Ab initio molecular orbital calculations on ion pair-water complexes of metal halides and oxides

Ab initio MO calculations are performed on a series of ion-molecular and ion pair-molecular complexes of H₂O + MX (MX = LiF, LiCl, NaCl, BeO and MgO) systems. BSSE-corrected stabilization energies, optimized geometrical parameters, internal force constants and harmonic vibrational frequencies have been evaluated for all the structures of interest. The trends observed in the geometrical parameters and other properties calculated for the mono-hydrated contact ion pair complexes parallel those computed for the complexes of the individual ions. The bifurcated structures are found to be saddle points with an imaginary frequency corresponding to the rocking mode of water molecules. The solventshared ion pair complexes have high interaction energies. Trends in the internal force constant and harmonic frequency values are discussed in terms of ion-molecular and ion-pair molecular interactions.     

Rh2(CO)4(μ-Cl)2和Rh4(μ-CO)3(CO)4的简正振动分析

金属簇合物具有独特的结构和成键方式。本文对铑簇合物的简正振动分析进行了研究。通过红外光谱用石蜡油糊涂KBr和聚乙烯窗口, 在Nicolet 200SXV FT-IR光谱上测定了Rh2(CO)4(μ-Cl)2的构型, 并使用分子振动全分析程序MVTA(Basic语言), 在PC机上进行计算。     

An Extension of the Consistent Valence Force Field (CVFF) with the Aim to Simulate the Structures of Vanadium Phosphorus Oxides and the Adsorption of n‐Butane and of 1‐Butene on their Crystal Planes

A specific force field of Consistent Valence Force Field type was developed with the aim to simulate the structures of catalysts of vanadium phosphorus oxide type and the reversible adsorption of organic compounds on specific crystallographic planes of such catalysts by molecular modeling. The appropriate parameters were derived for the bonded (stretching, bending, and torsional deformations) and nonbonded (attractive and repulsive van der Waals and Coulomb forces) atomic interactions for V—O and P—O bonds in typical fragments of these catalysts with the vanadium atom in the oxidation state IV. The parameters for bonded interactions were computed from Hessian matrices, supplied by the program DMol for performing Density Functional Theory, by means of a program for non‐linear regression. The DMol program was applied to energy minimize structures of known vanadium phosphorus oxides, which were compared with X‐ray structures, and to obtain their Hessian matrices as a basis for the force constants needed. Some hypothetical structural models had to be added. The van der Waals parameters were estimated by means of correlations between van der Waals radii and the repulsive parameters and between polarizabilities and the dispersive parameters from the literature. The force field obtained was applied to simulate the crystal structure of vanadyl pyrophosphate and to compute the heat of adsorption of n‐butane and of 1‐butene on its (100) plane (computer codes of company Biosym/MSI/Accelrys). The experimental crystal structure and the adsorption energies were fairly well reproduced, except that the a lattice constant proves somewhat too large.     

Force constants in molecular crystals of methyl-and perdeuteriomethylmercury(II) halides

Force constants for the internal vibrations involving the metal and for the lattice vibrations of Hg(CH₃)X and Hg(CD₃)X (X = Cl, Br or I) are calculated on the basis of a D_4h⁷ layer structure. The internal HgX stretching force constants are much lower than for these molecules in solution, but HgC stretching force constants are slightly higher. The HgX and longitudinal translatory force constants within the lattice layer are close in value to the strong and weak HgX bond stretching force constants respectively in the unsymmetrical [Hg(CH₃)X₂]^? complex ions.     

Determination of force fields for formaldehyde,acetaldehyde and acetone by the CNDO/force method

CNDO/Force calculations have been done for formaldehyde, acetaldehyde and acetone, and the theoretical force fields evaluated. Experimental force fields are obtained from vibrational frequencies using the least-squares refinement method. The initial force fields considered are based on the bending and interaction force constants obtained from the CNDO/Force calculations and the stretching force constants transferred from chemically related molecules. Vibrational frequencies of H₂CO, D₂CO, HDCO, H₂¹³CO and D₂¹³CO for formaldehyde, CH₃CHO, CH₃CDO, CD₃CHO, CD₃CDO and CH₂DCHO for acetaldehyde, and CH₃COCH₃ CD₃COCH₃ and CD₃COCD₃ for acetone are employed in the force field refinements. The final force fields obtained are found to be reasonable with respect to the diagonal and interaction force constants.     

