Potential energy surface for combined system

Having obtained a sufficient impression of the electronic structure of the medium (M-system) we can address the PES of the complex system. From the point of view of substantiation of the hybrid methods, it is the main problem [65], The entire PES U(q) of the molecular system is the sum of its electronic energy 0(q) given by eq. (1.247) and of the Coulomb repulsion U(q) of nuclei (or cores)  

Employing the distribution eq. (1.230) of the nuclear (core) charges between the subsystems eq. (1.251) the repulsive contribution to the energy can be written  

To get the PES of a complex system we supply the electronic energy So (q) with the sum of the core repulsions eq. (1.252) which yields the required PES of the complex system  

Now with the precision up to the second order in the small perturbations we can write the estimate for the energy of the M-system  

Inserting the estimates for the densities ((m m ))M obtained above using perturbation theory in the expression for the average Coulomb interaction between the electronic distributions of the subsystems we get  

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