CHAPTER 4: MOLECULAR ORBITAL THEORY It is clear that hybridized valence bond theory does not explain much of the observed phenomena for small molecules such as paramagnetism or UV absorption and a better theory needs to be introduced to rationalize these experimental observations. In molecular orbital (MO) theory, electrons occupy orbitals each of which spans the entire molecule. Molecular orbitals each hold up to two electrons and obey Hund’s rule, just like atomic orbitals. Ground-rule of MO theory: number of MOs that can be formed must equal the number of atomic orbitals of the constituent atoms. Each MO has an associated energy and to derive the electronic ground state of a molecule, the available electrons are placed in MOs according to the aufbau principle, beginning with the lowest energy. CHEM210/Chapter 4/2014/01

ΨMO (in-phase) = ΨMO = N[Ψ1 + Ψ2] BONDING IN HYDROGEN An approximate description of the MOs in hydrogen can be obtained by considering them a linear combinations of atomic orbitals (LCAOs). Each of the H atoms has 1s atomic orbital with associated wave functions, Ψ1 and Ψ2 and the signs of the wavefunction associated with the 1s orbital may be either + or -. The possible combinations of the two 1s orbitals are given by equations: ΨMO (in-phase) = ΨMO = N[Ψ1 + Ψ2] ΨMO (out-of-phase) = Ψ*MO = N*[Ψ1 - Ψ2] where N and N*are the normalization factors, ΨMO is an in-phase (bonding) interaction and Ψ*MO is an out-of-phase (antibonding) interaction 1sA + 1sB = MO1 1sA – 1sB = MO2 constructive interference destructive interference CHEM210/Chapter 4/2014/02

The label for a molecular orbital tells us three things: its shape. the parent atomic orbitals from which it was formed. its stability (bonding or anti-bonding): antibonding character is designated with an asterisk (*) The interaction between the H 1s AOs on forming H2 may be represented by the MO diagram shown below. CHEM210/Chapter 4/2014/03

CHEM210/Chapter 4/2014/04

H2 molecule is diamagnetic. The ground state electronic configuration of H2 may be written as using the notation; σg (1s2). The orbital interaction diagram can be used to predict several properties of the H2 molecule: H2 molecule is diamagnetic. Bond order = 1. Bond order = ½[(number of bonding electrons) – ( number of antibonding electrons)] CHEM210/Chapter 4/2014/05

The He2 molecule is not a stable species HELIUM (He2) σg (1s2) σu* (1s2) The bonding effect of the σg (1s2) is cancelled by the antibonding effect of σu* (1s2) Electrons in the anti-bonding MO (1sA-1sB) offset the energy gained by placing electrons in the bonding orbitals. The He2 molecule is not a stable species CHEM210/Chapter 4/2014/06

↑ ↑↓ ↑↓ ↑ ↑↓ ↑↓ Bond order = 0 A high bond order indicates high bond energy and short bond length. Consider H2+, H2, He2+, He2: first row diatomic molecules and ions H2 H2+ He2+ He2 Magnetism Dia- Para- - Bond order 1 ½ Bond energy (kJ/mol) 436 225 251 Bond length (pm) 74 106 108 σg (1s2) ↑ ↑↓ E ↑↓ ↑ ↑↓ ↑↓ σu* (1s2) CHEM210/Chapter 4/2014/07

LITHIUM (Li2) Remember Li: 1s22s1 Both the 1s and 2s overlap to produce s bonding and anti-bonding orbitals σg (1s2) σu* (1s2) σg (2s2) BO = ½(nb - na) = ½(4 - 2) = 1 = a single bond CHEM210/Chapter 4/2014/08

The molecule is not stable! BERYLLIUM (Be2) Remember Be: 1s22s2 σg (2s2) σu* (2s2) BO = ½(nb - na) = ½(4 - 4) = 0 No bond! The molecule is not stable! What about p orbitals? If the overlap lies along the major bond axis then must constitute a σ bond. If they overlap perpendicular to the axis they will form π bonds. FLUORINE (F2) AND OXYGEN (O2) The valence shell of a fluorine atom contains 2s and 2p AOs and the formation of the F2 molecule involves 2s – 2s and 2p – 2p interactions. CHEM210/Chapter 4/2014/09

CHEM210/Chapter 4/2014/10

We expect F to use 2p orbitals this time (valence electrons). For F: 1s22s22p5 We expect F to use 2p orbitals this time (valence electrons). subtraction addition subtraction addition CHEM210/Chapter 4/2014/01

F2 - It has 14 valence electrons O2 – has the same MO configuration but has two electrons less. This makes O2 paramagnetic as you will have unpaired electrons Determine the bond orders CHEM210/Chapter 4/2014/12

This leads to another arrangement of the molecular orbitals. Fluorine and oxygen follow the simple logic of LCAO as they are both very electronegative and the energy difference between the 2s and 2p is large. With boron, carbon and nitrogen a slightly different story emerges: for these elements, a degree of “s and p orbital interaction” occurs, whereby a change in the energy of the relative molecular orbitals occurs This leads to another arrangement of the molecular orbitals. σ2p* π2p* π2p* E σ2p 2p 2p π2p π2p CHEM210/Chapter 4/2014/13

↑ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ HETERONUCLEAR DIATOMICS Even when the atoms in a diatomic molecule are different, we use the homonuclear diatomic diagram with the s-p interaction as an approximation. NITRIC OXIDE (NO) Valence electrons = 5 + 6 = 11 σ2p* Bond order = 2.5 π2p* ↑ Molecule is stable and paramagnetic – agrees with experimental data. σ2p ↑↓ π2p ↑↓ ↑↓ σ2s* ↑↓ σ2s ↑↓ CHEM210/Chapter 4/2014/14

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ NO+: Number of valence electrons: 5 + 6 - 1 = 10 CN–: Number of valence electrons: 4 + 5 + 1 = 10 These structures are isoelectronic σ2p* π2p* σ2p ↑↓ Bond order = 3.0 π2p ↑↓ ↑↓ σ2s* ↑↓ σ2s ↑↓ CHEM210/Chapter 4/2014/15

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ Question: Can NeO exist? Number of valence electrons: 8 + 6 = 14 σ2p* π2p* ↑↓ ↑↓ σ2p ↑↓ Bond order = 1.0 π2p ↑↓ ↑↓ σ2s* ↑↓ σ2s ↑↓ What about NeO2-? CHEM210/Chapter 4/2014/16