Electronic structure computations anharmonic frequencies

For many reactions the calculated structures for potential energy minima are as accurate as those found experimentally. Ab initio and experimental harmonic vibrational frequencies usually agree to within 10-15% at the Hartree-Fock level and 5% at the MP2 level (Hehre et al., 1986). It has been found that Hartree-Fock harmonic frequencies computed with a medium-size basis set ean be scaled by the factor 0.9 to give approximate anharmonic n = 0 — 1 transition frequencies (Hehre et al., 1986). A detailed study has been made of how the computed ab initio frequencies for benzene depend on the size of the basis set and the treatment of electron correlation (Maslen et al., 1992). 

Unfortunately, measured vibrational frequencies have some anharmonic component, and the vibrational frequencies computed in the manner above are harmonic. Thus, even the most accurate representation of the molecular structure and force constant will result in the calculated value having a positive deviation from experiment (Pople et al. 1981). Other systematic errors may be included in calculations of vibrational frequencies as well. For instance, Hartree-Fock calculations overestimate the dissociation energy of two atoms due to the fact that no electron correlation is included within the Hartree-Fock method (Hehre et al. 1986 Foresman and Frisch 1996). Basis sets used for frequency calculations are also typically limited (Curtiss et al. 1991) due to the requirements of performing a full energy minimization. Thus, errors due to the harmonic approximation, neglect of electron correlation and the size of the basis set selected can all contribute to discrepancies between experimental and calculated vibrational frequencies. 

After an optimized structure has been obtained, the vibrational frequencies are calculated to characterize the structure as a local minimum (with no imaginary frequencies) and provide the data needed to evaluate (i) the zero-point energy, (ii) the thermal vibrational contribution to enthalpy and (iii) the vibrational entropy. A6 initio harmonic vibrational frequencies are typically larger than the values measured spectroscopically. A major soiuce of this disagreement is the neglect of anharmonicity effects in the calculations (errors also arise because of the incomplete incorporation of electron correlation and the use of finite basis sets). It is customary to scale ab initio values for the imperfect calculations. A set of scale factors has been recommended [51 ]. A better approach is to compute the anharmonic... 

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