⚛Molecular Physics Unit 5 – Molecular Geometry and Hybridization

Key Concepts and Definitions

• Molecular geometry describes the three-dimensional arrangement of atoms in a molecule
• Valence shell electron pair repulsion (VSEPR) theory predicts molecular geometries based on minimizing electron pair repulsion
• Hybridization involves the mixing of atomic orbitals to form new hybrid orbitals with specific shapes and orientations
• Sigma (σ) bonds are formed by the overlap of atomic orbitals along the internuclear axis
  • Stronger and more stable than pi bonds
• Pi (π) bonds are formed by the sideways overlap of atomic orbitals
  • Weaker and more reactive than sigma bonds
• Molecular orbitals are formed by the combination of atomic orbitals from multiple atoms in a molecule
• Polarity refers to the uneven distribution of charge in a molecule due to differences in electronegativity
• Intermolecular forces are attractive or repulsive forces between molecules, including van der Waals forces, hydrogen bonding, and dipole-dipole interactions

Molecular Geometry Basics

• Molecular geometry is determined by the number and arrangement of atoms and electron pairs around a central atom
• The shape of a molecule affects its physical and chemical properties, such as melting point, boiling point, and reactivity
• Electron pairs, both bonding and nonbonding (lone pairs), influence the geometry of a molecule
• Bonding electron pairs are shared between atoms and form chemical bonds
• Nonbonding electron pairs (lone pairs) are not shared between atoms and tend to occupy more space than bonding pairs
• The electron domain geometry considers both bonding and nonbonding electron pairs
• The molecular geometry only considers the arrangement of atoms, ignoring lone pairs
• Bond angles are the angles formed between the central atom and two adjacent atoms, and they vary depending on the molecular geometry (e.g., 109.5° in a tetrahedral arrangement)

VSEPR Theory and Molecular Shapes

• VSEPR theory states that electron pairs will arrange themselves around a central atom to minimize repulsion and maximize stability
• The theory predicts molecular geometries based on the number of electron domains (bonding and nonbonding) around the central atom
• Electron domains can be classified as AX$_n$E$_m$, where A is the central atom, X is a bonded atom, n is the number of bonded atoms, E represents a lone pair, and m is the number of lone pairs
• Common molecular geometries include linear (AX$_2$), trigonal planar (AX$_3$), tetrahedral (AX$_4$), trigonal bipyramidal (AX$_5$), and octahedral (AX$_6$)
  • Linear: CO$_2$, HCN
  • Trigonal planar: BF$_3$, SO$_3$
  • Tetrahedral: CH$_4$, NH$_4^+$
  • Trigonal bipyramidal: PCl$_5$
  • Octahedral: SF$_6$
• The presence of lone pairs can distort the ideal geometry, leading to bent (AX$_2$E), trigonal pyramidal (AX$_3$E), seesaw (AX$_4$E), and T-shaped (AX$_3$E$_2$) geometries
• Lone pairs occupy more space than bonding pairs, causing a decrease in bond angles compared to the ideal geometry

Hybridization of Atomic Orbitals

• Hybridization is the mixing of atomic orbitals to form new hybrid orbitals with specific shapes and orientations
• Hybrid orbitals are formed to minimize electron pair repulsion and maximize orbital overlap for bonding
• The type of hybridization depends on the number of electron domains around the central atom
  • sp hybridization: 2 electron domains, linear geometry
  • sp$^2$ hybridization: 3 electron domains, trigonal planar geometry
  • sp$^3$ hybridization: 4 electron domains, tetrahedral geometry
• Hybridization explains the observed geometries and bond angles in molecules that cannot be accounted for by the simple overlap of atomic orbitals
• The hybridization of the central atom can be determined by the number of sigma bonds and lone pairs it possesses
• Hybrid orbitals have a specific orientation and shape, which influences the overall molecular geometry
• Unhybridized p orbitals can form pi bonds, which are important in molecules with multiple bonds (e.g., ethene, benzene)