Formulation of the vibrational theory in terms of redundant internal coordinates

Using the generalized inverse of matrices and the method of canonical matrices, this paper develops an unambiguous formulation of the theory of small vibrations of molecules which is valid when redundant internal coordinates are used. Such treatment includes the attainment of unambiguous relationships relating the compliance matrix (the generalized inverse of the canonical force constants matrix) with experimental data (vibrational frequencies, Coriolis coupling constants, centrifugal distortion constants and mean-square amplitudes). Moreover, expressions for the elements of the Jacobian matrices of the above magnitudes with respect to the compliance constants have been also obtained as well as some sum rule relationships.     

Calculation of optimum geometries and force fields by the CNDO/force method

CNDO/Force calculations have been performed on a series of molecules, H₂CO, F₂CO, CF₄, CHF₃, CH₂F₂ and CH₃F. The optimum geometries and force fields are reported. It is found that the method can successfully predict the geometries of polyatomic molecules. The bending force constants and interaction force constants are, in general, comparable with experimental values both with respect to sign and magnitude. The stretching force constants have higher values than the experimental force constants. However, the trend in stretching force constants of a series of molecules is comparable with that of the corresponding experimental values.     

The vibrational spectra of cyanoethylenes

The frequencies and forms of the vibrations of acrylonitrile, cis- and trans-dicyanoethylenes, tricyanoethylene, and tetracyanoethylene have been calculated using various sets of force constants which take account of bond interaction. It has been shown that the vibrational spectra of all the cyanoethylenes (like those of cyanoacetylene and cyanogen studied earlier) are described by means of force constants which are extremely similar to those for simple molecules containing the same bonds. The observed values of the force constants characterizing the C=C, C-C, and C=N bonds and their interaction have been compared with the constants in hydrocarbons with analogous structures and in simple molecules. It has been concluded that in cyanoethylenes the intramolecular mutual influence of the multiple bonds leads to very slight delocalization of the electrons, compared with that for conjugated hydrocarbons.     

Chiral force constants: Recommendations for the presentation of internal coordinate force constants

Some force constants associated with the internal coordinates that sense handedness or chirality can have opposite signs in the enantiomers of chiral molecules. Examples of such force constants include interaction force constants between a torsional and stretching or bending internal coordinates. The sign reversal for these force constants in the enantiomers of chiral molecules or in opposite-handed molecular segments is best recognized by labeling them as chiral force constants. Recognition of chiral force constants suggests that certain guidelines are to be followed in the presentation of internal coordinate force constants. © 1993 by John Wiley & Sons, Inc. © John Wiley & Sons, Inc.     

Force Constants and Bond Orders of Nitrogen Bonds

The force constants and the corresponding bond orders of nitrogen bonds have been calculated from the vibrational spectra (infrared and Raman spectra) of a great number of nitrogen compounds. Plotting the maximum bond order of stable nitrogen bonds against the sum of Pauling's electronegativities of the bonding partners (Σx) leads to one continuous curve for the N? X bonds where X represents elements of the first and the second short period of the periodic table. Furthermore, when the bonds formed between these elements are arranged in a coordinate system in such a way that the position of each bond is determined by the difference between the electronegativities of the bonding partners (Δx along the ordinate) and the sum of the electronegativities of the bonding partners (Σx along the abscissa), the bonding partners capable of forming multiple bonds all lie within a closed domain, where their position can be correlated with their polymerizability and other reactivities of the multiple bonds. Also discussed are the orders of bonds between nitrogen and some transition elements. In an appendix, the present methods used to calculate force constants and bond orders are surveyed.     

