Pseudo-exchange repulsion

The first two terms describe each subsystem dressed with the interaction of each other. It is now apparent that exchange forces between the two subsystems have to be included in order to get the total force acting on the nuclei. This latter force is usually mimicked with a repulsive short range potential. A pseudo potential method can also be used in a microscopic approach to the surrounding medium effects [104,105],... 

We now wish to establish the general fxmctional form of possible wavefxmctions for the two electrons in this pseudo helium atom. We will do so by considering first the spatial part of the wavefunction. We will show how to derive fimctional forms for the wavefunction in which the exchange of electrons is independent of the electron labels and does not affect the electron density. The simplest approach is to assume that each wavefunction for the helium atom is the product of the individual one-electron solutions. As we have just seen, this implies that the total energy is equal to the sum of the one-electron orbital energies, which is not correct as it ignores electron-electron repulsion. Nevertheless, it is a useful illustrative model. The wavehmction of the lowest energy state then has each of the two electrons in a Is orbital ... 

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