The interaction of two atoms, each with one $2p$ electron, is studied by a method similar to that used by Kemble and Zener. An atomic wave function whose radial part is of the form const. $r{e}^{\ensuremath{-}\frac{\mathrm{kr}}{2}}$ (that is, with no nodes) is used. Complete potential energy curves are obtained for the twelve possible states, which are $^{1}\ensuremath{\Delta}_{g}$, $^{3}\ensuremath{\Delta}_{u}$, $^{1}\ensuremath{\Pi}_{g}$, $^{1}\ensuremath{\Pi}_{u}$, $^{3}\ensuremath{\Pi}_{g}$, $^{3}\ensuremath{\Pi}_{u}$, $^{1}{\ensuremath{\Sigma}}_{u}^{\ensuremath{-}}$, $^{3}{\ensuremath{\Sigma}}_{g}^{\ensuremath{-}}$, two $^{1}{\ensuremath{\Sigma}}_{g}^{+}$, and two $^{3}{\ensuremath{\Sigma}}_{u}^{+}$. The most stable states are $^{3}{\ensuremath{\Sigma}}_{u}^{+}$ (lowest) and $^{1}{\ensuremath{\Sigma}}_{g}^{+}$, which arise from ${m}_{{l}^{a}}=0$ and ${m}_{{l}^{b}}=0$, and in which there is the maximum overlapping of charge. The states with least overlapping of charge are those where ${m}_{{l}^{a}}=\ifmmode\pm\else\textpm\fi{}1$ and ${m}_{{l}^{b}}=\ifmmode\pm\else\textpm\fi{}1$, resulting in $^{1}\ensuremath{\Delta}_{g}$, $^{3}\ensuremath{\Delta}_{u}$, $^{1}{\ensuremath{\Sigma}}_{g}^{+}$, $^{1}{\ensuremath{\Sigma}}_{u}^{\ensuremath{-}}$, $^{3}{\ensuremath{\Sigma}}_{g}^{\ensuremath{-}}$, $^{3}{\ensuremath{\Sigma}}_{u}^{+}$, which are all repulsive. The II states lie in between, and are attractive. The present work gives precision to the ideas of Heitler on orbital valency, yields a positive exchange energy integral for the lowest states, and may be taken as supporting the conceptions of Slater about directed valency.