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.     

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.     

Calculation of Normal Vibrations of the Tetraazaporphin Molecule and Interpretation of Quasiline Spectra

Quasiline fluorescence and fluorescence-excitation spectra of tetraazaporphin and its N-deuterated derivative in n-octane at 77 K have been investigated, and the frequencies of normal vibrations in electronic states S ₀ and S ₁ have been determined. Calculation of normal vibrations of these molecules has been done and, on its basis, the experimental data are interpreted. It is shown that in the spectra, predominantly the totally symmetric vibrations of type A _g symmetry of the point D _2h symmetry group are active. Some activation of the nontotally symmetric B _1g vibrations in the fluorescence-excitation spectra is explained by the nonadiabatic interaction of the vibrational sublevels of the excited electronic state S ₁ with the purely electronic level S ₂.     

Calculation of Normal Vibrations and Interpretation of the Quasiline Spectra of Tetraazachlorin

Quasiline fluorescence and fluorescence-excitation spectra of tetraazachlorin and its N-deuterated derivative in n-octane at 77 K have been investigated and the frequencies of the normal vibrations for the electronic states S ₀ and S ₁ have been determined. Calculation of the normal vibrations of these molecules has been done and used to interpret the experimental data. Based on the results of analysis of the intensities in the spectra, the change in the structure of the molecule in the electronic state S ₁ is discussed.     

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.     

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.     

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.     

Anharmonic resonances in the vibrational spectra of pyrazine

The quartic force field of pyrazine has been calculated in the B3LYP/6-31G(d) hybrid density-functional approximation. Based on the results of this calculation, the total IR (250–3800 cm^–1) and Raman (400–3200 cm^–1) spectra of pyrazine have been interpreted with consideration for the Fermi and Darling-Dennison resonances and their spectral manifestations. A precision method is proposed for anharmonic analysis of the vibrational states of polyatomic molecules on the basis of consideration of their theoretical anharmonicity constants in combination with the corresponding experimental frequencies. The method of linear scaling of frequencies has been theoretically substantiated.__________Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 1, pp. 13–22, January–February, 2005.     

2-巯基噻二唑的拉曼、红外光谱、DFT计算和简正振动分析

采用B3LYP混合泛函和6-311G基函数组,并对重原子和轻原子使用离散函数和极化函数,利用密度泛函理论计算了2-巯基噻二唑的分子振动频率。实验测量了2-巯基噻二唑分子的拉曼、红外光谱,以实验频率为标准对分子内力场进行了标度,采用简正振动分析方法得到了各振动模的势能分布,从而对该分子的振动频率归属做出了全面指认。     

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 the IR Spectrum of Ethyl Chlorophyllide a by the Method of Density Functional

The structure, frequencies of normal vibrations, and the absolute IR intensities of ethyl chlorophyllide a have been calculated by the DFT/B3LYP/6-31G(d) density functional method. The force constants have been scaled by the Pulay method. The force field of ethyl chlorophyllide a has been obtained in independent and dependent natural coordinates. The vibrational IR spectrum of ethyl chlorophyllide a has been modeled. The experimental IR spectrum of chlorophyll a has been interpreted on the basis of the calculation performed.     

2+1维SU(3)格点纯规范场的真空态计算

用连续极限截断的格点本征值方法^[1],研究2+1维SU(3)的格点规范理论的真空态.在强耦合区,上述方法的结果与强耦合展开一致.在过渡区,上述方法的结果显示出较好的标度行为.     

Theoretical interpretation of the vibrational spectra of methyl-substitutedS-triazine

The problems of normal vibrations of mono-, di-, and trimethyl-substituted S-triazine are solved. Assignments of the frequencies of fundamental vibrations for an aromatic ring and methyl groups are suggested. Corrections for methyl substitution for the force constants of S-triazine are determined. The groups of characteristic and noncharacteristic vibrations of the aromatic ring of S-triazine on substitution of hydrogen are established. Saratov State University, 83, Astrakhanskaya St., Saratov, 410601, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 3, pp. 322–325, May–June, 1998.     

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.     

