Density Functional Theory Calculations of Normal Modes and Infrared Intensities for Tetraazaporphin

By the DFT/B3LYP method with a 6-31G(d) basis set, the structure, normal vibration frequencies, and band intensities in the IR spectra of porphin, tetraazaporphin (TAP), and three of its isotopomers have been calculated. Scaling of the force constants for porphin vibrations in nonredundant natural coordinates has been performed. The obtained scaling factors are used to predict the force field and normal modes of TAP and three of its isotopomers. To carry out a reliable assignment of the TAP frequencies, two alternative methods have been used: a wavenumber-linear scaling method and the frequency-shift method. There is good agreement between the frequencies predicted by the three methods used. The IR absorption spectrum of TAP has been simulated. Assignments of the observed experimental frequencies of TAP of odd symmetry types are suggested.     

Calculation of Normal Vibrations of Chlorin by the Method of Density Functionals

Using the DFT/B3LYP method with a 6-31G(d) basis set, the structure, normal vibration frequencies, and the absolute band intensities in the IR spectra of the chlorin molecule and its four symmetric isotopomers have been calculated. Scaling of the force field by the Pulay method in independent and natural coordinates has been carried out. A method for obtaining effective force fields without using experimental data on the fundamental vibration frequencies is proposed. By comparing the vibration modes and constructing special matrices, complete assignment of the fundamental frequencies of porphin and chlorin has been carried out. It has been shown that the majority of porphin macroring vibrations upon pyrrolenine ring hydrogenation are frequency-characteristic and only 12 vibrations change considerably. A frequency correlation with regard for the mode transition between chlorin and all its isotopomers under consideration has been established. Comparative analysis of the force fields of porphin and chlorin in dependent natural coordinates has revealed the unique nonlocal character of the change in force constants of the macroring upon hydrogenation of one pyrrolenine ring. Modeling of the IR spectra of chlorin and its isotopomers has been performed. Assignment and interpretation of the normal vibrations of the molecules under consideration have been carried out.     

Ab initio Calculation of Normal Vibrations of Chlorobenzene in the First Singlet Electron-Excitebd State 1 B 2

An analysis of experimental assignments of the frequencies of normal vibrations of chlorobenzene in the first singlet electron-excited state ¹ B ₂ has been performed with the use of two quantum-mechanical prediction methods — the method of frequency shifts and the method of transfer of scaling factors. Based on the data of this analysis, a new assignment of a number of vibration frequencies has been made. Normal vibrations of the chlorobenzene molecule in the excited state have been calculated by the CIS method with a 6-311 + G ^** basic set. An algorithm of autoscaling in dependent natural coordinates has been proposed. The force field of chlorobenzene has been scaled in dependent natural coordinates. It is shown that the scaling factors of benzene in the electron state ¹ B _2u can be used for calculating the frequencies of normal vibrations of chlorobenzene in the first singlet excited state ¹ B ₂.     

Quantum-mechanical calculation of the frequencies of the normal vibrations and intensities of the IR and Raman bands of pyridine N-oxide

The frequencies of the normal vibrations and the intensities of the bands in the IR and Raman spectra of pyridine N-oxide and three of its isotopomers are calculated with the density functional theory by using the Becke exchange and Lee-Yang-Parr correlation functionals with the 6?311+G(d, p) basis set. The scaling of the force constants in independent natural coordinates is performed. The force field of pyridine N-oxide in independent symmetry coordinates is obtained. A new assignment of the frequencies of some vibrations in the isotopomers is proposed. On the basis of the calculated frequencies and intensities, the vibrational IR and Raman spectra of pyridine N-oxide are modeled.     

Calculation of Plane Vibration Frequencies of the Porphin Molecule

By the DFT/B3LYP method with a 6-31G^** basis set the frequencies of normal vibrations of porphin and its five derivatives have been calculated. Scaling of the force constants for plane vibrations in independent natural coordinates has been carried out. Symmetry coordinates have been introduced and a force field for plane vibrations of the porphin molecule in independent symmetry coordinates has been obtained. Based on an analysis of special matrices and the potential energy distribution, complete matching of the plane vibration frequencies of porphin and its four isotopomers has been performed.     

