Band Convergence Research Articles

Rapid convergence of crystalline energy bands by use of a plane-wave-gaussian mixed basis set

All of the crystalline electron wave functions are expanded in an analytic mixed LCAO-PW basis. The LCAO'S, expressed as contracted sets of non-overlapping even-tempered Gaussians, describe the short wave length part of the electron wave functions, while the plane waves describe the long wave length part. One LCAO is obtained from each isolated atom electron state (neglecting electron spin) for each atom in the unit cell. About 65 plane waves give valence and low conduction band convergence to 0.2 eV for both C and zinc-blende ZnO, whereas over a thousand terms would be required for comparable OPW convergence. The analytic mixed basis set should be applicable to the calculation of electron energy bands in a wide variety of crystalline compounds.

Zinc(II) Tetraarylporphyrins Anchored to TiO2, ZnO, and ZrO2 Nanoparticle Films through Rigid-Rod Linkers

A series of six Zn(II) tetraphenylporphyrins (ZnTPP), with a phenyl (P) or oligophenyleneethynylene (OPE = (PE) n ) rigid-rod bridge varying in length (9-30 A) and terminated with an isophthalic acid (Ipa) anchoring unit, were prepared as model dyes for the study of sensitization processes on metal oxide semiconductor nanoparticle surfaces (MO(n) = TiO(2), ZnO, and insulating ZrO(2)). The dyes were designed such that the electronic properties of the central porphyrin chromophore remained consistent throughout the series, with the rigid-rod anchoring unit allowing each porphyrin unit to be located at a fixed distance from the metal oxide nanoparticle surface. Electronic communication between the porphyrin and the rigid-rod unit was not desired. Rigid-rod porphyrins ZnTPP-Ipa, ZnTPP-P-Ipa, ZnTPP-PE-Ipa, ZnTPP-(PE)(2)-Ipa, ZnTPP-(PE)(3)-Ipa, and ZnTMP-Ipa (with mesityl substituents on the porphyrin ring) were synthesized using combinations of mixed aldehyde condensations and Pd-catalyzed cross-coupling reactions. Their properties, in solution and bound, were compared with that of Zn(II) 5,10,15,20-tetra(4-carboxyphenyl)porphyrin ( p-ZnTCPP) as the reference compound. Solution UV-vis and steady-state fluorescence spectra for all six rigid-rod-Ipa porphyrins were almost identical to each other and to that of p-ZnTCPP. Cyclic voltammetry and differential pulse voltammetry scans of the methyl ester derivatives of the six rigid-rod-Ipa porphyrins, recorded in dichloromethane/electrolyte, exhibited redox behavior typical of ZnTPP porphyrins, with the first oxidation in the range +0.99 to 1.09 V vs NHE. All six rigid-rod-Ipa porphyrins and p-ZnTCPP were bound to metal oxide (MO(n) = TiO(2), ZnO, and insulating ZrO(2)) nanoparticle films. The Fourier transform infrared attenuated total reflectance spectra of all compounds bound to MO n films showed a broad band at 1553-1560 cm(-1) assigned to the v(CO(2)(-)) asymmetric stretching mode. Splitting of the Soret band into two bands at 411 and 423 nm in the UV-vis spectra of the bound compounds, and broadening and convergence of both fluorescence emission bands in the fluorescence spectra of the porphyrins bound to insulating ZrO(2) were also observed. Such changes were less evident for ZnTMP-Ipa, which has mesityl substituents on the porphyrin ring to prevent aggregation. Steady-state fluorescence emission of rigid-rod-Ipa porphyrins bound to TiO(2) and ZnO through the longest bridges (>14 A) showed residual fluorescence emission, while fluorescence quenching was observed for the shortest compounds.

The terminal tendon of the digital extensor mechanism: Part I, anatomic study

The purpose of this study was to examine the anatomy of the terminal tendon (TT) and its relationship to adjacent structures. The extensor tendons of 56 cadaveric digits (52 fresh-frozen and 4 formalin-preserved) underwent anatomic dissection. The TT is a segment between the convergence of the lateral bands proximally and the bony insertion in the phalanx distally. The ulnar lateral bands were thicker than the radial bands. The average distance from the TT insertion to the germinal matrix of the nail bed was 1.4 mm. The triangular ligament (TL) is a thin layer of transverse fibers between the lateral bands proximal to the TT. The dimensions of the TT and the TL vary relative to the size of the digit with the largest often occurring in the middle, followed by the ring, index, and small finger. The transverse retinacular ligament (TRL) had a dorsal attachment to the lateral bands and was much more defined and distinct than the oblique retinacular ligament. The ulnar TRL often was thicker than the radial TRL. The TT is the primary structure responsible for extending the distal interphalangeal (DIP) joint. The function of the adjacent retinacular structures is to provide stability to the TT. The thin nature and proximity of the TT to the nail matrix must be kept in mind during surgery. Knowledge of the TT anatomy is necessary for further study of its kinematics and pathology and for diagnosis and management of its disorders.

