MOLECULAR ORBITAL THEORY Chapter 10.8, Morrison and Boyd

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1 MOLECULAR ORBITAL THEORY Chapter 10.8, Morrison and Boyd more understanding: why oxygen is paramagnetic, why H2 + exists; explanation of excited electronic states (e.g., visible spectra) eliminates need for resonance structures rather than orbitals localized on an atom, uses molecular orbitals which are delocalized over several, if not all, of the atoms in a molecule => electrons are delocalized recognizes that conjugated π electron systems have added stability from delocalization of electrons Molecular Orbital (MO) Theory: Electron Delocalization molecular orbitals formed by adding or subtracting (linear combination) of atomic orbitals (AOs) centered on the nuclei being bonded (LCAO) for a homonuclear diatomic (atom 1 = atom 2) the MO (ψmolecular) is formed from overlap of waves (atomic orbitals) on atom 1 and atom 2 where the coefficient c 1 = ± c 2 ψmolecular orbital = c 1 ψatomic orbital on atom 1 + c 2 ψatomic orbital on atom 2 1. the number of MOs is equal to the number of atomic orbitals combined 2. when c 1 = c 2 there is in-phase constructive interference and a bonding molecular orbital results which is lower in energy than the parent atomic orbitals; when c 1 = c 2 there is out-ofphase destructive interference and an antibonding molecular orbital results which is higher in energy than the parent AOs and there is a node between the nuclei being bonded 3. electrons are assigned to the MOs with the same rules as electrons fill atomic orbitals they are assigned in increasing energy (aufbau principle) according to Hund's rule (equal energy orbitals first half fill with parallel electron spins before pairing) and Pauli exclusion principle (no more than two electrons per MO) 4. the most effective combination is when the parent atomic orbitals are of similar energy (the combination of a 1s AO and a 2s AO is not effective) the relative energies and parentage of MOs are visualized in a molecular orbital energy diagram (correlation diagram) where the bond order = 1/2 (# e-'s in bonding MOs # e-'s in antibonding MOs) (+, denotes phase of Ψ) (a) MO energy (correlation) diagram for the H 2 molecule. (b) Shapes of the MOs and the electron probability distribution are obtained by squaring the wave functions for MO 1 and MO 2. Positions of the nuclei are indicated by in energy diagram: bonding MO 1 has the greatest electron probability between nuclei while antibonding MO 2 s density lies outside this area bonding MO 1 has no node between nuclei while antibonding MO 2 does bonding MO 1 lower in energy than 1s orbitals of free H atoms; antibonding MO 2 higher in energy than the 1s orbitals average energy of a pair of bondingantibonding MOs is approximately at the energy of the original AOs

2 - 2 - Period Two Homonuclear Diatomic Molecules Homonuclear Diatomics (H Be 2 ) FIG I σ, σ* MOs Formed from s AO s FIG II MO Energy Diagram for FIG I The bonding MO formed by the constructive combination (overlap) of the two 1s orbitals has cylindrical symmetry with respect to the molecular axis (every slice of the MO perpendicular to the molecular axis will be a circle). Furthermore the MO is formed by singly connecting the atomic orbitals so that the two atoms are free to rotate about the molecular axis. Such a bond is called a sigma bond, σ. The antibonding bond is denoted as σ*. EX 1. Describe the bonding in H 2 +, H 2, He 2 +, He 2, Li 2 +, Li 2, Be 2 +, Be 2, give the bond order, and draw the appropriate energy-level diagrams. 2s orbital significantly higher in energy than 1s so there is no combination of 1s and 2s to form a molecular orbital. Furthermore there is no overlap of the 1s orbitals and they are considered to be isolated on the individual atoms. orbitals must overlap to form a bond

3 - 3 - Homonuclear Diatomics (B2 + Ne2) What about B 2? 1) Ways two p atomic orbitals can combine: head-on or sideways (parallel) FIG III - σ MOs formed from p AOs FIG IV - π MOs formed from p AOs Head-on overlap produces a σ 2p bond and sideways overlap forms a doubly connected pi bond, π. Rotation about the moleccular axis containing a π bond breaks the overlap and the bond! 2) σ2p orbital expected to be lower in energy than π2p since electrons in the sigma orbital are closest to the two positive nuclei and the head-on p overlap is greater than the sideways p overlap. This yields the symmetrical filling pattern in FIG V. EX 2. Fill in the MO energy diagram for O 2. Give the ground state electron configuration for the O 2 molecule. How many sigma bonds are there? How many pi bonds? What is the bond order? Is O 2 paramagnetic, diamagmentc, or ferromagnetic?

