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.     

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     

TYROSINE-SENSITIZED PHOTODIMERIZATION OF THYMINE IN AQUEOUS SOLUTION

Abstract. Photodimerization of thymine in aqueous solution in the presence of tyrosine was studied with monochromatic UV irradiation. The total dimer formation was sensitized in the presence of tyrosine. The action spectrum of sensitized total dimer formation has a peak near 280 nm corresponding to the absorption maximum of tyrosine. Triplet quenchers reduced the sensitization substantially. It seems probable that tyrosine-sensitized photodimerization of thymine occurred via triplet-triplet energy transfer from tyrosine to thymine.     

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.     

Selective permeation of CO2 through poly 2-(N,N-dimethyl)aminoethyl methacrylate membrane prepared by plasma-graft polymerization technique

A membrane having an amine moiety was prepared by plasma-grafting 2-(N,N-dimethyl)aminoethyl methacrylate (DAMA) onto a microporous polyethylene substrate. Permselectivity of the membrane for CO₂ over N₂ was achieved in both dry and water swollen conditions. When the CO₂ partial pressure in the feed gas was 0.047 atm, the selectivity of CO₂ over N₂ reached 130 for the highly swollen water containing membrane. This value was found to agree with that obtained with a mobile carrier membrane (supported liquid membrane) using DAMA as the carrier. The effects of several experimental conditions such as degree of grafting, feed partial pressure and temperature on the membrane performance were studied. It was suggested that the membrane acted as a fixed carrier membrane for CO₂ facilitated transport in under the dry condition and acted as a fixed reaction site membrane in the water swollen condition. The carrier transport mechanism is discussed for dry and aqueous membranes.     

Reaction of selenobenzophenones with olefins. Formation of 1H-2-benzoselenopyrans. Reaction of 1H-2-benzoselenopyrans with diazoalkanes

Selenobenzophenone reacts as a diene with dimethyl acetylenedicarboxylate (DMAD) to lead to dimethyl 1H-1-diphenylmethyl-1-phenyl-2-benzoselenopyran-3,4-dicarboxylate (5c) in moderate yield; the initial [4 + 2] cycloaddition is followed by the addition of another 1 mol equiv of selenobenzophenone. The reaction might proceed through carbene insertion of the primary cycloadduct. On the other hand, 4,4'-dimethoxyselenobenzophenone combines as a diene with DMAD furnishing dimethyl 1H-1-p-methoxyphenyl-6-methoxy-2-benzoselenopyran-3,4-dicarboxylate (4a). The reaction of benzoselenopyran derivative (4) with diaryldiazomethanes afforded another type of carbene insertion product.     

Kinetics of polymer translocation through a pore

We theoretically study kinetics of a polymer threading through a pore embedded in a flat membrane. We numerically solve three coupled kinetic equations for the number n(1) of polymer segments in one side of the membrane and expansion factors of the polymer chain in each side of the membrane. We find the time evolution n(1) proportional to t(1/(1+nu)) at late stages and the translocation time tau(t) is scaled as tau(t) proportional to 1+nu) for large number n of the polymer segments, where nu is the effective size exponent of the radius of gyration of the polymer. When the polymer is translocated into a region with a good solvent condition (nu=3/5), we obtain n(1) proportional to t(5/8) and tau(t) proportional to n(8/5).     

Chemical structure of iodine-doped polyisoprene

A nonconjugated conducting polymer (1,4-rans-polyisoprene) at different iodine doping levels has been studied with the 27.7-keV Mössbauer resonance of¹²⁹I. At the light doping level, almost all iodines are covalently bonding to the carbon atoms, breaking the double bonds of the main chain. At the medium doping level, other iodine species are found, which are idendified as anion species, l^?, l ₃ ^? and l ₃ ^? .At the heavy doping level, polyiodide anions, l ₃ ^? and l ₅ ^? , increase as compared to the covalently bonding iodine atoms and addtionally molecular iodine l₂ exists.