How to interpret a singlet term symbol for an s¹p¹ configuration?
The two states you have drawn correspond to the (antisymmetrised) wavefunctions

$$\begin{align}
\Psi_i &amp;= \mathrm{s}(1)\alpha(1) \cdot \mathrm{p}(2)\beta(2) \\
\Psi_j &amp;= \mathrm{s}(1)\beta(1) \cdot \mathrm{p}(2)\alpha(2)
\end{align}$$

Neither of the two states above are valid, as they do not obey the requirement for indistinguishability. For fermions such as electrons (spin-1/2), this is achieved by making the wavefunction antisymmetric upon permutation of any two electron labels. However, neither $\Psi_i$ nor $\Psi_j$ obey this:

$$\begin{align}
\mathcal{P}(\Psi_i) &amp;= \mathrm{s}(2)\alpha(2) \cdot \mathrm{p}(1)\beta(1)  \neq -\Psi_i \\
\mathcal{P}(\Psi_j) &amp;= \mathrm{s}(2)\beta(2) \cdot \mathrm{p}(1)\alpha(1)  \neq -\Psi_j
\end{align}$$

The appropriate wavefunction is a linear combination of these states (and a couple more):

$$\Psi_\text{singlet} = \frac{1}{\sqrt 2}[\mathrm{s}(1)\mathrm{p}(2) + \mathrm{p}(1)\mathrm{s}(2)] \cdot \frac{1}{\sqrt 2}[\alpha(1)\beta(2) - \beta(1)\alpha(2)]$$

If you expand these you can see the constituent wavefunctions

$$\begin{align}
\Psi_\text{singlet} &amp;= \frac{1}{2} [\mathrm{s}(1)\alpha(1) \cdot \mathrm{p}(2)\beta(2) \\
&amp;\qquad + \mathrm{p}(1)\alpha(1) \cdot \mathrm{s}(2)\beta(2) \\
&amp;\qquad - \mathrm{s}(1)\beta(1) \cdot \mathrm{p}(2)\alpha(2) \\
&amp;\qquad - \mathrm{p}(1)\beta(1) \cdot \mathrm{s}(2)\alpha(2)] \\
\end{align}$$

You need four "simple" wavefunctions in total because you have to account for the spatial indistinguishability of the two electrons (hence need a linear combination of two spatial wavefunctions) as well as the spin indistinguishability (linear combination of two spin wavefunctions).