Path integral formulation for many-electron system

The Feynman path integral method is applied to the many-electron problem of quantum chemistry. We begin with constructing new closure relations in terms of the linear combination of atomic orbital (LCAO) coefficients and investigate the transition amplitude and the partition function of the system in question; then a “classical path of electrons,” which is described by the time-dependent Hartree-Fock-Roothaan equation, is obtained by minimizing the action integral of the system with respect to the “electron coordinate.” The next order approximation is obtained by evaluating the deviation from this classical path, which is approximately written by a Gaussian integral. The result is expected to be the random-phase approximation. © 1996 John Wiley & Sons, Inc.     

Reactions of 2-Pyridyl Substituted Phosphine Oxides and Phosphonium Salts with Organometallic Reagents and in Aqueous Media

Phosphine oxides bearing two or three 2-pyridyl groups react with organometallic reagents affording 2,2′-bipyridyl, 2-substituted pyridines and pyridine in good yields. Phosphonium salts and phosphine oxides, bearing at least two 2-pyridyl or substituted 2-pyridyl groups also give the corresponding 2,2′-bipyridyls and pyridines upon treatment with acid or neutral solvents such as water and alcohols in substantial yields. The 2,2′-bipyridyls are considered to be formed by ligand coupling within the pentacoordinated phosphorus intermediate formed incipiently during the reaction.     

Studies on the syntheses of polymetalloxanes and their properties as a precursor for amorphous oxide. IV. Properties of SiO2–TiO2 oxide fibers from polytitanosiloxane

From polytitanosiloxanes (PTS), SiO₂–TiO₂ oxide fibers with fairly good tensile strength were prepared, and their mechanical and thermal properties were investigated. The precursor fibers PTS-0.5 and PTS-1.0 were obtained by dry spinning of a highly viscous PTS solution which were formed as the reaction mixture of silicic acid (SA) with bis(2,4-pentanedionato)titanium diisopropoxide (PTP) in the molar ratios (SA/PTP) of 0.5 and 1.0. The precursor fibers PTS-0.5 were too brittle to measure their tensile strength, whereas PTS-1.0 and the heat-treated fibers were found to have tensile strength of 130 (precursor), 540 (500°C), and 450 (900°C) MPa, respectively. Heat-treatment of the fibers PTS-1.0 at above 1000°C forms anatase and rutile of titanium dioxide. The crystallization is resulted from the unreacted PTP which is not incorporated into the polymer network.     

Spectroscopic and theoretical studies of optically active porphyrin dimers: a system uninterpretable by exciton coupling theory.

The electronic excited states of a meso-meso beta-beta doubly linked bis-porphyrin are comprehensively investigated by measuring its circular dichroism (CD) and magnetic circular dichroism (MCD) spectra. The observed spectroscopic properties are rationalized by DFT calculations. The frontier molecular orbitals (MOs) are constructed by the linear combinations of the constituent monomers' four MOs. Comparison of a theoretical CD spectrum based on time-dependent DFT (TDDFT) with the experimental spectra resulted in the assignment of the helical conformation of the dimer. This assignment is contrary to the previous assignment based on the point-dipole approximation (exciton coupling theory).     

Full fitting analysis of the relative intermediate form factor measured by neutron spin echo

This paper describes the dynamics of a water-in-oil microemulsion from the dilute to the dense droplet region. Using the relative intermediate form factor method for neutron spin echo data analyses [M. Nagao, H. Seto, Phys. Rev. E 78 (2008) 011507], the shape and structure fluctuations of a droplet microemulsion are successfully decoupled. In the previous paper, we used the first cumulant analysis of the shape fluctuation model, while the full fitting form of the same model is applied in this paper. The final results of the fittings using the first cumulant approximation and the full form of the model are almost identical, and therefore, the validity of the method is strengthened. The estimated bending modulus of the surfactant membrane, κ, is basically the same, within the experimental errors, in the previous and present results. The κ is not affected much by an increase of the droplet concentration. A clear dynamic slowing down of the water droplets is highlighted at the length scale corresponding to the inter-droplet distance from the structure fluctuation analysis.     

Mono-aromatic ring-fused versus adjacently di-aromatic ring-fused tetraazaporphyrins: regioselective synthesis and their spectroscopic and electrochemical properties

A method which preferentially produces adjacently di-aromatic ring-substituted tetraazaporphyrins (TAPs) has been developed, and their electrochemical and spectroscopic properties have been studied and compared with those of the corresponding series of mono-aromatic ring-fused TAPs. Mono-aromatic ring-fused TAPs show a split Q-band, and the splitting energy increases with increasing size of the aromatic ring. In addition, for the split Q-bands, the relative intensity of the band at longer wavelength decreases with increasing molecular size of the fused aromatics, compared with the shorter wavelength band. In the di-aromatic ring-fused TAPs, this kind of splitting is not seen, and only a shift of the band is observed. The intensity and band position of the split or unsplit Q-bands are quantitatively evaluated by simultaneous band deconvolution analysis, using both electronic absorption and magnetic circular dichroism spectra. The preparation of these TAP compounds has made it possible to adjust the Q-band position in a stepwise manner between ca. 600 and 750 nm. The first reduction and oxidation potentials of the TAP ring shift negatively with increasing number and size of the fused aromatics. The extent of the shift is found to be very small for the LUMOs but significant for the HOMOs. These spectroscopic and electrochemical properties are almost perfectly reproduced by molecular orbital calculations within the framework of the Pariser-Parr-Pople approximation. In particular, a small variation of the LUMO level and large destabilization of the HOMO level on ring expansion are rationalized from the extent of stretch of molecular orbitals: i.e., since the LUMOs are localized in the central TAP moiety irrespective of the molecular size, while the HOMOs have appreciable coefficients even over the fused aromatics, the HOMO level destabilizes while the LUMO level remains constant with increasing molecular size. In one CoTAP derivative, Co(III/II) and the first ligand oxidation couples occur experimentally at the same potential.     

Origin of the stability of Ge(105) on si: a new structure model and surface strain relaxation

The structure of Ge(105)-(1 x 2) grown on Si(105) is examined by scanning tunneling microscopy (STM) and first-principles calculations. The morphology evolution with an increasing amount of Ge deposited documents the existence of a tensile surface strain in Si(105) and its relaxation with increasing coverage of Ge. A detailed analysis of high-resolution STM images and first-principles calculations produce a new stable model for the Ge(105)-(1 x 2) structure formed on the Si(105) surface that includes the existence of surface strain. It corrects the model developed from early observations of the facets of "hut" clusters grown on Si(001).