Molecular Orbital Theory, Liquids, Solids, and Intermolecular Forces

Molecular Orbital Theory

• Lewis dot structures are useful for understanding bonding but are not perfect.
• Resonance is needed to explain equal bond lengths, for example, in ozone.
• Oxygen is paramagnetic, indicating it has unpaired electrons.

Molecular Orbitals

• Valence atomic orbitals (AO’s) combine to form molecular orbitals (MO’s).
• The number of MO’s equals the number of AO’s.
• MO’s are arranged in increasing energy levels.
• Electrons are distributed with a maximum of 2 per MO, starting from the lowest energy MO.
• Hund’s rule applies: for degenerate orbitals, electrons are added singly with the same spin before pairing.

Forming MO’s

• Orbitals as waves can add constructively:
  • Leads to increased electron density between nuclei, forming a bonding s MO.
• Orbitals can subtract destructively:
  • Leads to reduced electron density between nuclei, forming an antibonding s^* MO.

Hydrogen (H2)

• Bond order calculation:
  • Bond order = number of bonds = \frac{1}{2} (nB – nA)
  • n_B = number of electrons in bonding orbitals
  • n_A = number of electrons in antibonding orbitals
  • For H2: Bond order = \frac{1}{2} (2 - 0) = 1

He2 and He2+

• He2+:
  • Bond order = \frac{1}{2} (2 - 1) = \frac{1}{2}
  • Ion exists.
• He2:
  • Bond order = \frac{1}{2} (2 - 2) = 0
  • No bond, molecule does not exist.

Li2 and Be2

• Li2:
  • Bond order = \frac{1}{2} (2 - 0) = 1
• Be2:
  • Bond order = \frac{1}{2} (2 - 2) = 0
  • No bond – no molecule.

p Orbitals

• End-to-end overlap of p orbitals forms sigma (\sigma) bonding MO’s and sigma star (\sigma^*) antibonding MO’s.
• Side-to-side overlap of p orbitals forms pi (\pi) bonding MO’s and pi star (\pi^*) antibonding MO’s.
• Degenerate pairs of bonding and antibonding MO’s are formed.

2s – 2p Mixing

• Mixing occurs between 2s \sigma and 2p \sigma MO’s, similar to sp hybridization.
• Mixing decreases across the periodic table as the energy difference between 2s and 2p orbitals increases.

MO Diagrams for 2nd Period Diatomics

• Diagram shows atomic orbitals on the sides and molecular orbitals in the center, arranged by energy level.
• The order of MO’s varies for different molecules (B2, C2, N2 vs. O2, F2, Ne2) due to 2s-2p mixing.
• Energy levels are labeled as \sigma{2s}, \sigma{2s}^, \pi{2p}, \sigma{2p}, \pi{2p}^, \sigma{2p}^*.

Oxygen (O2)

• 12 valence electrons.
• 2 unpaired electrons – paramagnetic.
• Bond order = \frac{1}{2} (8-4) = 2
• Electronic configuration: \uparrow\downarrow \uparrow \uparrow \uparrow\downarrow \uparrow \uparrow \uparrow\downarrow \uparrow\downarrow \uparrow\downarrow \uparrow\downarrow \uparrow\downarrow \uparrow\downarrow \uparrow \uparrow

Bonding in 2nd Period Diatomics

• The table summarizes the bond order, bond energy, and bond length for various diatomic molecules.
• Large 2s-2p interaction affects the energy levels and properties of B2, C2, and N2.
• Small 2s-2p interaction affects the energy levels and properties of O2, F2, and Ne2.
• Bond order increases from Li2 to N2, then decreases from O2 to Ne2.
• Bond energy and bond length correlate with bond order.

Ions

• Adding an electron to a bonding MO or removing one from an antibonding MO increases the bond order by 0.5, strengthening and shortening the bond.
• Adding an electron to an antibonding MO or removing one from a bonding MO decreases the bond order by 0.5, weakening and lengthening the bond.

Heteronuclear Diatomics

• Atomic orbital energies decrease from left to right across the periodic table.
• For example, O orbital energies are lower than N.
• Bonding MO’s have more O atomic character, while antibonding MO’s have more N atomic character.
• Electron density is higher on the O side, consistent with the dipole moment.

