I am not an expert on this area, but I suggest that the section should start with the use of ab initio methods to calculate the potential energy hypersurface in detail and provide a surface for classical dynamics.
12.
Following the classical dynamics of Euler, the motion of a material body is produced by the action of externally applied forces which are assumed to be of two kinds : surface forces \ mathbf F and body forces \ mathbf b.
13.
Following the classical dynamics of Euler, the motion of a material body is produced by the action of externally applied forces which are assumed to be of two kinds : surface forces \ mathbf F _ C and body forces \ mathbf F _ B.
14.
It is a concept derived from classical mechanics that on the one hand can serve to refine certain methods of relativity still discussed today, to the Ehrenfest model, and to Ehrenfest time, the time characterizing the departure of quantum dynamics for observables from classical dynamics.
15.
Important observations often associated with classically chaotic quantum systems are spectral level repulsion, dynamical localization in time evolution ( e . g . ionization rates of atoms ), and enhanced stationary wave intensities in regions of space where classical dynamics exhibits only unstable trajectories ( as in scattering ).
