Theoretical study of dynamical properties on reaction path in molecular internal coordinates

The dynamical properties on reaction path (IRC) in internal coordinates have been obtained, which in. clude ω_K (frequencies orthogonal to IRC), L_K (vibrational modes), B_(KF) (coupling constants between the IRC and vibra tions orthogonal to it), B_(KL) (coupling constants between every two vibrations orthogonal to IRC). A set of theory of teac. tion path in molecular internal coordinates has been also constructed. The dynamical properties, including ω_K, B_(KF) B_(KL) of the reaction H~1O~2H~3 H~4→H~1O~2 H~3H~4 have been calculated, which explicitly explain the interaction, chang ing trend and contribution of each chemical bond (including bond angle) in the reaction.     

Force field for in-plane vibrations of isophthalonitrile

Summary The general quadratic force field for the in-plane vibrations of isophthalonitrile was calculated by the semi-empirical MINDO/3 method. This force field was refined to the frequencies observed experimentally for isophthalonitrile and isotopic shifts of isophthalonitrile-¹⁵N₂. The normal coordinates and the force field in internal coordinates were also calculated from the refined field.

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Kräftefeld für die nichtebenen Schwingungen von Isophthalsäuredinitril

Zusammenfassung Das allgemeine quadratische Kräftefeld für die nichtebenen Schwingungen von Isophthalsäuredinitril wurde mit der halbempirischen MINDO/3-Methode berechnet. Das Kräftefeld wurde aufgrund der experimentalen Frequenzen von Isophtalsäuredinitril und der Isotopen-Verschiebungen von Isophtalsäuredinitril-¹⁵N₂ verfeinert. Die Normalkoordinaten und das Kräftefeld in inneren Koordinaten wurden auch vom verfeinerten Kräftefeld berechnet.

     

Ab initio calculations of the ultraviolet resonance Raman spectra of uracil

An equation been derived to calculate, ab initio, the frequencies and intensities of a resonant Raman spectrum from the transform theory of resonance Raman scattering. This equation has been used to calculate the intensities of the ultraviolet resonance Raman spectra from the first π-π* excited state of uracil and 1,3-dideuterouracil. The protocol for this calculation is as follows: (1) The force constant matrix elements in Cartesian coordinate space, the vibrational frequencies, and the minimum energy ground and excited state geometries of the molecule are calculated ab initio using the molecular orbital program Gaussian 92, (2) the force constants in Cartesian coordinates are transformed into force constants in the space of a set of 3N – 6 nonredundant symmetrized internal coordinates, (3) the G matrix is constructed from the energy minimized ground state Cartesian coordinates and the GFL = LΛ eigenvalue equation is solved in internal coordinate space, (4) the elements of the L and L^?1 matrices are calculated, (5) the changes in all of the internal coordinates in going from the ground to the excited state are calculated, and (6) these results are used in combination with the transform theory of resonance Raman scattering to calculate the relative intensities of each of the 3N – 6 vibrations as a function of the exciting laser frequency. There are no adjustable parameters in this calculation, which reproduces the experimental frequencies and intensities with remarkable fidelity. This indicates that the Dushinsky rotation of the modes in the excited state of these molecules is not important and that the simplest form of the transform theory is adequate. © 1995 John Wiley & Sons, Inc.     

Peculiarities of the vibratioanl spectra of molecules adsorbed on the surface of heterogeneous catalysts: theoretical analysis

The vibrational spectra of adsorption complexes resulting from the adsorption of ammonia on the surface of heterogeneous catalysts are interpreted by computation of frequencies and forms of normal vibrations. The characteristics of normal vibrations are computed from the state of separate fragments of adsorption complexes. It is shown that an interaction of internal coordinates, associated with the adsorption bond, with internal coordinates of the adsorbed molecule leads to a decrease of characteristics of vibrations sensitive to the surface area. A correlation is established between the characteristics of such vibrations and the changes in their frequencies in comparison with the free molecule.     

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.     

