Electronic structure computations vibrational frequencies

Hartree-Fock theory is very useful for providing initial, first-level predictions for many systems. It is also reasonably good at computing the structures and vibrational frequencies of stable molecules and some transition states. As such, it is a good base-level theory. However, its neglect of electron correlation makes it unsuitable for some purposes. For example, it is insufficient for accurate modeling of the energetics of reactions and bond dissociation. 

Calculations are needed for every species. For example, for H2O the B3LYP/6-31G(d)-optimized structure has rotational constants of 787.96, 431.85, and 278.96GHz (1 GHz0.033356cm ) and an electronic energy of —76.408953 hartree. The structure also has an external symmetry number cr — 2, which affects the entropy. The computed vibrational frequencies are 1713.1, 3724.3, and 3846.6 cm (unsealed), so the scaled ZPE is 4552.0 cm — 54.45kJmoP The enthalpy function... 

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... 

One of the main aims of such computations is the prediction and rationalization of the optoelectronic spectra in various steric and electronic environments by either semiempirical or ab initio methods or a combination of these, considering equilibrium structures, rotation barriers, vibrational frequencies, and polarizabilities. The accuracy of the results from these calculations can be evaluated by comparison of the predicted ionization potentials (which are related to the orbital energies by Koopman s theorem) with experimental values. 

Statistical mechanics affords an accurate method to evaluate ArSP, provided that the necessary structural and spectroscopic parameters (moments of inertia, vibrational frequencies, electronic levels, and degeneracies) are known [1], As this computation implicitly assumes that the entropy of a perfect crystal is zero at the absolute zero, and this is one of the statements of the third law of thermodynamics, the procedure is called the third law method. 

Rotational and vibrational partition functions can be computed from the geometry and vibrational frequencies that are calculated for a molecule or TS. The entropy can then be obtained from these partition functions. Thus, electronic structure calculations can be used to compute not only the enthalpy difference between two stationary points but also the entropy and free energy differences. 

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