Lecture+24_MO+Theory+Heteronuclear+Diatomics_Practice+Problems

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Announcements for October 27 th , 2023 • Homework 8 due Sunday, October 29 th , 11:59 PM • Quiz 8 is available this weekend from Saturday to Sunday @ 5pm • Recitation 7 is tomorrow • Exam 2 is scheduled for Monday, October 30 th 7:00 – 9:00 pm • Covers Lectures 11 – 24 (MO Theory is final topic) • Note sheet for exam: 1 page, front and back, HANDWRITTEN ONLY (on paper in pen or pencil)!!! No typing, no computer-generated figures. • Review Session is Sunday, October 29 th from 4 pm – 6 pm in Chem 102 with Taehwan This Week Reading: Chapter 9, Sections 7 – 8 Monday Reading: Chapter 23, Sections 1 — 3 and 5 — 6 Wednesday Reading: Chapter 23, Sections 5 – 6 and Chapter 3, Section 3 Friday Reading: Chapter 3, Sections 1, 2, 5, and 6 Our objective is to explore a 2 nd approach to describe chemical covalent bonding The plan: • MO Theory • HX molecules • Practice Problems • π systems and delocalization

Consider the heteronuclear diatomic molecule, [BO] - . Use MO theory (z-axis is the bonding axis) to predict the [BO] - bond order and sketch the HOMO and LUMO . Draw both the best Lewis structure based on formal charge considerations and the octet abiding Lewis structure. Is either structure consistent with your MO diagram?

Identify all bonding interactions that occur in [BO] - as predicted by (a) MO Theory and (b) hybridization theory. Use the octet abiding Lewis structure for your answer to (b) and use the z- axis as the bonding axis. 2s Energy 2s 2p 2p MOs of [BO] - 𝝈 ?? ∗ 𝝈 ?? 𝝅 ?? 𝝅 ?? ∗ 𝝈 ?? 𝝈 ?? ∗ AOs of B AOs of O Lewis (octet): 𝑯?𝒃/𝑽????: 𝑴? ??????:

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Chemical bonding between AOs is orientation dependent and MO structure is influenced by atom identity: HF + + = = In-phase combination Constructive interference e - density between nuclei σ -bond σ *-antibond Node Out-of-phase bonding Destructive interference Greater e - density on ______ Greater e - density on ______ F H F H

3. More EN atom’s AOs are lower in energy → greater contribution to bonding MO 4. Less EN atom’s AOs are higher in energy → greater contribution to antibonding MO Heteronuclear diatomic molecules: HF Energy 2s 2p 1s AOs of H AOs of F MOs of HF -13.6 eV -18.6 eV -40.2 eV Polarity: Lewis: 1 σ -bond & 3 identical LPs MO Theory: BO = 1 & 3 LPs; only 2 identical LPs 2. Bonding symmetry of orbitals is critical 1. Bonding between 1s H and 2s F is negligible – too different in energy! e - density builds up on F due to ________________

We care about relative molecular orbital structure and HOMO/LUMO because these explain reactivity! HF reacts with OH - via acid-base (proton transfer) reaction to make H 2 O and F - Arrows depict e - flow • O donates e - pair to H to bond • HF bond breaks, shifting e - to F MO says: HOMO of HO - donates e - density to LUMO of HF 𝝈 ∗ ? ?,? 𝝈 HF MO Diagram 𝝈 ∗ ? ?,? 𝝈 OH - MO Diagram HOMO LUMO Energy HOMO = Highest energy MO containing e - (most reactive e - ) LUMO = Lowest energy unoccupied MO (lowest energy place to put e - )

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𝝈 ∗ ? ?,? 𝝈 𝝈 ∗ ? ?,? 𝝈 HOMO LUMO Energy When σ * gains e - , what is HF bond order? What happens between O and H? High probability of e - High probability of e - _________ overlap HF reacts with OH - via acid-base (proton transfer) reaction to make H 2 O and F - +

General principles of forming MOs 1. Symmetry of orbitals important for forming an MO 2. The closer in energy AOs are, the more they mix to form MOs + → + → • 1s H + 2p F mixing occurs to make the chemical covalent bond • Negligible mixing between 1s H and 2s F due to large energy differences • Orbital size weighted toward AO closest in energy (EN effect) + → Orbitals overlap and interact via wave interference • Constructive interference generates bonding orbitals • Destructive interference generates non-bonding or antibonding orbitals + → ??????? : Bigger orbital on more EN atom: ????𝒃?????? : Bigger orbital on less EN atom:

