Rigid Rotor Harmonic Oscillator Approximation Research Articles

Vibrational spectra and torsional barrier of pentafluorophenol

The vibrational spectra of pentafluorophenol (PFP) have been investigated in the gaseous and solid states and as solutions in nonpolar solvents. An assignment of the thirty-three fundamental modes is proposed using the band contours and Raman depolarization ratios. Thermodynamic properties, calculated for a rigid-rotor harmonic oscillator approximation, are also reported. The potential barrier restricting the internal rotation about the phenyl-O bond was evaluated to be 1273 cm −1.

Ideal gas thermodynamic properties of CH4−(a+b+c+d)FaClbBrcId Halomethanes

The available molecular parameters, fundamental frequencies, and enthalpies of formation at 298.15K (ΔHf ° (298) for halomethanes of the type CH4−(a+b+c+d)FaClbBrcId have been critically evaluated and recommended values selected. Molecular parameters and ΔHf ° (298) for some halomethanes have been estimated as the experimental values for these compounds are not available. This information has been utilized to calculate the ideal gas thermodynamic properties Cp°, S°, H°−H°0,−(G°−H0°)/T, ΔHf °, ΔGf °, and logKf from 0 to 1500 K and at a pressure of one atmosphere using the rigid rotor-harmonic oscillator approximation for the following compounds: CH2FBr, CH2ClBr, CH2CH, CH2BrI, CHF2Br, CHFClBr, CHFBr2, CHCl2Br, CHClBr2, CF3Br, CF3I, CF2ClBr, CF2Br2, , CF2I2, CFCl2Br, CFClBr2, CFBr3, CCl2Br, CCl3I, CCl2Br2, CClBr3.

Ideal gas thermodynamic properties of phenol and cresols

The standard chemical thermodynamic properties of phenol, o-cresol, and m-cresol, and p-cresol were calculated by use of the rigid rotor harmonic oscillator approximation. The partition functions for internal rotation of -OH and -CH3 groups were calculated as a direct sum over the internal rotation energy levels. It was assumed that o-cresol is a mixture of two rotational isomers. Values of molecular parameters, fundamental frequencies, potential barriers to internal rotation and enthalpies of formation were selected from among those reported in the literature and from some additional molecular orbital calculations.

A vibration assignment of tetrabromothiophene

The i.r. and Raman spectra of tetrabromothiophene were recorded in the region 4000–40 cm −1. An assignment of the fundamentals has been proposed on the basis of band intensities and comparison with spectra of related molecules. The molar thermodynamic properties have been obtained at several temperatures for a rigid-rotor harmonic oscillator approximation.

Molecular constants of XeO3F2

The force constants of XeO3F2 have been evaluated using the general valence force field. The mean square amplitudes of vibration, the generalised mean square amplitudes and shrinkage constants, Coriolis coupling coefficients and centrifugal distortion constants have also been calculated for the first time using the vibrational frequencies and the structural parameters. The thermodynamic properties have been computed for the ideal gaseous state at 1 atmospheric pressure for 11 temperatures from 100° to 1000°K using a rigid rotor harmonic oscillator approximation.

Ethylene glycol: Infrared spectra, AB initio calculations, vibrational analysis and conformations of 5 matrix isolated isotopic modifications

An extension of earlier ab initio calculations is reported which consists in a more detailed structure optimization of conformations investigated earlier, using the previously described as well as a more flexible basis set. The measurement and analysis of infrared spectra of five isotopic modifications, isolated in Ar and Xe matrices, are described. The analysis of the spectra, carried out within the framework of two H-bonded conformations r e1 and r e2 predicted by ab initio calculations to be the most stable ones, is complicated by the occurrence of unusually large matrix splittings and irreversible changes of the spectra under irradiation by infrared light. The spectra are interpreted in terms of essentially two slightly different conformers of type r e1, deformed by the matrix field. The 18O isotope shifts prove to be important for correct assignment and the least squares fit. A valence force field is given, whose dependence on the conformation of the OH groups and especially on H-bonding is discussed. According to normal coordinate analysis, the effect of the internal H-bond is most pronounced in the COH bend and OH torsion region. The differences of the potential constants of free and bonded OH groups are responsible for a zero point energy differences of about 20 cm −1 of two isomers of the modification CH 2ODCH 2OH. From experimental evidence for at least a partial equilibration of these two isomers at liquid helium temperature, internal rotation of the OH groups in an Ar matrix may be deduced. Thermodynamic functions of the r e1 conformation of glycol in the rigid rotor-harmonic oscillator approximation are reported.