4 - 4 - FIG V MO Energy Diagram for Z 8 FIG VI MO Energy Diagram for Z 7(and many heteronuclear diatomics) E Still need description of B 2! 3) A σ2s orbital on one atom can interact with a σ2p orbital on another. The result is a change from the simple symmetrical ordering given in FIG V. This mixing or hybridization leads to a type of interaction called sp mixing. It only occurs in σ MOs and is shown in FIG VI. When an electron is added to a σ2p MO it experiences repulsions from electrons in the σ2s MO as both orbitals have electron probability distributions in the same region of space between the nuclei being bonded. If the repulsion is large enough (and the orbitals have the same symmetry σ2s/σ2p or σ*2s/σ*2p) the σ2p orbital can be pushed above the π2p in energy by sp mixing. This repulsion decreases going across a period (row). Atomic size decreases across a period due to an increase in effective nuclear charge (increasing nuclear charge and poor screening of the 2p electrons by electrons in the 2s subshell) so that the 2s and 2p atomic orbitals both decrease in energy from Li2 to F2. While the energy of both decrease across a period, the separation in energy between the 2s and 2p orbitals increases. Therefore the mixing of the 2s and 2p atomic orbitals in MO formation decreases (repulsions decrease). The filling pattern of FIG VI shows the effect of mixing especially on the ordering of the σ2p and π2p molecular orbitals. EX 3. Fill in the MO energy diagram for B 2 and N 2. Give the ground state electron configurations, number of sigma bonds, number of pi bonds, and comment on the magnetic properties.

5 - 5 - Second Period Heteronuclear Diatomic Molecules Heteronuclear diatomics whose atoms are roughly the same size and do not differ much in electronegativity generally follow the MO energy diagram in FIG VI. CO below exemplifies the trend. σ*2p π*2p σ2p π2p σ*2s σ2s with 2s-2p mixing in energy diagram: AOs of more electronegative element lower in energy (attracts valence electrons more strongly) bonding MOs closer in energy to more electronegative (lower energy) O AOs and anti-bonding MOs closer in energy to less electronegative C AOs => bonding MO larger on O end (greater probability) and smaller on C end; reversed for antibonding MOs red dashed lines indicate s (p) AOs which mix with p (s) in forming MO When there exists a large difference in electronegativity, as shown in the MO diagram below for HF, one can be guided by the fact that orbitals of different symmetry or very different energies do not interact. The H 1s is much higher in energy than the F 2s so there is no overlap. The F 2p along the molecular axis can overlap with the H 1s but the two perpendicular p s cannot. Consequently HF has lone pairs in a σ2s and two unhybridized p orbitals (π2p). σ*2p 1s π2p 2p σ2p σ2s 2s You are not responsible for such MO diagrams

6 - 6 - summary for diatomics homonuclear and heteronuclear 1) draw molecular orbital energy diagram atomic orbitals of more electronegative element lower in energy: MO energies: σ s < σ s * < σ p < π p < π p * < σ p * for Z 8 (O 2, F 2, Ne 2 ) sp mixing causes π p < σ p for Z 7 and most heteronuclear diatomics 2) fill with valence electrons following the Pauli principle and Hund s rule 3) determine bond order, paramagnetism, etc Polyatomics: Combining Localized Electron and Molecular Orbital Models π Electron Systems 1) ethylene: CH 2 = CH 2 EX 4. Explain all of the bonding: hybridization, overlap to form bonds, type of bonds, bond angles

7 - 7-2) trans-1,3-butadiene: CH 2 = CH CH = CH 2 (conjugated molecule)

8 - 8-3) ozone: O 3 (conjugated molecule) 4) nitrate NO 3 - It becomes relatively easy to sketch the lowest energy MOs. 5) benzene C 6 H 6 (cyclic) (conjugated molecule)

9 - 9 - Conjugated π Electron Systems Conjugation phenomenon where lower energy is provided by delocalization of electrons in three or more adjacent, parallel, over-lapping p orbitals. Generally observed when double or triple bonds alternate with single bonds in a molecule. Also occurs in molecules that are resonance hybrids. vitamin C allyl cation allyl radical allyl anion conjugated atoms vitamin A