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The eigenvalue spectrum of the fractional quantum harmonic oscillator is calculated numerically, solving the fractional Schrödinger equation based on the Riemann and Caputo definition of a fractional derivative. The fractional approach allows a smooth transition between vibrational and rotational type spectra, which is shown to be an appropriate tool to analyze IR spectra of diatomic molecules.

The near-stoichiometric In:Fe:LiNbO₃ crystals (In:Fe:SLN) were grown by the TSSG technology for the first time. The infrared spectra and the photo-scattering resistance ability were measured. The threshold concentration of In³⁺ decreased to 2 mol% from 3 mol% of the congruent In:Fe:LiNbO₃(In:Fe:CLN) crystal. The mechanism of OH^- absorption peak shift was studied with the infrared spectra. The diffraction efficiency, writing time and erasure time were studied by using the two-wave coupling method, and the photorefractive sensitivity and dynamic range were calculated. The comprehensive indexes of the photorefractive properties of In:Fe:SLN crystals were superior to those of Fe:LN and In:Fe:CLN crystals. The In:Fe:SLN crystal was used as the storage material and the relative recognition of photorefractive volume holographic images was first realized with the material and good results were obtained.

Powder X-ray diffraction, Raman scattering and infrared spectra at different doping (x = 0 ~ 0.5) on polycrystalline Pr_1-xSr_1+xCoO₄ were performed. With increasing x, the shift of Raman scattering spectra is due to the enhancement of electron–phonon interaction along the c-axis. The contrary variation of infrared in wavenumber comes from the weakening electron–phonon interactions in the ab plane. There is a dramatic variation in resistivity as x increases, which is also caused by increasing carrier concentration and is related to the band shift. For Pr_1-xSr_1+xCoO₄, both A_1g bands shift to low frequency and reach a minimum when x = 0.3 and the resistivity of Pr_0.7Sr_1.3CoO₄ is the smallest at room temperature.

The neutral, anionic and cationic bismuth clusters with the size n up to 14 are investigated by using B3LYP functional within the regime of density functional theory and the LAN2DZ basis set. By analysis of the geometries of the Bi${}_n$ (n = 2–14) clusters, where cationic and anionic bismuth clusters are largely similar to those of neutral ones, a periodic effect by adding units with one to four atoms into smaller cluster to form larger cluster is drawn for the stable structures of bismuth clusters. An even–odd alteration is shown for the properties of the clusters, such as the calculated binding energies and dissociation energies, as well as frontier orbital energies, electron affinities, ionization energies. All the properties indicate that the Bi₄ cluster is the most possible existence in bismuth-containing materials, which supports the most recent experiment. The orbital compositions, infrared and Raman activities and the ultraviolet absorption of the most possible tetramer bismuth cluster are given in detail to reveal the periodic tendency of adding bismuth atoms and the stability of tetramer bismuth cluster.

We present an extended self-consistent charge density-functional tight-binding (SCC-DFTB) method that allows for computing vibrational infrared spectra. The extension is based on introducing an additional term in the SCC-DFTB energy formula that describes effectively the interaction of external electric field with molecular electron density distribution. The extended SCC-DFTB method is employed to model vibrational infrared spectra of 16 organic molecules. The calculated spectra are compared to experiment and to spectra obtained with density functional theory. For most of the molecules, the SCC-DFTB method reproduces the experimental spectra in a very satisfactory manner. We discuss the drawbacks and possible applications of this new scheme.

