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Announcements

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  • Recitation this evening
    • Intends on going through problems from test 2 that gave people trouble

Clicker 1

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  • Give the hybridization for the O in OF2
  • A) sp
  • B) sp3
  • C) sp2
  • D) sp3d
  • E) sp3d2

Clicker 2

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  • Give the hybridization for the S in SO3
    • A) sp
    • B) sp3
    • C) sp2
    • D) sp3d
    • E) sp3d2

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Clicker 3

  • How many of the following molecules have sp2 hybridization on the central atom?
  • HCN SO2 OCl2 XeCl2
  • A) 4
  • B) 3
  • C) 2
  • D) 1
  • E) 0

Ex: Multi-Central Atom Lewis Structures Isomers of C2H4O

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  • Acetaldehyde: CH3CHO,
  • Ethenol (aka vinyl alcohol): CH2CHOH
  • oxirane (aka ethylene oxide): CH2OCH2
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  • Explaination of the Bonds to O
    • (More complicated example than what you’ll see in this class)

Molecular Orbital (MO) Theory: Electron Delocalization

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  • In MO theory:
    • Applies Schrödinger’s wave equation to the molecule to calculate a set of molecular orbitals
      • The equation solution is estimated.
      • The estimated solution is evaluated and adjusted until the energy of the orbital is minimized.
  • In this treatment, the electrons belong to the whole molecule, so the orbitals belong to the whole molecule.
    • Delocalization

LCAO: Linear Combination of Atomic Orbitals

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  • The simplest guess starts with the atomic orbitals of the atoms adding together to make molecular orbitals; this is called the linear combination of atomic orbitals (LCAO) method.
    • Weighted sum
  • Because the orbitals are wave functions, the waves can combine either constructively or destructively.

Molecular Orbitals

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  • When the wave functions combine constructively, the resulting molecular orbital has less energy than the original atomic orbitals
    • Called a bonding molecular orbital
    • Designated: σ, π
    • Most of the electron density between the nuclei
  • When the wave functions combine destructively, the resulting molecular orbital has more energy than the original atomic orbital.
    • Called an antibonding molecular orbital
    • Designated: σ, π
    • Most of the electron density outside the nuclei
    • Nodes between nuclei

Interaction of 1s Orbitals

Molecular Orbital Theory

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  • Use Aufbau approach for MO’s (as we did for individual atoms)
  • electrons go into lowest energy MO’s first
  • pair up when they have to
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  • Electrons in bonding MOs are stabilizing.
    • Lower energy than the atomic orbitals
  • Electrons in antibonding MOs are destabilizing.
    • Higher in energy than atomic orbitals
    • Electron density located outside the internuclear axis
    • Electrons in antibonding orbitals cancel stability gained by electrons in bonding orbitals.

MO and Properties

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  • Bond order = ½ (# Bonding Electrons – # Antibonding Electrons)
  • Bond order = difference between number of electrons in bonding and antibonding orbitals
    • Only need to consider valence electrons
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    • May be a fraction
    • Higher bond order = stronger and shorter bonds
    • If bond order = 0, then the bond is unstable compared to individual atoms and no bond will form.
  • A substance will be paramagnetic if its MO diagram has unpaired electrons.
    • If all electrons are paired, it is diamagnetic.
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  • Ex:
  • Bond order = ½ (# Bonding Electrons – # Antibonding Electrons)
  • Bond Order H2 = ½ (2 – 0) = 1
    • Corresponds to a sigma bond
    • Also coincides with Lewis models

Why Doesn’t the Molecule He2 Exist?

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  • Bond order = ½ (# Bonding Electrons – # Antibonding Electrons)
  • Bond Order He2 = ½ (2 – 2) =0
    • Because the bond order is zero, dihelium doesn’t exist

Why Does the Molecule He2+ Exist?

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  • Bond order = ½ (# Bonding Electrons – # Antibonding Electrons)
  • Bond Order He2+ = ½ (2 – 1) =1/2
    • Nonzero, so it works

Summarizing LCAO–MO Theory

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  • Molecular orbitals (MOs) are a linear combination of atomic orbitals (AOs).
    • The total number of MOs formed from a particular set of AOs always equals the number of AOs in the set.
  • When two AOs combine to form two MOs, one MO is lower in energy (the bonding MO) and the other is higher in energy (the antibonding MO).
  • When assigning the electrons of a molecule to MOs, we fill the lowest energy MOs first with a maximum of two spin-paired electrons per orbital.
  • When assigning electrons to two MOs of the same energy, Hund’s rule is followed to fill the orbitals singly first, with parallel spins, before pairing.
  • The bond order in a diatomic molecule is the number of electrons in bonding MOs minus the number in antibonding MOs divided by two.
    • Stable bonds require a positive bond order (more electrons in bonding MOs than in antibonding MOs).
  • MOs are named by type: σ, π, with a subscript to indicate what AOs they were formed from.

Practice Problem on Bond Order H2-

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Period Two Homonuclear Diatomic Molecules

Interaction of p Orbitals

Molecular Orbital Energy Ordering

Practice Problem on Molecular Orbital Theory N2- ion. Determine the electron configuration, and whether the ion is para or diamagnetic

Molecular Orbital Energy Diagrams for SecondPeriod-p-Block Homonuclear Diatomic Molecules

Heteronuclear Diatomic Molecules and Ions

  • When the combining atomic orbitals are identical and of equal energy, the contribution of each atomic orbital to the molecular orbital is equal.
  • When the combining atomic orbitals are different types and energies, contributions to the MOs are different:
  • The more electronegative an atom is, the lower in energy are its orbitals.
  • Lower energy atomic orbitals contribute more to the bonding MOs.
  • Higher energy atomic orbitals contribute more to the antibonding MOs.
  • Nonbonding MOs remain localized on the atom donating its atomic orbitals.

Second-Period Heteronuclear Diatomic Molecules

Practice Problem on Molecular Orbital Theory CN-

MO and Polyatomic Molecules

  • When many atoms are combined together, the atomic orbitals of all the atoms are combined to make a set of molecular orbitals, which are delocalized over the entire molecule.
  • Gives results that better match real molecule properties than either Lewis or valence bond theories

Bonding in Metals and Semiconductors

Bonding in Metals and Semiconductors

  • The simplest theory of metallic bonding involves the metal atoms releasing their valence electrons to be shared as a pool by all the atoms/ ions in the metal.
    • An organization of metal cation islands in a sea of electrons
    • Electrons delocalized throughout the metal structure
  • Bonding results from attraction of cation for the delocalized electrons.

Semiconductors and Band Theory

  • Band Theory:
  • Electrons become mobile when they make a transition from the highest occupied molecular orbital into higher energy empty molecular orbitals.
  • These occupied molecular orbitals are referred to as the valence band.
  • The unoccupied orbitals the conduction band.

Vocab

molecular orbital theory applies Schrödinger’s wave equation to the molecule to calculate a set of molecular orbitals
molecular orbital orbitals which hold electrons which belong to an entire molecule
linear combination of atomic orbitals (LCAO) weighted sum of orbitals which helps predicting the optimal energy/shape of orbitals (aka let’s take 10% of s and 90% of p)
bonding molecular orbital molecular orbitals which have wave functions which combine constructively
bonding molecular orbitals result in an orbital which has (more or less?) energy than the originals less
antibonding molecular orbitals bonding molecular orbitals which have wave functions which combine destructively
bond order half of the difference of the number of bonding electrons and antibonding electrons