Cartesian Dynamics of Simple Molecules IV Centrosymmetric Linear Quadratomics

A simple spring model for molecular vibrations, which uses Cartesian co-ordinates for both longitudinal and transverse displacements, is applied to centrosymmetric linear quadratomic molecules, such as cyanogen and acetylene and its halogenated derivatives. Analytical expressions for the three stretching and two bending mode frequencies are obtained in terms of five independent force constants. By substitution of Raman and infrared frequencies, values of these force constants are obtained and briefly discussed. The validity of the model is confirmed by the satisfactory agreement between calculated and observed frequencies of isotopic species.     

Cartesian Dynamics of Simple Molecules. IX. Pyramidal Quadratomics (C3v Symmetry)

The vibrations of pyramidal AB₃ type molecules with C_3v symmetry are analyzed in terms of Cartesian co-ordinates, and analytical expressions for the four normal mode frequencies are derived as functions of two stretching and two bending force constants. Optimized values of these force constants are obtained for a number of tri-hydride and tri-halide molecules by substitution of available spectroscopic and geometric data. The physical validity of the model is confirmed by comparing the calculated and observed frequencies of several isotopic species.     

Cartesian Dynamics of Simple Molecules X Linear Quadratomics (C∞v Symmetry)

The vibrations of linear ABC₂ type molecules with C_∞V point group are analysed in terms of Cartesian co-ordinates. Algebraic expressions for the three stretching and two bending normal mode frequencies are derived in terms of longitudinal and transverse force constants, atomic masses and bond lengths. Values of non-valence interaction parameters are transferred from A₂B₂ (D_∞h) molecules, and values of the principal force constants are adjusted to reproduce the observed frequencies for a number of asymmetric halogen derivatives of acetylene. Normal mode frequencies of various isotopic species are also calculated. The nature of the computed eigenvectors for these molecules is briefly discussed. It is found that the carbon-carbon and carbon-hydrogen valence interactions remain approximately constant for these molecules, whereas the carbon-halogen bonds show a weakening trend with increasing halogen mass.     

Zone center frequencies of the orthorhombic NdMnO3 perovskite

A short range force constant model has been applied for the first time to investigate the phonons in NdMnO₃ perovskite in the orthorhombic phase. The calculations with nine stretching and eight bending force constants provide good agreement for the observed Raman frequencies. The infrared frequencies have been assigned for the first time.     

Cartesian Dynamics of Simple Molecules III Non-Linear Triatomics (C2v Symmetry)

A simple spring model for the molecular vibrations of non-linear triatomic molecules with C_2v symmetry is described in terms of Cartesian co-ordinates. Analytical expressions for the stretching and bending mode frequencies are obtained and compared with previous derivations. Optimized values of force constants are calculated for models involving two or three adjustable parameters. The validity of the model is demonstrated by the satisfactory agreement between calculated and observed frequencies of isotopic species. The model provides a simple explanation of the near degeneracy of the symmetric and asymmetric stretching frequencies of H₂S and H₂Se.     

Calculation and interpretation of the oscillation spectra of the naphthenes. spiropentane

The frequencies and forms of the normal oscillations of spiropentane are calculated on the basis of the system of force constants of cyclopropane and an interpretation of its oscillation spectrum is given. The characteristic frequencies corresponding to the quaternary atom of carbon in spiropentane are established.     

Phonons at the zone center for α-NaAlH4

A short-range force constant model has been applied for the first time to investigate the phonons in α-NaAlH₄ having body centered tetragonal Scheelite structure .The normal symmetry coordinates for the Scheelite structure were computed to investigate the phonons at the zone center. The phonons for α-NaAlH₄ have been calculated involving five stretching and two bending force constants .The calculated Raman frequencies exhibit good agreement with the available measured values. The infrared frequencies have been assigned proper modes for the first time.     

Cartesian Dynamics of Simple Molecules VIII planar quadratomics (D3h symmetry)

The vibrations of planar A₃B type molecules with D_3h symmetry are analysed, by treating these molecules as a special case of A₂BC types with C_2v symmetry. Analytical expressions for the four normal mode frequencies are derived in terms of four force constants, and optimized values of the latter for the boron trihalides and sulphur trioxide are obtained and briefly discussed. Frequencies of various isotopic species are also calculated.     

Estimates of the elastic characteristics of graphenes

The central and noncentral force constants have been calculated within the previously proposed model of the binding energy of carbon atoms in graphene, which is based on the Harrison bonding orbital method. The results obtained have been used to estimate the characteristic phonon frequencies and elastic constants of graphene materials.     