Atypical intensity distribution in the Raman spectrum of 9,10-anthraquinone

The structure, the frequencies of the normal vibrations, and the absolute intensities of the bands in the IR and Raman spectra of 9,10-anthraquinone and its four symmetrical isotopomers are calculated in terms of the DFT/B3LYP method with the 6-31G(d) basis set. The effective harmonic force field of 9,10-anthraquinone is found by the Pulay method. A technique for directly obtaining the effective force fields without using experimental data on the frequencies of fundamental vibrations is proposed. An atypical intensity distribution in the Raman spectrum of 9,10-anthraquinone between two totally symmetric A _g and two nontotally symmetric B _3g vibrations is found. A new interpretation of these four experimentally observed vibrational Raman bands is proposed.     

Calculation of the Normal Vibrations of Benzene in the First Singlet Electron-Excited State 1 B 2u

Using the CIS/6-311+G^** method, the normal vibrations of the benzene molecule in the first singlet electron-excited state ¹ B _2u have been calculated. The algorithm of calculation of the force field in dependent coordinates by the method of generalized inversion is described. A method of autoscaling in dependent natural coordinates is suggested. For six groups of natural coordinates scaling factors have been obtained, the use of which has led to agreement between the calculated and experimental frequencies of the vibrations of benzene. The frequencies of the B _1u -symmetry-type vibrations, for which there is no experimental assignment, have been calculated. The problem of selection of the force field in dependent coordinates is discussed.     

Influence of spin-orbit coupling on vibronic spectra of metalocomplexes porphin: Manifestation of out-of-plane vibrations

In fine-structure phosphorescence spectra of metallocomplexes of porphin with ions of the Pd(II) and Pt(II) and their meso-deuterated derivatives additional lines have been detected which have no analogs in fluorescence and resonance Raman spectra of metalloporphyrins and in phosphorescence spectra of metallocomplexes of porphin with light ions of the Mg(II) and Zn(II). For Zn-porphin, quantum-chemical calculations of frequencies and forms of in-plane and out-of-plane vibrations have been performed. Based on experimental data and calculation results it has been found, that in vibronic phosphorescence spectra of metallocomplexes of porphin, out-of-plane gerade modes of the E _g symmetry (D _4h symmetry group) are manifested. The activity of out-of-plane vibrations increases with enhancing spin-orbital coupling upon changing to heavier chelated metal ions. Vibronic transitions with participation of out-of-plane gerade E _g vibrations manifest in the T ₁ → S ₀ transition through the vibronic intensity borrowing from the triplet-triplet ³ E _u -³ E _g transition.     

Effect of the Central Atom of a Metal on the Structure and Frequencies of the Normal Vibrations of the Porphin Ligand

The structure and frequencies of the normal vibrations of the molecules of porphin, Mg-, Zh-, and Ni-porphin were calculated by the density-functional method in the B3LYP/6-31G(d) approximation, and correlation of their frequencies was made. The force fields have been obtained in dependent natural coordinates. It is shown that the majority of changes in the vibrational frequencies in transition from porphin to its metal complexes correlate with changes in the structure of the pyrrole and pyrrolenine rings of the porphin ligand.     

Calculation of Out‐of‐Plane Vibrations of a Porphin Molecule

Using the DFT/B3LYP method with the base set 631G^**, we carried out calculation of the frequencies of the normal vibrations of porphin and of its five isotopic types. Scaling of force constants for outofplane vibrations has been performed in independent natural coordinates. The symmetry coordinates are introduced and a force field for outof plane vibrations of a porphin molecule in independent coordinates of symmetry is obtained. A new correlation of the frequencies of vibrations in the type of the symmetry B _1u for the isotopic type of the d ₂ porphin molecule is suggested on the basis of discrete analysis of the distribution of a potential energy.     

