Some cross-section theorems on the tangent bundle over a finslerian manifold

Summary Let T(M) be the tangent bundle over a Finslerian manifold M of n-dimension endowed with the Cartan connection ∇. One makes T(M) into a 2n dimensional affinely connected manifold by assigning a connection ∇^c to T(M). The cross-section of a vector field V defined in M reveals in T(M) an n-dimensional submanifold and its geometry is developed by means of the affine subspace theory and of the affine collineations in the base Finsler manifold. This work was supported by the National Research Council of Canada, 1970–1971, A-4037. Entrata in Redazione il giorno 8 maggio 1971.     

The role of the doubly excited configurations in the π-electronic structure of the croconate anion

The electronic structure of the croconate anion is investigated by the semi-empirical VESCF method with CI including up to the doubly excited configurations. The effect of the doubly excited configuration is quite large in the lowest singlet state which turns out to be a ground state, while the calculation including only singly excited configurations produces a triplet ground state. The calculated first transition energy (¹ A₁ ¹ E₁) is in fair agreement with the observed value. The interpretation of the transition moment in case that the doubly excited configurations are included is also discussed.

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Zusammenfassung Die Elektronenstruktur des Croconat-Anions wurde mit der halbempirischen VESCF-Methode mit Konfigurationswechselwirkung, die bis zu zweifach angeregte Konfigurationen einschloß, untersucht. Der Einfluß der zweifach angeregten Konfigurationen ist im niedrigsten Singulettzustand, der sich als Grundzustand herausstellt, sehr stark. Schließt die Rechnung hingegen nur einfach angeregte Konfigurationen ein, so erhält man einen Tripletgrundzustand. Die berechnete erste Übergangsenergie (¹ A₁ ¹ E₁ stimmt gut mit dem beobachteten Wert überein. Ebenso wird die Interpretation des Übergangsmomentes für den Fall, daß auch zweifach angeregte Konfigurationen berücksichtigt werden, diskutiert.

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Resumé La structure électronique de l'anion croconique est étudieé par la méthode VESCF semi-empirique avec IC, configurations diexcitées comprises. L'effet des configurations diexcitées est très important sur l'état singulet le plus has qui est un état fundamental, alors que si l'on ne tient compte que des configurations monoexcitées on obtient un état fundamental triplet. La premiére énergie de transition calculée (¹ A₁ ¹ E₁ est en bon accord avec la valeur observee. Le moment de transition est interprété dans les cas où l'on tient compte des configurations diexcitées.

     

High-spin radical cations of a dendritic oligoarylamine

A new dendritic oligoarylamine, N,N,N',N',N",N"-hexakis[4-(di-4-anisylamino)phenyl]- 1,3,5-benzenetriamine (BTA) 2, which contains a 1,3,5-benzenetriamine molecular unit as an potential precursor of a high-spin molecule and three oligoarylamine moieties as spin-carrying units surrounding the core BTA, has been prepared by the sequential palladium-catalyzed amination reactions. The redox property has been investigated by cyclic voltammetry, and the highly charged states up to the hexacation are accessible to 2. The polycationic high-spin species have been generated by stepwise chemical oxidation, and the electronic structures have been examined in detail by the continuous wave (CW) and pulsed ESR spectroscopy in comparison with the previously studied 1. The pulsed ESR technique enabled us to determine the definite spin multiplicity of the generated polycationic species of 2. It was confirmed that the dominant oxidized species observed by the two- and three-electron oxidations were assigned to the spin triplet 2(2+) and the spin quartet 2(3+), respectively. Moreover, these high-spin polycationic species turned out to be far more stable as compared to 1, and the isolation of 2(3+) as the SbCl(6)(-) salt has been accomplished. The temperature dependence of the magnetic susceptibility for the 2(3+)(SbCl(6)(-))(3) salt revealed that the intramolecular ferromagnetic interaction exists in 2(3+), and moreover, the trication 2(3+) was found to be deformed in the solid state.     

A theoretical study on the third-order nonlinear optical properties of pi-conjugated linear porphyrin arrays

By using the Pariser-Parr-Pople (PPP) theory, the second hyperpolarizabilities (gamma) have been calculated for various pi-conjugated porphyrin arrays including "porphyrin tapes": the meso-beta doubly linked porphyrin array Dn and the meso-meso, beta-beta, beta-beta triply linked array Tn. The validity of the PPP theory is checked via a comparison with both the ab initio Hartree-Fock and the B3LYP theories in the case of porphyrin monomers and dimers. It is found that Dn and especially Tn exhibit much more remarkable evolution of gamma/n along with an increasing number of porphyrin units n compared with the butadiyne-bridged array, Yn. As a result, the static third-order susceptibilities chi((3)) of Dn and Tn are expected to be 1 and 3 orders of magnitude larger than that of Yn in the limit n --> infinity, and these advantages of porphyrin tapes become more prominent by taking into account geometrical relaxations of porphyrin units in the arrays. The structure-property relationship in various conjugated polymers including porphyrin arrays is interpreted on the basis of the scaling behaviors of chi((1)) and chi((3)) with the effective conjugation length (ECL) as well as the reciprocal HOMO-LUMO energy gap (1/E(g)). In particular, from the master plot of chi((3)) (and even chi((1))) versus 1/E(g), the pi-conjugation of Tn is noted to indeed be exceptional, because its large susceptibilities cannot be expected from the scaling behavior of ordinary one-dimensional conjugated systems. We also point out that the theory of scaling relationship, chi((3)) approximately 1/E(g)(x)(), is significantly improved by taking into account electron-electron interactions based on the comparison with experiments.     

