Rotational harmonicity

In the rigid-rotator, harmonic-oscillator approximation Eq. (72) becomes... 

The theory of rotational and vibrational Raman intensities is discussed in detail elsewhere (e.g.. References 1-6). Relative rotational Raman intensities are proportional to Raman line strength factors (S ). For rigid rotator, harmonic oscillator diatomic molecules S (J.,Jf) = 3(Jj+1)(Jj+2)/(2(2L+3)) where J is a rotational quantum number. However, real molecules are not rigid rotators and S must be... 

IV. Nonlinear Polyatomic Molecule (Rigid Rotator, Harmonic Oscillator]... 

Spectroscopic constants used in calculating corrections to rigid rotator-harmonic oscillator approximation (cm ) ... 

Spectroscopic constants used In calculating corrections to the rigid-rotator harmonic oscillator model (cm" ) ... 

Gordon (2) has used the constants listed above to calculate C from 298.15 to 6000 K by the method of Pennington and Kobe (3), which takes anharmonicity. vibration-rotation interaction, and centrifugal stretching into account. The constants have been taken from ( , 5, 6, 7, 8). The thermodynamic functions below 298.15 K have been calculated for the rigidly rotating harmonic oscillator. 

Functions were calculated from the constants given above using the rigid rotator harmonic oscillator method. The entropy was increased by R tn 2 because two rotameric forms are implied by use of the torsional frequency. Small but arbitrary adjustments were made in the assignment of the bending mode frequencies in order to reproduce the vapor pressure data of Scott et al. (1 ) as closely as possible. Calculated values of S (298.15 K) = 57.03 and S (340 K) = 58.70 cal k" raol" may be compared with 56.99 and 58.69, respectively, derived from the data of Scott et al. Internal rotation calculations would require a complex potential function in order to fit the data. The barrier to inversion (990 cm 2.8 kcal mol ) is slightly less than the barrier to... 

Rosenblum, E.l.Dashevskaya, E.E.Nikitin, and I.Oref, On the sampling of microcanonical distributions for rotating harmonic triatomic molecules, Chem. Phys. 213, 243 (1996)... 

The infra-red band spectra of molecules were first "explained in terms of whole-molecule rotation and intramolecular atomic vibrations by Bjerrum (/) in 1912. This explanation was consolidated by Kratzer (2) in 1920 who used the classical formulation (Bohr-formahsm), and confirmed by the calculations of the quantum mechanics of Schrodinger and Heisenberg in the rigid-rotator, harmonic-oscillator, ligid-rotator-CMW-harmonic oscillator, and non-rigid-rotator-CMW-anharmonic oscillator approximations 3). 

Leaute B, MarciUiacy G (1986) On the Schrodinger equation of rotating harmonic, three-dimensional and doubly anharmonie oscillators and a class of confinement potentials in connection with the biconfluent Heun differential equation. J Phys A Math Gen 19 3527-3533... 

Disregarding the tunnel effects (see Sect. 1.5) and staying within the approximation rigid rotator-harmonic oscillator, one may, for the biomolecular reaction A -h B), calculate the kinetic isotopic effect (ratio between the reaction rate constant of the compound with the light isotope and the rate constant K2 of the compound containing the heavy isotope) from the Bigeleisen equation ... 

When the rigid rotator-harmonic oscillator model was applied to molecules with two configurations separated by an energy barrier, the results obtained by Godnev (1953) were used. This author showed in... 

The selected molecular constants and electronic state excitation energies were used to calculate the thermodynamic functions in the rigid rotator-harmonic oscillator approximation over the temperature range 298.15-3000 K at standard pressure. These functions are gathered in Table A2 in the form of the coefficients of the polynomial (see Appendix). 

McCarthy et al., 1996 Melville et al., 2000 Robbins and Barrow, 1974 Rubinoff et al., 2003 Sauer et al., 1996 Schall et al., 1983, 1987 Shenyavskaya et al., 1965, 1968 Simard and James, 1992 Uttam and Joshi, 1995 Uttam et al., 1997 Verges et al., 1999 Xin and Klynning, 1994), molecular constants for most fluorides RF and some chlorides RCl have been determined only for the ground electronic state. These data are sufficient for reasonably estimating molecular constants for unknovm compounds in this state. Thus, the possibility appears to use the rigid rotator-harmonic oscillator model in calculations of the thermodynamic functions for the entire series of RF and RCl molecules. 

In the second method, the thermodynamic functions were calculated in the rigid rotator-harmonic oscillator approximation with additional inclusion of the anharmonicity of oscillations by the method of Mayer and Goeppert-Mayer (Gurvich et al., 1978-1984) and correction for centrifugal... 

Figures 36 and 37 show the plots of the reduced Gibbs energy versus temperature. Curves a were plotted from the data obtained by Krasnov and Danilova (1969) by calculation of statistical sums only for the ground states of LaF and LaCl in the rigid rotator-harmonic oscillator approximation.

The thermodynamic functions for LaF2 used for determining ArH (l, 0) and ArH°(2, 0) have been described in Section 3. They were calculated in the rigid rotator-harmonic oscillator approximation with the inclusion of electronic excitation observed for the free La ion. 

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