Orbital Valency

Abstract

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. $r{e}^{-\frac{\mathrm{kr}}{2}}$ (that is, with no nodes) is used. Complete potential energy curves are obtained for the twelve possible states, which are ${}_{}{}^1{}_{}{}^{}\Delta _g^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}\Delta _u^{}{}_{}{}^{}$, ${}_{}{}^1{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$, ${}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, ${}_{}{}^1{}_{}{}^{}{\Sigma }_u_{}^{-}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}{\Sigma }_g_{}^{-}{}_{}{}^{}$, two ${}_{}{}^1{}_{}{}^{}{\Sigma }_g_{}^{+}{}_{}{}^{}$, and two ${}_{}{}^3{}_{}{}^{}{\Sigma }_u_{}^{+}{}_{}{}^{}$. The most stable states are ${}_{}{}^3{}_{}{}^{}{\Sigma }_u_{}^{+}{}_{}{}^{}$ (lowest) and ${}_{}{}^1{}_{}{}^{}{\Sigma }_g_{}^{+}{}_{}{}^{}$, which arise from $m_{l^a}=0\mathrm{}$ and $m_{l^b}=0\mathrm{}$, and in which there is the maximum overlapping of charge. The states with least overlapping of charge are those where $m_{l^a}=\pm 1$ and $m_{l^b}=\pm 1$, resulting in ${}_{}{}^1{}_{}{}^{}\Delta _g^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}\Delta _u^{}{}_{}{}^{}$, ${}_{}{}^1{}_{}{}^{}{\Sigma }_g_{}^{+}{}_{}{}^{}$, ${}_{}{}^1{}_{}{}^{}{\Sigma }_u_{}^{-}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}{\Sigma }_g_{}^{-}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}{\Sigma }_u_{}^{+}{}_{}{}^{}$, 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.