Potential energy surface analytical form

Smooth COSMO solvation model. We have recently extended our smooth COSMO solvation model with analytical gradients [71] to work with semiempirical QM and QM/MM methods within the CHARMM and MNDO programs [72, 73], The method is a considerably more stable implementation of the conventional COSMO method for geometry optimizations, transition state searches and potential energy surfaces [72], The method was applied to study dissociative phosphoryl transfer reactions [40], and native and thio-substituted transphosphorylation reactions [73] and compared with density-functional and hybrid QM/MM calculation results. The smooth COSMO method can be formulated as a linear-scaling Green s function approach [72] and was applied to ascertain the contribution of phosphate-phosphate repulsions in linear and bent-form DNA models based on the crystallographic structure of a full turn of DNA in a nucleosome core particle [74],... 

As is already clear, a reliable functional representation of the potential-energy surface is of extreme importance. Such a functional form must be as simple as possible in order to facilitate solving the dynamical problem, but must contain sufficient complexity that the reliability of the representation will not be jeopardized.105 In this spirit we have suggested models which have physical motivation and allow a simple, yet reliable, representation of the EHF and corr two-body17 136 140 and three-body17,21141 energy terms. Since the EHF terms are, in principle, calculable by ab initio methods (and subsequently represented in analytic form) whereas the corr terms are calculated semi-... 

The reliability of high-dimensional quantum calculations based on ab initio potential energy surfaces is also demonstrated in Fig. 6, where the sticking probability of H2/Cu(l 0 0) obtained by sixdimensional wave packet calculations [32] is compared to experimental results derived from an analysis of adsorption and desorption experiments [27]. The measured experimental sticking probabilities and, via the principle of detailed balance, also desorption distributions had been fitted to the following analytical form of the vibrationally resolved sticking probability as a function of the kinetic energy ... 

Murrel and co-workers [39] have developed a functional form in which the global analytic potential energy surface is written as a sum of N-body terms... 

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. 

In order to investigate the dynamics of chemical reactions by means of classical mechanical trajectory calculations it is desirable to have an analytic form for the potential energy surface so as to permit efficient calculation of the potential and its derivatives. All the empirical and most of the semi-empirical surfaces mentioned so far have been of this form, but all of them have been based on theoretical or physical models. In attempting either to find potential surfaces to describe specific reactions, or to investigate the effect of different features of a surface on the energy and angular distribution of the reaction products, several convenient and flexible functional forms for potential energy surfaces have been proposed. 

---