Cartesian Dynamics of Simple Molecules VI Centrosymmetric Linear Pentatomics

A simple spring model for molecular vibrations, which uses Cartesian co-ordinates for both longitudinal and transverse displacements, is applied to centresymmetric linear pentatomic molecules such as carbon suboxide and carbon subsulphide. Analytical expressions for the four stretching and three bending mode frequencies are derived in terms of seven independent force constants. By substitution of Raman and infrared frequencies, values of these force constants are obtained and briefly discussed. Eigenvectors of the normal modes and eigenfrequencies of various isotopic species are also calculated.     

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 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.     

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 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.     

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.     

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.     

Lattice vibrational modes in potassium thiocyanate

Calculations on long-wavelength lattice vibrations have been made for cystallline KNCS within the framework of the rigid ion model. The short range force constants and effective charges of the ions have been determined from the observed frequencies. Unobserved frequencies are predicted, and normal coordinates have been obtained and schematized.     

Born-von Kármán force constants of face-centred cubic metals studied by means of phonon frequency sums

Information concerning the Born-von 'Karmán (BvK) force constants of selected cubic metals are obtained from measured phonon frequencies by means of the gradual form of the frequency sum rule. Published model values of the BvK constants are commented on.     

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。     

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。     

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.     

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.     

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.     

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.     

Lattice dynamics of wurtzite-type crystals—II

We evaluated, in the preceding paper, the effective ionic charge and electronic polarizability for wurtzite-type crystals on the basis of the polarizable-ion model given by Born and Huang. With use of the quantities so evaluated, we here estimated the short-range force constants from observed frequencies, elastic constants, and piezoelectric constants after simplifying Born and Huang's procedures. The resulting set of force constants can reproduce the observed data except for the piezoelectric constants. This poor reproduction of the piezoelectric constants is due to the fact that the long-range force is emphasized in the polarizable-ion model.     

Direct determination of born — von Kármán force constants for face-centred cubic elements from measured phonon frequencies

Born — von Kármán force constants are shown, by refining a procedure developed recently, to depend linearly on certain squared phonon frequencies. A 17x17 matrix of coefficients in such linear equations for crystals with the copper structure is given. An illustrative example (Pd) exhibits good agreement with reliable published model force constants; moreover, a higher degree of precision has probably been obtained. Some problems concerning extensions of the procedure to other structures and to more realistic lattice-dynamical models are outlined.The author wishes to thank J. Bok and D. Frei for valuable technical assistance.     

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.     

Consistent shell model parameters for the rocksalt structure alkali halides

A set of shell model parameters for the rocksalt structure alkali halides is presented in which the shell charges and polarization force constants are taken to be crystal independent properties. The high and low frequency dielectric constants and the transverse optic frequencies for the whole family of crystals are reproduced with high accuracy.     

Interatomic forces in the b.c.c. transition metals

Using information obtained from X-ray scattering data, a model for the charge density in the transition metals is constructed. In this model the charge density is given by the sum of the charges situated at the ionic and bond centre sites. Within this framework, expressions for the second order elastic constants and the phonon frequencies in the cubic transition metals are obtained. These quantities have been calculated with and without the bond charge contributions for iron. The comparison with the experimental results shows that the introduction of bond charges, and hence angularity in the force-fields, in iron leads to distinctly better agreement with experiment. From a study of the elastic constants of the other b.c.c. transition metals some observations as to the nature of the angular force fields are made.