# Lesson 3. Chemical Bonding. Molecular Orbital Theory

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1 Lesson 3 Chemical Bonding Molecular Orbital Theory 1

2 Why Do Bonds Form? An energy diagram shows that a bond forms between two atoms if the overall energy of the system is lowered when the two atoms approach closely enough that the valence electrons experience attraction to both nuclei It is important to consider both the attractive and repulsive forces involved! Also, remember that atoms are in constant motion above 0 K. Bonds are NOT rigid! 2

3 Why do bonds form? Lennard-Jones potential energy diagram for the hydrogen molecule. E Energy of two separate H atoms r

4 The Quantum Mechanics of H 2 + To get a better understanding of bonding, it s best to start with the simplest possible molecule, H 2+. What forces do we need to consider? This is a three-body problem, so there is no exact solution. The nuclei are much more massive than the electrons (1 u for a proton; u for an electron). To simplify the problem, we use the Born-Oppenheimer approximation. We assume that the motion of the nuclei is negligible compared to the motion of the electrons and treat the nuclei as though they were immobile. 4

5 The Quantum Mechanics of H 2 + If we set the internuclear distance to R, we are then able to solve for the wavefunction of the electron in H 2 + and its energy: Electron energy = kinetic energy + electron-nuclear attraction This is possible because H 2 + has only one electron and simple (cylindrically symmetric) geometry. The resulting ground-state orbital looks like this: 5

6 The Quantum Mechanics of H 2 + The energy of this ground state orbital depends on R. If we calculate the potential energy of the system (both the electron and the internuclear repulsion) at different values of R, we arrive at an energy diagram just like the one on the first slide of this lecture. Important Points to Note: In H 2+, the electron doesn t belong to either atom. In H 2+, the electron is in an orbital which spans the molecule a molecular orbital! Just as atoms have many atomic orbitals (1s, 2s, 2p, etc.), molecules can have many molecular orbitals. In H 2+, the higher energy molecular orbitals are all empty. The energy of a molecular orbital depends in part on the relative positions of the nuclei. 6

7 The Molecular Orbitals of H 2 It was possible to solve the Schrödinger equation exactly for a hydrogen atom, but a helium atom had too many electrons. We encounter the same problem with H 2. While H 2 + can be solved, as soon as a second electron is introduced, there are too many moving bodies and the wavefunction cannot be solved exactly. This does not mean we re finished with quantum mechanics! Instead, we make more approximations So, what s a reasonable approximation? We know that, when two hydrogen atoms are far apart (i.e. R is large), they behave like two free hydrogen atoms. If we were able to bring them together such that the nuclei overlapped (i.e. R = 0 pm), we would have : 7

8 The Molecular Orbitals of H 2 If we imagine the initially separate hydrogen atoms approaching each other (as in the diagram at the right), we see the electrons begin to lean in to begin making the H-H bond. What is responsible for this behaviour? 300 pm 250 pm 220 pm 200 pm 150 pm 100 pm 73 pm 8

9 The Molecular Orbitals of H 2 The orbitals of a hydrogen molecule (R = ~74 pm) must be somewhere between those two extremes. We often approximate molecular orbitals by describing them as combinations of atomic orbitals. This is termed Linear Combination of Atomic Orbitals (LCAO) and gives an LCAO-MO such as that below: By adding the two atomic orbitals, we obtain a sigma bonding orbital (σ). Bonding: lots of electron density between the two nuclei Sigma symmetry: high electron density along the axis connecting the nuclei 9

10 The Molecular Orbitals of H 2 We can also subtract the two atomic orbitals (equivalent to adding them after inverting the phase of one just as subtracting 5 is equivalent to adding -5): This is a sigma antibonding orbital (σ * ). Antibonding: depleted electron density between the two nuclei (look for a node perpendicular to the axis connecting the nuclei) Sigma symmetry: high electron density along the axis connecting the nuclei 10

11 Molecular Orbital Diagram for H 2 We can draw an energy level diagram showing molecular orbitals and the atomic orbitals from which they were derived. This is referred to as a molecular orbital diagram (MO diagram). Note that the energy difference is larger between the atomic orbitals and the antibonding orbital than between the atomic orbitals and the bonding orbital. 11

12 Molecular Orbital Diagram for H 2 MO diagrams relate the energies of molecular orbitals to the atomic orbitals from which they were derived. If the total energy of the electrons is lower using molecular orbitals (the middle column), the molecule forms. If the total energy of the electrons is lower using atomic orbitals (the two outside columns), no molecule is formed. To fill a molecular orbital diagram with electrons, use the same rules as you would to fill in an atomic orbital diagram: Fill σ first. Pauli s exclusion principle still applies Hund s rule still applies 12

13 Molecular Orbital Diagram for H 2 Thus, the orbital occupancy for H 2 in the ground state is and the orbital occupancy for He 2 in the ground state is We can calculate bond orders for these two molecules from their MO diagrams: 13

14 Molecular Orbital Diagram for H 2 If a molecule of H 2 was irradiated with light, exciting an electron from 1σ to 2σ *, what would happen? Should it be possible for H 2 - to exist? What about He 2+? 14

