Chapter 1: Covalent Bonding and Shapes of Molecules

Covalent Bonding and Shapes of Molecules

1.1 Electronic Structure of Atoms

  • Atoms consist of a nucleus (protons and neutrons) surrounded by electrons.
  • The nucleus has a diameter of 10−1410^{-14} to 10−1510^{-15} meters.
  • Electrons have a diameter of 10−1010^{-10} meters.
  • Shells: Define the probability of finding an electron in specific regions of space around the nucleus.
  • Principal quantum numbers (n) identify shells.
  • Each shell holds up to 2n22n^2 electrons, where n is the shell number.
  • Shells are divided into subshells, which contain orbitals.
  • Orbitals: Regions of space holding up to two electrons with specific quantized energy.

1.2 Lewis Model of Bonding

  • Atoms interact to achieve a complete outer-shell electron configuration, resembling the nearest noble gas.
  • Atoms may gain or lose electrons to become ions (anions or cations), forming ionic bonds.
  • Atoms may share electrons to complete their valence shells, forming covalent bonds.
  • Electronegativity: An atom's attraction for shared electrons in a chemical bond (Pauling scale).
  • Electronegativity increases from left to right and decreases from top to bottom in the Periodic Table.
  • Electron Affinity: Energy change when an electron is added to an atom or molecule.
  • Ions form if electronegativity difference is >= 1.9.
  • Covalent Bonds:
    • Simplest example is H2, where each atom's single electron combines to form an electron pair.
    • ΔH0=−435 kJ (−104 kcal)/molΔH^0 = -435 \text{ kJ }(-104 \text{ kcal})/\text{mol}
    • This shared pair fills each atom's valence shell.
  • Bond Length: Distance between nuclei in a chemical bond.
  • Multiple covalent bonds (double, triple) occur when atoms share more than two electrons.
  • Polar Covalent Bonds: Occur when electronegativity difference is approximately 0.5 to 1.9.
    • The more electronegative atom gains a greater fraction of electrons (δ−\delta^−).
    • The less electronegative atom gains a smaller fraction of electrons (δ+\delta^+
  • Bond Dipole Moment ($\mu$): Measure of covalent bond polarity.
    • Product of charge (e) and distance (d) between nuclei: μ=e⋅d\mu = e \cdot d
    • SI unit: coulomb ∙ meter, commonly reported in debyes.
  • Lewis structure guidelines:
    • Determine total valence electrons.
    • Determine atom connectivity.
    • Connect atoms with single bonds.
    • Arrange remaining electrons to complete valence shells.
    • Represent shared electrons as lines and nonbonding electrons as dots.
  • Formal Charge: Charge on an atom in a polyatomic ion or molecule.
    • Steps: Draw Lewis structure, assign unshared electrons and half of shared electrons to each atom, compare with valence electrons in neutral atom.
    • Sum of formal charges equals the total charge.
  • Molecules with Group 3A elements (B, Al) may be apparent exceptions to the octet rule.
  • Dative Bonds (Coordinate Covalent Bonds): Both electrons come from a single atom.
    • Example: B-N bond in BF<em>3BF<em>3 and NH</em>3NH</em>3.
    • An Arrow indicates the direction of the electron pair donation

1.3 Functional Groups

  • Atoms or groups of atoms within a molecule that exhibit characteristic physical and chemical properties.
  • Allow division of organic compounds into classes.
  • Serve as the basis for naming organic compounds.
  • Alcohols: Contain an -OH (hydroxyl) group bonded to a carbon atom with four single bonds; classified as primary (1°), secondary (2°), or tertiary (3°) based on the number of carbon atoms bonded to the carbon atom bearing the -OH group.
  • Amines: Contain an amino group (N bonded to one, two, or three carbon atoms); classified as primary (1°), secondary (2°), or tertiary (3°) amines.
  • Aldehydes and Ketones: Contain a carbonyl (C=O) group.
  • Carboxylic Acids: Contain a carboxyl (-COOH) group.
  • Carboxylic Esters: Derivatives of carboxylic acids where the carboxyl hydrogen is replaced by a carbon containing group, commonly known as esters.
  • Carboxylic Amides: Derivatives of carboxlyic acids where the -OH of the carboxyl group is replaced by an amine, commonly known as amides.

1.4 Bond Angles and Shapes of Molecules

  • Valence-Shell Electron Pair Repulsion (VSEPR) Theory: Predicts bond angles based on electron pair repulsion, where electron pairs stay as far apart as possible.

1.5 Polar and Nonpolar Molecules

  • Determining molecular polarity requires considering:
    • Polar bonds.
    • Arrangement of atoms in space.
  • Molecular Dipole Moment ($\mu$): Vector sum of individual bond dipoles.

