A Self-Consistent Field Variational Calculation of IP for the Helium Atom

A Self-Consistent Field Variational Calculation of IP for the Helium Atom 

One approach to the problem of the ri2 temi is a variational self-consistent field approximation. Our treatment here follows that by Rioux (1987), in which he starts 

The kinetic energy operator for the one-electron system of the H atom is — fi /2m) /r ) d/dr)r d/dr) [Eq. (6-21)] and the potential energy is —e /r for attr action of a single electron to the hydrogen nucleus. It is reasonable to use the same operator for a single electron in a separated helium orbital, either /(I) or v /(2). In atomic units we have 

Although we are solving for one-electron orbitals, r /i and r /2, we do not want to fall into the trap of the last calculation. We shall include an extra potential energy term Vi to account for the repulsion between the negative charge on the first electron we consider, electron I, exerted by the other electron in helium, electron 2. We don t know where electron 2 is, so we must integrate over all possible locations of electron 2 

The same treatment produces a similar operator for elechon 2. 

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