Anharmonicity properties, vibrationally averaged

Vibrational corrections. For energies, this would typically be inclusion of zero point energies while for properties this may correspond to a vibrational averaging. The corrections may again be done at several levels of accuracy, for example using a harmonic approximation or also including anharmonic effects. 

Dracinsky et investigated relative importance of anharmonic corrections to SSCCs for a model set of methane derivatives, differently charged alanine forms, and sugar models. They systematically estimated the importance of the first and second-order property derivatives of SSCCs for vibrational corrections in model compounds. For a vibrational wave function j/ , the vibrationally averaged SSCC was calculated as... 

Kongsted, J., Christiansen, O. (2006). Automatic generation of force fields and property surfaces for use in variational vibrational calculations of anharmonic vibrational energies and zero-point vibrational averaged properties. Journal of Chemical Physics, 125,124108. 

Prediction of properties affected by vibrational averaging can only be accomplished if an accurate representation of the molecular PES is available at least around the equilibrium position(s). Anharmonic force fields provide the most convenient source for such a representation on which most interconversions of the many distance types are based. Thus, the use of anharmonic force fields in accurate structural studies of small molecules has a long hi story Furthermore, a... 

Another technique to obtain the effects of the anharmonic terms on the excitation frequencies and the properties of molecular crystals is the Self-Consistent Phonon (SCP) method [71]. This method is based on the thermodynamic variation principle, Eq. (14), for the exact Hamiltonian given in Eq. (10), with the internal coordinates not explicitly considered. As the approximate Hamiltonian one takes the harmonic Hamiltonian of Eq. (18). The force constants in Eq. (18) are not calculated at the equilibrium positions and orientations of the molecules as in Eq. (19), however. Instead, they are considered as variational parameters, to be optimized by minimization of the Helmholtz free energy according to Eq. (14). The optimized force constants are found to be the thermodynamic (and thus temperature dependent) averages of the second derivatives of the potential over the (harmonic) lattice vibrations ... 

---