Dispersion correction to PES of complex system

Estimates of the electronic energy of the complex system employed in the expressions eqs. (1.254), (1.256) for its PES can be further improved. For this let us notice that the solutions of the self consistent system eq. (1.246) are used as multipliers in the basis functions eq. (1.216) of the subspace Im/. It turns out that the effective Hamiltonian Heff eq. (1.232) has nonvanishing matrix elements between the ground state of eq. (1.246) and the basis product states of the subspace ImP, differing from it by two multipliers simultaneously by the wave function for the R-system and by that for the M-system ( A p. p f 0). Indeed  

These matrix elements result in an additional energy correction which can be taken into account by the moves similar to those used when we took into account the interactions of the states with the fixed electron distribution with the states with the charge transfers between the subsystems. As previously, we consider the projection operator V on the single configuration ground state of the complex system  

The first term equals the energy So multiplied by the ground state projection operator V. The second gives the correction to it. Different terms in // behave differently under this projection. Taking into account that V projects to the product of the eigenstates of the operators Hff and eq. (1.246) one can see that  

Restricting ourselves for the simplicity in eq. (1.264) by the reduced Coulomb operator 

Atkins. Physical Chemistry, Oxford University Press, Oxford, 1979. 

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