Unformatted text preview: Lecture 4 Molecular Orbital Theory So far we have been using a "Localized Bonding Approach" This model was very helpful because... because... It is simple and easy to use It takes us a long way We can describe the geometries of many molecules However, there are some problems with this approach 1 Limitations of Lewis Theory and VESPR Theory These theories assume that electrons are localized between pairs of atoms It is necessary to use the idea of resonance because some predicted structures are incorrect The model/approach does not deal effectively with molecules containing unpaired electrons It does not give us direct information about bond energies Now We Turn to a Better Approach Molecular Orbital Theory It is more complicated When considering many atom molecules, extensive computer calculations are necessary Now we will look at ... Homonuclear diatomics Heteronuclear diatomics Later in the course we will look at ... Polyatomic molecules Transition metal complexes 2 What is Molecular Orbital Theory? The theory says that when two atoms approach each other their atomic orbitals mix. The electrons no longer belong to one of the atoms but to the molecule as a whole Overlap of orbitals occurs in 3 ways (draw examples) 3 Types of overlap
Lobes + + - + Equal # of pos. And neg overlap Overlap positive positive negative Result zero Energy-Level Diagram Once we consider the magnitude of the overlap we can draw an energy level diagram Whenever two atomic orbitals mix, two molecular orbitals are formed, one which is bonding and the other antibonding. The bonding orbital is always lower in energy (more stable) than the A.B. orbital For significant mixing to occur, the atomic orbitals must be of similar energy Each orbital can hold a maximum of 2 electrons, one 1/2, one -1/2 When electrons are placed in different molecular orbitals of equal energy, the parallel arrangement (Hund's Rule) will have the lowest energy (Hund' 4 Let's first consider the simple diatomic molecule H2+ When two orbitals overlap positively their electron density is higher than just the sum of the electron densities of the two separate orbitals Linear Combination of Atomic Orbitals for H2+ draw 5 Electron Density Distribution Diagram (before and after) draw 6 Steps to constructing the MO diagram
Draw the atomic orbitals for each atom Label all parts of the diagram (including energy!) Insert electrons into the AO's AO' Mix the AO's to get MO's - draw the AO' MO' MO's, label the Mo's and insert electrons MO' Mo' MO diagram for H2+ 7 What happens once we construct the molecular orbital energy diagram? We can determine the bond order of a diatomic molecule Bond order - an attempt to judge the number of bonds between pairs of atoms in a molecule (bond strength) B.O. = 1/2 (NB - NA) NB = # of e in bonding orbitals NA = # of e in antibonding orbitals Bond order increases - bond length decreases Bond order decreases - bond length increases H2 Atomic orbitals Molecular orbitals Atomic orbitals 8 Practice Let's do Let' + He2 He2 9 Period 2 Diatomics
A little bit more complicated due to p- orbitals and -bonding p-orbitals can mix in 2 ways (Let's draw) (Let' 10 An MO has -symmetry if it is symmetrical with respect to a line joining the two nuclei. If you rotate the orbital about the internuclear axis there is no phase change -symmetry - asymmetric with respect to a line joining the two nuclei. If you rotate the orbital about the internuclear axis there is a phase change 11 In -bonding the increased electron density of the bonding orbital is not between the two nuclei, but above and below the plane containing the nuclei Any atom with p-orbitals will form the set 2pz *2pz 2px *2px 2py *2py Energies of 2s and 2p orbitals for period 2 elements In going from Li to F the effective nuclear charge (Z*) experienced by an electron in a 2s or 2p atomic orbital increases and the orbital energy decreases The trend is nonlinear and the s-p separation increases significantly from B to F This difference in energy affects the energies of the molecular orbitals (such that the ordering of the MOs in Li2-N2 differ from that in F2 and O2) Two kinds of MO energy diagrams Li2 - N2 O2 and F2 12 Let's draw the two diagrams
Li2 N2 Some s,p mixing O2 and F2 No s, p mixing 13 14 "- crossover" Study the diagrams the way that we draw them in class!
Read your text or other books to help reinforce the concepts that we are learning; however, the diagrams are slightly different and contain different notations and neglect some details (like mixing) Stick with one way and stay with it 15 What about the core electrons
We can ignore the interaction between core 1s atomic orbitals since the net bonding is determined by the interaction between valence atomic orbitals There are an equal number of electrons in bonding and antibonding orbitals Magnetic Properties
Diamagnetic - all electrons are spinpaired A diamagnetic substance is repelled by a magnetic field Paramagnetic - contains one or more unpaired electron(s) A paramagnetic substance is attracted by a magnetic field 16 Let's now look more carefully at the molecular orbital diagrams of some of the diatomics of period 2 What are their bond orders What are their magnetic properties The difference between homonuclear diatomic and heteronuclear diatomics
In homonuclear diatomics the resulting MOs were constructed from equal contributions from each of the sets of atomic orbitals In heteronuclear diatomics the MOs may contain different atomic orbital contributions 17 Heteronuclear Diatomic - HF Things to consider...
Zeff(F) > Zeff(H) The F 2s and 2p atomic orbital energies are significantly lowered with respect to the H 1s atomic orbital Which atomic orbital interactions are symmetry-allowed? Are the atomic orbitals sufficiently well matched in terms of energy? How do we do this?
First define the axis set for the orbitals; let the nuclei lie on the z-axis Overlap between the H1s and F2s orbitals is allowed by symmetry but the energy separation is very large 18 HF continued ... Overlap between the H1s and F2pz atomic orbitals is also symmetry-allow There is a reasonable orbital energy match This leads to and * MOs with the orbital having greater F than H character and the * orbital having greater H than F character The two F 2px and 2py atomic orbitals become non-bonding orbitals in HF since no net bonding interaction with the H1s atomic orbital is possible The orbitals interactions to consider for the heteronuclear diatomic HF 19 From the orbital energy diagram we can calculate that the Bond order for HF = 1 Let's Try the Diatomic CO
Zeff (O) > Zeff(C) The energy of the O2s atomic orbital is lower than that of the C 2s atomic orbital The 2p level in O is at lower energy than that in C The 2s-2p energy separation in O is greater than that in C 20 Remember this diagram? Orbital Interactions in CO
Complicated There are two MO diagrams in our book One is more simplified One is obtained computationally but is also over simplified Let's look at the simpler model Let' 21 Simpler Orbital Energy Diagram for CO More intricate Orbital energy diagram for CO (but still over simplified) 22 Understanding the MO diagram
Would I expect you to come up with this on your own? No Given this diagram would I expect you to understand and interpret it? Yes Let's try Let' Interpretation.... The highest occupied MO (HOMO) is bonding and possesses predominantly carbon character A degenerate pair of MOs make up the lowest unoccupied MOs (LUMOs), these MOs possess more C than O character The O 2s orbital is too low in energy to interact w/C2s or C2pz (which would be symmetry allowed ) and so it forms a nonbonding orbital The C2s and C2pz orbitals interact with the O2pz orbital to form 3 MOs The C2py and the O2py interact to form and * MOs The C2px and the O2px interact to form and * MOs 23 A pictorial representation of the HOMO and LUMO in CO These MOs have more Carbon character than O character. 24 ...
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