Model calculations of the vibrations of bonded water molecules

Model calculations have been made of the vibrational frequencies and normal modes of a water molecule vibrating in a combined internal and external field. A constant internal force field has been used together with an external central force field from four or three nearest-neighbour atoms to the water molecule. These neighbour atoms have been arranged either tetrahedrally or trigonally around the water molecule. The external force field has been further restricted by the use of five possible site symmetries for the water molecule, C_2v, C₂, C_s(σ_xz, C_s(σ_yz) and C₁. A series of calculations have been made where the external force constants have been varied within the range 1—80 Nm^?1.The nine calculated normal modes can be divided into three groups: intra-molecular, rotational and translational vibrations. Among the rotational vibrations it is found that, in the tetrahedral environment, the rocking mode occurs at lower frequencies than the twisting and wagging modes, whereas the opposite occurs for the trigonal environment. Frequency ratios have been calculated using the isotopic species H₂O, D₂O, HDO and H,¹⁸O. The twisting and wagging modes have the vH₂O/vD₂O ratio in the range 1.35-3-1.41 and the rocking mode in the range 1.26—1.41.     

General methods of analysing molecular vibrations

An acute need may arise to develop for the complete analysis of molecular vibrations practically convenient general methods based on coordinates other than “chemical coordinates”. One reason is the proven proposition: Among independent internal coordinates corresponding to a molecule, there cannot be one which describes a small displacement of a chemical group as a whole relative to a certain molecular plane, provided this group contains more than two linearly or three non-linearly arranged atoms. Two methods are presented in some detail. The first is based on the use of X⁰_δ coordinates which are components of “bond vectors” in the “sown” (for each “bond”) Cartesian coordinate system. The second method utilizes X⁰ coordinates, i.e. the components of atomic displacements in the “down” (for each atom) Cartesian coordinate system. Computation of the torsional vibration of transdichloroethane is given as an example illustrating the first method. The Mayants treatment of the symmetry of a molecule, proceeding from elementary considerations which do not use the group theory explicitly and are valid for any coordinates, is expounded in a somewhat improved version. The peculiarities arising when considering the mean-square amplitude matrix, Σ, in X⁰_δ and X⁰ coordinates are also discussed.     

The exact isotope rule for symmetrically substituted molecules

The vibrational frequencies of isotopically substituted molecules are related exactly and explicitly to the parent molecules through a mixing parameter, following the method developed by Sheth (C. V. Sheth, J. Phys. B: Atom. molec. Phys. 8, 121 (1975)) using Cartesian displacement coordinates. It is shown that the explicit expressions for vibrational frequencies for symmetrical isotopic substitution of a non-linear X Y²-molecule coincide with that of DeWames and Wolfram (R. E. DeWames and T. Wolfram, J. chem. Phys. 40, 853 (1964)) derived from Green's function. The present procedure has the advantage of working with only symmetry coordinates belonging to genuine vibrations as compared to Green's function technique. Explicit expressions for vibrational frequencies for symmetrically substituted pyramidal X Y³-and tetrahedral X Y⁴-molecules are given for the first time involving properly defined mixing parameters. Using these expressions a theoretical justification of Noether's empirical rule (G. Herzberg, Infrared and Raman Spectra. Van Nostrand, New York (1945); H. D. Noether, J. chem. Phys. 11, 97 (1943)) is given for the first time in the cases considered.     

Infrared spectra of bis(trifluoromethanesulfonyl)imide based ionic liquids: Experiments and DFT simulations

We measured the far- and mid-infrared spectra of three ionic liquids having bis(trifluoromethanesulfonyl)imide anions and three different cations of the families of pyrrolidinium and ammmonium ions. The molecular vibrations of the individual ions were calculated by means of DFT theory at the B3LYP/6-31G** level: we found good agreement between the experimental and the computed frequencies. The infrared lines are ascribable to molecular vibrations of the single ions, suggesting an extremely weak interaction between anions and cations. The spectral lines found experimentally between 760 and 1050 cm⁻¹ are fingerprints for different cations. The comparison with the calculated frequencies allows the assignment of the experimental spectral lines to specific molecular vibrations of anions and for the first time of the specific cations of the measured ionic liquids.     