Classify each of the following orbital interactions as σ, σ*, π, or π* . Additionally, determine if the atom on the left or right is more electronegative . For which of the following diatomic molecules would the inverted MO diagram be followed? Strategy: 1. Identify whether bonding occurs along internuclear axis or above and below 2. Identify whether a node occurs in space between atoms 3. More EN atom’s AOs are lower in energy → greater contribution to bonding MO 4. Less EN atom’s AOs are higher in energy → greater contribution to antibonding MO (i) (ii) (iii) (iv) O 2 +2 NBe CN – BNe PN SiP - Strategy: 1. The inverted diagram is the exception! ( σ 2p above π 2p ) 2. DIATOMIC MOLECULES containing at least 1 Li, Be, B, C, or N atom and another 2 nd period element follow it due to sp-mixing Why? The low EN of these atoms allows 2s and 2p in bonding region to “hybridize” Large atoms too big to form strong π - bonds!!!

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Consider the set of orbital interactions below which describe chemical bonding between Cr and Cl. Using MO theory ( x-axis is the bonding axis ), predict the structure of the molecular orbitals (NO MO DIAGRAM IS NEEDED!). If the electronegative effect is involved, please sketch your orbitals to unambiguously reflect it. Cr – Cl +x +y +z 1. Who is more EN, Cr or Cl? 2. More EN atom’s AOs are lower in energy. Which MOs have a greater contribution from it? 3. Less EN atom’s AOs are lower in energy. Which MOs have a greater contribution from it? (a) Out-of-phase Cr ?? ? ? −? ? and Cl ?? ? (b) In-phase Cr ?? ?? and Cl ?? ? (c) Out-of-phase Cr ?? ? and Cl ?? ?

For which of the following diatomic molecules would the bond strength increase (or bond length decrease) upon adding an electron? Strategy: 1. Determine whether the “regular” or “inverted” is followed and make a QUICK sketch 2. Count electrons and place them into MO diagram 3. Determine bond order before and after 1 e - added (or removed) B 2 P 2 + NO CN – Li 2 Determine whether the following molecules are paramagnetic or diamagnetic

σ p σ s Constructed below is the molecular orbital diagram for BeH 2 – the molecule that started us on our orbital-based bonding journey. Based on the relative placement of MOs to AOs, sketch each of the bonding and antibonding orbitals. (Hint: Electronegativity effect will be at play!) 2s Energy 2p MOs of BeH 2 𝝈 ? ∗ 𝝈 ? 𝝈 ? 𝝈 ? ∗ AOs of Be H1s n 2p H1s σ * p σ * s

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The delocalized approach to MO theory avoids introducing resonance structures O 3 (Ozone): • Central O is sp 2 hybridized, while bonding O is between sp 2 /sp 3 • Bond order of 1.5 for both O – O bonds VSEPR/Hybridization Theory: • Since 1 π -bond and lone pair (4 e - ) are involved in resonance, 3 AOs needed (2p x ) • Ignore remaining lone pairs and σ -bonds • Add 1 __________ to each MO as we climb the energy ladder Molecular Orbital Theory: 3 AOs → 3 MOs Bonding __ nodes Antibonding __ nodes Nonbonding __ node __________ ________ __________ _______ __________ ________

MO theory predicts that the π -bonds in conjugated organic molecules are delocalized across the entire molecule as opposed to localized between 2 atoms. This gives rise to color in many organic pigments (Ex: β -carotene and organic LEDs). Given below are the delocalized π -orbitals for 1,3-butadiene (structure right). Arrange them in order of increasing energy and determine which are occupied by electrons in 1,3-butadiene. (i) (ii) (iii) (iv) 1. Count the number of nodes between 2p-orbitals that produce the delocalized electronic structure. 2. Rank the orbitals in order of increasing energy based on node count! 3. Count the number of π -electrons in 1,3-butadiene. Which orbitals are occupied?

MO theory naturally accounts for delocalization • MOs constructed from sideways overlap of atomic p-orbitals account for delocalized π -bonding • MOs spread across all atoms involved in resonance (# AOs in = # MOs out) • Only 1 true structure Energy 0 nodes 1 nodes HOMO 2 nodes LUMO 3 nodes 1 2p-orbital per C → 6 π MOs • 6 π e - ’s, so lowest 3 MOs occupied • Node count increases by 1 as MO energy increases • Cyclic structure introduces degeneracy

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We just learned hybridization theory! Now MO theory! How do we know which is right? We never do! Experiments can only be designed to test our hypotheses/theories. Once we gather enough evidence to support or refute our theory, we continue testing or developing a new explanation of our world. AFM with molecular sized tip probes molecular structure (through e- density) STM uses tunneling current to probe Ψ 2