# 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 H3+ molecule? According to the LCAO method, I feel the lowest energy MO will be 1s(A) + 1s(B) + 1s(C). Where 1s(A) is the wave function of the 1s orbital of one of the Hydrogen atoms. This has 0 nodes and has the lowest energy.

Isn't this correst?

• Welcome to chemistry.se! This seems to be a homework question according to our policy, please share your thoughts and attempts towards the solution. For formatting help visit the help center and for more information take the tour. – Martin - マーチン Dec 19 '14 at 6:22
• Yes, you are correct: This will be the orbital with lowest energy. – Philipp Dec 19 '14 at 10:32
• Why are you asking about hypothetical linear H₃⁺ molecule, when there is real triangular H₃⁺? – Mithoron Dec 19 '14 at 11:03
• @Mithoron I can't change my homework question, can I ? 😉 – Praveen Sriram Dec 19 '14 at 11:25

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.