Introduction to Alkanes and Molecular Orbitals

Bonding, orbitals, and basic ideas

• Two atoms in an approach allow only two electrons per orbital (whether atomic or molecular) and lead to the formation of a bonding and an antibonding orbital.
  • When two atomic orbitals combine, you get two new molecular orbitals: one bonding (lower in energy) and one antibonding (higher in energy).
  • The bonding orbital is named a sigma bonding orbital (σ), and its counterpart is the sigma antibonding orbital (σ*).
  • In a simple two-atom example, both new orbitals are formed, but electrons will occupy the lowest-energy one first; the antibonding orbital may remain empty depending on the total electrons.
• Consequences for more complex systems:
  • For a system with two interacting parts, the pairing of electrons in the bonding framework leads to stabilizing interactions, while electrons in antibonding orbitals destabilize the system.
  • In a three-atom system, geometry follows rules based on electron-pair repulsion around the central atom (a precursor to VSEPR ideas): linear when two substituents, trigonal planar with three substituents, and tetrahedral with four substituents around the central atom.
  • Carbon often forms four bonds, resulting in a tetrahedral arrangement; this is because the electrons in bonds try to maximize the distance from each other (to minimize repulsion).
  • Although some molecules undergo octahedral arrangements, those involve d-orbitals and are less common for main-group elements discussed earlier.
• Summary of chapter focus and terminology:
  • Alkanes: hydrocarbons composed only of carbon and hydrogen.
  • Bonding concepts: sigma (σ) bonds from end-to-end overlap; pi (π) bonds from sideways overlap of p orbitals; bonding vs antibonding, and energy considerations.
  • The geometry of a molecule is influenced by how orbitals overlap and how electrons distribute in bonding versus antibonding combinations.

Electron waves: wavelength, amplitude, and phase

• Waves have three related properties:
  • Wavelength: the distance between successive peaks (the spatial periodicity).
  • Amplitude: how far a wave deviates from its center line (a measure of intensity in many contexts).
  • Phase: the sign/offset of the wave (conceptually plus vs minus; relevant when comparing two waves).
• Analogies to visualize these concepts:
  • Ocean waves have amplitude and wavelength, with peaks and troughs representing deviation from the center line.
  • A plucked guitar string similarly has displacement up or down; phase describes whether two vibrating parts are moving in the same direction at a given moment.
• Importance of phase:
  • When two waves encounter each other, phase alignment matters:
  • In phase (peaks align with peaks) -> constructive interference, amplitude increases.
  • Out of phase (peaks align with troughs) -> destructive interference, amplitude decreases or cancels.
  • Practical example: noise-cancelling headphones create an “antiphase” wave to cancel incoming sound.
• Electron density and energy:
  • Electron density corresponds to amplitude; higher amplitude regions correspond to higher electron density and, in a charge picture, more negative charge density.
  • Frequency relates to energy (as discussed in the context of light waves): higher frequency light carries more energy.
  • Phase is about interference and does not imply charge on its own; plus/minus labels in wave visuals indicate phase, not charge.
• Interference in molecular orbitals:
  • When two atomic orbitals combine, regions where they are in phase give higher electron density between atoms (bonding interaction).
  • Regions in which they are out of phase create a node where electron density is zero (antibonding interaction).
  • The overall molecule’s stability depends on constructive overlap in bonding orbitals vs. destructive overlap in antibonding orbitals.
• Quantitative reminder:
  • For a pair of interacting orbitals, you effectively create a bonding orbital and an antibonding orbital; electrons fill the lower-energy bonding orbital first if available.

Valence vs. core electrons and orbital pictures

• In larger atoms and molecules, the core electrons are deeply bound and largely do not participate in bonding at the energy scales usually considered; chemistry primarily involves valence electrons.
• For carbon, the second electron shell (the valence shell) is most important for bonding; core electrons are largely inert in typical chemistry discussions.
• The chemistry of elements in the same group (e.g., carbon vs. silicon) shares the idea that valence electrons drive bonding behavior, though orbital energies and available d-orbitals can differ for heavier elements.
• This framework is a simplification (a model) to help visualize what happens when atoms approach and form bonds; real molecules involve many interacting electrons and dynamic rearrangements.