Raman polarization analysis of highly crystalline polyethylene fiber

The complex orientation dependence in space of Raman active vibrations in the orthorhombic structure of polyethylene (PE) is discussed in terms of Raman tensor elements as intrinsic physical parameters of the lattice. Building upon the symmetry assignment of these vibrational modes, we systematically studied, from both theoretical and experimental viewpoints, the changes of polarized intensity for the A_g and the B_2g + B_3g vibrational modes with respect to PE molecular orientation. After explicitly expanding the Raman selection rules associated with the A_g and the B_2g + B_3g modes, introducing them into general expressions of the orientation distribution function, and validating them by means of a least‐square fitting procedure on experimental data, we compare here two mesostructural models for a highly crystallized and self‐aligned PE fiber structure. Stereological arguments are shown concerning the arrangement of orthorhombic fibrils in such a sample that unfold the correct values of five independent Raman tensor elements for orthorhombic PE. Copyright © 2010 John Wiley & Sons, Ltd.     

Raman active modes of NiSi crystal

Raman scattering intensities of the NiSi Raman-active modes have been calculated with three Raman measurement configurations, which can be used for the symmetry assignment of the NiSi Raman peaks. Raman-active vibrations of the NiSi crystal have also been theoretically studied. Results show that the lattices with A_g and B_2g modes vibrate only in the plane normal to the NiSi[0 1 0] direction while the lattices with B_1g and B_3g modes vibrate only along the NiSi[0 1 0] axis. Based on such study, the relationship between the anisotropic strain distribution in the NiSi thin film and the Raman peak shifts has been briefly discussed.     

Excited Even-Symmetry States of Metallocomplexes of Porphin and Its Derivatives

Based on calculations by the CNDO/S method, data on the excited molecular states of even parity of the magnesium complexes of porphin (P), tetraazaporphin (TAP), tetrabenzoporphin (TBP), and phthalocyanine (Phc) are obtained. It is only in MgP that the first excited g-state 1¹ B _2g (29,000 cm^–1) is located 300 cm^–1 higher than the B level (28,700 cm^–1). In MgTBP, the two states 1¹ B _1g (24,700 cm^–1) and 1¹ B _2g (25,500 cm^–1) are found to be near the B level (27,500 cm^–1), while the states 1¹ B _2g (25,500 cm^–1) in MgTAP and 1¹ B _2g (21,000 cm^–1) and 1¹ B _1g (23,100 cm^–1) in MgPhc are located much lower than the B level; the energy of the latter is 31,900 and 32,400 cm^–1 in MgTAP and MgPhc respectively. The results obtained are in good agreement with experimental data on two-photon absorption: in the zinc complex of tetraphenylporphin (TPhP), the g-state is detected in the region of the B level, while in ZnPhc, two bands at 20,400 and 21,700 cm^–1 show up.     

Comparison of Theoretical Methods and Basis Sets for ab initio and DFT Calculations of the Structure and Frequencies of Normal Vibrations of Polyatomic Molecules

The dependence of the quality of calculation of the geometric parameters and frequencies of normal vibrations on the choice of the theoretical method and the basis set of Gaussian functions has been investigated within the framework of four approximations (DFT/B3LYP, HF, MP2, MP3), using benzene and s-triazine molecules as an example. It has been shown that the molecular parameters calculated using the basis set without polarization functions within the framework of any of the above theoretical methods agree poorly with the experimental data. It has been concluded that the use of the basis set 6-31G(d) within the framework of these methods with allowance for the electron correlation for calculating the geometric parameters and frequencies of normal vibrations of polyatomic cyclic compounds is most optimum in terms of the relation between the expenditure of time and the quality of the calculation. The coefficients of linear scaling of frequencies have been obtained by the DFT/B3LYP method for 22 basis sets that were tested on porphin, pyrrole, indene, and pyridine molecules. Atypically large errors in determining the frequencies of some benzene and s-triazine vibrations have been obtained in a number of quantum-mechanical calculations with large basis sets. The changes in the force field for these cases have been investigated with the example of the benzene molecule.     

