Molecular vibrations thermodynamic corrections

Anharmonicity of molecular vibrations presents one of the most vexing problems in studies of molecular structure. Anharmonic corrections (of first order, involving the cubic force constants) are required in accurate determinations of the equilibrium structures of molecules from rotational spectra, as well as from electron diffraction measurements. To obtain accurate harmonic force fields, it is necessary first to correct the vibrational data for anharmonicity (using second-order corrections, involving cubic and quartic force constants). Information on anharmonic force fields obtained from experimental data is also important as a basis for comparison in quantum chemical investigations of molecular forces as well as in studies of high-temperature thermodynamic properties and of rate and dissociation processes. Yet detailed studies of anharmonic force fields have hitherto been limited to small molecules with N = 2-4 atoms (in isolated cases to N = 6). 

The molecular and spectroscopic constants were obtained from Gayles and Self (2). The vibrational frequencies were corrected to the average isotropic species. The molecular configuration was reported to be staggered, analogous to that observed for B Cl.(g). The angle between two B-BF planes is approximately 90 . The thermodynamic functions were evaluated based on an... 

Electronic levels (T ) and vibrational-rotational constants of the observed states are from the optical study of Barrow et al. (J ) and the microwave work of Tiemann et al. (2). Other low-lying electronic states and their vibrational-rotational constants are estimated in isoconfIgurational groups by analogy with BaO (8) and from trends observed in the known states of the other alkaline-earth oxides and sulfides. Thermodynamic functions are calculated using first-order anharmonlc corrections to and in the partition function Q = exp(-c ej /T). Uncertainty in the energy and molecular constants for the... 

Methods to apply quantum corrections for this inadequacy of classical mechanics when applied to crystals, as well as other phases, have been explored (124-127), but there is not yet general agreement on how best to calculate thermodynamic properties for these types of systems. The practical solution of Berens and co-workers (124) entails. . calculating the velocity spectrum S(v) from molecular dynamics and then integrating S(v) over all frequencies with a weighting fimction which is the difference between the quantum and classical harmonic weighting functions for the thermodynamic variable of interest. However, as the statement avers, anharmonic contributions to the vibrational modes will not be captured correctly this relatively minor shortcoming was addressed by Hardy and co-workers (128). 

But molecules have other energy states that atoms don t. They have rotational and vibrational energy states that can have an important impact on q. Indeed, we found in our discussion of rotational spectroscopy that molecules occupy excited (that is, / > 0) rotational energy levels at normal temperatures This suggests, correctly, that the existence of such energy levels has an impact on q, and correspondingly on the thermodynamic properties of molecular gases. 

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