Effect of pressure on the vibrational structure of insensitive energetic material 5-nitro-2,4-dihydro-1,2,4-triazole-3-one

The Raman spectra of alpha form 5-nitro-2,4-dihydro-1,2,4-triazole-3-one (alpha-NTO, space group P) were measured in a high-pressure vessel diamond anvil cell (DAC). The pressure was increased to 27.6 GPa. In general, Raman bands show a blue shift because of the nature of the molecule packing as a high-pressure effect, but some particular bands exhibited a red shift, disappearance, split, or slight shifting in our experiments. Those red-shifting bands concerning hydrogen bonds, i.e., carbonyl and amino groups, are likely to work as a stabilizer against stimuli to the molecule or crystal. This stabilizing nature might characterize the insensitivity of NTO. Molecular dynamic (MD) calculations were performed to reveal the high-pressure effect of the alpha-NTO crystal. The coordinates of individual atoms in the crystal structure were obtained using X-ray diffraction analysis. The pressure dependence of the power spectra of the correlation functions of the C=O bond length in NTO was calculated. A unique high-pressure effect of the alpha-NTO crystal was found on the power spectra. The peak frequency in the power spectrum of the C=O stretching vibration exhibited a red shift with an increase in pressure to 10.0 GPa, while the peak intensity considerably decreased under the same pressure process, because this bond length increased with an increase in pressure to 10.0 GPa. At a pressure of >20.0 GPa, a blue shift appeared. These results of the MD calculations are in good agreement with our experimental data.     

Generation of subpicosecond vacuum ultraviolet pulses at 126 nm by using harmonics of a subpicosecond Ti:Sapphire laser

Subpicosecond vacuum ultraviolet (VUV) pulses at the wavelength of 126 nm have been generated in rare gases as a result of the 7th harmonic radiation of a subpicosecond Ti:Sapphire laser oscillating at 882 nm. The VUV harmonic intensity was optimized in Xe at the pressure of 1.2 Torr. The behavior of the harmonic emission was qualitatively reproduced by the classical nonlinear optics. The increase of the harmonic intensity was limited by multiphoton ionization of Xe.     

Theoretical analysis of oxygen reduction reaction and H2O2 formation and the impact of CF3SO3H coverage on Pt (111)

Theoretical analysis of ORR on Pt (111) was carried out with the combined technique of DFT calculation and the UBI-QEP method in order to understand the overall ORR pathways, behavior of H₂O₂ formation, and the impact of trifluoromethane sulfonic acid (CF₃SO₃H and TfOH) coverage, the alternative material of Nafion^®, on the reactivity on the Pt surface. The ORR scheme consisting of elementary reactions was then modeled to determine the dominant path and the limiting step based on their activation energies. The results showed that the dominant ORR path included the H₂O₂ formation step and OOH formation step was limiting. When TfOH covered the Pt surface, it was revealed that the adsorption energy of an O₂ molecule on Pt (111) was decreased due to the lower Fermi level and the d-band center, resulting in decreasing the activation energy of the limiting step. TfOH, however, could suppress the O₂ adsorption on the Pt surface. In addition, with the TfOH coverage, it was indicated that the limiting step of ORR was shifted to H₂O-production step which was after the H₂O₂ production, resulting in the enhancement of the H₂O₂ formation.     

Photoluminescence spectral change in layered titanate oxide intercalated with hydrated Eu3+

A number of interesting photoluminescence properties of titanate layered oxide intercalated with hydrated Eu3+ have been demonstrated. Photoluminescence intensity of Eu3+ decreased rapidly with time during irradiation by UV light having energy higher than the band gap energy of the host TiO (Ti(1.81)O4) layer. This is presumably due to the decrease in energy transfer from the host TiO layer to Eu3+ as a result of the change in the hydration state of water molecules surrounding Eu3+, which is caused by the hole produced in the TiO valence band. When irradiation was discontinued, the emission intensity gradually recovered. The recovery time increased when the water in the interlayer is removed by heat treatment. This indicates that the state of interlayer water changes during irradiation and returns to its initial state after discontinuation of irradiation. The excitation spectra changed drastically at any given wavelength upon irradiation with UV light. A comparison of the excitation spectra before and after irradiation reveals that only the excitation peak at around the irradiation wavelength decreased upon irradiation, as in the case of spectral hole burning. The hydration state of water molecules surrounding Eu3+ presumably changes depending on the irradiation wavelength, leading to the above spectral change because the Eu/TiO film has a superlattice structure producing holes with different energies.