What are the molecular orbitals of the hypothetical linear H₃⁺ molecule?


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> What would be the wave function of the lowest energy molecular orbital of a hypothetical linear $\ce{H3+}$ molecule?
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According to the LCAO method, I feel the lowest energy MO will be $\mathrm{1s(A) + 1s(B) + 1s(C)}$, where e.g. $\mathrm{1s(A)}$ is the wave function of the $\mathrm{1s}$ orbital of one of the Hydrogen atoms. This has $0$ nodes and has the lowest energy.


Isn't this correct?




The lowest energy MO is : $\psi\_1 = (1/2)(\phi\_A+ \sqrt2\phi\_B+\phi\_C)$.


Then comes the MO: $\psi\_2 = (1/\sqrt2)(\phi\_A- \phi\_C)$.


The highest energy MO is $\psi\_3 = (1/2)(-\phi\_A+ \sqrt2\phi\_B-\phi\_C)$.


Where $\phi$ denotes the atomic orbital $1s$ on each hydrogen atom. $A$, $B$ and $C$ denote hydrogen atoms, where $B$ is the central one.


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