Ideal gas thermodynamic properties of six chlorofluoromethanes

Spectroscopic and thermal data were reviewed. The selected values for the principal moments of inertia, the vibrational fundamentals, and the standard enthalpy of formation at 298.15 K for each of the six chlorofluoromethanes were used to derive the chemical thermodynamic properties of molecules from 0 to 1500 K, based on the rigid-rotor harmonic-oscillator approximation. The calculated values are in accord with experimental heat capacities and entropies.

Infrared and raman spectra of 2,4,6-trichlorobenzonitrile

The infrared and Raman spectra of 2,4,6-trichlorobenzonitrile have been measured in the solid state and in solution. A complete vibrational assignment based on aC 2v symmetry was made using the Raman polarization data and by comparison with the spectra of benzonitrile. In the solid state, the spectra are consistent with the centrosymmetric monoclinic structure reported for the molecule. Thermodynamic functions have been calculated for the temperature range 1500-200 ° K for a rigid-rotator harmonic oscillator approximation.

Ideal gas thermodynamic properties of the eight bromo- and lodomethanes

The available molecular parameters, fundamental frequencies, and enthalpy of formation for eight bromo- and indomethanes have been critically evaluated and recommended values selected. This information has been utilized to calculate the ideal gas thermodynamic properties. C°p, S°, H°−H°0, (G°−H°0)/T, ΔHℱ°, ΔGℱ°, and log Kℱ from 0 to 1500 K using the rigid rotor-harmonic oscillator approximation.

Rotational Cut-Off and Anharmonicity Effects on Thermodynamic Properties of Gases at High Temperatures

SummaryThe exact expressions for the partition function Q and the coefficient of specific heat at constant volume Cv for a rotating-anharmonic oscillator molecule, including coupling and rotational cut-off, have been formulated and values of Q and Cv have been computed in the temperature range of 100°K to 100 000°K for O2, N2 and H2 gases. The exact Q and Cv values are also compared with the corresponding rigid-rotator harmonic-oscillator (infinite rotational and vibrational levels) and rigidrotator anharmonic-oscillator (infinite rotational levels) values. The rigid-rotator harmonic-oscillator approximation can be accepted for temperatures up to about 5000°K for O2 and N2. Beyond these temperatures the error in Cv will be significant, owing to anharmonicity and rotational cut-off effects. For H2, the rigid-rotator harmonic-oscillator approximation becomes unacceptable even for temperatures as low as 2000°K.

Kraftkonstanten, mittlere Schwingungsamplituden, Coriolis-Kopplungskonstanten und thermodynamische Funktionen der Moleküle WOCl4 und WOBr4 / Force Constants, Mean Amplitudes, Coriolis Coupling Constants, Thermodynamic Functions, WOCl4 , WOBr4

A normal co-ordinate analysis of the molecules W 0Cl4 and WOBr4 has been carried out following W ilson’s FG matrix method. Valence force constants based on known (WOCl4) and estimated (WOBr4) molecular parameters have been evaluated. The results support the assignment of the known Raman spectra of W0Cl4 . Also the mean amplitudes of vibration and the perpendicular amplitude correction coefficients K have been computed for the temperatures T = 0 and T = 298 °K. Furthermore the Coriolis coupling constants of the ζz(EaxEb)- type have been determined. Some thermodynamic functions have also been calculated for an ideal gas state at one atmosphere pressure and different temperatures using the rigid rotor harmonic oscillator approximation.

