How are molecular orbitals determined?

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.

![http://www.chemexplore.net/]()

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:

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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").