Molecular Orbital Theory, Light Absorption, and Conjugated Systems

Molecular Orbital Comparison of Diatomic Oxygen and Nitrogen

• Orbital Configurations ($O_2$ vs. $N_2$):     * A primary difference between the molecular orbital (MO) diagrams of Oxygen ($O_{2}$) and Nitrogen ($N_{2}$) is the relative energy of the $\sigma_{2p}$ orbital.     * In some molecules, the $\sigma_{2p}$ is higher in energy than the $\pi_{2p}$ orbitals, while in others, it is lower. This is often referred to as the "switcheroo."     * The second major difference is the number of valence electrons. Nitrogen has fewer electrons than oxygen, meaning its MO diagram is not filled as high as oxygen's.

• Energy Gaps and Light Absorption:     * The gap between the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO) determines the energy of light a molecule can absorb.     * Species with a relative smaller gap, such as Oxygen ($O_{2}$), can absorb lower energy light.     * This concept is an extension of atomic theory where electrons jump between energy levels; the same principle applies to molecular orbitals.

• Spectral Data:     * The absorbance spectra for $N_{2}$ and $O_{2}$ show distinct peaks.     * Observational data shows one peak around $300 \, nm$ and another peak slightly higher than $600 \, nm$.     * Large Energy Gap: Requires high-energy light (shorter wavelengths) to facilitate an electronic jump.     * Small Energy Gap: Requires low-energy light (longer wavelengths).     * Note: It is important to be careful with horizontal axes on spectra, as they are often measured in wavelength ($nm$) rather than frequency or energy.

Frontier Molecular Orbitals in Halogens

• Trends in Halogen Diatomics ($Cl_{2}$, $Br_{2}$, $I_{2}$):     * The halogens are part of the "HONCLBRIF" group (Hydrogen, Oxygen, Nitrogen, Chlorine, Bromine, Iodine, Fluorine), meaning they exist naturally as diatomic molecules.     * Because they reside in the same column of the periodic table, they possess the same number of valence electrons and fill molecular orbitals to the same extent.

• HOMO-LUMO Transitions in Halogens:     * The identity of the frontier orbitals changes as one moves down the periodic table:         * Chlorine ($Cl_{2}$): HOMO is $\pi^<em><em>{3p}$; LUMO is $\sigma^</em></em>{3p}$. Gap is Big.         * Bromine ($Br_{2}$): HOMO is $\pi^<em><em>{4p}$; LUMO is $\sigma^</em></em>{4p}$. Gap is Medium.         * Iodine ($I_{2}$): HOMO is $\pi^<em><em>{5p}$; LUMO is $\sigma^</em></em>{5p}$. Gap is Small.     * The gap size "collapses" as you move down the group. Chlorine has the largest gap, while Iodine has the smallest.

• Atomic Radii and Energy Displacement:     * Bonding molecular orbitals represent a displacement downward from a central energy line (representing atomic orbitals), and anti-bonding orbitals (the "stars in the sky") represent a displacement upward.     * Iodine atoms have very large radii; their atomic orbitals are far from the nucleus. This results in a smaller "delta" ($\Delta E$) when atomic orbitals combine to form molecular orbitals.     * Chlorine has a much larger change (way down for bonding, way up for anti-bonding), resulting in a massive energy gap.

Physical Observations and Color Predictions (Class Demonstration)

• Determining Observed Color:     * The color we observe is the complement of the color absorbed by the molecule.     * Calculations and predictions require the use of the color wheel from Unit 4.

• Diatomic Molecule Reveal:     * Fluorine ($F_{2}$): Has a very small radius. This creates a very large energy gap for the jump. The energy needed is so high it corresponds to a wavelength shorter than visible light (Ultraviolet). Because it doesn't absorb visible light, it appears clear/white.     * Chlorine ($Cl_{2}$): The gap is slightly smaller than $F_{2}$. It absorbs light in the purple range. The complement of purple is yellow. In more concentrated samples, it can appear "redder" or darker yellow.     * Bromine ($Br_{2}$): The gap shrinks further, allowing it to absorb blue light. The complement of blue is orange.     * Iodine ($I_{2}$): Possesses the smallest gap. It absorbs yellow light strongly. The complement of yellow is violet.

