Basic Ideas Concerning MOs 1. Number of MOs = Number of AOs. 2. Bonding (lower energy) and antibonding (higher energy) MOs formed from AOs. 3. e- fill the lowest energy MO first (aufbau process) 4. Maximum 2 e- per orbital (Pauli Exclusion Principle) 5. Degenerate orbitals fill singly before they pair up (Hund’s Rule). Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 11 Slide 1 of 57 Molecular Orbitals – Learning Objectives • 1. Construct molecular orbital diagrams for diatomic molecules composed of elements from the first period elements (H and He) and the second period elements (Li, Be, B, C, N, O F and Ne). This includes species with +ve and -ve charges. (Eg. O2+ and CN-). • 2. Label MOs in the MO diagram and show their relative energies. Indicate whether MOs are bonding or anti-bonding. Molecular Orbitals – Learning Objectives • 3. Use the molecular formula (for neutral molecules and diatomic ions) and charge to determine the total number of electrons that we must accommodate using the MO picture. • 4. Distribute all of the electrons among the available MOs – starting with the lowest energy MOs (sound familiar?). Molecular Orbitals – Learning Objectives • 5. After counting the number of electrons in both bonding and anti-bonding orbitals determine the bond order. • 6. Use the MO diagram (and the number of electrons in the various molecular orbitals) to determine whether a molecule is diamagnetic or paramagnetic. Molecular Orbitals – Learning Objectives • 7. Understand a surprising feature of molecular orbital theory. We can accommodate all of the valence electrons in various molecular orbitals for a diatomic species and end up with a bond order of zero! Bond Order • Stable species have more electrons in bonding orbitals than antibonding. No. e- in bonding MOs - No. e- in antibonding MOs Bond Order = 2 Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 11 Slide 6 of 57 Molecular Orbitals – Nomenclature: • For the simplest atoms (H, He, Li, Be) only 1s and 2s orbitals are occupied in the ground electronic state. The overlap of two 1s orbitals can only produce a sigma (σ) bond. In the H2 molecule, for example, two 1s atomic orbitals can combine to form a σ1s bonding molecular orbital and a σ1s* anti-bonding molecular orbital. When 2p orbitals come into play we can form both σ and π molecular orbitals. Simplest Diatomics – MO Diagrams • MO diagrams are initially a bit confusing because they represent the formation of chemical bonds using both a “before picture” (showing the relative energies of the various atomic orbitals) and an “after picture” (showing the relative energies of the molecular orbitals). We’ll illustrate this with the molecules H2, He2, H2+ and He2+. Diatomic Molecules of the First-Period BO = (e-bond - e-antibond )/2 BOH + = (1-0)/2 = ½ 2 BOH = (2-0)/2 = 1 2 BOHe + = (2-1)/2 = ½ 2 FIGURE 11-22 BOHe = (2-2)/2 = 0 2 •Molecular orbital diagrams for the diatomic molecules and ions of the firstperiod elements Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 11 Slide 9 of 57 Class Examples • Draw molecular orbital diagrams for Li2 and Be2. Using the MO diagrams determine the bond order for both molecules and, as well, indicate from the MO diagrams whether the molecules are diamagnetic or paramagnetic. Molecular Orbitals of the Second Period Elements • First period use only 1s orbitals. • Second period have 2s and 2p orbitals available. • p orbital overlap: – End-on overlap is best – sigma bond (σ). – Side-on overlap is good – pi bond (π). Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 11 Slide 11 of 57 Molecules with 2nd Period Atoms • The simplest possible molecular orbital diagram that one could imagine for second row elements having 2p electrons is shown on the next slide. This slide would necessarily apply only to homonuclear diatomics. Note the “symmetrical disposition” of bonding and nonbonding orbitals. FIGURE 11-25 (PART A) Possible molecular orbital energy-level scheme for diatomic molecules of the second-period elements Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 11 Slide 13 of 57 MO Diagrams - Surprises • The MO diagram presented on the previous slide does not adequately explain all properties of diatomic molecules formed from second period elements. Overlap of 2p atomic orbitals produces six MOs whose order energy order can vary with atomic number of the bonded atoms. Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 11 Slide 14 of 57 MO Diagrams – Surprises – C2: • Two possible MO diagrams are illustrated for the C2 molecule on the next slide. The presentation of MOs here is similar to that used in drawing orbital diagrams for atoms. By experiment we know that the C2 molecule (4 valence electrons contributed by each C atom for a total of 8) is diamagnetic. Which of the MO diagrams accounts for this diamagnetism? •Experiment shows C2 to be diamagnetic, supporting a modified energy-level diagram Expected MO Diagram for C2 Modified MO Diagram for C2 Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 11 Slide 16 of 57 Rationalization of the C2 “Problem”: • With homonuclear molecules constructed from atoms having only ns electrons the visualization/construction of MOs is simple. For diatomic molecules containing both 2s and 2p electrons MOs can be “constructed” using four atomic orbitals as opposed to two. This accounts for variations in the order of MO energies and we speak of s and p mixing. (Any swimming pool analogies?) FIGURE 11-25 (PART B) Modified molecular orbital energy-level schemes for diatomic molecules of the second-period elements Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 11 Slide 18 of 57 FIGURE 11-26 (PART 1) Molecular orbital occupancy diagrams for the homonuclear diatomic molecules of the second-period elements Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 11 Slide 19 of 57 Homonuclear Molecules Containing 2nd Period Atoms (MO Diagrams) • The next few slides represent the MO diagrams (molecular energy levels) for a series of homonuclear diatomics. The MO diagrams for O2, F2 and Ne2 are what we would expect to see in the absence of 2s and 2p orbital mixing. Why? These diagrams account for the bond order of each molecule and also magnetic properties. We can construct similar diagrams for O2+ and O2- (and other molecules). Molecular orbital occupancy diagrams for the homonuclear diatomic molecules of the second-period elements (Symmetrical disposition of Mos) Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 11 Slide 21 of 57 Molecular Oxygen is Paramagnetic • We discussed earlier the fact that Lewis structures do not account satisfactorily for the paramagnetism of the O2 molecule. The MO picture of chemical bonding does account fro this paramagnetism. A really “cool” experiment to demonstrate paramagnetism in oxygen involves trapping liquid oxygen between the poles of a permanent magnet. A Special Look at O2 FIGURE 10-3 Paramagnetism of Oxygen Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 11 Slide 23 of 57 Heteronuclear Diatomics – cont’d: • In heteronuclear diatomics the different energies of the 2s and 2p orbitals on the two bonded atoms make “s and p mixing” more favourable. Why? Here we use new designations for the MOs since the s and p subscripts used for homonuclear diatomics (eg. σ2s) now have little meaning. A Look at Heteronuclear Diatomic Molecules FIGURE 11-27 •The molecular orbital diagram of CO Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 11 Slide 25 of 57 Tests 2 and 3 • We’ll examine solutions for a few of the questions on yesterday’s test. The final term test is on November 16th. The material for this test will have been largely covered by the end of today’s class. In the first instance I’ll ask you to look at sp3d and sp3d2 hybridization schemes at home.