Krypton's Hartree-Fock ground configuration is : a closed shell with six equivalent…

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · Many-electron atoms and the periodic table · Many-electron atoms and the periodic table

Deriving the Spectrum, Ch Self-consistent fields and correlation

Problem

Krypton's Hartree-Fock ground configuration is [Ar]3d104s24p6[\mathrm{Ar}]3d^{10}4s^24p^6: a closed shell with six equivalent 4p4p electrons filling the three spatial orbitals 4p−1,4p0,4p+14p_{-1},4p_0,4p_{+1}, each doubly occupied. ((a)) In the closed-shell Hartree-Fock energy EHF=2∑a⟨a∣h∣a⟩+∑a,b(2Jab−Kab)E_{\rm HF}=2\sum_a\langle a|h|a\rangle+\sum_{a,b}(2J_{ab}-K_{ab}), state which pairs of 4p4p electrons contribute an exchange integral KabK_{ab} and how many such pairs there are, given three doubly-occupied spatial orbitals. ((b)) The Hartree-Fock orbital energy of a 4p4p electron is ϵ4p=−0.524 Eh\epsilon_{4p}=-0.524\,E_{\rm h}. Estimate krypton's first ionisation energy by Koopmans' theorem, in eV. The measured value is 14.00 eV14.00\,\mathrm{eV}. State whether Koopmans over- or underestimates it, and explain the sign, contrasting with beryllium's 2s2s pair.

Browse the problem library