Separated internal force constants for the ethylene and ethane molecules and their use for calculation of the force field for the propylene molecule

We consider the question of separation of linear combinations of force constants for ethylene and ethane. Introduction of a perturbation into the matrix of the kinematic coefficients allows us to solve the inverted vibrational problem using the matrix method of successive approximations without eliminating dependent coordinates. Such an approach makes it possible to obtain a sufficient system of equations for determining the separated internal force constants. The separated internal force constants determined for ethylene and ethane are used to calculate the force field for propylene. The calculated separated internal force constants for propylene reproduce its vibrational spectrum and the spectrum or propylene-d₆ with average deviation from experimental frequencies of 8 cm^–1. The numerical influence coefficients for stretching vibrations of the C-H bond are linearly related to the lengths of these bonds.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 22, No. 1, pp. 118–122, Janauary–February, 1986.     

Explicit representation of anisotropic force constants for simulating intermolecular vibrations of multiply hydrogen-bonded systems

We investigated the mechanical nature of multiply hydrogen-bonded systems by means of ab initio quantum chemical calculations, and we derived a set of force constants to reproduce the anisotropic vibration modes of such systems. Twenty multiply hydrogen-bonded molecular dimers were selected for evaluation of the stiffness of their hydrogen bonds. By means of a multivariate analysis, the principal values of the stiffness tensor were divided into the contributions from each hydrogen bond. Force constants in the stretching directions were estimated to be 20.2 and 11.5 N m(-1) for NH...O and NH...N pairs, respectively. The obtained parameter set was used to reconstruct the various intermolecular vibration motions, and reasonable values in the low-frequency (ca. terahertz) region were obtained. Comparison of the multivariate analysis with the normal-mode analysis suggested that the off-diagonal terms for the transverse and rotational motions may appreciably contribute to the coupling of those basic motions.     

Scaled Quantum Mechanical Force Fields for the Peroxynitrates. II. Fluorocarbonyl Peroxynitrate and Chlorocarbonyl Peroxynitrate.

The vibrational properties of fluorocarbonyl peroxynitrate, FC(O)OONO₂ and chlorocarbonyl peroxynitrate, ClC(O)OONO₂ were studied by means of density functional theory (DFT) methods. The obtained results served to revise the reported experimental spectra and their corresponding assignments. Subsequently, the revised data were used in the definition of scaled quantum mechanics (SQM) force fields for these peroxynitrates. A set of internal force constants was also calculated from such force fields.     

Etude vibrationnelle des oxydes PbO α et PbO β: Interpretation en relation avec la dilatation thermique

A normal coordinate analysis of the Raman and ir vibrational spectra of PbO α and PbO β allowed us to calculate the force field for both phases. The cohesion between the structural layers is realized by means of attractive interactions involving the lone pair of the Pb^II atoms. The analysis of the potential energy distribution shows that these interactions are much weaker than the PbO bonds in the layers. The calculated force constants for these bonds vary inversely as a function of their distance and allow one to explain the value of the thermal expansion coefficients in the layers. On the other hand, the abnormally small value of the thermal expansion along the normal direction to the layers, particularly for PbO β, may be explained only in assuming the existence of a negative contribution due to a modification of the relative orientation of the dipoles (Pb^II-lone pair) situated on two adjacent layers.     

Bond stretching force constants and compressibilities of nitride,oxide, and sulfide coordination polyhedra in molecules and crystals

Molecular quadratic stretching force constants are calculated for a variety of MX bonds (X = N, O, S) in coordinated polyhedra containing row 1 and 2 metal atoms, M, using SCF molecular orbital methods and 6-31G^* basis sets. The resulting data scatter along three distinct trends, depending on whether the bonds involve row 1 atoms, row 1 and row 2 atoms, or row 2 atoms. When compared with spectroscopically determined force constants, the calculated force constants are found to be 20% larger. A single trend seems to obtain when the calculated force constants are plotted as a function of the effective nuclear charges of the bonded atoms and their interatomic separations. Scaled force constants calculated for the SiO bond are in rough agreement with values provided by spectroscopic measurements for silicic acid molecules and silicate crystals. Polyhedral compressibilities for nitride-, oxide-, and sulfide-coordinated polyhedra are inversely related with force constants calculated for their MX bonds. The close similarity of these compressibilities and those recorded for chemically similar crystals suggests that force constant-compressibility relationships in chemically similar molecular and crystalline systems are not significantly different.     

