= Helium variational effective charge
{title2=$\zeta_*=27/16$}
A product of two normalized $1s$ orbitals proportional to $e^{-\zeta r}$, combined with a <singlet state>, gives the fixed-nucleus <helium atom> trial <energy> $E(\zeta)=\zeta^2-4\zeta+5\zeta/8$ in <atomic units>. Minimization gives $\zeta=27/16$ and $E=-729/256$ Hartree. Nuclear charge remains two in the <Hamiltonian operator>; varying $\zeta$ changes only the trial orbitals. The reduced orbital charge describes screening, while explicit dependence on <electron> separation can further lower the trial <energy> under the <quantum variational principle>.
Back to article page
