Schrodinger equation reactive systems

This observation is fundamental, reveling the fact that the characteristic energies of the Fokker-Planck equation are reactive energies, and in the final, nonequilibrium energies. This aspect is directly correlated with the nonequilibrium character specific for the Fokker-Planck equation while modeling open systems (driven by drift diffusion and factors, stochastic noise, etc.). Moreover, if the analytical solution of the eigen-values for the Schrodinger equation with the potential ) is considered, the consecrated expression is obtained ... 

Abstract. We are investigating systematic the application of the finite element method (FEM) for solving the Schrodinger equation. The subsequent work is devoted to the calculation of vibrational transition probabilities for the collinear reactive system A + BC (i.e. H H2 and their isotopes, F - -H2 and Ne + ). We have performed an extensive analysis of FEM on the vector-computer... 

In principle, each of these can be used to formulate an exact theory of water. The choice of the particular level depends on the questions we want to ask about the system. If we are interested only in explaining some macroscopic thermodynamic properties of pure water, we might be satisfied with the choice of a relatively simple mixture model. If we want to compute the pair correlation function, then a rigid model for water molecules may be used. If we are also interested in the dielectric properties of pure water or the solvation of ions in water, we need to assign an electric dipole moment, or perhaps a quadrupole moment, to our rigid water molecule. If we want to allow for dissociation into ions, then clearly a rigid model for water molecules will not be appropriate, and we need to consider a lower level of treatment such as a collection of and 0 . Finally, if we are interested in the chemical reactivity of water molecules, we must start from the more elementary description of the system in terms of electrons and various nuclei and solve the Schrodinger equation for all the molecules involved in the chemical reaction. 

A useful method that can be used in both time-independent and time-dependent calculations on chemical reactions is to add a negative imaginary potential (NIP) to the overall potential in carefully selected regions. This enables reactive flux into particular channels to be absorbed by the NIP and it is then not necessary to integrate the SchrOdinger equation further in that channel as the total reactive flux into it has been obtained. This is useful when state-to-state information is not needed but an overall reactive cross-section is required. The NIP also obviates the need for complicated coordinate systems in chemical reactions (such as hyperspherical coordinates) but the most appropriate parameters for the NIP have to be carefully tested. 

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