Polarized Raman scattering and lattice eigenmodes of antiferromagnetic NdFeO3

The first‐ and second‐order Raman‐active phonons in the orthorhombic Pbnm NdFeO₃ single crystals were studied by means of polarized Raman scattering and lattice dynamics computations (LDC). The zone‐center phonons of A_g symmetry were distinguished from the B_1g eigenmodes by performing polarized Raman scattering experiments using two parallel polarization configurations, X′(ZZ)X′ and Z(X′X′)Z. With the help of LDC, we were able to assign most of the observed Raman‐active modes, including phonons of B_2g and B_3g symmetry. The LDC results indicated that among the 16 force constants employed, the one corresponding to the stretching vibration between the central Fe cation and the axial oxygen atom in a FeO₆ octahedron unit had the largest value. This suggests that the B‐site Fe cation is more tightly bound to the axial O1 ion than the other two equatorial O2 ions. It was further shown that at higher wavenumbers, the displacement of oxygen atoms contributed dominantly to the zone‐center vibrations. Copyright © 2008 John Wiley & Sons, Ltd.     

自旋梯状化合物Sr14(Cu1-yFey)24O41的拉曼散射谱研究

利用常规的固相合成法制备了三种Sr₁₄(Cu_1-yFe_y)₂₄O₄₁(y=0,0.03,0.05)多晶样品,其中y=0.03是单纯Fe³⁺掺杂,y=0.05是Fe³⁺和Fe²⁺混合掺杂.在100—1500cm^-1频移范围内测量了这三种样品的偏 关键词： 拉曼散射 电输运性质 自旋梯状化合物     

Application of a method of linear scaling of frequencies in calculations of the normal vibrations of polyatomic molecules

The frequencies of the harmonic vibrations of 88 compounds consisting of atoms of the first period are calculated in the approximation of the hybrid density functional B3LYP with the 6-31G* basis set. Using 1189 frequencies from experimental IR and Raman spectra of these compounds in the gas phase and the corresponding theoretical frequencies, the coefficients of the function of linear scaling are found by the least squares method. The method of linear scaling of frequencies is applied to the prediction of the 108 vibrational frequencies of a porphin molecule. A conclusion is made that this method is promising for the interpretation of vibrational spectra of complex molecules and, in combination with the Pulay method of scaling of a quantum-mechanical field, for the determination of harmonic force constants.     

Structural phase transition due to La substitution in Bi4Ti3O12

The structure of Bi_4?x La _x Ti₃O₁₂ (BLaTx) as a function of La content from x = 0.00 to 1.25 was studied by Raman spectroscopy and X-ray diffraction (XRD). It was observed that the Raman modes evolve discontinuously at about x = 1.00, which indicates a structural phase transition. Specifically, the B _2g and B _3g Raman modes shown evidences to coalesce into E _g modes with increasing La content. The evolution of Raman modes corresponds to the weakening of ferroelectric orthorhombic lattice distortion with increasing La substitution when x ≤ 1.00 and the final transition into the paraelectric tetragonal structure at higher La content. XRD and electrical measurement results confirm this phase transition by the observation that diffraction peaks from (200) and (020) planes of BLaT0.75 coalesce into one peak in BLaT1.25 and by the corresponding disappearance of remanent polarisation. The impact of La substitution on electrical properties of BLaTx is discussed briefly.     

Polarized Raman study of lattice modes in ammonium perchlorate at low temperatures

The Raman spectra of oriented single crystals of ammonium perchlorate have been measured as a function of temperature between 12 and 300 K. The results are consistent with the assignment of NH₄ClO₄ to the D_2h¹⁶ space group at all temperatures. A weak B_1g mode at 180 cm^?1 is assigned as an NH₄⁺ libration. Anomalous temperature dependence is observed for low frequency B_1g and B_3g lattice modes. Detailed results are presented for these modes in the range 18–80 K.     

Influence of magnetic ordering on the phonon Raman spectra in YCrO3 and GdCrO3

A_1g and B_2g phonon Raman lines with frequencies of ≈ 560 cm^-1 in YCrO₃ and GdCrO₃ show large blue shift from a little above the Néel temperature to lower temperatures. The contribution of the volume exchange striction to the frequency shift is estimated to be about 30 to 40 per cent for the A_1g and B_2g lines, respectively.