Methane: CH₄ and sp³ hybridization

• Methane as a prototype:
  • Carbon forms four equivalent bonds to hydrogens, leading to a tetrahedral arrangement.
  • This is commonly described by sp³ hybridization: one s orbital plus three of the p orbitals mix to form four equivalent sp³ hybrid orbitals.
• Visualizing sp³ orbitals:
  • An sp³ orbital is depicted as a lobed region with phase distinctions (colors in lecture visuals often indicate phase).
  • Each of the four sp³ lobes overlaps with a hydrogen 1s orbital to form a C–H sigma bond.
• Bonding geometry and energy:
  • The four C–H sigma bonds arrange themselves to maximize their mutual separation, consistent with tetrahedral geometry and minimization of electron pair repulsion.
  • In the bonding picture, electrons occupy the bonding sp³ orbitals; antibonding counterparts (σ*) exist but are unoccupied in methane under normal ground-state conditions.
• Overlap details (qualitative):
  • When two orbitals overlap in-phase, electron density builds up between the nuclei (bond formation).
  • When they overlap out-of-phase, antibonding character reduces electron density between the nuclei (node formation).
• Representations and conventions:
  • The four C–H bonds are equivalent and can be depicted with Lewis structures, ball-and-stick models, or condensed formulas; all representations connect in the same connectivity.
• Important caveat:
  • The sp³ picture is a useful fiction to explain observed geometry and bonding patterns; in real molecules, dynamic interactions and slight distortions can occur, but the model explains the observed tetrahedral geometry well.

Ethene (ethylene): C₂H₄ and sp² hybridization

• Geometry and bonding framework:
  • Each carbon in ethene is sp² hybridized, giving a trigonal planar arrangement around each carbon with bond angles of approximately 120^ ext{o}.
  • The molecule lies essentially flat (planar) with the carbons and hydrogens in the same plane.
• Orbital picture:
  • Each carbon uses one s orbital and two of the p orbitals to form three sp² hybrids; these hybrids form sigma (σ) bonds in the plane:
  • C–C sigma bond
  • Two C–H sigma bonds on each carbon
  • The remaining unhybridized p orbital on each carbon (perpendicular to the plane) overlaps with the other carbon’s p orbital to form a pi (π) bond, which is part of the C=C double bond.
• The pi bond and its orientation:
  • The pi bond arises from sideways overlap of the unhybridized p orbitals; it lies above and below the plane (electron density delocalized in that region).
  • When the p orbitals overlap in phase, electron density is concentrated around the bond region; when out of phase, a node appears and the overlap weakens.
• Bonding and antibonding in ethene:
  • For each sigma bond there is a corresponding sigma* antibonding orbital (unoccupied in ground-state ethene).
  • There is also a pi, and a pi* antibonding orbital as part of the molecular orbital set.
• Conceptual takeaway:
  • The geometry and bonding in ethene are explained by the combination of sp² hybridization (for sigma framework) and side-by-side p-orbital overlap (for the pi bond).

Acetylene (ethyne): C₂H₂ and sp hybridization

• Geometry and bonding framework:
  • Acetylene is linear, with a bond angle of 180^ ext{o} between the carbon–carbon–hydrogen framework.
  • Each carbon is sp hybridized, formed by mixing one s and one p orbital to produce two sp hybrid orbitals.
• Orbital picture:
  • Each carbon uses two sp orbitals to form two sigma bonds: one to hydrogen and one to the other carbon.
  • The remaining two p orbitals on each carbon (perpendicular to each other and to the bond axis) form two pi bonds between the carbons, giving a triple bond (one sigma + two pi bonds).
• Orientation of p orbitals:
  • The two remaining p orbitals on each carbon are oriented perpendicular to the bond axis and to each other; their sideways overlaps create the two pi bonds.
• Planarity and density:
  • The entire molecule is linear and planar along the axis; the perpendicular p orbital interactions create the pi-bonding region around the C≡C bond.
• Summary of bonding in C₂H₂:
  • There are three bonds between the two carbons: one sigma and two pi bonds.
  • Each carbon also forms a sigma bond with a hydrogen (C–H). The bonding picture is built from sp hybridization for the C atoms plus the 2 parallel pi interactions for the C≡C bond.
• Antibonding orbitals:
  • Just as with other bonds, there exist sigma* and pi* antibonding orbitals, which are higher in energy and unoccupied in the simplest ground-state description.

