Deformation of the potential energy

Piela L, Kostrowicki J and Scheraga H A 1989 The multiple-minima problem in the conformational analysis of molecules. Deformation of the potential energy hypersurface by the diffusion equation method J. Phys. Chem. 93 3339... 

L. Piela, J. Kostrowicki, and H. A. Scheraga,/. Phys. Chem., 93,3339 (1989). The Multiple-Minima Problem in Conformational Analysis of Molecules. Deformation of the Potential Energy Hypersurface by the Diffusion Equation Method. 

This type of representation of the potential energy in terms of the internal (valence) degrees of freedom is called a Valence Force Field. Valence force fields have long been used in vibrational spectroscopy in order to carry out normal mode analysis[j ]. Basically what the terms in equation (2) express are the energies required to deform each internal coordinate from some unperturbed... 

When, the geometry of the molecule is fully optimized at each conformation, the geometry of the whole molecule changes during the rotation. As a result, the rotational constants change with the rotation angles, and have to be fitted in a Fourier series. Since the deformation does not influence the dynamical symmetry properties of the molecule, the rotational B constants may be fitted to a symmetry adapted functional form identical to that of the potential energy function of (113). 

Fig. 8.1 Diagram showing the deformation of ionic potential-energy wells by an applied electric field.

Most of the potential energy surfaces reviewed so far have been based on effective pair potentials. It is assumed that the parameterization is such as to account for nonadditive interactions, but in a nonexplicit way. A simple example is the use of a charge distribution with a dipole moment of 2.ID in the ST2 model. However, it is well known that there are significant non-pairwise additive interactions in liquid water and several attempts have been made to include them explicitly in simulations. Nonadditivity can arise in several ways. We have already discussed induced dipole interactions, which are a consequence of the permanent diple moment and polarizability of the molecules. A second type of nonadditive interaction arises from the deformation of the molecules in a condensed phase. Some contributions from such terms are implicitly included in calculations based on flexible molecule potentials. Other contributions arises from electron correlation, exchange, and similar effects. A good example is the Axilrod-Teller three-body dispersion interaction ... 

Since a deformation of the potential Su can be expressed in terms of a set of changes of the normal coordinates dQi,..., dQa,..., dQsM-sorSM-e, the total differential of energy can be written as... 

As a conclusion, the simple analytical form of the potential energy surface allows to calculate the minimal energy path, step by step from HS to the LS energy minimum. It is obvious that along the path the contributions of the different modes will change. At HS only JT active modes contribute. After the first step the symmetry is lowered and the other modes as mentioned will mix in. This allows getting very detailed picture on the interaction between the deformation of the electron distribution and the displacements of the nuclei. 

The present chapter was devoted to the detailed consideration of the dynamic JT effect in the orbital triplet states for the 3d ions in a cubic crystal field, which included analysis of the spin-orbit splitting quenching (Ham effect) and geometry of the excited states (deformation of the equilibrium ligands configuration and cross-section of the potential energy surfaces). All necessary equations involved into such an analysis were given and explained. Theoretical description has been supported by... 

---