1.6 Quantum or Wave Mechanics

  • Albert Einstein: Postulated that light consists of photons of electromagnetic radiation.
    • E=hνE = h\nu
    • E: Energy,
    • $\nu$: Frequency,
    • h: Planck's constant.
  • Louis de Broglie: Advanced the idea that particles in motion exhibit wave properties.
    • λ=h/(mv)\lambda = h/(mv)
    • m: Mass,
    • v: Speed,
    • $\lambda$: Wavelength.
  • Wave Equation: Mathematical equation describing this wave.
  • Node: A point in space where the value of the solution of a wave equation is zero.
  • Nodal Plane: Any plane perpendicular to the direction of propagation that runs through a node.
  • Erwin Schrödinger: Developed an equation to describe wave properties of electrons in atoms or molecules.
  • Quantum (Wave) Mechanics: Studies particles and their wavelike properties.
  • Wave Function ($\psi$): Set of solutions to the Schrödinger equation, defining energy and spatial region of an electron in an atom that occupies three-dimensional space called an orbital.
  • Hybrid Orbitals: New atomic orbitals formed from combinations of atomic orbitals (hybridization).
  • $\psi^2 is proportional to the probability of finding an electron at a point in space.
  • Electron density is equal in regions with the same absolute value of $\psi$.
  • $\psi^2 is zero at a node.
  • Orbital Interactions: Interactions of waves (constructive or destructive).
  • Phasing: Sign of the wave function (+ or -).
  • Electrostatic Potential Maps: Display computed electronic charge density with colors representing electron density (red = high, blue = low).

1.7 A Combined Valence Bond and Molecular Orbital Theory Approach to Covalent Bonding

Both Valence Bond (VB) and Molecular Orbital (MO) Theories approximate the energetics of covalent bond formation.

  • Valence Bond (VB) Theory: Provides an easily visualized description of single bonds.
    • Bonds arise from the overlap of atomic orbitals on adjacent atoms.
    • Correlates with Lewis structures, where two electrons are visualized between atoms as a bond.
  • Molecular Orbital (MO) Theory: Most convenient for describing multiple bonds.
    • Electrons in molecules exist in molecular orbitals.
    • Combining n atomic orbitals yields n MOs.
    • MOs are arranged in order of increasing energy.
    • Filling MOs follows the same rules as atomic orbitals (Aufbau principle, Pauli exclusion principle).
      *Hybridization is used:
      *Mathematical combination of one 2s atomic orbital and three 2p atomic orbitals forms four equivalent sp3 hybrid orbitals.
      *Atoms with four sp3 hybrid atomic orbitals are referred to as sp3 hybridized.
      *Each sp3 orbital has 25% s-character and 75% p- character.
      *Mathematical combination of one 2s atomic orbital wave function and two 2p atomic orbital wave functions forms three equivalent sp2 hybrid orbitals.
      *Each sp2 orbital has 33% s-character and 67% p- character.
      *An atom possessing three sp2 hybrid orbitals and a single p atomic orbital is said to be sp2 hybridized.
      *Mathematical combination of one 2s atomic orbital and one 2p atomic orbital gives two equivalent sp hybrid orbitals.
      *Each sp orbital has 50% s-character and 50% p- character.
      *An atom possessing two sp hybrid orbitals and two 2p orbitals is said to be sp hybridized.
  • Bonding Molecular Orbital: MO where electrons have lower energy than in isolated atomic orbitals.
  • Sigma ($\sigma$) Bonding Molecular Orbital: MO with electron density concentrated between nuclei and cylindrically symmetric.
  • Antibonding Molecular Orbital: MO where electrons have higher energy than in isolated atomic orbitals (denoted with *).

1.8 Resonance

  • Many molecules and ions cannot be accurately represented by a single Lewis structure.
  • Theory of Resonance (Linus Pauling): Molecules are described as a composite of two or more Lewis structures (contributing structures or resonance structures).
  • Contributing structures are interconnected by double-headed arrows, indicating a resonance hybrid.
  • Curved arrows show the redistribution of valence electrons between contributing structures (electron pushing), either from a bond to an adjacent atom or from a lone pair to an adjacent bond.
  • Rules for Writing Contributing Structures: All structures must have the same number of valence electrons, obey covalent bonding rules, have the same number of paired and unpaired electrons, and have the same positions of all nuclei.
  • Relative Importance of Contributing Structures: Filled valence shells > maximum number of covalent bonds > least separation of unlike charges > negative charge on a more electronegative atom.

1.9 Molecular Orbitals for Delocalized Systems

  • Delocalization: Spreading of charge and/or electron density over a larger volume of space.
  • Occurs for conjugated systems, where there is a lack of atoms between π bonds or between π bonds and lone-pair electrons.

1.10 Bond Lengths and Bond Strengths in Alkanes, Alkenes, and Alkynes

  • Different hybridization implies different geometry, different bond length and different bond strength.