A Quantum Mechanical Progression of Understanding Hydrogen the atom (1 p+, 1 e-) modifications A Quantum Mechanical Progression of Understanding …Zeff and hydrogen-like orbitals Poly-electronic atoms (more than 1 p+ and more than 1 e-) Molecules comprised of atoms (the overlap of e-’s in atomic orbitals…the localized electron model) …resonance / hybridization Molecules from a holistic perspective (more than one nucleus and more than one electron) …molecular orbitals

The simplest molecule... H2 1s 1s

Constructive Overlap

Constructive Overlap 1sA + 1sB electron densities add together

Destructive Overlap

Destructive Overlap 1sA - 1sB electron densities cancel each other

Interaction of two atomic orbitals dictates the production of two molecular orbitals…. s1s* Probability distributions are on either side of nuclei s1s Probability distribution is in between the nuclei

stable molecule H2 s1s2 s1s* E 1s 1s s1s # of bonding e-’s - # of antibonding e-’s Bond Order = 2 s1s* antibonding M.O. E 1s 1s s1s Bond Order probonding M.O. = 1 (molecular orbital configuration notation) H2 s1s2

not a stable molecule He2 s1s* E 1s 1s s1s = 0 Bond Order antibonding probonding = 0 He2

Factors which influence the strength of the interactions between two atomic orbitals which produce 2 molecular orbitals is determined by: A. the energy difference between the orbitals. B. the magnitude of their overlap. In general…for the interaction to be strong…the energies of the orbitals must be ~ equal and the overlap should be large. Li2 Liatom 1s22s1 Liatom 1s22s1

stable molecule Li2 s1s2 s1s*2 s2s2 E Liatom 1s22s1 Liatom 1s22s1 s2s* Bond Order 1s 1s = 1 s1s Li2 Liatom 1s22s1 Liatom 1s22s1

Bonding and Antibonding All scientific models are perfect and in no need of modifications? Which of the following concepts would you associate with atomic orbitals? delocalized electrons or localized electrons 3. What type of orbitals would you associate with delocalized electrons? 4. When two atomic orbitals combine to give a set of molecular orbitals, the M.O.’s are differentiated from each other by what designation? 5. When molecular orbitals are symmetrical about the axis between two nuclei we call them by what designation? 6. Molecular orbitals, when being filled, follow the same rules as filling atomic orbitals…they are? FALSE Molecular Orbitals Bonding and Antibonding Sigma, s Aufbau, Pauli and Hunds

B2 Batom 1s22s22p1 Batom 1s22s22p1

stable molecule B2 all electrons are paired!!! E Batom 2s22p1 Diamagnetic p2p* p2p* 2p p2p p2p 2p E s2p s2s* Bond Order 2s 2s = 1 s2s B2 Batom 2s22p1 Batom 2s22p1

stable molecule B2 two electrons are unpaired!!! E Batom 2s22p1 Paramagnetic s2p* p2p* p2p* 2p 2p s2p E p2p p2p s2s* Bond Order 2s 2s = 1 s2s B2 Batom 2s22p1 Batom 2s22p1

C2 N2 O2 CN- s2p* p2p* p2p s2p s2p p2p s2s* s2s 2 3 2 3 dia dia dia B.O.→ New filling order due to s-p mixing C2 N2 O2 CN- s2p* p2p* E p2p s2p s2p p2p s2s* s2s dia dia dia para Magnetism?→

Liquid Oxygen

On bright sunny days, you may notice the fresh-air smell of this gas if it’s present in small concentrations. It’s name, however derives from a Greek word that means “to smell” because the normal odor in higher concentrations is disagreeable. You may notice this odor around faulty electrical equipment. It is a faintly blue gas that’s used a water disinfectant and bleach (especially in Europe). The gas is stable except at elevated temps or in the presence of a catalyst where it decomposes. Unfortunately, this happens to our dismay in the upper levels of our atmosphere where it’s very much needed… On bright sunny days, you may notice the fresh-air smell of this gas if it’s present in small concentrations. It’s name, however derives from a Greek word that means “to smell” because the normal odor in higher concentrations is disagreeable. You may notice this odor around faulty electrical equipment. It is a faintly blue gas that’s used a water disinfectant and bleach (especially in Europe O3 (OZONE)

The electron dot structure for this molecule is described as a resonance hybrid of the two resonance forms:

use MO theory to describe their behavior. To get a better view we separate out those electrons that appear to be in different locations in different resonance forms and use MO theory to describe their behavior. The other electrons are described using the localized electron model sp2 hybridization Uses the molecular orbital model Uses the localized electron model  

O→ 2s22px22py12pz1 unhybridized p orbital

 

The pi electrons in the non-bonding orbital spend half their time on molecule.   Pi MO’s:   Click here for Rotating Pi Orbitals of O3 Notice: only the bonding and non-bonding pi orbitals are occupied. We have only four electrons in the pi system and we fill up the possible pi energy levels in the same way that we do atoms, i.e. start at the lowest and use Pauli exclusion principle and Hund’s rule.   The total PI bond order is (2 - 0)/2 = 1 but since the bonding orbital is spread over two O-O bonds the pi bond order per O-O bond is ½ = 0.5 . The O-O sigma bonds contributes a sigma bond order of 1.0 to each O-O bond so the TOTAL bond order per O-O bond is 1.0 + 0.5 = 1.5 which again predicts the O-O bond is half way between O-O and O=O. The pi electrons in the non-bonding orbital spend half their time on one end oxygen and half their time on the other end oxygen. Adding in the sigma non-bonding pairs we get an average of 2 ½ non-bonding pairs per end O atom as was predicted by averaging the resonance forms.

6 molecular orbitals in benzene for 6 unhybridized p electrons (one on each carbon) Only the lowest energy orbitals (all pro-bonding) get filled. Makes for a very stable molecule!)