Tuesday, June 4, 2019

homework - 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?



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.


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