# How are molecular orbitals determined?

Aug 18, 2015

It's a bit unclear what you're asking for, but I assume you mean how do we determine which molecular orbitals (MOs) are formed from which atomic orbitals (AOs).

Let's say we looked at methane.

Carbon uses its $2 s$ and $2 p$ AOs to bond with hydrogen's $1 s$ AO. As it prepares to bond with hydrogen, carbon allows its $s$ and $p$ orbitals to mix, slightly lowering their energy levels, and creating a hybridized $s {p}^{3}$ MO from the $2 {p}_{x}$, $2 {p}_{y}$, $2 {p}_{z}$, and $2 s$ orbitals, which explains why it's called $s {p}^{3}$ ($1$ $s$-type and $3$ $p$-type AOs), and also why it is said to have roughly 75% $p$ character and 25% $s$ character.

The hybridization in carbon can be written out roughly like this:

When the orbital overlap occurs, carbon shares its $s {p}^{3}$ electrons with hydrogen's $1 s$ electron to make one $\sigma$ bond.

The overlap between a $1 s$ and a $2 p$ looks like this diagram I drew below (suppose the $2 {p}_{x}$ orbital is on the x-axis):

(The carbon is positioned where the $s {p}^{3}$ node is.)

The electron density increases where the $2 {p}_{\text{x/y/z}}$ and the $1 s$ have the same phase ($+$), and so that lobe gets bigger (think principle of superposition for standing waves).

Since a bond must be favorably made to be made often, the resulting MO must support a greater electron density in order to make the bond fairly strong (and therefore stable). Therefore, it is a bonding MO (antibonding MOs are due to opposite-phase overlap, decreasing electron density by creating nodes, and working against bonding, hence "anti").