Molecular vibrations of complexes with trigonal ligands: Part IX. Zr(BH4)4

The molecular vibrations of Zr(BH₄)₄ are analysed on the basis of a T_d model. Symmetry coordinates are described and classified into those of ligand vibrations and central-part vibrations. A simple force field is deduced, which gives satisfactory agreement with experimental vibrational frequencies and mean amplitudes of vibration. A continuation of the work by considering the probably more realistic T model is suggested.     

Infrared and Raman spectra of terephthalonitrile and terephthalonitrile-15N2. Force field for out-of-plane vibrations

A general assignment of the vibrational spectra of terephthalonitrile and terephthalonitrile-¹⁵N₂ is proposed on the basis of their infrared and Raman spectra. The relevant symmetry is found to be D_2h. The force field for the out-of-plane vibrations of these molecules was calculated by refining the general quadratic force field obtained by the semi-empirical MINDO/3 method, starting with a geometry optimized by this method. The refined force field reproduces the observed frequencies of the out-of-plane vibrations to better than ±0.5 cm⁻¹.     

Analyse en coordonnees normales des vibrations de la 4-nitropyridine N-oxyde

A 51-parameter force field is established for the vibrations of the 4-nitropyridine N-oxide (NPO) and the 4-nitropyridine-d₄ N-oxide (NPO-d₄) molecules. The mean error between the 72 observed and calculated frequencies is 4.8 cm⁻¹ for the in-plane vibrations and 2.1 cm⁻¹ for the out-of-plane vibrations. The NCA calculations confirm our previous assignments for the NPO spectra, but four frequencies were permuted for NPO-d₄. The force field calculations were extended to fit the vibrational frequencies of NPO in solution in CCl₄, MeOH and H₂O. The fact that a donor solvent favours one resonant form of NPO is clearly demonstrated by the variations of five force constants.     

Vibrational spectra and normal coordinate analysis of p-cresol and its deuterated analogs

I.r. and Raman spectra of p-cresol and its seven deuterated analogs were investigated in dilute solutions of hydrophobic solvents. Assignments of the observed i.r. and Raman bands were made on the basis of isotopic frequency shifts, Raman polarization properties, i.r. intensifies and normal coordinate calculations. The calculated normal frequencies are in good agreement with the experimental ones: the average error below 1700 cm⁻¹ is 3.8 cm⁻¹ for 164 in-plane vibrations and 3.3 cm⁻¹ for 59 out-of-plane vibrations. The calculated vibrational modes may be useful in analysing the vibrational spectra of tyrosine. It is suggested that several doublets due to Fermi resonance and a trio of Raman bands in the 1260-1160 cm⁻¹ region are potential probes for the micro-environments of tyrosine side chains in proteins.     

Efficiency of post-Hartree-Fock force field for the interpretation of vibrational spectra ofN,N-dimethylnitramine

Harmonic force fields for the molecule ofN,N-dimethylnitramine were calculated in the RHF/6-31G^* and MP2/6-31G^** approximations. Scaling of the force fields obtained made it possible to reliably interpret the vibrational spectra of light and perdeuterated compounds reported in the literature. The assignment is confirmed by good reproducibility of experimental isotope shifts upon¹⁵N-amino- and¹⁵N-nitrosubstitution. The frequencies of intramolecular vibrations in far IR and Raman spectra as well as in neutron inelastic scattering spectra for the light and perdeuterated samples of solidN,N-dimethylnitramine were identified using the force field calculated with the inclusion of electron correlation (MP2). Although general structures of the force fields calculated in the RHF and MP2 approximations are similar, considerable differences in the force constants of the NO and NN stretching vibrations and especially in the constants of the NO_str/NO_str and NO_str/NN_str interactions remain even after scaling the force fields.     

Theoretical IR,Raman and NMR spectra of 1,2- and 1,3-dimethylenecyclobutane

Equilibrium geometries, rotational constants, harmonic vibrational frequencies, infrared intensities, Raman activities, and ¹H and ¹³C NMR spectra were calculated for 1,2-dimethylenecyclobutane and its less stable isomer 1,3-dimethylenecyclobutane by using MP2, DFT (B3PW91), and RHF theoretical methods involving the 6-311++G⁷ basis set.The properties calculated theoretically have been compared with the experimental values. The internal coordinates defined for both isomers were used in the potential energy distribution (PED) analysis. The theoretical vibrational and NMR spectra form the basis to differentiate particular compounds in reaction mixture.     

