# Molecular orbitals of three or more atoms

1. Jul 3, 2014

### hokhani

In Molecular orbital theory, when two atoms A & B come close to each other, their atomic orbitals (say their s orbitals) combine and make two molecular orbitals, one bonding and the other anti-bonding. How about molecular orbitals of three or more atoms? For three atoms say A & B & C we would have three molecular orbitals obtained from their s atomic orbitals. Which of them are bonding and which anti-bonding?

2. Jul 3, 2014

3. Jul 3, 2014

### DrDu

For three equal s orbitals in a line with equal distance, there will be three molecular orbitals with coefficients of the atomic orbitals A, B and C equal to (up to overall normalization) (a,b,a), (1,0,-1), and (c,-d,c), where a, b, and c are positive numbers. The first one is bonding (positive overlap between all orbitals), the second one non-bonding (as there is no overlap between neighbouring atoms) and the third one anti-bonding (negative overlap). The first one has no nodes, the second one one node (change from plus to minus) and the third one two nodes. Correspondingly, for four atoms you get one with no nodes, one with one node, one with two nodes and one with three nodes which are consecutively higher in energy.

4. Jul 4, 2014

### hokhani

Thanks. Could You please introduce me an elementary reference that deals with molecular orbitals without using group theory?

Last edited: Jul 4, 2014
5. Jul 4, 2014

### DrDu

Look out for "qualitative molecular orbital theory". I can't help you with specific titles.