Eigenvector-following, potential energy

Once the normal coordinate of interest is known, it is possible to simultaneously move all atoms of the system, following the displacements indicated by the appropriate eigenvector. The total energy of the system as a function of the normal displacements results in potential curve similar to that described for the case of the chemisorbed CO. From this curve the force constant of the vibration can be easily obtained. In practice it is common to express the displacements defining each normal coordinate, Qi, as... 

The semi-empirical molecular orbital calculation software MOPAC in the CAChe Work System for Windows ver. 6.01 (Fujitsu, Inc.) was used in all of calculations for optimization of geometry by the Eigenvector Following method, for search of potential energies of various geometries of intermediates by use of the program with Optimized map, for search of the reaction path from the reactants to the products via the transition state by calculation of the intrinsic reaction coordinate (IRC) [10]. 

It is now assumed that the distance variable, p is also the variable in a harmonic cell potential with states (ln>, n = 0, 1,2,... and with energies, E = hco(n + 1/2). The zero-order states of the vibronic system are then the product states, (4 (x)ln>, n = 0, 1,.... The electronic ground state eigenvector is expanded about p = 0 as follows ... 

---