The vibrational spectra of N-Cl maleimide

The infrared spectra of N-Cl maleimide as a Nujol mull and dissolved in various solvents were recorded between 4000 and 30 cm^?1. Raman spectra of the crystalline solid and saturated solution in CH₃CN were recorded and semiquantitative polarization measurements were made.The fundamental frequencies have been tentatively assigned in terms of C_2V symmetry, based upon Raman polarization data and analogies with the spectra of maleimide and maleic anhydride. A force field was derived by initially transferring force constants from maleimide. After small iterations a satisfactory correspondance was achieved between the observed and calculated in-plane modes whereas larger discrepancies remained for some of the out-of-plane vibrations.     

FTIR and Raman studies on benzimidazole

The FTIR and laser Raman spectra of benzimidazole have been recorded. The observed frequencies were assigned to various modes of vibrations on the basis of normal coordinate calculations, assuming C_s point group symmetry. The potential energy distribution associated with normal modes is also reported here. The assignment of fundamental vibrations agrees well with the calculated frequencies.     

Low frequency vibrations in crystalline biphenyl: Model calculations and raman and neutron spectra

Vibrational frequencies of crystalline biphenyl have been calculated in the rigid phenyl approximation using the crystal structure at 110 K. The calculated results explain successfully the experimental infrared and Raman frequencies as well as the polarization data of the Raman bands at 80 K that have been observed in the present study for the first time. The frequency dispersion curves calculated in the b^* direction show that the coupling between the intramolecular CC torsion and the translational lattice vibrations changes drastically as the wave vector changes. The existence of a minimum frequency point located away from the Brillouin zone boundary indicates that the pulse transition near 40 K is a commensurate—incommensurate one in accordance with the results of neutron diffraction that have recently been reported. Incoherent inelastic neutron scattering spectra have also been investigated above and below the phase transition temperature.     

Vibrational analysis of l-alanine and deuterated analogs

Raman spectra of the polycrystalline l-alanine analogs CH₃CH(NH⁺₃)COO^?, CH₃CH(ND⁺₃)-COO^?, CD₃CD(NH⁺₃)COO^?, and CD₃CD(ND⁺₃)COO^? have been obtained. A normal coordinate analysis is carried out based on the experimental frequencies of the four isotopic analogs and a 34 parameter valence-type force field defined in terms of local symmetry coordinates. The final refinement, in which five stretching force constants are constrained to fixed values obtained from bond length data, results in an average error of 7 cm^?1 (0.9%) for the observed frequencies of the four isotopically substituted molecules. Band assignments are given in terms of the potential energy distribution for local symmetry coordinates. For non-deuterated l-alanine, the vibrations above 1420 cm^?1 and below 950 cm^?1 may be described as localized group vibrations. By contrast, the eight modes in the middle frequency range, viz. the three skeletal stretching, the COO^? symmetric stretching, one NH⁺₃ rocking, the symmetric CH₃ deformation, and the two methyne CH deformation vibrations, are very strongly coupled to one another. Some decoupling appears to take place in the perdeutero molecule, and all but five modes can be described as localized group vibrations.     

Normal coordinate analysis of H8Si8O12

Normal coordinate analysis of the fundamental vibrations of H₈Si₈O₁₂ has been carried out. Because of the octahedral symmetry, the 78 vibrational degrees of freedom lead to 33 different vibrations, six of which are infrared active, 13 are Raman active and 14 are inactive. From the internal coordinates one gets 116 symmetry coordinates. We describe a straightforward method for determining the internal symmetry coordinates of any molecular system. Internal coordinates, symmetry force constants, the full set of orthonormal symmetry coordinates as well as the 38 redundant orthonormal symmetry coordinates of H₈Si₈O₁₂ are tabulated. The potential energy distribution analysis shows that most of the fundamental vibrations can be very well interpreted in terms of the internal vibrations ν(SiH), ν(SiO), δ(SiH), δ(OSiO) and δ(SiOSi) which makes it easy to compare them with vibrations observed in other silsesquioxanes and similar silicon compounds.