Microscopic calculation of the magnetic field of neutron stars

Based on the Dirac equation describing an electron moving in a uniform and cylindrically symmetric magnetic field which may be the result of the self-consistent mean field of the electrons themselves in a neutron star, we have obtained the eigen solutions and the orbital magnetic moments of electrons in which each eigen orbital can be calculated. From the eigen energy spectrum we find that the lowest energy level is the highly degenerate orbitals with the quantum numbers pZ=0, n=0, and m≥0. At the ground state, the electrons fill the lowest eigen states to form many Landau magnetic cells and each cell is a circular disk with the radius λfree and the thickness λe, where λfree is the electron mean free path determined by Coulomb cross section and electron density and λe is the electron Compton wavelength. The magnetic moment of each cell and the number of cells in the neutron star are calculated, from which the total magnetic moment and magnetic field of the neutron star can be calculated. The results are compared with the observational data and the agreement is reasonable.     

Microscopic calculation of the magnetic field of neutron stars

Based on the Dirac equation describing an electron moving in a uniform and cylindrically symmetric magnetic field which may be the result of the self-consistent mean field of the electrons themselves in a neutron star, we have obtained the eigen solutions and the orbital magnetic moments of electrons in which each eigen orbital can be calculated. From the eigen energy spectrum we find that the lowest energy level is the highly degenerate orbitals with the quantum numbers pz = 0, n = 0, and m ≥0. At the ground state, the electrons fill the lowest eigen states to form many Landau magnetic cells and each cell is a circular disk with the radius λfree and the thickness λe, where λfree is the electron mean free path determined by Coulomb cross section and electron density and λe is the electron Compton wavelength. The magnetic moment of each cell and the number of cells in the neutron star are calculated, from which the total magnetic moment and magnetic field of the neutron star can be calculated. The results are compared with the observational data and the agreement is reasonable.     

导体球壳上感应电荷及空间电场的分布(2)

本文利用镜象法讨论了在不接地导体球壳附近有点电荷时，空间的电场分布和球壳表面上感应电荷的分布。     

Vibrational Structure of the Absorption Spectra and a Model of the HNO and DNO Molecules in the Excited State

The vibrational structure of the absorption spectra of the first n–^*–electron transitions of the HNO and DNO molecules is calculated in the Franck–Condon approximation. A structural model of the molecules in the excited electronic state is constructed on the basis of correlations and with the aid of a method of hybrid atomic orbitals. Evaluation of the influence of deuterium substitution on the intensities of the vibrational components upon electronic excitation is made. A comparison of the experimental and theoretical absorption spectra calculated for different models of the molecules is carried out.     

Normal and superconducting state in the presence of forward electron-phonon and impurity scattering

By assuming that the superconducting pairing is due to the forward E-P scattering (FEP pairing) it is shown that the critical temperature of clean systems depends linearly on the E-P coupling constant and the isotope effect is very small. Impurities with the pronounced forward scattering (FS impurities) change analytical properties of the quasiparticle Green's function substantially compared to the case of the isotropic scattering. The FS impurities are pair-breaking and affect in the same way s- and d-wave FEP pairing making in the dirty limit.The usual isotropic impurity scattering is pair-weakening for s-wave and pair-breaking for the d-wave FEP pairing. Received 1st July 1998     

2-烷基TCNQ的红外光谱和结构研究——CH_2剪式振动的双峰与晶体场分裂的关系(英文)

测量了2-烷基TCNQ(C8TCNQ,C12TCNQ,C18TCNQ)浇铸膜的红外光谱,发现这类化合物的红外CH2剪式振动在1 471和1 462 cm-1处显示2个峰。这2个峰的强度比(I1 471/I1 462)随着烷基链的长度增加而明显减少。另外,来自CH2的1 471 cm-1吸收峰与来自TCNQ环的1 529 cm-1吸收峰的相对强度随着碳链的长度增加而不发生变化。CnTCNQ系列化合物的红外光谱CH2的剪式振动行为与长链脂肪酸中CH2行为很不相同。在长链脂肪酸中,晶体场效应导致了剪式振动分裂。考虑C12TCNQ的晶体结构,而将1 471cm-1峰归属为非叉指对接的碳链,将1 462 cm-1峰归于叉指对接的碳链,双峰的出现与晶体场分裂无关。并且得到烷基TCNQ中,非叉指对接的碳链的长度与碳链总长度无关的结论。