Polyatomic systems elementary processes

If the end points are defined, the solution to the classical equations of motion corresponding to an elementary process can be sought the resulting system point trajectories represent the realistic evolution of the polyatomic system from reactants to products on the given potential energy surface Wm(QJ) at the total energy H — T + W(Q ). The solutions to the equations of motion can thus be considered as transformations leading from a set of boundary conditions in the reactant asymptote to a set of boundary conditions in the product asymptote. 

The calculation of reaction profiles is one of the main subjects of the static approach (see later) the relevance of reaction profiles in representing the potential energy determining the course of elementary processes is given by the adequacy of expansion Eq. (36) and of neglecting the second-order term. It is obvious that expansion Eq. (36) tends to be more adequate when the kinetic energy content in the evolving polyatomic system is small. 

In an alternative approach, exact (numerical) time-dependent quantum wave-packet methods have been employed since the early eighties of the last century to explore the d3mamics of ob-initio-haseA models of conical intersections, see Refs. 6-8 for reviews. It has been found by these calculations that the fundamental dissipative processes of population and phase relaxation at femtosecond time scales are clearly expressed already in fewmode systems, if a directly accessible conical intersection of the PE surfaces is involved. The results strongly support the idea that conical intersections provide the microscopic mechanism for ultrafast relaxation processes in polyatomic molecules. " More recently, these calculations have been extended to describe photodissociation and photoisomerization processes associated with conical intersections. The latter are particularly relevant for our understanding of the elementary mechanisms of photochemistry. 

The molecular electostatic potential (MEP) represent just one of the attempts of connecting in depth studies on molecular systems with basic and elementary concepts of chemistry. It is no mere coincidence that the first proposals of using detailed MEP values in the study of inter- and intra-molecular processes [2] has immediately followed the obtaining of effective computer codes for ab initio calculations of the electronic stucture of polyatomic molecules. 

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