On the energy difference between the ^l<i>P</i> and ³<i>P</i> states of the beryllium isoelectronic sequence

<jats:title>Abstract</jats:title><jats:p>Wave functions of the <jats:sup>1</jats:sup><jats:italic>S</jats:italic> (ground state), <jats:sup>3</jats:sup><jats:italic>P</jats:italic> and <jats:sup>1</jats:sup><jats:italic>P</jats:italic> states for the beryllium isoelectronic sequence have been obtained in various approximations.</jats:p><jats:p>The <jats:sc>HF</jats:sc> <jats:sup>2</jats:sup><jats:italic>p</jats:italic> orbitals for the <jats:sup>1</jats:sup><jats:italic>P</jats:italic> and <jats:sup>3</jats:sup><jats:italic>P</jats:italic> states are similar except for Be, where the <jats:sup>2</jats:sup><jats:italic>p</jats:italic> orbital is quite diffuse for the <jats:sup>1</jats:sup><jats:italic>P</jats:italic> state.</jats:p><jats:p>The difference between the experimental <jats:italic>E</jats:italic>(<jats:sup>1</jats:sup><jats:italic>P</jats:italic>) – <jats:italic>E</jats:italic>(<jats:sup>3</jats:sup><jats:italic>P</jats:italic>) and the <jats:sc>HF</jats:sc> <jats:italic>E</jats:italic>(<jats:sup>1</jats:sup><jats:italic>P</jats:italic>) – <jats:italic>E</jats:italic>(<jats:sup>3</jats:sup><jats:italic>P</jats:italic>) is 0.62 eV for Be and 1.17 ∼ 1.40 eV for B<jats:sup>+</jats:sup> ∼ F<jats:sup>5+</jats:sup>. The disagreements are attributed to the correlation effects between the 2<jats:italic>s</jats:italic> and 2<jats:italic>p</jats:italic> electrons. This is confirmed by ci calculations.</jats:p><jats:p>It is shown that a limited basis <jats:sc>SCF</jats:sc> calculation reproduces the above feature of the <jats:sc>HF</jats:sc> results if we treat the orbital exponents as the variational parameters. The use of the Slater values for the orbital exponents is shown to be inadequate especially for the Be <jats:sup>1</jats:sup><jats:italic>P</jats:italic> state.</jats:p><jats:p>The conclusions of this paper will be useful for discussing the <jats:sc>V–T</jats:sc> separations of H<jats:sub>2</jats:sub> and C<jats:sub>2</jats:sub>H<jats:sub>4</jats:sub>.</jats:p>