Vibrational spectra, normal modes, force field and barrier to inversion of phosphiran, phosphiran-1-d 1 and phosphiran-2,3-d 4

The infrared spectra over the range of intramolecular fundamentals of polycrystalline phosphiran and phosphiran-1-d 1 at 77 °K have been obtained and the observed frequencies assigned. Correlation field effects have been observed and analyzed in terms of the intermolecular forces operative in the unit cell. The intramolecular vibrations of phosphiran, phosphiran- 1-d 1, and phosphiran-2,3-d 4 have been subjected to simultaneous analysis in the approximation of harmonic forces and the resulting eigenvectors and potential energy distributions are presented. An estimate from the force field of the periodic barrier with inversion at phosphorus of 33 kcal mole −1 has been obtained and compared to results for similar molecules. Thermodynamic functions for phosphiran have been calculated in the rigid rotor harmonic oscillator approximation.

Normal Coordinate Treatments and Calculated Thermodynamic Properties of Phosphoryl Fluorodichloride, Phosphoryl Chlorodifluoride, Thiophosphoryl Bromide, Thiophosphoryl Fluorodibromide, and Thiophosphoryl Bromodifluoride

The Raman and ir spectra of phosphoryl dichlorofluoride, phosphoryl difluorochloride, thiophosphoryl tribromide, thiophosphoryl dibromofluoride, and thiophosphoiyl difluorobromide were collected and examined for the most probable values for the wavenumbers, intensities, and depolarization factors. The data are as follows: The Raman displacements Δσ in cm−1, the relative intensities I, and the depolarization factors ρ are for POFCl2: Δσ ( I) ρ = 207(3.6)0.55, 254(1.8)6/7, 330(1)0.6, 372(3.4)6/7, 386(5.5)0.3, 547(10)0.05, 620( w)6/7, 894( w)0.45, and 1331 ( m) p; for POF2Cl: 274(10)0.65, 274 (calculated), 410(17)0.23, 424(7)6/7, 424 (calculated), 618(10)0.05, 895( m)0.1, 948( w>)6/7, and 1358( m)0.2; for PSBr3: 115(5.5)6/7, 165(4.1)0.3, 179(5)6/7, 299(10)0.05, 438( w)6/7, and 718 ( m) p; for PSFBr2:129(7)0.6, 159.5(11)6/7, 219(10)0.5, 254(4)6/7, 274(5)0.3, 377(10)0.2, 470( w)6/7, 718( m) p, and 887 ( vw) p; and for PSF2Br: 175(28)0.5, 231(3)6/7, 288(29)0.3, 298( w)6/7, 384(7)0.25, 462( w)0.1, 474(10)0.1, 711(9)0.1, 899( w)0.75, and 930( w)0.75. No published ir spectral data were found for POFCl2, POF2Cl, PSBr3, PSFBr2, and PSF2Br. Also normal coordinate treatments were conducted for POFCl2, POF2Cl, PSFBr2, and PSF2Br on the basis of the Cs model and the one for PSBr3 on the basis of the C3 v model. The results of these treatments established the above listed wavenumbers as fundamentals and lend support for 424 and 274 cm−1 bands for POF2Cl as the missing Raman bands. The F matrix elements obtained for these molecules were determined in such a way that F matrix elements common to POF3, POF2Cl, POFCl2, and POCl3 had nearly the same values and those common to PSF3, PSF2Br, PSFBr2, and PSBr3 also had nearly the same values. Finally, the values of the thermodynamic properties for these substances were computed for the ideal gaseous state using the rigid rotator harmonic oscillator approximation at 1 atm from 200 to 1000 K.

Vibrational Spectra of Gaseous 1,1,1-Trifluoro-2-butyne

The infrared and Raman spectra of gaseous CH3C≡CCF3 have been recorded and all of the fundamental frequencies have been identified. A normal coordinate analysis indicates appreciable mixing among the symmetric CF3 vibrations and the C–C stretchings. The values of the Coriolis coefficients, ζ9 and ζ10, are consistent with those of a freely rotating methyl group. Strong Coriolis coupling has been suggested as the cause for the sharp doublet contour of the ν16 band in the Raman spectrum. The high intensities of some combination and overtone bands are explained in terms of Fermi resonance with fundamental levels. Thermodynamic functions at several temperatures have been determined in the rigid-rotor harmonic-oscillator approximation.

