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

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?

• Why are you asking about hypothetical linear H₃⁺ molecule, when there is real triangular H₃⁺? Dec 19 '14 at 11:03
• @Mithoron I can't change my homework question, can I ? 😉 Dec 19 '14 at 11:25

## 1 Answer

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.