Knowledge Bank

“Trial wave functions of the form $\varphi (r1)\varphi (r2)\chi (r12)$ and $[\varphi (r1)\psi (r2)+\varphi (r1)\psi (r2)\chi (r12)]$ have been used to represent the wave functions of the isoelectronic helium scries. The functions $\varphi$ and $\psi$ are taken in the forme $e-\zeta r\Sigma \lambda a\lambda r\lambda$ and $\chi$ in the form $\Sigma \lambda c\lambda r12\lambda ;\zeta ,a\lambda$ and $clambda$ were determined by minimizing the energy. Preliminary results indicate that about five terms for each expansion is equivalent to a full variational calculation of $\varphi ,\psi$ and $\chi$. For helium, the best closed-shell wave function accounts for 02%, and the best open-shell wave function for 98.6% of the correlation energy.”