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) 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) 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) 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) 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) 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 Li 2 Be 2 B2B2 C2C2 N2N2 O2O2 F2F2 Ne

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.