Vibrationally averaged potential energy surfaces for isotopic He–CO₂ complexes (He–¹⁸O¹³C¹⁸O and He–¹⁶O¹³C¹⁶O) are presented. Based on the latest ab initio potential of He–¹⁶O¹²C¹⁶O (Ran H, Xie D, J Chem Phys128:124323, 2008.) including the Q₃ normal mode for the v₃ antisymmetric stretching vibration of the CO₂ molecule, the averaged potentials for both He–¹⁸O¹³C¹⁸O and He–¹⁶O¹³C¹⁶O are obtained by integrating the potential energy surfaces over the Q₃ normal mode. The averaged potentials have T-shaped global minima and two equivalent linear local minima. The radial discrete variable representation/angular finite basis representation method and Lanczos algorithm are employed to calculate the related rovibrational energy levels. The calculated band origin shifts of He–¹⁸O¹³C¹⁸O and He–¹⁶O¹³C¹⁶O are 0.1066 and 0.0914 cm^-1, respectively, which agree very well with the observed values of 0.1123 and 0.0929 cm^-1. The calculated rovibrational transitions of He–¹⁸O¹³C¹⁸O and He–¹⁶O¹³C¹⁶O are also in very good agreement with the available experimental spectra.

Density functional theory has been employed to study the molecular geometries, energies, infrared vibrational spectra, and thermodynamic properties of the clusters (Cl₂AlN₃)_n(n = 1–4) at the B3LYP/6-311+G* level. The optimized clusters (Cl₂AlN₃)_n(n = 2–4) all possess cyclic structures formed by Al atoms bridged by the α-nitrogen of the azide groups, and azido in azides has linear structure. The relationships between geometrical parameters and oligomerization degree n are discussed. The gas-phase structures of the trimers prefer to exist in boat-twisting conformation. As for the tetramer, the S₄ symmetry structure is the most stable. The infrared spectra are obtained and assigned by vibrational analysis. Trends in thermodynamic properties with temperature and oligomerization degree n are discussed, respectively. A study of their thermodynamic properties suggests that monomer 1A forms clusters (2A, 3A and 3B) can occur spontaneously in the gas phase at temperatures up to 800 K. However, monomer 1A forms tetramers can occur spontaneously at temperatures below 600 K.

Quantum chemical calculations reproduced the experimental infrared spectra of NiPc, NiPc(AsF₆)_0.5, CoPc, and CoPc(AsF₆)_0.5. The agreement in the changes of line intensities supports the ligand-centered oxidation in both NiPc(AsF₆)_0.5 and CoPc(AsF₆)_0.5. Whereas, electron configurations of NiPc and NiPc⁺ as well as CoPc represent standard cases, i.e. they can be taken as a closed-shell and open-shell system, respectively, the electron configuration of CoPc⁺ must be taken as an open-shell system (while the number of electrons is even) to get an agreement of theoretical and experimental infrared spectra.

Ethylenediamine-N,N′-diacetic acid complexes of the covalent conjugates of octacarboxy-substituted cobalt phthalocyanine with one, two and three platinum atoms (3a–c) were synthesized and characterized by elemental analysis, electronic absorption, infrared and mass spectra data.

The infrared spectra of tetrakis(dibutylamino) phthalocyanine and octakis(dibutylamino) compounds were studied via theoretical investigations. The results reveal deep fusion of the peripheral alkylamino moieties with the phthalocyanine chromophore in the tetrakis(dibutylamino)- but not in the octakis(dibutylamino)-phthalocyanine compounds. The successive localized molecular orbitals (LMO) and bond order analyses give support for the infrared vibrational results.

The existence of an epitaxially stabilized tetragonal-like (“T -like”) monoclinic phase in BiFeO₃ thin films with high levels of compressive strain has been reported recently. While their structural and ferroelectric properties are different from those of rhombohedral-like (“R-like”) films with lower levels of strain, little information exists on magnetic properties. In this study we have applied a short range force constant model by using normal coordinates to investigate the Raman and the infrared wavenumbers in tetragonal BiFeO₃ having space group P4mm (C₄v¹). The calculation of zone center phonons has been made by using three stretching and six bending force constants. The calculated Raman and infrared wavenumbers are in very good agreement with the observed ones. The potential energy distribution has also been investigated for determining the significance of contribution from each force constant toward the Raman and the infrared wavenumbers.