Vibrational assignments and force field calculations for trimethylarsenic dichloride,dibromide and their deuterated analogs

Raman and infrared spectra have been recorded for trimethylarsenic dichloride, dibromide and their deuterated analogs and vibrational assignments were made for the skeletal modes of these compounds. The spectra of the dichloride and its deuterated analog were interpreted in terms of a trigonal bipyramidal structure, D_3h symmetry, whereas the spectra of the dibromides were interpreted using the ionic model, [(CH₃)₃AsBr]⁺Br⁻, having C_3v symmetry. Using a generalized valence force potential field, normal coordinate analyses data were obtained for the dichloride and the dibromide. Included in this data are potential energy distributions for a set of symmetry coordinates. The force fields obtained for the dichloride and dibromide were used to calculate frequencies for the corresponding deuterated compounds. The discrepancies between the observed and calculated frequencies for the deuterated compounds are discussed in terms of the assumptions made.     

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.     

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.     

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.     

In-plane force constants of the peptide group: Least-squares adjustment starting from ab initio values of N-methylacetamide

Least-squares adjustment of the force constants of N-methylacetamide belonging to the A′ symmetry block was carried out starting from the force constant values obtained by an ab initio SCF MO calculation with the 4–31G basis set. Fourteen diagonal force constants were adjusted by the use of 122 vibrational frequencies of 9 isotope derivatives in the liquid state observed in the region 2000-100 cm^?1. Here, all the off-diagonal elements were fixed at the initial values calculated with the 4–31G basis set. The greatest difference between the observed and calculated frequencies was 30 cm^?1, and the differences for 94 modes were less than 10 cm^?1. Most of the force constatns of bond stretching modes were reduced by 5–10%, and those of angle deformation modes by 20–30% in the course of the least-squares adjustment. The CO stretching force constant was lowered by 30% in the adjustment, and this is understandable because the adjustment involves the effect of bringing the peptide group from a free to a hydrogen-bonded state.     

Sextic force field of nitrous oxide

The sextic force field in the curvilinear internal coordinates has been studied for the nitrous oxide molecule from the spectroscopic data of ¹⁴N₂¹⁶O, ¹⁴N¹⁵N¹⁶O, and ¹⁵N¹⁴N¹⁶O. The bands below 6600 cm⁻¹ have been used. The force constants in the internal coordinates are converted to those in dimensionless normal coordinates by two successive transformations. The vibration Hamiltonian matrix for each symmetry species of a given isotopic species has been constructed from the harmonic oscillator basis functions, and it is then diagonalized numerically to give the vibrational energy levels and the wavefunctions. The latter have been used for the evaluation of ratational constants. The least-squares refinement has been very successful in the present study, and it is shown that the general quartic force field supplemented by the quintic and sextic stretching diagonal force constants estimated from the Morse function, provided that the terms up to sextic are kept in the dimensionless normal coordinate space, well reproduces the spectroscopic constants such as the vibrational levels, rotational constants, l-type doubling constants, and centrifugal distortion constants. The spectroscopic constants of the isotopic molecules which are excluded from the refinement process are also in good agreement with the computed ones. The bond dissociation energies of the NN and NO bonds estimated from the present results have been critically examined.     

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.     

Vibrational Spectra and Normal Coordinate Analysis for an Imidazole Bridged Copper,Zinc Binuclear Complex

Abstract

The normal coordinate analysis of a model compound for Cu, Zn-SOD: [(dtma)CuImZn(dtma)]CIO₄ · 2.5H₂O (where dtma = 4-diethylenetriamineacctate; Im = imidazolate) has been carried out by using a Urey-Bradley force field. According to the molecular structure, 240 internal coordinates were established and 174 theoretical vibrational frequencies were calculated. Due to introducing an appropriate set of internal coordinates and force constants in the course of calculation, the calculated frequencies agree well with the observed values, with the average difference 4.40cm^?1 and the maximum deviation 24.2cm^?1 between them, although the structure of the title compound is complicated. Some structural and spectral properties are here 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.     

The computed force constants and vibrational spectra of cubane

The geometry, complete harmonic force field, and dipole moment derivatives of cubane, C₈H₈, have been calculated at the Hartree-Fock level using a 4–21 Gaussian basis set. The infrared and Raman spectra of cubane and four deuterated derivatives were calculated and compared with previously observed spectra. A set of five scale factors for the calculated force constants was then derived by least-squares fitting of the fundamental vibrational frequencies calculated from the scaled force field to the frequencies obtained by direct experimental measurement. The resulting scaled quantum-mechanical (SQM) force field, containing 73 unique elements, is believed to give an accurate representation of the harmonic vibrational potential of cubane. In most cases, the spectral assignments previously made from purely empirical considerations were confirmed, but a few corrections are proposed. The only major alteration is for an A_2u mode revised to appear at 1030 cm^?1 in the undeuterated molecule. Coriolis constants and approximate infrared intensities are also calculated.     

