Molecular Shape and Bonding Theories

VSEPR and Molecular Geometry

Molecular Shape Overview * Lewis structures are two-dimensional models, whereas atoms and molecules exist in three dimensions. * The 3-D shape of a molecule determines its physical and chemical properties. * Case Study: $C_4H_{10}O$ Isomers * 1-Butanol: Density is $0.81\,g/mL$ . Melting point is $-89.8\,^\circ C$ . Boiling point is $117.7\,^\circ C$ . Solubility in water is $73\,g/L$ . Flash point is $29\,^\circ C$ . * 2-Butanol: Density is $0.81\,g/mL$ . Melting point is $-115\,^\circ C$ . Boiling point is $99.5\,^\circ C$ . Solubility in water is $125\,g/L$ . Flash point is $24\,^\circ C$ .
Valence Shell Electron Pair Repulsion (VSEPR) Model * The model predicts molecular shapes based on the number of electron domains around a central atom. * Electron Domains: Charge clouds composed of shared electrons (bonds) or lone-pair electrons. * Stability: The most stable arrangement minimizes repulsion by placing electron domains as far apart as possible while remaining connected to the central atom. * Geometries: * Electron Geometry (Domain Geometry): The arrangement of all electron domains. * Molecular Geometry: The shape occupied specifically by the atoms (excluding lone pairs, though their presence influences the shape).
Summary of Geometries (Table 11.1) * 2 Electron Domains: * $2$ Bonded Groups, $0$ Lone Pairs: Electron geometry is Linear; Molecular geometry is Linear; Bond angle is $180^\circ$ ; Example: $CO_2$ . * 3 Electron Domains: * $3$ Bonded Groups, $0$ Lone Pairs: Electron geometry is Trigonal planar; Molecular geometry is Trigonal planar; Bond angle is $120^\circ$ ; Example: $NO_3^-$ . * $2$ Bonded Groups, $1$ Lone Pair: Electron geometry is Trigonal planar; Molecular geometry is Bent; Bond angle is <120^\circ; Example: $NO_2^-$ . * 4 Electron Domains: * $4$ Bonded Groups, $0$ Lone Pairs: Electron geometry is Tetrahedral; Molecular geometry is Tetrahedral; Bond angle is $109.5^\circ$ ; Example: $CH_4$ . * $3$ Bonded Groups, $1$ Lone Pair: Electron geometry is Tetrahedral; Molecular geometry is Trigonal pyramidal; Bond angle is <109.5^\circ; Example: $NH_3$ . * $2$ Bonded Groups, $2$ Lone Pairs: Electron geometry is Tetrahedral; Molecular geometry is Bent; Bond angle is <109.5^\circ; Example: $H_2O$ . * 5 Electron Domains (Expanded Valence): * $5$ Bonded Groups, $0$ Lone Pairs: Electron geometry is Trigonal bipyramidal; Molecular geometry is Trigonal bipyramidal; Bond angles are $90^\circ$ , $120^\circ$ , $180^\circ$ ; Example: $PCl_5$ . * $4$ Bonded Groups, $1$ Lone Pair: Electron geometry is Trigonal bipyramidal; Molecular geometry is Seesaw; Bond angles are <90^\circ, <120^\circ, <180^\circ; Example: $SF_4$ . * $3$ Bonded Groups, $2$ Lone Pairs: Electron geometry is Trigonal bipyramidal; Molecular geometry is T-shaped; Bond angles are <90^\circ, <180^\circ; Example: $ClF_3$ . * $2$ Bonded Groups, $3$ Lone Pairs: Electron geometry is Trigonal bipyramidal; Molecular geometry is Linear; Bond angle is $180^\circ$ ; Example: $I_3^-$ . * 6 Electron Domains (Expanded Valence): * $6$ Bonded Groups, $0$ Lone Pairs: Electron geometry is Octahedral; Molecular geometry is Octahedral; Bond angles are $90^\circ$ , $180^\circ$ ; Example: $SF_6$ . * $5$ Bonded Groups, $1$ Lone Pair: Electron geometry is Octahedral; Molecular geometry is Square pyramidal; Bond angles are <90^\circ, <180^\circ; Example: $ClF_5$ . * $4$ Bonded Groups, $2$ Lone Pairs: Electron geometry is Octahedral; Molecular geometry is Square planar; Bond angles are $90^\circ$ , $180^\circ$ ; Example: $XeF_4$ .
Specific Domain Examples * Two Domains: Linear arrangement is most stable to minimize repulsion. Bond angle is $180^\circ$ . Examples include two single bonds ( $BeH_2$ ), two double bonds ( $CO_2$ ), or one single and one triple bond ( $OCN^-$ ). * Three Domains: Trigonal planar arrangement. Representative angles are $120^\circ$ , though nonidentical bonded groups can cause deviations. * Four Domains: A 3-D tetrahedron is formed to maximize distance beyond the $90^\circ$ available in a planar arrangement. Ideal angle is $109.5^\circ$ . * Five Domains (Trigonal Bipyramid): Includes Axial domains ( $180^\circ$ apart) and Equatorial domains ( $120^\circ$ apart). Lone pairs preferentially occupy equatorial positions because they exert greater repulsion; an equatorial lone pair is $90^\circ$ from only two neighbors, whereas an axial position is $90^\circ$ from three. * Six Domains (Octahedral): Adjacent domains are $90^\circ$ apart.
Larger Molecules * Complex molecule shapes are described as a series of connected smaller shapes. * Any nonterminal atom serves as a central atom for determining local geometry (number of domains, bonding groups, and lone pairs). * Propanal ( $CH_3CH_2CHO$ ): The $CH_3$ and $CH_2$ carbons have four bonding domains (tetrahedral). The $CHO$ carbon has three bonding domains (trigonal planar).

