Force Constants,Coriolis Coupling Constants,and Mean Amplitudes of Vibration of InCl6 3-

Abstract

The general quadratic force constants, coriolis coupling constants and mean amplitudes of vibration have been evaluated for InCl₆ ^3- using recent vibrational data. The results are employed to study the trend of variation in the isoelectronic sequences e.g. InCl₆ ^3-, SnCl₆ ^2- and SbCl₆ ^?.

In the present communication we report the force constants, coriolis coupling constants and mean amplitudes of vibration for InCl₆ ^3- which have not been reported so far. The results are used to study the trend of variation of the molecular parameters in the isoelectronic sequence e.g. InCl₆ ^3-, SnCl₆ ^2- and SbCl₆ ^?. The fundamental frequencies of InCl₆ ^3-, employed in this computation, have been reported on the basis of octahedral symmetry, from infrared and Raman Spectral Studies¹.     

Effect of Environmental Cations on Force Constants,Vibrational Mean Amplitudes and Bond Order of Metaloxygen Bonds in Some Octahedral Oxyanions

The general valenoe force field (GVFF), modified orbital valence force field (MOVFF), and modified Urey-Bradley force field (MUBFF) have been employed to calculate the force constants of octahedral Te⁶⁺o₆, and Ti⁴⁺o₆ anions in the presence of different environmental cations. The mean amplitudes and generalized mean square amplitudes of vibrations for these anions at temperatures; O°K,298. 16°K, and 500°K have also been calculated. Further, the metaloxygen bond order was estimated with the help of general valence stretching force constants. The effects of environmental cations on the force constants, mean amplitudes and π-bonding of metal-oxygen bonds have been critically discussed. The effect of atomic masses of anions on the ooriolis coupling constants of ‘f_iu species has also been outlined.     

Harmonic Force Field And Mean Amplitudes for Gallium Trichloride Dimer

A harmonic force field is developed and an assignment of the vibrational frequencies for Ga₂Cl₆ is proposed. The mean amplitudes of vibration are calculated.     

Mean Amplitudes Of Vibration For Aluminum And Ferric Chloride Dimers

Mean amplitudes of vibration were calculated from spectroscopic data for all the types of interatomic distances in Al_eCl_e and Fe₂Cl₆.     

Harmonic Force Fields and Mean Amplitudes for Aluminum Triiodide Dimer and Monomer

Harmonic force fields for AlI₃ (in-plane) and Al₂I₆ are developed from incomplete experimental assignments of vibrational frequencies and comparison with related molecules analysed previously. The missing frequencies are predicted from the calculations. Mean amplitudes of vibration are calculated.     

Harmonic Force Fields and Mean Amplitudes for Aluminum Trifluoride Monomer and Dimber

Recently, in this Journal, J. D. Macomber¹ has inquired into the mechanisms by which a signal is produced in a crossed-coil NMR spectrometer, His reflections led him to question the conventional explanation and to propose in its place a novel and more subtle one. The claim is made that the crossed-coil instrument is unique in its performance of a special form of emission spectroscopy-the detection of coherent spontaneous radiation (superradiance).² It is important to question fundamentals; however, we must disagree with the author's conclusions.     

Harmonic Force Field and Mean Amplitudes for Gallium Tribromide and Triiodide Dimers

Harmonic force fields are developed for the Ga₂Br₆ and Ga₂I₆ molecules. The analysis confirms previous assignments of experimental frequencies. Mean amplitudes of vibration are calculated.     

Harmonic Force Fields and Mean Amplitudes For Gallium And Indium Trihalide Monomers

Harmonic force fields (in-plane) for gallium and indium trihalides are developed from complete or incomplete experimental assignments of vibrational frequencies. The missing frequencies are predicted from the calculations Mean amplitudes of vibration are calculated.     

Mean Amplitudes of Vibration for Some Linear Gold(I) Complexes

Recently, Braunstein and Clark¹ described the synthesis and vibrational spectra of complexes containing the AuCl₂, AuBr² and AuI₂ ions. In order to obtain a deeper insight into the vibrational properties of these anions it seems interesting to calculate, using the available spectroscopic data, values for the mean amplitudes of vibration and some related quantities.     

Geometric Mean of States and Transition Amplitudes

The transition amplitude between square roots of states, which is an analogue of Hellinger integral in classical measure theory, is investigated in connection with operator-algebraic representation theory. A variational expression based on geometric mean of positive forms is utilized to obtain an approximation formula for transition amplitudes.     

Vibrational Mean Amplitudes of XY3 Pyramidal Molecules

The vibrational mean amplitudes for bonded as well as for nonbonded distances have been evaluated for AsP₃, SbP₃, and PAs₃ at temperatures : T = 0^oK, T = 298.15^oK and T=500 ^oK using recent vibrational data. The results have been briefly discussed.     

