Because of the repulsion of the two electrons one

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into the wavefunction. Because of the repulsion of the two electrons, one would expect the probability to be higher when the electrons are further apart, and this is accomplished by the additive term, which increases with increasing r 12 . 4. 1/2 3 4 . . 2 2 E a u Let's take the derivative and set it equal to 0 to find min 1/2 1/2 3 4 3 2 0 1/ 2 2 2 2 2 dE d   1/2 min min 1/2 min 2 3 4 16 0.293 2 18 2 3 2   1/2 1/2 min min 3 4 3 4(0.293) (0.293) 0.424 . . 2 2 2 2 E a u   As expected, this approximate energy is higher than the exact Hydrogen Ground State Energy: E exact = -0.500 a.u.
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