Molecular Orbital Theory Tutorial 8 Molecular Orbital Theory

Aim of Molecular Orbital Theory Valence bond theory cannot fully explain observed properties of molecules  e.g it shows that O2 is “Diamagnetic”, however O2 shows to be “Paramagnetic” in fact ! MO theory completes the picture of covalent bond formation

Molecular Orbital Theory Molecular orbital theory describes covalent bonds in terms of molecular orbitals, which result from interaction of the atomic orbitals of the bonding atoms and are associated with the entire molecule. Atomic Orbital = belongs to only one atom Molecular Orbital = belongs to the entire molecule

Molecular Orbital Theory MO theory considers the wave nature of electrons (electrons have a dual nature “particles and waves”) Waves interact in 2 ways Constructive interaction Destructive interaction

Molecular Orbital Theory Therefore, Electrons interact in 2 ways Bonding Molecular orbitals Lower energy (More stable) A constructive way & Anti-bonding Molecular orbitals Higher energy (Less stable) A destructive way N.B Bonding MO is of lower energy than individual atomic orbitals, that’s why bond formation is exothermic

H2 H σ 1s2 σ* 1s + σ 1s The molecular orbital diagram of H2 will be: destructive constructive H σ* 1s Higher energy (Less stable) σ 1s Lower energy (More stable) + The molecular orbital diagram of H2 will be: σ* 1s σ 1s The electronic configuration of H2 molecule: σ 1s2

MO diagram : P orbitals e.g N2 1s2 2s2 2p3 N + N 2px + 2px σ* 2px σ 2px 1s + 1s σ* 1s σ 1s 2py + 2py п 2py п* 2py 2s + 2s σ* 2s σ 2s 2pz + 2pz п 2pz п * 2pz

P orbitals

P orbitals overlap

How are molecular orbitals filled They are filled in order of increasing energy σ 1s σ* 1s σ 2s σ* 2s σ 2px п 2py п* 2py п 2pz п* 2pz σ* 2px Orbitals with equal energy are half-filled first “Hund’s Rule”

How are molecular orbitals filled Notes: The number of molecular orbitals formed is always equal to the number of atomic orbitals combined. Each molecular orbital can accommodate up to two electrons with opposite spins When there are several orbitals of equal energy, electrons enter singly with parallel spins, where no pairing occurs until the orbitals are half-filled. “Hund’s Rule” The number of electrons in the molecular orbitals is equal to the sum of all the electrons on the bonding atoms.

Molecular orbital model can predict the magnetic properties of the molecule All electrons paired Unpaired electrons Diamagnetic Paramagnetic

Molecular Orbital Energy Level diagram of O2 8O : 1s2 2s2 2p4 σ 1s σ* 1s σ 2s σ* 2s σ 2px п 2py п* 2py п 2pz п* 2pz σ* 2px O + O 8 + 8 = 16 electrons Paramagnetic HOMO = п* 2py & п* 2pz LUMO = σ* 2px N.B The valence MO diagram of O2 starts from σ 2s

HOMO : Highest Occupied Molecular Orbital LUMO : Lowest Unoccupied Molecular Orbital

Bond Order A calculation that gives an indication about the stability of the molecule 3 : triple bond 2 : double bond 1 : single bond 0 : molecule doesn’t exist

Bond Order Li2 Diamagnetic HOMO : σ 2s LUMO : σ* 2s 3 + 3 = 6 σ 1s σ* 1s σ 2s σ* 2s Diamagnetic HOMO : σ 2s LUMO : σ* 2s Bond order = ½ (4 – 2) = 1 Electronic configuration of Li2 : σ 1s2 σ* 1s2 σ 2s2

Exceptions B2, C2, N2 Light molecules in period 2 Have flipped σ 2p & п 2p molecular orbitals П 2py σ* 2s σ 2s σ* 1s σ 1s П* 2pz σ 2px П 2pz σ* 2px П * 2py

Question 1: B2 5 + 5 = 10 Bond order = ½ (6 – 4) = 1 П 2py σ* 2s σ 2s П* 2pz σ 2px П 2pz σ* 2px П* 2py Bond order = ½ (6 – 4) = 1

Question 2: NO+ 7 + 8 – 1 = 14 П 2py σ* 2s σ 2s σ* 1s σ 1s П* 2pz σ 2px П 2pz σ* 2px П* 2py Bond order = ½ (10 – 4) = 3 Diamagnetic HOMO: σ 2px LUMO: П* 2py & П* 2pz

Question 2: CN- 6 + 7 + 1 = 14 П 2py σ* 2s σ 2s σ* 1s σ 1s П* 2pz σ 2px П 2pz σ* 2px П* 2py Bond order = ½ (10 – 4) = 3 Diamagnetic HOMO: σ 2px LUMO: П* 2py & П* 2pz

Question 2: BN 5 + 7 = 12 П 2py σ* 2s σ 2s σ* 1s σ 1s П* 2pz σ 2px Bond order = ½ (8 – 4) = 2 Diamagnetic HOMO: П 2py & П 2pz LUMO: σ 2px

Question 2: F2 9 + 9 = 18 П 2py σ* 2s σ 2s σ* 1s σ 1s П* 2pz σ 2px Bond order = ½ (10 – 8) = 1 Diamagnetic HOMO: П* 2py & П* 2pz LUMO: σ* 2px