Force constant analysis of molecular groups in apatite solids

The results of normal coordinte analyses demonstrate that the simple Urey-Bradley force field gives a reasonable representation of the potential-energy function of PO₄^3? in pyromorphite (Pb₁₀(PO₄)₆Cl₂) but is unsatisfactory for AsO₄^3? and VO₄^3? in mimetite (Pb₁₀(AsO₄)₆Cl₂) and vanadinite (Pb₁₀(VO₄)₆Cl₂). respectively. Theoretical band assignments are made for PO₄^3? in pyromorphite using simple Urey-Bradley force field and based on a good frequency fit, a physically reasonable set of molecular force constants and some experimental confirmation. The general order of magnitude and trends in force constants are physically realistic. The theoretical analysis provides additional confirmation for the assignment of the v₂ bending mode to a higher-frequency, lower-intensity band at 436 cm^?1 in the infrared. Eigenvector calculations allow determination of which internal coordinates are major contributors to the various normal modes.     

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。     

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.     

The band spectrum of propynal at 4140 Å: Calculation of the structure from the Franck-Condon principle

The in-plane and out-of-plane vibrational modes in the ³A″ and ¹A′ electronic states of propynal were subjected to a normal coordinate treatment in the approximation of the Urey-Bradley force field. From the relative oscillator strengths of the transitions connecting the vibrationless ¹A′ state and the vibronic levels of the ³A″ state, the differences in equilibrium configuration were evaluated by an approximate Franck-Condon analysis based on the ground state normal coordinates. As this treatment gave 512 possible geometrical structures for the upper state, it was necessary to resort to a comparison of the observed and calculated moments of inertia along with chemical intuition to isolate the structure. A test of the correctness of the calculated structural change and the vibrational assignment was made by evaluating the intensities of the in-plane and out-of-plane fundamental, sequence, and cross sequence transitions by the exact Franck-Condon method.     

Density functional and experimental studies on the FT‐IR and FT‐Raman spectra and structure of benzoic acid and 3,5‐dichloro salicylic acid

FT‐IR and FT‐Raman spectra of benzoic acid (BA) and 3,5‐dichloro salicylic acid (SA) have been recorded in the regions of 4000–400 and 4000–50 cm⁻¹ respectively. The spectra were interpreted with the aid of normal coordinate analysis following the full structure optimizations and force field calculations based on density functional theory (DFT) using standard B3LYP6‐31G** method and basis set combinations. The DFT force field transformed to natural internal coordinates was corrected by a well‐established set of scale factors that were found to be transferable to the title compounds. The infrared and Raman spectra were also predicted from the calculated intensities. Comparison of the simulated spectra with the experimental spectra provides important information about the ability of the computational method to describe the vibrational modes. Copyright © 2008 John Wiley & Sons, Ltd.     

Determination of force fields for two conformers of nitromethane bycndo/Force method

cndo/Force method is used to evaluate the redundancy free internal valence force fields for two conformers of nitromethane. The initial force field is set up by taking the interaction and bending force constants from this method and transferring the stretching force constants from the force fields of chemically related molecules. The final force field is obtained by refining the initial force field using vibrational frequencies of isotopic speciesviz CH₃NO₂, CD₃NO₂, CH₃ ¹⁵NO₂ and CH₃N¹⁸O₂. The final force field thus obtained is reasonable on the basis of frequency fit and potential energy distribution. The barrier to internal rotation is found to be 0.048 kcal mol⁻¹.     

Electrostatic potential: A new approach for some mixed boundary value problems

A new approach to the solution of problems of electrostatics, some of them with mixed boundary conditions, is presented. The proposed scheme can be used in cases were we have a formal solution in the form of a series in Legendre polynomials and the boundary or matching conditions are given not on the whole interval (0, π) of the polar variable, θ, but only over the interval (0, π/2) or (π/2, π). Truncation of the series after the Nth term and the projection on the subspace generated by the set of the first N even (or odd) Legendre polynomials allows us to determine the unknown coefficients of the approximate solution. The results show rapid convergence toward the exact values as we increase the number of terms, N, included in the approximate solutions. The procedure allows to solve approximately some problems whose exact solutions, we believe, are not yet known.