15 15

16 Molecular Orbitals of Homonuclear Diatomics As the two hydrogen atoms approach, we can see that the orbitals change from looking like two separate 1s orbitals (one per H) to looking like a σ molecular orbital: The picture for the development of the antibonding σ * molecular orbital is similar except that, instead of the two 1s orbitals appearing to reach in toward each other, they appear to push away from each other. 300 pm 250 pm 220 pm 200 pm 150 pm 100 pm 73 pm 16

17 Molecular Orbitals of Homonuclear Diatomics We can combine higher energy atomic orbitals in the same way. Compare the σ and σ * orbitals made from the 2s orbitals in F 2 to the σ and σ * orbitals made from the 1s orbitals in H 2 : σ * 1s (H) 1s (H) σ σ * 2s (F) 2s (F) σ 17

18 Molecular Orbitals of Homonuclear Diatomics Note that as the distance between nuclei increases, the overlap between the 1s orbitals decreases. That s why we can t just compare 1s and 2s for F 2! σ * 1s (F) 1s (F) σ σ * 2s (F) 2s (F) σ This is also why, for the most part, we focus on valence molecular orbitals. The core MOs look just like core AOs. 18

19 Molecular Orbitals of Homonuclear Diatomics p orbitals can also be combined to make molecular orbitals. The type of molecular orbital formed will depend on the orientation of the p orbitals. p orbitals that overlap head-on (usually defined as the p z orbitals) give σ molecular orbitals: 19

20 Molecular Orbitals of Homonuclear Diatomics p orbitals that overlap side-on (usually defined as the p x or p y orbitals) give π molecular orbitals and here are the pretty computer-generated pictures of those orbitals: 20

21 General Rules for LCAO-MOs Linear Combination of Atomic Orbitals (LCAO) can only be used to generate molecular orbitals when the atomic orbitals have compatible symmetry. e.g. Combination of an s orbital and a p orbital allowed disallowed When atomic orbitals are added in phase (constructive interference), a bonding orbital is made. When added out of phase (destructive interference), an antibonding orbital is made. THE NUMBER bonding OF MOLECULAR ORBITALS IS antibonding ALWAYS EQUAL TO THE NUMBER OF ATOMIC ORBITALS INCLUDED IN THE CALCULATION!!! 21

22 22

23 The MO Diagram for Li 2 -N 2 4σ 2p 2π 2p 2π 2p 2p 3σ 2pz 2p 1π 2p 1π 2p 2σ 2s 2s 2s 1σ 2s

24 Li 2 and Be 2 Li 2 BO: Bond energy: 106 kj/mol Be2 BO: 2σ 2s 2σ 2s 2s 2s 2s 2s 1σ 2s 1σ 2s

25 Correlation diagram for homonuclear diatomics, Z up to 7 (Li 2 -N 2 ) B 2 Bond order = BDE = 290 kj 4σ 2p 2π 2p 2π 2p 2p 2p 1π 2p 1π 2p 2σ 2s 2s 2s 1σ 2s

26 Paramagnetic unpaired electrons Diamagnetic all electrons paired 2p 2p 26

27 C 2 Bond order BDE 620 kj 2π 2p 4σ 2p 2π 2p 2p 2p 1π 2p 1π 2p 2σ 2s MOEC: 2s 2s 1σ 2s

28 N 2 Bond order BDE 945 kj 4σ 2p 2π 2p 2π 2p 2p 2p 1π 2p 1π 2p 2σ 2s MOEC: 2s 2s 1σ 2s

29 Molecular Orbitals of Homonuclear Diatomics O 2 29

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31 31

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33 33

34 Molecular oxygen is paramagnetic

35 Singlet oxygen ( 1 O 2 ) BO = (6-2)/2 = 2 Singlet Oxygen is an excited state of the ground state triplet 3 O 2 molecule. It is much more reactive, and will readily attack organic molecules. O O 2 O The O 2 molecule in its excited singlet state which is 25 kcal/mol in energy above the ground triplet state. Irradiation with IR light causes excitation to the singlet state, which can persist for hours because the spin-selection rule (see later) inhibits transitions that involve a change of spin state.

36 Recap

37 Molecular Orbitals of Heteronuclear Diatomics The molecular orbitals of heteronuclear diatomics (HF, CO, CN -, etc.) can be predicted using the same principles that we used to construct the molecular orbitals of homonuclear diatomics: Ignore the core electrons Total number of MOs = Total number of AOs Only AOs of similar energy combine to make LCAO-MOs Only AOs of compatible symmetry combine to make LCAO-MOs: σ-type AOs (s and p z orbitals) make σ MOs π-type AOs (p x and p y orbitals) make π MOs 37

38 Molecular Orbitals for HF Consider the valence atomic orbitals of hydrogen and fluorine: Which AOs will combine to make MOs? Which AOs will not mix (and therefore still look like an AO)? 38

39 Molecular Orbitals for HF Using symmetry and energy as our guide, we predict that we will make LCAO-MOs that look something like: There can be no π bonding in HF. Why not? There will still be orbitals with π symmetry in HF. 39

40 Molecular Orbitals for HF 40

41 41

42 The MOs of CO 4σ 2p 2π 2px 2π 2py 2p C 3σ nb 2s-2pz 1π 2px 1π 2py 2p O 2s C 2σ 2s-2pz 1σ 2sO 2s O

43 43

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