree-Fock results for the 357 subshells show that there are approximate but accurate linear relations between <u ^k > _nl and <r ^k > _nl and between <v ^k > _nl and <p ^k > _nl , in which the proportionality constant in each space depends on n,l, and k. Received: 27 April 1998 / Accepted: 29 May 1998 / Published online: 28 August 1998     

all-Z-Tetrabenzo

Crystal structures of the silver complexes derived from tetrabenzo[16]annulene with AgOTf and AgClO(4) are different, although these two complexes show similar (1)H NMR spectra reflecting a similar clathrate structure in solution. The silver complex of pentabenzo[20]annulene with AgClO(4) adopts a clathrate structure both in the solid state and in solution.     

Single-bubble sonochemiluminescence in aqueous luminol solutions

Sonochemiluminescence (SCL) of luminol due to a single bubble is studied through spectral measurement. No SCL was observed from a stable single bubble that emitted high-intensity sonoluminescence (SL). In contrast, SCL was observed under conditions of an unstable dancing bubble, where a bubble grows and ejects tiny bubbles, making it "dance" by counteraction. Furthermore, SCL was observed from dancing bubbles even when SL was not observed, depending on the dissolved gas content. The instability of bubble collapse is the key parameter governing SCL.