Question

write down the slater determinant For the ground state of Beryllium (4 electrons )and indicate which states are allowed or not? Explain on of the terms ? does the wave function that is given satisfy the pauli exclusion principle ? Explain your reasons to

Answer 1

The ground state configuration of Be is 1 s2 2 s2. Because all of the shells are "closed" (electrons have been assigned to all available orbitals and spins), the Hartree-Fock wave function can be represented by a single Slater determinant. To construct a Slater determinant, write a different spin-orbital in each column (for simplicity, write "1s" in place of f1 s), and write a different electron's coordinates (label) in each row. If the atomic orbital functions are drawn from an orthonormal set, the normalization constant N equals 1/sqrt(4!).

Wolfram's mathematica software was used to optimize energy value for beryllium atom, using different confinement radii r0, provided the value for nuclear charge Z = 4.

Using four and six variational parameters, energy values and their respective variational parameters for beryllium atom's electronic configuration 1s22s2 are shown in tables 1 and 2, using the direct variational method and an antisymmetric wave function, where confinement radius r0 is measured in Bohr and energy EH in Hartrees.