Konvergenz von Absorption und Fluoreszenz bei gekreuzt konjugierten Oligomeren aus Chalkon-Bausteinen

The absorption and fluorescence spectra of two series of chalcone oligomers (1a–d) and (2a–d) are reported. Due to small or vanishing orbital coefficients (HMO calculation) within the cross-conjugated systems, the bathochromic shifts caused by the extension of the chains are modest. The effective conjugation lengths amount to 6 and 14 chalcone building blocks in the absorptions of the series 1 and 2. The convergence of the fluorescence bands is already reached in 1d and 2d with 4 and 8 enone units, respectively. Besides the uniform or alternate arrangement of the chalcone building blocks, the positions of the propoxy substituents show a considerable influence on the electronic transitions provided that push–pull effects are operating.

Konvergenz von Absorption und Fluoreszenz bei gekreuzt konjugierten Oligomeren aus Chalkon-Bausteinen

The absorption and fluorescence spectra of two series of chalcone oligomers (1a–d) and (2a–d) are reported. Due to small or vanishing orbital coefficients (HMO calculation) within the cross-conjugated systems, the bathochromic shifts caused by the extension of the chains are modest. The effective conjugation lengths amount to 6 and 14 chalcone building blocks in the absorptions of the series 1 and 2. The convergence of the fluorescence bands is already reached in 1d and 2d with 4 and 8 enone units, respectively. Besides the uniform or alternate arrangement of the chalcone building blocks, the positions of the propoxy substituents show a considerable influence on the electronic transitions provided that push–pull effects are operating.

The bond length of ZrAr +

The photodissociation spectrum of isolated ZrAr + has been observed. The bond length in the vibrationless ground state is r 0 = 2.718 ± 0.01 A ̊ with Ω″ = 3 2 . The c state of this ion has Ω′ = 5 5 , an electronic origin at T 00 = 15580 cm −1, a vibrational frequency of ω e = 74.9 cm −1, an anharmonicity of ω e x e = 1.15 cm −1, an equilibrium rotational constant of B e = 0.0655, and a rotation-vibration constant of α e = 0.00154 cm −1. The bond length of this excited state is r 0 = 3.050 ± 0.01 A ̊ with a diabatic bond energy of 1170 ± 20 cm −1. Assignment of the c-X band convergence places the adiabatic binding energy of ground state of ZrAr + at D 0 = 2706 ± 20 cm −1.

Polarized Raman spectra for the full range of isotopic dilution for ice Ic and amorphous ice: Mixtures of intact H2O and D2O

The 90 K polarized Raman scattering of thin films of ice Ic and ice Ia containing mixtures of intact H2O and D2O have been measured using the interference-enhanced internal-reflection technique. The effects of isotopic dilution reported for samples with a D2O content ranging from 0% to 100% are consistent with the commonly held view that intermolecular coupling produces collective vibrational modes that determine the appearance of the Raman spectra in the stretching mode region of crystalline and amorphous ice. The convergence of bands produced by the collective modes on the isotopically decoupled mode frequencies of both ν1 and ν3 is displayed in this study. Bands at 3323 and 3209 cm−1 in the anisotropic scattering of protiated ice Ic are shown to converge on the decoupled antisymmetric stretch frequency of 3370 cm−1. The gradual shift of the dominant isotropic scattering at 3085 cm−1 towards the frequency of the decoupled ν1 mode is also revealed, with bands for the first stage in the evolution of the in-phase ν1 collective mode, i.e., the neighbor coupled mode, observed at 3180 (H2O) and 2340 cm−1 (D2O). The data also suggest that the shift of the in-phase coupled ν1 band begins with the first traces of added diluent, a behavior that indicates a macroscopic extension of the resonant coupling for both crystalline and amorphous ice. By contrast, the insensitivity of isotropic scattering near 3420 cm−1 to isotopic dilution suggests that the overtone of the bending mode is the likely source.

Continuous absorption below the band convergence limit in the I2 B ← X transition

The I2 B(3Π0u+) ← X (1Σg+) transition displays both continuous and discrete spectral features. Because of absorption from thermally excited levels of the ground state, the continuum of such a system extends a considerable distance into the discrete spectrum below the spectroscopic dissociation limit D0. The extinction coefficient for B ← X absorption in I2 is resolved quantitatively into discrete and continuous contributions near D0, with application to several recent studies of this transition.

Convergence of Reciprocal-Lattice Expansions and Self-Consistent Energy Bands of NaF

A convergence study is made of the reciprocal-lattice expansion of linear-combination-of-atomic-orbitals integrals in NaF. Converged integrals are obtained by direct summation and by extrapolation after different numbers of terms. It is found that extrapolation procedures give simple accurate results and substantially reduce labor involved. Comparison is made with other methods for obtaining convergence. Converged integrals are used as a basis for a self-consistent Hartree-Fock-Slater energy-band calculation for NaF using methods previously developed. Some transition energies are presented and correlated with available optical data. Self-consistent charge densities in NaF differ only slightly from a linear combination of ionic charge densities, confirming the ionic nature of NaF.