Polar and Nonpolar Molecules

Bond Dipoles and Molecular Dipoles * Electronegativity differences ( $\Delta EN$ ) determine bond polarity. * Individual bond dipoles can sum to create a molecular dipole or cancel out due to symmetry. * Molecular dipoles result in dipole moments, which influence intermolecular forces.
Predicting Polarity * Molecules with one bond: Direct prediction. $HF$ is polar; $F_2$ is nonpolar. * Molecules with multiple bonds: * Symmetry: $CO_2$ is nonpolar because its two polar bonds cancel in a linear geometry. $SF_6$ is nonpolar due to its symmetrical octahedral geometry and strongly polar bonds ( $\Delta EN = 1.5$ ). * Asymmetry: $H_2O$ is polar as its bond dipoles add together in a bent geometry. $NH_3$ is polar (Trigonal pyramidal, $\Delta EN = 0.9$ ). $CH_2F_2$ is polar (Tetrahedral, $C-H \, \Delta EN = 0.4$ , $C-F \, \Delta EN = 1.5$ ). $BrF_5$ is polar (Square pyramidal, $\Delta EN = 1.2$ ).

Valence Bond Theory: Hybrid Orbitals and Bonding

Basics of Valence Bond (VB) Theory * Covalent bonds form via the overlap of valence orbitals. * As atoms approach, potential energy reaches a minimum at the specific bond length. * Electrons in the overlap region must be spin-paired. * Atomic orbitals involved are usually half-filled, but a coordinate covalent bond occurs when a filled orbital overlaps with an empty one.
Hybridization of Orbitals * Hybrid orbitals are mathematical combinations of atomic orbitals (AOs) to achieve maximum overlap. * The number of hybrid orbitals produced equals the number of AOs combined. * $sp^3$ Hybridization: Combination of one $2s$ and three $2p$ orbitals. Forms four identical orbitals. Found in tetrahedral geometries (e.g., $CH_4$ , $NH_3$ , $H_2O$ ). * $sp^2$ Hybridization: Combination of one $2s$ and two $2p$ orbitals. Forms three identical orbitals for sigma bonding and leaves one unhybridized $p$ orbital for pi bonding. Found in trigonal planar geometries (e.g., Ethene $C_2H_4$ , Formaldehyde $CH_2O$ ). * $sp$ Hybridization: Combination of one $2s$ and one $2p$ orbital. Forms two identical orbitals and leaves two unhybridized $p$ orbitals. Found in linear geometries (e.g., Ethyne $C_2H_2$ ).
Sigma ( $\sigma$ ) and Pi ( $\pi$ ) Bonds * Sigma Bond: Formed by head-to-head overlap along the internuclear axis. All single bonds are sigma bonds. * Pi Bond: Formed by side-to-side overlap of unhybridized $p$ orbitals, existing in two regions above and below the internuclear axis. * Multiple Bonds: * Double bond = $1 \, \sigma$ bond + $1 \, \pi$ bond. * Triple bond = $1 \, \sigma$ bond + $2 \, \pi$ bonds.
Advanced VB Concepts * Extended Valence: Previously, $sp^3d$ and $sp^3d^2$ were proposed for trigonal bipyramidal and octahedral shapes, but $d$ orbitals are energetically unfavorable for this. VB theory lacks a simple explanation for expanded octets. * Fractional Hybridization: In $H_2O$ , research suggests the oxygen may be $sp^2$ hybridized with a lone pair in an unhybridized $p$ orbital. Increased $p$ character in bonding orbitals explains the $104.5^\circ$ angle, bringing it closer to the $90^\circ$ of pure $p$ orbitals.