Mean-Square Amplitudes of Vibration of the Metal Atom in Iron-Organometallics

Hyperfine Interactions - 57Fe Mössbauer effect data for ferrocene over the temperature range 90≤T&;lt;370 K have been analyzed in detail to yield the mean-square amplitudes of...     

Intramolecular Force Fields and Vibrational Amplitudes of Disulfur Monoxide Isotopes

The force constants of S₂O have been calculated smploying GVFF and UBFF models. The reliability of the set of force constants have been examined. The mean amplitudes of vibration have also been evaluated at three temperatures, viz., 0°K, 298·15°K and 500°K. The results have been briefly discussed. The mean amplitude values will be helpful in interpretation of the electron diffraction data whenever available.     

Calculation of the Interatomic Force Constants of Pyrazole

In the frame of a more complete study on the tautomery of the pyrazolines-5-ones, the authors determined the normal vibration modes of pyrazole. They calculate the interatomic force constants by means of a “simplex” optimisation procedure (1).     

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.     

由QCD求和规则计算π介子和K介子twist-3分布振幅的归一化常数

本文用QCD求和规则计算了π介子和K介子的两个twist-3分布振幅的归一化常数m_{0π}^p和m_{0K}^p. 与运动方程的要求不同, 我们的计算结果表明(把求和规则微扰部分的α_s修正考虑之后), m_{0π}^p=1.00±0.17GeV,m_{0K}^p=1.46±0.23GeV. 应该指出的是, 它们与运动方程给出的结果相比要小不少. 比如π介子的情形, QCD求和规则给出的上述结果约是运动方程要求的值的50%左右.在exclusive的一些过程中, 人们发现, 一直到Q²较大(2—40GeV²)的区域,本应受到抑止的非首要的(比如, non-leading twist的贡献)贡献还可以跟首要的贡献(比如, leading twist的贡献)相比, 甚至可以超过. 这是难以相信的. 而较小的归一化常数将有助于弱化这个矛盾. 我们的计算结果支持这一点.     

Scaled DFT Force Constants and Vibrational Spectrum of Cyclopropylamine

Abstract

The molecular structure and harmonic vibrational frequencies of cyclopropylamine have been calculated using the B3LYP density functional method with the 6‐31G(2d,2p) basis set. The scaled DFT force field gives very good reproduction of the experimental vibrational frequencies. Several of the vibrational fundamental modes assigned previously are reassigned on the basis of the B3LYP/6‐31G(2d,2p) method and the scaled force field calculations. The optimized scaling factors were used to scale the B3LYP/6‐31G(2d,2p) force field of cyclopropane and cyclopropylamine (–ND₂) molecules.     

Determination of Water Force Constants with Fuzzy Methods

The paper proposes a new approach to the determination of moleculare force fields from observed vibrational frequencies for the case, that observed frequencies are only given in more or less sharp expectation ranges (intervals). Starting from a physically reasonable force constant space, we determine force fields so that the calculated eigenfrequencies are near by the experimental ones. However, in contrast to classical least squaress methods, we will model the uncertainty expressed by the statement “near by” with special triangle functions where the experimental values stand in the head of the triangles. In the sense of the fuzzy set theory, these functions are interpreted as membership functions. Within the force constant space we carry out Normal Coordinate Analyses in the usual way and determine a force field so that the eigenfrequencies have the least possible deviation from the experimental values. The deviation is evaluated with the help of the triangle membership functions. Hence, the selected force field with least deviation is called a fuzzy-optimal one. The water molecule is selected as a model case, because its least-squares force field is precisely known. Following the Born-Oppenheimer-Approximation, we treat all water isotopes in the same manner and select fuzzy-optimal force fields so that the evaluations for each water isotope are approximately similar and as high as possible. We will see that the fuzzy approach is always applicable, even if the assumptions for application of least squares methods are failed. This is a main advantage of the fuzzy method.

     

Mean-Square Amplitudes of Vibration and Anisotropic Motion of Metal Atoms in Iron Organometallics

Hyperfine Interactions - Inelastic nuclear resonant scattering spectra of 57Fe atoms were measured on Pt3 57Fe and Pd3 57Fe with the L12 crystal structure, and with the same crystallographic sites...     

Condensed Aromatics. Part XVII. Mean Amplitudes and Perpendicular Amplitude Coefficients for Anthracene

Mean amplitudes of vibration (Z) and perpendicular amplitude correction coefficients (K) are computed from spectroscopic data. They are consistent with the most recently observed vibrational frequencies. The values of K are reported here for the first time.