Covalent Bonding, Valence Bond Theory, and Molecular Hybridization

Fundamentals of Covalent Bonding and Chemical Representations

• Covalent Bond Definition: A covalent bond occurs when two atomic nuclei share electrons, positioning the electron density between the two nuclei.

• Electron Shorthand Notation: The standard shorthand notation for an electron is $e^-$ (or $2\,e^-$ for an electron pair).

• Representations of Covalent Bonds:

  • Lewis Dot Structures: Depict each electron as an individual dot. Placing two dots between atom symbols indicates that those two electrons are shared covalently between the atoms (e.g., $C : H$).

  • Line Bond / Kekulé Structures: Represent a shared pair of electrons as a solid line. Each individual line represents $2\,e^-$ shared between atoms. Line structures are preferred in organic chemistry because they eliminate the need to draw individual dots.

Valence Bond Theory (VBT)

• Core Concept: Valence Bond Theory posits that a covalent bond forms when atomic orbitals of two approaching atoms physically overlap, causing the atoms to adhere to one another.

• Electrostatic Interactions:

  • Electrons possess a negative charge ($-$).

  • Atomic nuclei possess a positive charge ($+$) due to protons (neutrons carry no charge).

  • An electron is initially attracted to its original nucleus. When brought into close proximity with another atom, it becomes attracted to the second nucleus as well.

  • Shared electrons serve as an electrostatic bridge that holds two positively charged nuclei near each other.

• Orbital Overlap Mechanism: Overlapping atomic orbitals create a shared region where electrons simultaneously stabilize both positively charged nuclei.

Atomic Orbitals and Hybridization in Methane ($CH_4$)

• Carbon Framework: Carbon forms the foundational framework for organic chemistry.

• Ground-State Electron Configuration of Carbon:

  • Atomic number $Z = 6$.

  • Inner shell: $1s$ orbital is completely filled ($1s^2$).

  • Valence shell: $4$ total valence electrons—$2$ in the $2s$ orbital ($2s^2$) and $2$ in the $2p$ orbitals ($2p^2$).

• Limitations of Pure Atomic Orbitals:

  • Unhybridized atomic orbitals ($2s$ sphere and three $2p$ dumbbell lobes) cannot explain carbon forming four equivalent, symmetrical bonds.

  • Pure atomic orbitals cease to exist once molecular bonding occurs.

• $sp^3$ Hybridization Process:

  • The $2s$ orbital and all three $2p$ orbitals ($2p_x, 2p_y, 2p_z$) mix and rehybridize.

  • This mixing produces four identical, degenerate (equal energy) $sp^3$ hybridized orbitals.

  • Each $sp^3$ orbital holds $1$ valence electron prior to bonding.

• Spatial Geometry and VSEPR Theory:

  • According to Valence Shell Electron Pair Repulsion (VSEPR) theory, electron pairs maximize spatial separation to minimize electrostatic repulsion.

  • Arranging four equivalent orbital domains as far apart as possible yields a tetrahedral geometry.

Three-Dimensional Conventions and Molecular Geometry

• Spatial Perception:

  • Standard human spatial perception defaults to $90^\circ$ Cartesian coordinates.

  • Tetrahedral carbon bonds exist in a non-standard $109.5^\circ$ spatial coordinate system.

• 2D Drawing Conventions for 3D Representations:

  • Solid / Flat Line: Represents a bond residing entirely within the two-dimensional plane of the paper or board.

  • Wedge Bond: Represents a bond pointing outward from the plane directly toward the viewer.

  • Dash Bond: Represents a bond pointing backward behind the plane away from the viewer.

  • Standard $sp^3$ Carbon Convention: Drawn using two flat bonds in the plane, one wedge bond, and one dash bond.

• Methane ($CH_4$) Parameters:

  • $H-C-H$ Bond Angle: Exactly $109.5^\circ$ (due to four identical substituents).

  • $C-H$ Bond Length: $109\,\text{pm}$ ($1\,\text{pm} = 10^{-12}\,\text{m}$).

Single Bonding in Ethane ($C_2H_6$) and Sigma Bonds

• Orbital Overlap in Ethane:

  • Carbon Atoms: Both carbons are $sp^3$ hybridized with tetrahedral geometry.

  • Hydrogen Atoms: Exist with unhybridized $1s$ spherical orbitals; hydrogen does not rehybridize because it forms only one bond.

  • $C-H$ Bond Overlap: Formed by the overlap of a carbon $sp^3$ orbital with a hydrogen $1s$ orbital ($sp^3\text{--}1s$).

  • $C-C$ Bond Overlap: Formed by the head-on overlap of two carbon $sp^3$ orbitals ($sp^3\text{--}sp^3$).

• Sigma ($\sigma$) Bond Definition:

  • A $\sigma$ bond occurs when orbital overlap is concentrated directly along the internuclear axis between two nuclei.

  • All single covalent bonds are $\sigma$ bonds.

• Ethane ($C_2H_6$) Parameters:

  • Consists of two connected tetrahedral carbons.

  • $C-C-H$ Bond Angle: Approximately $112^\circ$ (slightly distorted from $109.5^\circ$ because substituents are non-identical).

  • $C-C$ Bond Length: $153\,\text{pm}$.

Double Bonding in Ethylene ($C_2H_4$) and Pi Bonds

• Ethylene Framework:

  • Molecular formula: $C_2H_4$.

  • Structure contains a carbon-carbon double bond ($H_2C=CH_2$), sharing a total of $4$ electrons ($2$ electrons per bond line).

  • Each carbon is attached to $3$ distinct items/atoms.

• $sp^2$ Hybridization:

  • To attach to $3$ items, carbon mixes its $2s$ orbital with two of its $2p$ orbitals.

