Vibrational frequency alternations

Next, Ah and Ad are written in terms of partition functions (see Section 5.2), which are in principle calculable from quantum mechanical results together with experimental vibrational frequencies. The application of this approach to mechanistic problems involves postulating alternative models of the transition state, estimating the appropriate molecular properties of the hypothetical transition state species, and calculating the corresponding k lko values for comparison with experiment.""- " "P... 

Vibrational spectroscopy is of utmost importance in many areas of chemical research and the application of electronic structure methods for the calculation of harmonic frequencies has been of great value for the interpretation of complex experimental spectra. Numerous unusual molecules have been identified by comparison of computed and observed frequencies. Another standard use of harmonic frequencies in first principles computations is the derivation of thermochemical and kinetic data by statistical thermodynamics for which the frequencies are an important ingredient (see, e. g., Hehre et al. 1986). The theoretical evaluation of harmonic vibrational frequencies is efficiently done in modem programs by evaluation of analytic second derivatives of the total energy with respect to cartesian coordinates (see, e. g., Johnson and Frisch, 1994, for the corresponding DFT implementation and Stratman etal., 1997, for further developments). Alternatively, if the second derivatives are not available analytically, they are obtained by numerical differentiation of analytic first derivatives (i. e., by evaluating gradient differences obtained after finite displacements of atomic coordinates). In the past two decades, most of these calculations have been carried... 

As it is now very well known, accurate studies of the water-water interaction by means of ab-initio techniques require the use of larger and flexible basis sets and methods which consider correlation effects [85,94-96], Since high level ab-initio post-Hartree-Fock calculations are unfeasible because of their high computational cost for systems with many degrees of freedom, Density Functional Theory, more economical from the computational point of view, is being more and more considered as a viable alternative. Recently, we have presented [97] results of structural parameters and vibrational frequencies for the water clusters (H20) , n=2 to 8, using the DFT method with gradient corrected density functionals. 

All of the theoretical methods that allow for geometry optimization predict the bowl-shaped conformation of 8 to predominate over the planar alternative. However, the calculated energy differences between the two conformations differ drastically and span the range of 0.8 to 84 kcal/mol. Moreover, the calculated energy difference between the plants and bowl-shaped conformers is quite important since it represents the barrier for bowl-to-bowl inversion if (a) planar corannulene represents the transition state (TS) for the process, and (b) the entropic term in AG is negligible. Condition (a) seems to be fulfilled, since vibrational frequency calculations give one and only one imaginary frequency for the planar structure... 

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