低温相HI分子晶体振动光谱计算

本文用弹性力常数模型计算了低温相ＨＩ晶体的振动光谱。利用９个可调参数计算出３７个晶格模式和８个内部模式晶场分裂谱线频率，结果与实验值甚符合，同时结合群论分析对晶体拉曼和红外光谱进行了全面指认，计算还给出晶体中各类相互作用力参数。     

CUO分子结构与势能函数

用密度泛函理论的B3LYP方法,对铀原子采用14个价电子的准相对论有效原子实势及(6s5p2d4f)[3s3p2d2f]收缩价基集合,碳、氧原子采用6311G全电子基集合,应用Gaussian98程序对一氧化碳气体与铀表面相互作用的可能分子结构CUO(角形Cs和线形C∞v构型)分子进行几何优化计算,得到了稳定结构的几何构形、能量、谐振频率、力学性质和电性质,并用微观可逆性原理分析了其可能的离解极限.结果表明,势能函数等值势能面图能清晰地再现CUO分子的结构特征和离解能;铀原子与一氧化碳的反应是势垒较低、容易进行的反应 关键词： CUO 密度泛函理论 分子结构 势能函数     

Raman and Infrared Spectra of Crystals with the Cadmium Iodide Structure

Abstract

Raman and far infrared spectra (in the frequency range 20–360 cm^?1) have been recorded for polycrystalline samples of six crystals having the cadmium iodide layered structure. The four fundamental zone-center vibrational frequencies are assigned for CoBr₂, FeBr₂, MgBr₂, MnBr₂, CdI₂ and MgI₂. Values of the principal interlayer force constants are deduced from a simple linear chain dynamical model, and comparisons are made with recent results from spectroscopic studies of crystals with the related cadmium chloride structure.     

The Harmonic and Anharmonic Force Fields of Nitrosyl Halides

Harmonic and anharmonic symmetry force constants matrices have been calculated using a stepwise coupling method for the twelve isotopic species of nitrosyl fluoride, chloride and bromide. The valence force fields derived from the above matrices were used to recalculate the normal frequencies and the potential energy distribution among force constants. The valence force fields are compared with others previously reported obtained by different methods.     

The application of the matrix method of successive approximations to the calculation of the force constants of tetramethylmethane

A study is made of the applicability of the matrix method of successive approximations to the calculation of force constants under conditions of insufficient experimentally measured vibrational frequencies using as an example the molecule tetramethylmethane and its deuteron modifications. A solution is guaranteed by fixing some of the force constants in each approximation. A procedure is proposed for the selection of the force constants to be fixed, and the assignment of values to them. The force constants obtained in this way completely satisfactorily reproduce the experimental vibration frequencies.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 7, pp. 59–62, July, 1971.     

多原子分子力场的量子化学研究

本文报道了一种由量子化学方法获得的笛卡尔力场F_x矩阵转换成内坐标力场F_r矩阵的方法。利用该方法获得的力场和Wilson-GF矩阵方法对多原子分子和离子的力场、振动模式和频率进行了研究,获得了十分满意的结果。     

Comparison of empirical and ab initio force fields for phosphine

Existing experimental data on frequencies, Coriolis coupling constants, and centrifugal distortion constants for phosphine can be reconciled by means of a harmonic force field, provided substantial vibrational dependences of the distortion constants are permitted. Such dependences are indicated in a recent high-resolution study of PD₃. The resulting empirical force constants are then in excellent agreement with existing predicted values from a sophisticated ab initio study, including electron correlation.     

Study on the force field of pyrite

A normal coordinate treatment is made for pyrite on the basis of a Urey-Bradley force field. The i.r. frequencies used in the calculation have been reported by Verble and Wallis and the Raman frequencies by Ushioda. The values obtained for the Fe-S and S-S force constants are discussed.     

Properties and application of the reduced isotopic product rule for molecular vibration frequencies

The well-known approximate separation of low molecular vibrational frequencies from high frequencies has in the past been combined with the Redlich-Teller isotopic product rule to split the latter into separate rules for the high and for the low frequencies (reduced isotopic product rules). A number of variants and properties of these rules are discussed, along with some modifications applicable when redundant coordinates are involved. A discussion is given of the use of nonbonded distances instead of the related bond angles, and the employment of computer programs which calculate normal frequencies from postulated force constants. A comparison is made of the relative advantages of using these reduced product rules for testing assignments of observed vibration frequencies as opposed to the use of frequencies or frequency product ratios calculated from transferred force constants. Finally benzene, ethylene, methyl isocyanide, and cyclohexane are worked out as examples and some suggestions made of possible remaining uncertainties in the assigned fundamental frequencies.     

Gas phase vibrational fundamentals and vib-rotational parameters of AsCl3

Contour simulation of the gas phase infrared fundamental bands of AsCl₃ led to estimated values for the first-order Coriolis constants, the vibrational frequencies, and the relative values of the vibrational transition moments. Improved values of the six independent force constants of a general quadratic force field were determined on the basis of the observed frequencies, mean amplitudes of vibration, and Coriolis and centrifugal distortion constants. The potential energy distribution over the normal modes is reported.     

PO2自由基的光谱常数和非谐力场的理论研究

利用B3PW91、B3LYP和B3P86方法以及cc-pvQz和6-311++G(3df,3pd)基组计算了PO2自由基的光谱常数。先将计算的平衡几何结构、转动常数、谐频和基频、四次离心畸变常数和六次离心畸变常数与已有的相应实验或理论数据进行了比较。在此基础上,从理论上预测了非谐性常数、振转相互作用常数、科里奥利耦合常数、三次和四次力常数。计算结果表明,B3PW91/G理论水平得到的PO2自由基的光谱常数是可靠的。