Problem 2

Write the Hamiltonian operator for the boron B+ cation (4 electrons) when the nucleus is assumed stationary. Use atomic units.

Write a zero-order wavefunction ?0(1234) for the ground state of the cation. The wavefunction must incorporate the spatial and spin coordinates of each electron and it must be antisymmetric with respect to the exchange of the labels of any pair of electrons.

What is the energy of the cation if we completely neglect the repulsion between the electrons?

What is the first order correction to the energy of the B3+ ion if the perturbation Hamiltonian only includes the electron-electron repulsion.

What is the ground state energy of the B3+atom according to a variational approximation approach similar to the one used for the ground state energy of the He atom?

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