Molecular Orbital Construction for Polyatomic Molecules: Ethene ($C_{2}H_{4}$)

• Hybridization and Pure p Orbitals:     * Hybridization and Molecular Orbital theory are compatible and can be used simultaneously.     * For Ethene ($C_{2}H_{4}$), each carbon is surrounded by three regions of electron density (two single bonds to Hydrogen, one double bond to Carbon), making it trigonal planar with $sp^2$ hybridization.     * Every $sp^2$ hybridization leave one "pure p orbital" unused on the shelf.

• The Component Orbitals of Ethene:     * The molecule has six total atoms, meaning six atomic orbital sources feed into the MO diagram.     * Sigma Bonding ($\sigma$) occurs from the overlap of the $sp^2$ hybridized orbitals of Carbon with the $1s$ orbitals of Hydrogen.     * This creates multiple $\sigma$ bonding orbitals and multiple $\sigma^<em>$ anti-bonding orbitals in the "sky."      The pure p orbitals on the carbon atoms combine to form $\pi$ (bonding) and $\pi^*$ (anti-bonding) orbitals.

• Delocalization Principles:     * Molecular orbitals belong to the whole molecule, not individual atoms. Electrons in these orbitals are shared across the entire structure ("There is no me in you, it's just us").     * In a diagram, atomic orbitals are shown on the far sides as work-in-progress, and molecular orbitals are shifted toward the center to represent the shared identity of the molecule.

Conjugated Systems and Carbon Chains

• Focusing on the HOMO-LUMO Gap:     * In large molecules, the HOMO-LUMO gap is typically the transition between the $\pi$ and $\pi^<em>$ orbitals.      For light absorption studies, we can often ignore the $\sigma$ frame and focus solely on the pure p orbitals remaining after hybridization.

• Effect of Chain Length on Energy Gaps:     * 4-Carbon Chain: If four carbons are $sp^2$ hybridized in a row, they provide four pure p orbitals. These combine to create four MOs (two $\pi$ bonding, two $\pi^<em>$ anti-bonding).      10-Carbon Chain: If ten carbons are $sp^2$ hybridized in a row, they provide ten pure p orbitals. These create ten MOs (five $\pi$ bonding, five $\pi^<em>$ anti-bonding).      As more molecular orbitals are "crammed" into the energy diagram, the energy gap between the HOMO and LUMO becomes smaller (teeny tiny).     * Rule: Longer chains of alternating single and double bonds lead to smaller HOMO-LUMO gaps.

Specialized Case Studies: Lycopene and Bleach

• Lycopene ($C_{40}H_{56}$):     * The molecule responsible for the red color in tomatoes.     * It contains an uninterrupted chain of 22 $sp^2$ hybridized carbons.     * This creates 22 molecular orbitals (11 bonding, 11 anti-bonding) with a very small gap.     * It absorbs green light (sufficient energy for the tiny gap), and thus its complement—red—is what we see.

• The Chemistry of Bleaching:     * Molecules that have interrupted single-double-single chains (Molecule A in the slides) have larger gaps and absorb in the Ultraviolet range, appearing white/colorless.     * Bleach does not necessarily remove the stain molecule from the fabric.     * Instead, bleach (containing $OH$ and $Cl$ groups) chemically reacts with the double bonds, converting them into single bonds.     * By breaking the conjugated chain, the HOMO-LUMO gap increases so significantly that the molecule no longer absorbs visible light. The stain remains, but it is invisible to the eye because it only absorbs UV light.

Academic Spotlight: Professor Harold Freeman

• Biography: Professor Harold Freeman is a researcher at North Carolina State University.
• Field of Study: Colorful compounds and sustainable dye community.
• Key Initiative (Color Yes, Cancer No):     * Many molecules with long conjugated chains and small gaps resemble human hormones (endocrine disruptors), which can lead to cancer.     * Professor Freeman's work involves creating single-double chain structures that retain their color properties but do not mimic biological molecules, thereby reducing health risks.

Questions & Discussion

• Interviewer/Student Question: Are you going to travel with the tracking or you have to pay?
• Response: I'm taking the bus with the… that way. It is kind of an underwhelming demonstration.
• Discussion on Logic: The class discussed how the opposite of what is absorbed is observed, but MO theory is required to know which specific wavelength is actually absorbed.
• Unit 4 Summary Goals:     * Where does color come from in diatomic molecules? (MO Gap size).     * What is the deal with soap?     * How do we power a car?     * How do we separate components in a mixture to determine if they make rats sick or not sick?