Torsional band structure determination

Torsional Band Structure Determination of Electronic Spectra... 

Rigid Molecule Group theory will be given in the main part of this paper. For example, synunetry adapted potential energy function for internal molecular large amplitude motions will be deduced. Symmetry eigenvectors which factorize the Hamiltonian matrix in boxes will be derived. In the last section, applications to problems of physical interest will be forwarded. For example, conformational dependencies of molecular parameters as a function of temperature will be determined. Selection rules, as wdl as, torsional far infrared spectrum band structure calculations will be predicted. Finally, the torsional band structures of electronic spectra of flexible molecules will be presented. 

Another difficulty with the infrared method is that of determining the band center with sufficient accuracy in the presence of the fine structure or band envelopes due to the overall rotation. Even when high resolution equipment is used so that the separate rotation lines are resolved, it is by no means always a simple problem to identify these lines with certainty so that the band center can be unambiguously determined. The final difficulty is one common to almost all methods and that is the effect of the shape of the potential barrier. The infrared method has the advantage that it is applicable to many molecules for which some of the other methods are not suitable. However, in some of these cases especially, barrier shapes are likely to be more complicated than the simple cosine form usually assumed, and, when this complication occurs, there is a corresponding uncertainty in the height of the potential barrier as determined from the infrared torsional frequencies. In especially favorable cases, it may be possible to observe so-called hot bands i.e., v = 1 to v = 2, 2 to 3, etc. This would add information about the shape of the barrier. 

In practice, one usually defines a training set of molecules and associated experimental properties and fits the relevant data with an assumed force field.The next step is to test the results on molecules and data outside the training set. Experimental data that depend on the energy surface and that may be used to determine the parameters of the intramolecular interactions consist mainly of gas-phase structural data derived from microwave spectra or electron diffraction patterns, crystal structures derived from X-ray and inelastic neutron scattering measurements, and vibrational frequencies obtained from infrared and Raman spectra. Torsional barriers are derived from NMR band shapes and relaxation times, whereas conformational energies are determined from spectroscopic and thermochemical data. Nonbonded parameters are determined mainly from... 

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