  • Yields three equivalent $sp^2$ hybridized orbitals and leaves one unhybridized $2p$ orbital untouched.

  • Notation $sp^2$ indicates the mixing of one $s$ orbital and two $p$ orbitals.

• Geometry:

  • Trigonal Planar Geometry: The three $sp^2$ orbitals lie in a flat plane oriented $120^\circ$ apart to minimize repulsion.

  • Perpendicular $p$ Orbital: The unhybridized $2p$ orbital sits perpendicular ($90^\circ$) to the trigonal plane formed by the $sp^2$ orbitals.

• Bonding Composition in Ethylene:

  • $C-H$ Bonds: Formed via $sp^2\text{--}1s$ overlap ($\sigma$ bonds).

  • $C-C$ $\sigma$ Bond: Direct end-to-end overlap between one $sp^2$ orbital from each carbon ($sp^2\text{--}sp^2$ overlap), sharing $2$ electrons along the internuclear axis.

  • $C-C$ $\pi$ Bond: Side-by-side overlap of the unhybridized $2p$ lobes above and below the internuclear axis, sharing an additional $2$ electrons.

• Ethylene Structural Parameters and Energy Comparison:

  • $H-C-C$ Bond Angle: Approximately $121^\circ$.

  • $C=C$ Bond Length: $134\,\text{pm}$ (shortened by approximately $19\,\text{pm}$ compared to single bonds).

  • Bond Dissociation Energies:

  • Ethane ($C-C$ single bond): $377\,\text{kJ\,mol}^{-1}$.

  • Ethylene ($C=C$ double bond): $728\,\text{kJ\,mol}^{-1}$.

  • Relative Bond Strengths:

  • A double bond ($728\,\text{kJ\,mol}^{-1}$) is stronger than a single bond ($377\,\text{kJ\,mol}^{-1}$), but less than twice as strong.

  • Individual $\pi$ bonds are weaker than $\sigma$ bonds due to side-by-side overlap being less efficient than direct head-on overlap.

Triple Bonding in Acetylene ($C_2H_2$)

• Acetylene Framework:

  • Molecular formula: $C_2H_2$ (used as fuel in welding torches).

  • Contains a carbon-carbon triple bond ($H-C \equiv C-H$), sharing a total of $6$ electrons ($3$ pairs).

  • Each carbon is attached to $2$ distinct items (one hydrogen atom and one carbon atom).

• $sp$ Hybridization:

  • Carbon combines its $2s$ orbital with one $2p$ orbital.

  • Yields two equivalent $sp$ hybridized orbitals and leaves two unhybridized $2p$ orbitals.

• Geometry:

  • Linear Geometry: The two $sp$ orbitals orient $180^\circ$ apart along a straight line.

  • Mutually Perpendicular $p$ Orbitals: The two unhybridized $2p$ orbitals sit at right angles ($90^\circ$) to each other and to the linear $sp$ axis—one set aligned vertically (up/down) and the second set aligned horizontally (front/back).

• Bonding Composition in Acetylene:

  • $C-C$ $\sigma$ Bond: Direct head-on overlap of two $sp$ orbitals ($sp\text{--}sp$), sharing $2$ electrons along the internuclear axis.

  • First $C-C$ $\pi$ Bond: Side-by-side overlap of vertical unhybridized $2p$ orbitals, sharing $2$ electrons above and below the axis.

  • Second $C-C$ $\pi$ Bond: Side-by-side overlap of horizontal unhybridized $2p$ orbitals, sharing $2$ electrons in front of and behind the axis.

  • Total: $1\,\sigma$ bond + $2\,\pi$ bonds = $6$ shared electrons.

Heteroatoms and Hybridization in Methylamine ($CH_3NH_2$)

• Heteroatom Definition: Any atom in an organic molecule that is neither carbon nor hydrogen (frequently atoms with lone pairs like nitrogen or oxygen).

• Methylamine Framework ($CH_3NH_2$):

  • Structure consists of a methyl group ($-CH_3$) attached to an amine group ($-NH_2$).

  • Nitrogen starts with $5$ valence electrons.

  • Nitrogen forms $3$ covalent bonds to achieve an octet ($8$ valence electrons total), leaving $1$ non-bonding lone pair ($2$ electrons).

• Hybridization and Geometry of Nitrogen:

  • Nitrogen contains $4$ total domains of electron density: $1$ carbon atom, $2$ hydrogen atoms, and $1$ non-bonding lone pair.

  • To accommodate four electron domains, nitrogen undergoes $sp^3$ hybridization.

  • The non-bonding lone pair resides in an $sp^3$ hybridized orbital.

  • Electronic Geometry: Tetrahedral electronic geometry surrounds the nitrogen atom.

Questions & Discussion

• Question: Is the hydrogen atom hybridized in organic molecules?

  • Answer: No. Hydrogen forms only a single bond using its spherical $1s$ orbital and does not undergo rehybridization. Hydrogen hybridization is excluded from hybridization analysis.

• Question: How does the bond strength of a sigma bond compare to a pi bond?

  • Answer: A $\pi$ bond is weaker than a $\sigma$ bond because side-by-side orbital overlap is less effective than direct head-on overlap. However, a double bond containing both a $\sigma$ and a $\pi$ bond is overall stronger and shorter than a single $\sigma$ bond alone.

• Question: How is hybridization depicted on an orbital energy diagram?

  • Answer: Hybridization in valence bond theory shows equal-energy (degenerate) hybridized orbitals resulting from the mixing of lower-energy $s$ orbitals and higher-energy $p$ orbitals, distinct from molecular orbital theory diagrams.