# Tips On Building Molecular Orbitals

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Molecular orbitals give students a lot of trouble. Here’s some tips on how they work.

•  adjacent p orbitals overlap to build up larger “pi systems” (so long as they’re oriented in the same plane).
•  the lowest energy pi system will have always have all its p orbitals lined up the same way.
• The number of molecular orbitals corresponds to the number of adjacent p orbitals (i.e. number of atoms in conjugation). So ethene, for instance, has 2 p orbitals and 2 molecular orbitals. Butadiene has 4 p orbitals in conjugation and 4 energy levels.
•  the “color” of the lobe indicates the “sign” of the wave (think of a wave with positive or negative amplitude).
• Adjacent lobes with the same sign will have “constructive interference”. Like two waves with the same sign, they will combine to form a larger wave.
• Adjacent lobes with opposite signs will have “destructive interference”.
• Between adjacent lobes with opposite signs is an area where the “sign” (amplitude) of the wave is zero. This is called a node.
• The more nodes an orbital has, the higher in energy it will be (less “stable”). On the right hand diagram, notice how the energy increases with the number of nodes (0, 1, 2, 3)
• Each orbital can fit two electrons, and the lowest energy orbital is filled first (this is the “building up principle” or “Aufbau principle”.).

P.S. The three-orbital case often throws people off… notice that the second energy level has a node right on top of the carbon. This means there is zero electron density on this atom. Don’t worry too much if this seems weird: for our purposes, the consequences of this are not so important.

P.P.S. Also note that we can’t put the nodes just “anywhere”, but that they are arranged symmetrically around the center of the Pi system. The reason for this is not crucially important for our purposes, but comes from properties of the Schrodinger wave equation (the equation produces symmetrical waves)