Differentiated Chemistry:  Molecular Orbital Notes

A theory based on Schrödingers Wave Function Equation

Describes the distribution (densities) and energies of bonded electrons

Analogous to quantum model of atoms

Electrons are delocalized about entire molecule- Molecular Orbitals

A. Molecular Orbitals-

1.Formed from the mixing of atomic orbitals- Number of M.O.s is equal to the number of atomic orbitals they are formed.

a.      When two orbitals are mixed; one orbital is the bonding orbital and one is the nonbonding orbital

Bonding orbital- electron distribution is between nuclei, Stabilize bonds

Nonbonding orbital- electron distribution is away from internuclear region, Destabilize bonds

b.     Sigma and Pi bonds are the types of covalent bonds.

Therefore we must have bonding and antibonding sigma and pi bonds.

c.     For M.O.s to form, the atomic orbitals must have similar energies.

2.     As with atomic orbitals:

a.      One molecular orbital will hold 2 electrons with opposite spins (Pauli’s Exclusion Principle).

b.     Molecular orbitals that have the same energy (degenerate) will singly fill with electrons before electrons are allowed to pair up and their spins will be parallel (Hund’s Rule).

c.     Electron Configurations are constructed by using the Aufbau process for Molecular Orbitals.

B. Homonuclear Diatomic Molecules.  

1.     Molecular Orbital Energy Diagrams for 1st energy level molecules

-used to represent the relative energies of the molecular orbitals (Aufbau)  

Ex. H₂  

Electron Configuration-  (s_1s)²(s_1s*)

a. Bond Order- Used to identify the bonding stabilization of electrons

Bond order =  ½ (# of bonding electrons - # of nonbonding electrons)

1. Bond order is related to bond dissociation energy.  

The greater the bond order the higher the dissociation energy.

Ex. He₂

Electron Configuration :    (s_1s)²(s_1s*)²

Bond Order: (2-2)/2 = 0  

**Bond orders of zero show no bond stabilization and therefore molecule won’t exist.  

2.     Second Energy Level Orbital Diagrams  

a. Non-valence shell orbitals can be omitted from energy level diagrams.  WHY?

Example. Li₂ & Be₂

Electron Configurations:  KK(s_2s)²   &  KK(s_2s)²(s_2s*)²

The 1^st energy levels are designated by their assigned letter value (K,L,M,…)  

** Li₂ exists when lithium is in the vaporous state near the boiling point. What about Be₂?

b. Molecular Orbitals involving p-type orbitals  

- 2 sets of p-type orbitals (3 each) will produce 6 molecular orbitals  

(1-   s_p, 2 - p_p, 1- s_p*, 2- p_p*)

Degenerate molecular orbitals (2 - p_p) fill according to Hund’s Rule  

Example. F₂

  Electron Configuration  KK(s_2s)²(s_2s*)²(s_2p)²(p_2p)⁴(p_2p*)⁴  

Bond Order:  ½(6-4) = 1  

3. Interesting Notes (Not necessarily exceptions)  

a. O₂

Recall-  Bond order is proportional to bond dissociation energy  

Examples:   Generalization for n=2 elements  

C—C à 345 kJ/mol                                   (200-300 kJ/mol)

C=C à 611 kJ/mol                                    (500-600 kJ/mol)  

CºC à 837 kJ/mol                                    (900-1000 kJ/mol)

So where does Oxygen fit with it’s bond dissociation energy of 495 kJ/mol?  

Bond energy (495 kJ/mol) and bond length (1.21 A as compared to 1.31A for C—C) suggests that O₂ has a double bond, but where does the paramagnetic property come from?  

Electron Configuration  KK(s_2s)²(s_2s*)²(s_2p)²(p_2p)⁴(p_2p*)²

Bond Order:  ½(6-2) = 2

Lewis Structure:  O=O

Notice that in O₂, there are two half-filled p_2p* orbitals.  These singly filled orbitals creates a net magnetic charge, thus oxygen is paramagnetic.

  b. Diboron (B₂)  

  In some diatomic molecules (B₂, C₂, & N₂) special circumstances have evolved.

** Due to 1-3 electrons in the p orbitals and fewer protons, the 2s and 2p orbitals are considerably closer in energies than the 2s and 2p orbitals in atoms like oxygen and fluorine.  

**This causes a mixing of the s & p orbitals thus causing a reversal of the s_2p and p_2p molecular orbitals  

c.  N₂  

Configuration:  KK(s_2s)²(s_2s*)²(p_2p)⁴(s_2p)²  

Bond order:  ½(6-0) = 3  

Lewis Structure  :NºN: