Subsystems effective subsystem Schrodinger

Energy and Effective Schrodinger Equationsfor Separable Subsystems... 

For both methods, we describe the interactions between the quantum subsystem and the classical subsystem as interactions between charges and/or induced charges/dipoles and a van der Waals term [2-18]. The coupling between the quantum subsystem and the classical subsystem is introduced into the quantum mechanical Hamiltonian by finding effective interaction operators for the interactions between the two subsystems. This provides an effective Schrodinger equation for determining the MCSCF electronic wave function of the molecular system exposed to a classical environment, a structured environment, such as an aerosol particle. 

Schrodinger equation with the appropriate Bloch s boundary conditions. For the general case an analytical solution is not possible and one needs to solve the equation numerically. But we found that, for our purposes, one can get qualitatively the same results if the grained films considered, which have the hexagonal symmetry, are represented by an effective 2D set of interacting square wells with rectangular barriers. Thus, to estimate the values of and I y, for the square lattice inside the unit cell one has two independent Kronig-Penney equations for both electron and hole subsystems. 

The merit of the generalized SCRF theory is that it correctly describes polarization effects on the solute subsystem which may be important, e.g. in enzymatic reactions. The fact that the solute nonlinear Schrodinger equation is explicitly solved, allows one to have special solvent induced electronic states, which could appear otherwise as excited states for the isolated system. 

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