Maximum Interaction Model Force Constant Calculation of the Mlx (Co)6-x Type Molecule

C—O stretching frequency of inorganic carbonyl molecules is quite characteristic in the vibrational spectroscopy (the IR and Raman). Since such stretching modes are quite different from the skeletal modes, a non-mechanical coupling model has been proposed by Cotton¹⁾. The C—O stretching force constants and their interaction constants may be calculated semiquantitatively from their characteristic frequencies. The trouble is that the number of vibrational frequencies is always less than the number of force constants, whenever a symmetry irreducible representation contains more than one frequency. Cotton suggest that the interaction constants for octahedral type molecule from the dpπ bonding point of view^1-2). Instead of this, a model of maximum interaction between M—C—O bonds is proposed in this paper. Such model not only gives better remedy to the problem of octahedral complexes, but also is useful to solve the normal modes in molecules of trigonal bipyramidal and many other symmetries.     

Vibrational spectra,force fields and NMR-data for triorganyl-tetrelomethanes CH4−n(TtR3)n (Tt = Sn and Pb)

Based on vibrational spectra normal coordinate calculations have been carried out for trimethyltetrelomethanes CH_4−n(TtMe₃)_n (Tt = Sn and Pb, n = 2 and 4). The resulting comparable force constants of the two distinguishable types of carbon-metal bonds for Tt = Sn (range K(C-Sn) 220 - 180 Nm⁻¹) are 10 – 15% higher than for Tt = Pb (K(C-Pb) 190 - 170 Nm⁻¹). These force constants K(C-Tt) are similar to the K(C-Hg) values of corresponding methylmercuriomethanes CH_4−n(HgMe)_n. The force constants K (C-Tt), and also the coupling constants ¹J(Tt,C) from NMR spectra, indicate weakening of the carbon-metal bonds in the central CTt_n groups with growing n, whereas the peripheral TtMe bonds are almost unaffected by variations of n.     

Force fields and assignments of the vibrational spectra of acridine and phenazine—an ab initio study

A complete set of force constants and their corresponding scale factors in non-redundant local coordinates were obtained by fitting the in-plane ab initio Hartree–Fock (HF) vibrational frequencies computed using 4-21G and 6-31G^** basis sets to the experimental ones. Using these force constants the potential energy distribution (PED) of the normal modes was obtained and based on the PED the earlier empirical assignments were either confirmed or reassigned for all the in-plane fundamentals. The force constants of acridine and phenazine are compared to those of anthracene to study the similarities and differences. Probable assignment is proposed for the out-of-plane fundamentals of acridine based on Durig's simple scaling of the local force constants.     

INFRARED SPECTROSCOPIC STUDIES OF SOME URANYL NITRATE COMPLEXES

Abstract

The infrared spectra of ammonium, potassium, rubidium and cesium uranyl trinitrates (NH₄UO₂(NO₃)₃, KUO₂(NO₃)₃, RbUO₂(NO₃)₃ and CsUO₂(NO₃)₃) have been measured in the region from 4000 cm^?1 down to 30 cm^?1. A normal coordinate analysis of the complexes has been made as a six-body problem (UO₂ X₃) (X=NO₃) neglecting the outer cations. Force constants of U-O and U-X bonds in UO₂X₃ anion have been approximately obtained on the basis of a modified valence force field including an additional force constant of opposite U[sbnd]O bond-bond interaction. In addition, bond order of the uranyl bonds of the complexes has been determined from the U[sbnd]O stretching force constants and compared with those of other uranium compounds such as metal uranates and uranium oxides.