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What would be the wave function of the lowest energy molecular orbital of a hypothetical linear $\ce{H3+}$ molecule?

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?

Buck Thorn
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Praveen Sriram
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1 Answers1

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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.

Yomen Atassi
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