1. Lecture 15 Molecular Bonding Theories 1) Molecular Orbital Theory Considers all electrons in the field of all atoms constituting a polyatomic species, so that all molecular orbitals (MO’s) are multicenter. The most common way to build MO’s,  MO,j, is by using a linear combination of all available atomic orbitals  AO, i (LCAO): Consider dihydrogen molecule ion H 2 + as an example. We can form two molecular orbitals from two hydrogen’s atomic orbitals  A and  B : The probability to find an electron on the  g orbital is then where S is the overlap integral for atomic orbitals  A and  B and N is normalizing constant. S > 0 corresponds to a bonding (  g ) and S < 0 (  u ) – to antibonding situations.

2. 2) Molecular Orbital Theory. Dihydrogen molecule In dihydrogen molecule we have 2 electrons, 1 and 2. Assuming that 1 and 2 are independent one from another (one-electron approximation), we can get: The first term corresponds to ionic contribution and the second one – to covalent contribution to the bonding (compare with VB theory).

3. 3) Atomic orbital overlap and covalent bonding Interaction between atomic orbitals leads to formation of bonds only if the orbitals: –1) are of the same molecular symmetry; –2) can overlap well (see explanation of the overlap integral below); –3) are of similar energy (less than 20 eV energy gap). Any two orbitals  A and  B can be characterized by the overlap integral, Depending on the symmetry and the distance between two orbitals, their overlap integral S may be positive (bonding), negative (antibonding) or zero (non-bonding interaction).

4. 4) Simplified MO diagram for homonuclear diatomic molecules (second period) Combination of 1s, 2s, 2p x, 2p y and 2p z atomic orbitals of two atoms A of second row elements leads to ten molecular orbitals.  * 2p =  2pA –  2pB (3  u )  * 2py =  2pyA –  2pyB (  g )  * 2px =  2pxA –  2pxB (  g )  2py =  2pyA +  2pyB (  u )  2px =  2pxA +  2pxB (  u )  2p =  2pA +  2pB (3  g )  * 2s =   sA –   sB (2  u )  2s =   sA +   sB (2  g )  * 1s =   sA –   sB (1  u )  1s =   sA +   sB (1  g )

5. 5) Orbital mixing and level inversion in homonuclear diatomic molecules Orbitals belonging to the same atom mix if all of the following is true: 1) they are of the same symmetry; 2) they are of similar energy (less than 20 eV difference). Note that there is no  -orbitals of the same symmetry in diatomic homonuclear molecules (  g and  u only). So, they energy levels will remain unaffected by mixing.

6. 6) MO diagrams of homonuclear diatomic molecules Filling the resulting MO’s of homonuclear diatomic molecules with electrons leads to the following results: Bond order = ½ (#Bonding e’s - #Antibonding e’s) AB# of e’sBond order # unpair. e’s Bond energy, eV 6 8 10 12 14 16 18 20 Li 2 Be 2 B2B2 C2C2 N2N2 O2O2 F2F2 Ne 2 1 0 1 2 3 2 1 0 0 0 2 0 0 2 0 0 1.1 - 3.0 6.4 9.9 5.2 1.4 -

7. 7) Molecular Orbital Theory. Energy levels in N 2 molecule Photoelectron spectroscopy of simple molecules is an invaluable source of the information about their electronic structure. The He-I photoelectron spectrum of gaseous N 2 below proves that there is the  -  level inversion in this molecule. It also allows identify bonding (peaks with fine vibronic structure) and non-bonding MO (simple peaks) in it.