Molecular constants of tungsten chloride pentafluoride

A normal co-ordinate analysis of the tungsten chloride pentafluoride molecule has been carried out following Wilson's FG matrix method using a general quadratic potential function, and a set of potential energy constants is reported. The analysis supports the assignments given by Adams et al. Thermodynamic properties—heat content, free energy, entropy and heat capacity—for ideal gas state at one atmosphere pressure and with usual rigid rotor harmonic oscillator approximation have been calculated for twelve temperatures from 100 to 1000°K.

Molecular constants of SiH3C ≡ CH and SiD3C ≡ CH

A normal co-ordinate analysis of silylacetylene and silylacetylene-d3 has been carried out following Wilson'sF-G matrix method. The potential energy constants obtained therefrom have been used to evaluate rotational distortion constants and mean square amplitudes of vibration for these molecules. Thermodynamic functions, such as heat content, free energy, entropy heat capacity for the ideal gaseous state at one atmosphere pressure and with the usual rigid rotor harmonic oscillator approximation, have also been calculated for 12 temperatures from 100°K to 1000°K.

Potential Energy Constants, Rotation Distortion Constants and Thermodynamical Properties of GeH3CN and GeD3CN

AbstractThe force constants, obtained from a normal coordinate analysis of the molecules GeH3CN and GeD3CN using Wilson's F.G. matrix method, have been made use in the evaluation of rotational distortion constants for these molecules. Molar thermodynamic properties of these molecules for the ideal gaseous state at one atmospheric pressure, with rigid rotor harmonic oscillator approximation have also been obtained.

Raman spectra, normal coordinate treatment, and calculated thermodynamic properties for hydrazine and tetradeuterohydrazine

Raman displacements, relative intensities, and depolarization factors have been obtained for liquid hydrazine at room temperature. All available data concerning the structure, Raman and infrared spectra, frequency assignments, and dipole moment measurements were collected and examined for the most reliable values. Results of normal coordinate treatment based on the C 2 model are given and frequency assignments are reviewed. Also, calculated thermodynamic properties for 273.16°K to 1000°K on the basis of the rigid rotator harmonic oscillator approximation are listed. The C 8 model (suggested by others) also was considered.

Potential Energy Constants, Rotational Distortion Constants, and Thermodynamic Properties of Methylacetylenes

A special iterative method of obtaining the potential energy constants from vibrational and rotational spectra has been developed. The method has been applied to determine the potential energy constants of some methylacetylenes. The fundamental vibrational frequencies of the deuteriated and tritiated isotopic forms of the acetylenes have been calculated by transferring the force constants. The nonvanishing moments of the inertia tensor derivatives have been obtained for a CY3C≡CX type of molecule. Using a perturbation treatment, the rotational distortion constants DJ, DJK, and DK for these symmetric rotor molecules have been evaluated. These values have been compared with the values from microwave experiments where such data are available. The thermodynamic properties (heat capacity, heat-content function, free-energy function, and entropy) have been computed from the vibrational wave numbers for all the molecules. These calculations are based on a rigid-rotor harmonic-oscillator approximation for the ideal gaseous state at 1 atm pressure and for the range 100° to 1000°K.

Infrared Spectrum and Thermodynamic Properties of Gaseous Sulfur Trioxide

The infrared spectrum of sulfur trioxide was obtained under prism resolution in the gaseous state and in xenon matrices at liquid-nitrogen temperature. In both cases a satisfactory vibrational assignment of the monomeric SO3 spectrum could be made on the basis of a simple D3h symmetry model. The observed gas phase fundamentals were v3(e′) = 1391, v4(e′) = 529, and v2(a2″) = 495 cm—1. The matrix fundamentals were essentially the same as those of the gas phase except that the v2(a2″) mode was shifted to 464 cm—1. A normal coordinate treatment of the SO3 molecule was carried out and potential constants were determined for both Urey-Bradley and simplified valence force fields. Three weak absorption bands of S3O9 were also detected in the gas-phase spectrum. From the temperature and pressure variation of the intensities of these bands it was estimated that for the trimerization reaction at 298°K, Kp was approximately 1 atm—2 and ΔH298° was approximately 30 kcal/mole of S3O9. The values of the thermodynamic properties of monomeric SO3 were computed for the ideal gaseous state using the rigid rotor harmonic oscillator approximation at 1 atm from 100° to 1500°K.