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.     

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 IV Centrosymmetric Linear Quadratomics

A simple spring model for molecular vibrations, which uses Cartesian co-ordinates for both longitudinal and transverse displacements, is applied to centrosymmetric linear quadratomic molecules, such as cyanogen and acetylene and its halogenated derivatives. Analytical expressions for the three stretching and two bending mode frequencies are obtained in terms of five independent force constants. By substitution of Raman and infrared frequencies, values of these force constants are obtained and briefly discussed. The validity of the model is confirmed by the satisfactory agreement between calculated and observed frequencies of isotopic species.     

The vapour phase Raman spectra,Raman band contour analyses,Coriolis coupling constants,and e-species force constants for the molecules HCF3, ClCF3, BrCF3, and ICF3

The vapour phase Raman spectra of the molecules HCF₃, ClCF₃, BrCF₃, and ICF₃ have been recorded at pressures of up to 1 atmosphere over the fundamental frequency regions. The Raman band contours of the e-species fundamentals have been analysed to yield first-order Coriolis coupling constants from which, together with the fundamental frequencies, e-species force constants of the general harmonic potential function have been evaluated. One force field was found for fluoroform, but two different ones were found for the molecules ClCF₃, BrCF₃ and ICF₃.     

Calculation of force constants and mean amplitudes of vibration of octahedral XY6 molecules using frequencies and zeta constants

Expressions involving vibrational frequencies, Coriolis coupling constants and masses of the atoms of the molecule that are invariant under symmetrical isotopic substitutions are derived for octahedral XY₆ molecules following the method given by Jagannathan and others. These invariants are used to calculate the force constants, compliance constants and mean amplitudes of vibration of 13 molecules of XY₆-type.     

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.     

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.     

The Degenerate Vibrations of BCl3, BBr3 and BI3 with Application of Keating Coordinates

The experimental works of vibrational spectroscopy and normal coordinate analyses for BCl₃, BBr₃ and BI₃ are reviewed extensively. Harmonic force fields of the E' species are produced using isotopic frequencies and Coriolis constants as additional data, respectively. The usefulness of Keating coordinates versus valence coordinates as basis of force field approximations is discussed. The conclusions are not unequivocal, but they go in favour of the Keating coordinates when the reliability of the different computations is taken into account. Boron trichloride is treated specifically in some detail. Final force fields are proposed for the title molecules with the aid of the mass influence on Coriolis constants.     

Geometrical structures,vibrational frequencies,force constants and dissociation energies of isotopic water molecules （H2O,HDO, D2O,HTO, DTO,and T2O） under dipole electric field

The dissociation limits of isotopic water molecules are derived for the ground state. The equilibrium geometries, the vibrational frequencies, the force constants and the dissociation energies for the ground states of all isotopic water molecules under the dipole electric fields from -0.05 a.u. to 0.05 a.u. are calculated using B3P86/6-311++G(3df,3pf). The results show that when the dipole electric fields change from -0.05 a.u. to 0.05 a.u., the bond length of H-O increases whereas the bond angle of H-O-H decreases because of the charge transfer induced by the applied dipole electric field. The vibrational frequencies and the force constants of isotopic water molecules change under the influence of the strong external torque. The dissociation energies increase when the dipole electric fields change from -0.05 a.u. to 0.05 a.u. and the increased dissociation energies are in the order of H2O, HDO, HTO, D2O, DTO, and T2O under the same external electric fields.     

Force field calculations of acetonitrile using CNDO/force method

The redundancy-free internal valence force field (RFIVFF) of acetonitrile is reported using CNDO/force method. The initial force field is set up by taking the interaction and bending force constants from CNDO force field and transferring 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 harmonic frequencies of CH₃CN,¹³CH₃CN, CH₃ ¹³CN, CH₃C¹⁵N, CD₃CN and CD₃ ¹³CN. The final force field thus obtained is found to be excellent on the basis of frequency fit and potential energy distribution.     

Normal co-ordinates through coriolis coupling constants

Normal co-ordinates, force fields and isotopic frequencies have been calculated for someXY ₃ andXY ₄-type molecules using coriolis coupling constants.     

Force field calculation for inplane vibrations of ethylene usingcndo/Force method

cndo/Force method is used to evaluate redundancy-free internal valence force field (rfivff) for inplane vibrations of ethylene. The bending force constants, the stretch-band and bend-bend interaction force constants are predicted reasonably well in magnitude and sign by this method; whereas stretching force constants and stretch-stretch interactions are overestimated. Initial force field is set up by transferring stretching force constants from structurally-related molecules and including the rest of the force constants fromcndo force field. The field so constructed is subjected to refinement by the least square method. A total of 64 vibrational frequencies of C₂H₄, C₂D₄, C₂H₂D₂ and their¹³C isotopic modifications are used to determine force field containing 15 parameters. The final force field is found to be reasonable on the basis of frequency fits, potential energy distribution and band assignments.     

Microwave spectra of HPO and DPO: molecular structure

Microwave spectra of the unstable phosphorus containing molecule, HPO, and its deuterated species were measured in the frequency range of 70-380 GHz. The molecule was produced by a DC-glow discharge of a gas mixture of PH₃, CO₂, and H₂(D₂). Rotational constants and centrifugal distortion constants for HPO and DPO were determined accurately. Harmonic force constants were evaluated from the centrifugal distortion constants determined in the present study, and with vibrational frequencies reported previously. The zero-point average structure for HPO was obtained by taking the isotopic difference of the PH bond length into consideration: r_z(PH)=1.473(7) Å, r_z(PO)=1.4843(9) Å, and θ_z=104.57(16)°. The errors were estimated from the residual inertial defect. Equilibrium bond lengths for the PH and PO bonds were derived as 1.455(7) and 1.4800(9) Å, respectively, by assuming anharmonic constants of the corresponding diatomic molecules.     

The vapor phase Raman spectra,Raman band contour analyses,Coriolis coupling constants,and e-species force constants of the molecules SPF3, FCCl3, and BrCCl3

The vapor phase Raman spectra of the molecules SPF₃, FCCl₃, and BrCCl₃ have been recorded at pressures of up to 1 atm over the fundamental frequency regions. The Raman band contours of the e-species fundamentals have been analyzed to yield first-order Coriolis coupling constants from which, together with the fundamental frequencies, e-species force constants of the general harmonic potential function have been evaluated. The results for thiophosphoryltrifluoride are compared with those deduced previously on the basis of infrared band contour analyses.     

Calculation and interpretation of vibrational spectra of halogen-substituted ethanes

The frequencies, forms of the normal vibrations, and the potential energy constants of the CH₃CHF₂, CH₃CHCl₂, and CH₃CHBr₂ molecules were calculated. The interpretation of the vibrational spectra existing in the literature was refined, and the characteristics of the force field in these molecules were established.     

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.     

Correlation Relationships Between Geometric and Vibrational Parameters of Simple Sulphone Molecules

Empirical correlation relationships are presented between vibrational frequencies and force constants on one hand and bond lengths on the other, characterizing the SO₂ group for a series of simple sulphone molecules.     

Use ofD J,DJK constants for the unique fixing of intramolecular forces inXY 3 pyramidal molecules

A mathematical formalism is developed to evaluate all the possible sets of intramolecular force fields fitting fundamental vibrational frequencies and centrifugal distortion constants in the case ofXY ₃ pyramidal type molecules. The method is applied to PF₃ molecule as an example. It is found that there exist as many as four sets of force field fitting all the above experimental data. A few general criteria are suggested to eliminate the suprious sets, thus making further experimental data unnecessary to fix the true physical force field.