Representations and practical notes

• Representations of molecular structure:
  • Lewis structures: show connectivity and valence electron pairs.
  • Ball-and-stick models: convey geometry and relative bond lengths/angles.
  • Condensed formulas: provide a compact way to denote connectivity and composition.
  • These representations are different views of the same underlying connectivity and bonding patterns.
• The role of these models in chemistry:
  • They help predict geometry, reactivity, and properties; as molecules become larger (e.g., C₅H₁₀ and beyond), you may not memorize every arrangement and instead rely on a mix of representations.
  • For reaction chemistry, antibonding orbitals (σ* and π*) become important when considering breaking and forming bonds.

Practical and conceptual takeaways

• Bonding follows simple rules at the level discussed: electrons occupy bonding orbitals first, with antibonding orbitals generally remaining empty unless extra energy is involved.
• Hybridization (sp³, sp², sp) provides a convenient way to rationalize molecular geometry and bonding patterns in hydrocarbons, even though it is a model rather than a literal picture.
• The distinction between sigma and pi bonds explains the difference in bond strength and reactivity: sigma bonds are generally stronger and provide the framework, while pi bonds contribute to multiple bond character and reactivity (e.g., in alkenes and alkynes).
• Phase concepts in orbital overlap reflect the sign of lobes in orbital shapes; when lobes of the same sign overlap, bonding occurs; opposite signs produce antibonding interactions and nodes.
• Core vs. valence electrons emphasize that chemistry mostly involves valence electrons, with core electrons largely remaining spectators in many bonding and valence interactions.

Connections to broader ideas and context

• Geometry rules (linear, trigonal planar, tetrahedral) tie into the orientation of orbitals and the minimization of repulsion among electron pairs (an early form of what becomes VSEPR theory).
• The progression from s and p orbitals to hybridized sp, sp², sp³ orbitals captures the idea that atoms rearrange their valence electron density to form stable, energy-favorable bonds in molecules.
• Real molecules can exhibit variations and complexities (bond lengths, partial double-bond character, resonance) beyond the simplified pictures, but the core concepts explained in these notes underpin much of organic chemistry and molecular physics.

Quick reference of key terms and ideas

• Bonding orbital: a lower-energy orbital formed by constructive overlap; electrons stabilize the molecule.
• Antibonding orbital: a higher-energy orbital formed by destructive overlap; electrons in this orbital destabilize the molecule if occupied.
• Sigma bond (σ): end-to-end overlap along the bond axis; single bonds are σ bonds.
• Pi bond (π): sideways overlap of p orbitals; multiple bonds involve pi bonding in addition to sigma bonding.
• Sigma star (σ), Pi star (π): antibonding counterparts to σ and π bonds.
• Hybridization: mixing of atomic orbitals (s and p) to form degenerate, directional bonding orbitals (sp³, sp², sp).
• Valence vs. core electrons: chemistry largely involves valence electrons; core electrons are more tightly bound and less reactive.
• Orbital phase: the sign of the lobes of an orbital; in-phase overlap increases electron density between nuclei; out-of-phase overlaps create nodes.
• Planarity and angles in hydrocarbons:
  • Linear: 180° (e.g., acetylene C≡C arrangement)
  • Trigonal planar: 120° (e.g., ethene C=C framework)
  • Tetrahedral: no single fixed angle stated here (e.g., methane CH₄)
• Examples discussed: CH₄ (methane), C₂H₄ (ethylene), C₂H₂ (acetylene).