Bonding and Molecular Orbitals

• Molecular orbitals (MOs) are formed by the combination of atomic orbitals from multiple atoms in a molecule
• MOs can be classified as bonding, antibonding, or nonbonding
  • Bonding MOs have lower energy than the constituent atomic orbitals and contribute to the stability of the molecule
  • Antibonding MOs have higher energy than the constituent atomic orbitals and can weaken the bond
  • Nonbonding MOs have similar energy to the constituent atomic orbitals and do not significantly affect bonding
• The linear combination of atomic orbitals (LCAO) method is used to construct MOs
• The shape and symmetry of MOs determine the electron distribution and bonding properties in a molecule
• Bonding MOs are filled with electrons first, followed by nonbonding and antibonding MOs, according to the Aufbau principle and Hund's rule
• The bond order can be calculated from the number of bonding and antibonding electrons, indicating the strength and stability of the bond
  • Bond order = (number of bonding electrons - number of antibonding electrons) / 2
• MO theory can explain the properties of molecules that cannot be accounted for by valence bond theory, such as the paramagnetism of O$_2$ and the stability of H$_2^+$

Polarity and Intermolecular Forces

• Polarity arises from the uneven distribution of charge in a molecule due to differences in electronegativity between atoms
• Polar molecules have a net dipole moment, with a positive end (δ+) and a negative end (δ-)
  • Examples: H$_2$O, HCl, NH$_3$
• Nonpolar molecules have a balanced distribution of charge and no net dipole moment
  • Examples: CO$_2$, CH$_4$, benzene
• Intermolecular forces are attractive or repulsive forces between molecules, which influence properties such as melting point, boiling point, and solubility
• Dipole-dipole interactions occur between polar molecules, where the positive end of one molecule attracts the negative end of another
• London dispersion forces (induced dipole-induced dipole interactions) occur between nonpolar molecules due to temporary fluctuations in electron distribution
  • These forces are weaker than dipole-dipole interactions but are present in all molecules
• Hydrogen bonding is a strong type of dipole-dipole interaction that occurs when a hydrogen atom bonded to an electronegative atom (N, O, or F) interacts with another electronegative atom
  • Hydrogen bonding is responsible for the unique properties of water and the secondary structure of proteins and DNA

Applications in Chemistry and Physics

• Understanding molecular geometry and hybridization is crucial for predicting the reactivity and properties of molecules
• Molecular geometry influences the accessibility of reactive sites and the stereochemistry of reactions
  • Example: the SN2 reaction mechanism requires a backside attack, which is favored by a tetrahedral geometry
• Hybridization affects the strength and orientation of bonds, which can impact the stability and reactivity of molecules
  • Example: the planar structure of benzene, resulting from sp$^2$ hybridization, contributes to its unique aromatic properties
• Polarity and intermolecular forces play a significant role in determining the physical properties of substances, such as melting point, boiling point, and solubility
  • Example: the high boiling point of water compared to other hydrides is due to extensive hydrogen bonding
• Molecular orbital theory is essential for understanding the electronic structure and properties of molecules, particularly in spectroscopy and quantum chemistry
  • Example: the color of transition metal complexes can be explained by the splitting of d orbitals in different ligand fields
• Knowledge of molecular geometry and hybridization is applied in fields such as drug design, materials science, and nanotechnology
  • Example: the design of enzyme inhibitors often involves considering the shape and electronic properties of the active site

Problem-Solving and Practice

• Determine the electron domain geometry and molecular geometry for a given molecule or ion based on its Lewis structure
  • Example: for the NH$_3$ molecule, the electron domain geometry is tetrahedral, and the molecular geometry is trigonal pyramidal
• Predict the hybridization of the central atom in a molecule or ion based on the number of electron domains
  • Example: in the H$_2$O molecule, the oxygen atom has four electron domains (two bonding and two lone pairs), so it is sp$^3$ hybridized
• Draw the shape of hybrid orbitals and predict the bond angles in a molecule based on its hybridization
  • Example: in the BF$_3$ molecule, the boron atom is sp$^2$ hybridized, resulting in a trigonal planar geometry with bond angles of 120°
• Use molecular orbital theory to determine the bond order and stability of molecules or ions
  • Example: in the O$_2$ molecule, there are eight bonding electrons and four antibonding electrons, resulting in a bond order of (8 - 4) / 2 = 2
• Predict the polarity of a molecule based on its geometry and the electronegativity differences between atoms
  • Example: the CO$_2$ molecule is nonpolar because it is linear and has equal electronegativity on both oxygen atoms
• Identify the types of intermolecular forces present in a substance and explain their impact on its properties
  • Example: in liquid water, hydrogen bonding leads to a high surface tension and a high specific heat capacity
• Practice drawing Lewis structures, predicting molecular geometries, and assigning hybridization for a variety of molecules and ions
• Solve problems involving the application of molecular geometry and hybridization concepts to real-world situations, such as the structure of biomolecules or the properties of materials