# Question 5862e

Mar 18, 2016

We use the convention that the $3 {p}_{y}$ orbitals of the outer atoms point directly towards the ($s {p}^{2}$) hybrid orbitals of the central atom.

color(blue)("["KK_(sigma)"]"("nb 3"s)^2 ("nb 3"s)^2 ("nb 3"s)^2 (sigma sp^2)^2 (sigma sp^2)^2 (sigma sp^2)^2 ("nb 3"p_z)^2 ("nb 3"p_z)^2 ("nb 3"p_z)^2 ("nb 3"p_x)^2 ("nb 3"p_x)^2 ("nb 3"p_x)^2)

Note that the nonbonding orbitals are not all completely nonbonding.

Some have bonding character that lower their energies relative to a typical nonbonding orbital, which ideally has energies similar to the original atomic orbital because of the lack of orbital-orbital interactions.

${\text{AlCl}}_{3}$ is isoelectronic with ${\text{BF}}_{3}$, boron trifluoride. So, we can expect them to:

• Have similar molecular orbital (MO) diagrams (except for any differences with respect to energy gaps between the $s$ of the central atom vs. that of the outer atoms, which, for ${\text{AlCl}}_{3}$, may or may not allow $3 s - 3 s$ interactions and give that MO more bonding character)
• Have similar structures (trigonal planar)
• Have similar Lewis acid behavior

Here is the MO diagram for ${\text{BF}}_{3}$ (Inorganic Chemistry, Miessler et al., pg. 160):

What you should notice are the electrons in the $3 {a}_{1} '$, $2 e '$, $4 {a}_{1} '$, $3 e '$, $1 {a}_{2} ' '$, $1 {a}_{2} '$, $1 e ' '$, $4 e '$ MOs. Those are filled orbitals. Also, remember that we are looking at ${\text{AlCl}}_{3}$.

In order to write the electron configuration for this molecule, we use the names of the orbitals from lowest to highest energy, with superscripts for the number of electrons. So we get:

$\textcolor{g r e e n}{\text{["KK_(sigma)"]} {\left(3 {a}_{1} '\right)}^{2} {\left(2 e '\right)}^{2} {\left(2 e '\right)}^{2} {\left(4 {a}_{1} '\right)}^{2} {\left(3 e '\right)}^{2} {\left(3 e '\right)}^{2} {\left(1 {a}_{2} ' '\right)}^{2} {\left(4 e '\right)}^{2} {\left(4 e '\right)}^{2} {\left(1 {a}_{2} '\right)}^{2} {\left(1 e ' '\right)}^{2} {\left(1 e ' '\right)}^{2}}$

Note that $K {K}_{\sigma}$ means the core $\sigma$ MOs are filled and aren't valence.

I know you aren't used to this $a \text{/"b"/"e"/} t$ notation for orbitals, so here's a way to write it that is more on the level of General Chemistry.

We use the convention that the $3 {p}_{y}$ orbitals of the outer atoms point directly towards the hybrid orbitals of the central atom (hence the $\sigma s {p}^{2}$ involves the $\sigma$ bonding of the $s {p}^{2}$ hybridized orbitals and the implied $3 {p}_{y}$ of chlorine).

color(blue)("["KK_(sigma)"]"("nb 3"s)^2 ("nb 3"s)^2 ("nb 3"s)^2 (sigma sp^2)^2 (sigma sp^2)^2 (sigma sp^2)^2 ("nb 3"p_z)^2 ("nb 3"p_z)^2 ("nb 3"p_z)^2 ("nb 3"p_x)^2 ("nb 3"p_x)^2 ("nb 3"p_x)^2)#

That tells you which orbitals are primarily nonbonding, and what kind of orbitals they are ($s {p}^{2}$ from aluminum, $3 {p}_{x}$ from chlorine, etc).

Some overarching observations:

• You can see that there are $18$ electrons accounted for by the mostly nonbonding MOs, which correlates with the number of lone pairs of electrons in each chlorine in total ($6 \times 3 = 18$). Note that a mostly nonbonding orbital doesn't necessarily have the same energy as the original atomic orbital; if it has bonding character, it will be lower in energy than usual.
• You can also see the three $\sigma \left(s {p}^{2}\right)$ MOs that account for the three single bonds on ${\text{AlCl}}_{3}$, since trigonal planar molecules have $s {p}^{2}$ hybridization.
• Finally, ${\text{AlCl}}_{3}$ can act as a Lewis acid by accepting electrons into its LUMO, meaning its $2 {a}_{2} ' '$ (or ${\pi}^{\text{*}}$) MO, which makes sense because accepting electrons demonstrates Lewis acid behavior.

(That $2 {a}_{2} ' '$ antibonding MO corresponds to the first $\text{nb 3} {p}_{z}$, or $1 {a}_{2} ' '$, by the way, which has some bonding character. You can tell they're related because they both have the label ${a}_{2} ' '$.)