Using Valence Bond Theory

Reactivity and Rotation * Reactivity: Molecules with multiple bonds are more reactive than those with single bonds because side-to-side $\pi$ overlap is less extensive than head-on $\sigma$ overlap, making $\pi$ bonds easier to break. * Bond Rotation: Sigma bonds allow free rotation because overlap is not disrupted. Pi bonds restrict rotation because rotation would break the required parallel alignment of the $p$ orbitals. * Comparison: Propane ( $CH_3CH_2CH_3$ ) has only $10 \, \sigma$ bonds. Propene ( $CH_3CH=CH_2$ ) has $7 \, \sigma$ and $1 \, \pi$ bond, making it more reactive.
Limitations of VB Theory * Does not explain molecular electronic energy levels different from atomic ones. * Cannot explain paramagnetism (e.g., the unpaired electrons in oxygen, $O_2$ ).

Molecular Orbital Theory

Basics of MO Theory * Atomic orbitals combine to form molecular orbitals (MOs) delocalized over the entire molecule. * Constructive Interference: Additive combination of wave functions results in bonding MOs (lower energy). * Destructive Interference: Subtractive combination results in antibonding MOs (higher energy; contains a node).
Bond Order Calculation * Bond order determines molecule stability: $\text{Bond Order} = \frac{1}{2}(\text{Bonding } e^- - \text{Antibonding } e^-)$ . * A bond order of $1$ is equivalent to a single bond. A bond order of $0$ indicates no stability.
Diatomic Molecules and Period 2 Trends * $H_2$ : Two electrons in $\sigma_{1s}$ ; Bond order = $1$ . Configuration: $(\sigma_{1s})^2$ . * $He_2$ : Two electrons in $\sigma_{1s}$ , two in $\sigma^<em><em>{1s}$ ; Bond order = $0$ (unstable). $H_2^-$ : Bond order = $\frac{1}{2}(2 - 1) = 0.5$ ; less stable than $H_2$ but can exist. * $B_2$ , $C_2$ , $N_2$ : Have a different ordering of energy levels ( $\pi</em>{2p}$ below $\sigma_{2p}$ ) compared to $O_2$ , $F_2$ , $Ne_2$ ( $\sigma_{2p}$ below $\pi_{2p}$ ). * Nitrogen ( $N_2$ ): Bond order of $3$ ; diamagnetic (all electrons paired). * Oxygen ( $O_2$ ): Bond order of $2$ . MO diagram reveals unpaired electrons in $\pi^<em>_{2p}$ orbitals, explaining its paramagnetism (weak attraction to magnetic fields). Peroxide ( $O_2^{2-}$ ): All electrons paired (diamagnetic); bond order = $\frac{1}{2}(8 - 6) = 1$ . The $\text{O-O}$ bond is longer and weaker than in $O_2$ .
Heteronuclear Diatomics and Resonance * Nonbonding Orbitals: Unshared valence electrons retain atomic orbital energy levels. They do not contribute to bond order (e.g., in $HF$ and $NO$ ). * Resonance: Described as delocalization of $\pi$ bonds over adjacent atoms. * Ozone ( $O_3$ ): A single bonding MO encompasses all three oxygen atoms. * Benzene ( $C_6H_6$ ): All six $\pi$ electrons are delocalized across the hexagonal ring. All $\text{C-C}$ bond lengths are identical.

Summary of Bonding Models (Table 11.3)

Lewis Theory: Focuses on octet rule/valence shells. Simple 2D model. Drawback: No 3D info or explanation of why bonds form.
VSEPR: Predicts 3D shapes and polarity based on electron domains. Drawback: Does not explain "how" bonds form.
Valence Bond Theory: Explains bond strength (overlap), reactivity/rotation ( $\pi$ bonds), and molecular geometry. Drawback: Cannot explain paramagnetism or expanded octet geometries well.
Molecular Orbital Theory: Explains energy levels, paramagnetism, and delocalization/resonance. Drawback: Computationally complex for large molecules.

Questions & Discussion

Example 11.9 (Bond Counting): Determine the total $\sigma$ and $\pi$ bonds in acetylsalicylic acid ( $C_9H_8O_4$ ). * Response: There are $16$ single bonds and $5$ double bonds. Since each double bond contains one $\sigma$ and one $\pi$ , the total is $21 \, \sigma$ bonds and $5 \, \pi$ bonds.
Example 11.13 (Bond Order Comparisons): Calculate the bond order of nitric oxide ( $NO$ ) via MO theory vs Lewis structure. * Response: MO diagram calculations result in a bond order of $2.5$ , whereas the Lewis structure predicts a bond order of $2$ .