Question

How are molecular orbitals determined?

Answer 1

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 `2s` and `2p` AOs to bond with hydrogen's `1s` 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 `sp^3` MO from the `2p_x`, `2p_y`, `2p_z`, and `2s` orbitals, which explains why it's called `sp^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 `sp^3` electrons with hydrogen's `1s` electron to make one `sigma` bond.

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

(The carbon is positioned where the `sp^3` node is.)

The electron density increases where the `2p_("x/y/z")` and the `1s` 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").