Polyatomic Molecules

• MO’s extend throughout the molecule.
• Electron density is concentrated between pairs of atoms.
• Molecules with resonance structures have delocalized MO’s that encompass all the atoms in the different resonance forms.

Examples

• Benzene: \pi electrons are in MO’s that look like rings above and below the molecule.
• Ozone: \pi electrons are in an MO that covers all three O atoms.

Chapter 12: Liquids, Solids, and Intermolecular Forces

States of Matter

• Gas:
  • Molecules widely spaced.
  • Highly compressible.
• Liquid:
  • Molecules closely spaced.
  • Not easily compressible.
• Liquids are approximately 1000 times as dense as gases.

Properties of Liquids

• As the temperature of a gas decreases, the kinetic energy of the molecules reduces until it can no longer overcome intermolecular forces (imf).
• The substance then condenses into a liquid.
• Whether a substance is solid, liquid, or gas at a given temperature and pressure depends on the strength of imf.

Phase Changes

• Adding a small amount of heat can loosen imf in a solid, while a significant amount is needed to break imf in a liquid.
• Liquids boil when their vapor pressure reaches atmospheric pressure.
• Boiling can also occur by sufficiently lowering the pressure.

Intermolecular Forces

• Intermolecular forces (imf) hold molecules together.
• Without sufficient imf, liquid molecules would separate into a gas.
• Covalent bonds have energies ranging from 150-1000 kJ/mol.
• imf have energies ranging from 0.05-40 kJ/mol.
• imf are much weaker and more easily broken than covalent bonds.

Factors Affecting Intermolecular Forces

• As thermal energy increases, it can overcome imf, leading to a phase change to gas.
• The strength of imf determines the state of matter (solid, liquid, or gas) at a given temperature.
• Substances that are gases at room temperature have low imf and are often low molecular mass or nonpolar.
• Molecular mass and polarity influence imf.

Intramolecular Forces

• Large molecules, especially biological ones, exhibit forces between different parts of the molecule – intramolecular forces.
• Intramolecular forces hold proteins into their biologically relevant structures (e.g., Chymotrypsin).

Coulombic Attraction

• Coulomb’s Law for the energy of attraction between ions in a crystal lattice:
  • E = \frac{1}{4\pi\epsilon0} \frac{q1q_2}{r}
• Similar attractions occur between partial charges in molecules (\delta^+ \delta^-).
• The imf between water molecules is strong due to their high polarity.

Dispersion Force

• Electrons in an atom (e.g., Helium) move randomly.
• Temporary dipoles occur when electrons are momentarily on the same side of the atom.

Induced Dipoles

• A temporary dipole in one atom attracts electrons in a nearby atom, inducing a temporary dipole.
• Neighboring sides have opposite charges, resulting in attraction.
• These fleeting attractions always contribute and add up.

Factors Affecting Dispersion Forces

• Strength of dispersion forces depends on molecular polarizability – distortion of the electron cloud of the atom or molecule.
• Polarizability increases with the number of electrons, so dispersion forces increase with increasing number of electrons or molar mass.

Boiling Points and Molar Mass

• Boiling points of noble gases increase with molar mass, demonstrating the effect of dispersion forces.
• Example:
  • He (4.00 g/mol, 4.2 K)
  • Ne (20.18 g/mol, 27 K)
  • Ar (39.95 g/mol, 87 K)
  • Kr (83.80 g/mol, 120 K)
  • Xe (131.30 g/mol, 165 K)

Boiling Points of Linear Alkanes

• Boiling points of linear alkanes increase roughly linearly with molar mass due to increased dispersion forces.
• Example:
  • n-Pentane (C5H12)
  • n-Hexane (C6H14)
  • n-Heptane (C7H16)
  • n-Octane (C8H18)
  • n-Nonane (C9H20)

Structure and Intermolecular Forces

• Long, skinny molecules can interact more readily with other molecules than short, fat ones of similar mass.
• They have larger imf.
• Example:
  • b.p. = 36.1°C
  • b.p. = 9.5°C