Chapter 9 Molecular Geometry and Bonding Theories Notes

Molecular Shapes

• Lewis structures depict bonding and lone pairs but not shape.
• Lewis structures aid in determining molecular shapes.
• Common shapes exist for molecules with two or three atoms connected to a central atom.

The VSEPR Model

• Molecular shape is determined by bond angles and bond lengths.
• Electron pairs repel each other.
• Electron pairs position themselves as far apart as possible, allowing for prediction of molecular shape.
• This concept is the valence-shell electron-pair repulsion (VSEPR) model.

Electron Domains

• Electron domains are regions where electrons are most likely to be found.
• Bonding electron domains include single, double, and triple bonds between two atoms.
  • Multiple bonds count as one electron domain.
• Nonbonding electron domains (lone pairs) are centered on one atom.
• A central atom can have multiple electron domains.

Valence-Shell Electron-Pair Repulsion (VSEPR) Model

• The optimal arrangement of electron domains minimizes repulsions among them.
• Balloon analogy: Balloons tied together demonstrate how maximizing distances minimizes repulsions.

Electron-Domain Geometries

• Electron-domain geometries for two to six electron domains around a central atom are shown in Table 9.1.
  • The arrangement results in a specific shape.
  • Each electron domain geometry corresponds to specific bond angles.
• To determine electron-domain geometry, count the total number of bonding and nonbonding electron domains on the central atom.
  • Multiple bonds count as one electron domain.

Electron-Domain Geometries Table 9.1

• 2 Electron Domains
  • Arrangement: Linear
  • Geometry: Linear
  • Predicted Bond Angle: 180 degrees
• 3 Electron Domains
  • Arrangement: Trigonal Planar
  • Geometry: Trigonal Planar
  • Predicted Bond Angle: 120 degrees
• 4 Electron Domains
  • Arrangement: Tetrahedral
  • Geometry: Tetrahedral
  • Predicted Bond Angle: 109.5 degrees
• 5 Electron Domains
  • Arrangement: Trigonal Bipyramidal
  • Geometry: Trigonal Bipyramidal
  • Predicted Bond Angles: 90 and 120 degrees
• 6 Electron Domains
  • Arrangement: Octahedral
  • Geometry: Octahedral
  • Predicted Bond Angle: 90 degrees
• Coordination number refers to the number of electron domains around an atom.

Applying VSEPR to Determine Molecular Shapes

1. Draw the best Lewis structure.
2. Determine the electron-domain geometry.
3. Use the arrangement of bonded atoms to determine the molecular geometry.
   • Tables 9.2 and 9.3 show potential molecular geometries.

Linear Electron Domain

• In the linear domain, there is only one molecular geometry: linear.
• A molecule with only two atoms will be linear regardless of the electron domain.

Trigonal Electron Domain

• Two possible molecular geometries:
  • Trigonal planar: all electron domains are bonding electrons.
  • Bent: one of the electron domains is a lone pair.

Tetrahedral Electron Domain

• Three possible molecular geometries:
  • Tetrahedral: all bonding pairs.
  • Trigonal pyramidal: one lone pair.
  • Bent: two lone pairs.

Nonbonding Pairs and Bond Angles

• Nonbonding pairs are physically larger than bonding pairs.
• Their repulsions are greater, compressing bond angles.

Multiple Bonds and Bond Angles

• Double and triple bonds have larger electron domains than single bonds.
• They exert a greater repulsive force, increasing bond angles.

Molecules with Expanded Valence Shells

• Elements in periods 3 through 6 can break the octet rule and form more than four bonds (or have more than four electron domains).
• These elements utilize d-orbitals for bonding.
• This results in two more possible electron domains:
  • Five: trigonal bipyramidal.
  • Six: octahedral.

Trigonal Bipyramidal Electron Domain

• Four distinct molecular geometries:
  • Trigonal bipyramidal
  • Seesaw
  • T-shaped
  • Linear

Positions in Trigonal Bipyramidal Geometry

• Axial positions
• Equatorial positions
• Lone pairs preferentially occupy equatorial positions.

Octahedral Electron Domain

• All positions are equivalent in the octahedral domain.
• Three molecular geometries:
  • Octahedral
  • Square pyramidal
  • Square planar

Shapes of Larger Molecules

• VSEPR can be applied to complex molecules.
• For larger molecules, consider the geometry about each atom.

Molecular Shape and Polarity

• Use bond polarity (based on electronegativity) to assign dipole moments using vectors.

  • Polar: bond dipoles are not symmetrical.
  • Nonpolar: bond dipoles cancel due to equal magnitude and symmetrical arrangement.

• Steps to determine molecular polarity:

  1. Draw the Lewis structure.
  2. Determine the electron-domain geometry by counting central atom pairs.
  3. Determine molecular geometry by distinguishing between bonding and nonbonding electron domains.

Covalent Bonding and Orbital Overlap

• VSEPR doesn't explain why bonds exist.
• Valence-bond theory explains why bonds exist.
• Electrons of two atoms occupy the same space, resulting in orbital overlap.
• Sharing space between two electrons of opposite spin creates a covalent bond.

Valence-Bond Theory

• Increased overlap brings atoms together until a balance is reached between charge repulsions and electron-nucleus attraction.
• Atoms cannot get too close due to internuclear repulsions.
• Minimum energy: Bond strength.
• Minimum distance: Bond length.

Hybrid Orbitals

• Hybrid orbitals form by mixing valence-bond theory atomic orbitals to create new orbitals of equal energy.
• Orbitals of equal energy are called degenerate orbitals.
• This process is hybridization.
• Shape of hybrid orbitals differs from that of atomic orbitals.
• Mixing two orbitals creates two hybrid orbitals; mixing three creates three, and so on.

Be: sp Hybridization

• Beryllium (Be) has only paired electrons in full sublevels.
• Be forms compounds with two bonds.
• sp hybridization: mixing one s orbital and one p orbital.

sp Hybrid Orbitals

• Mixing s and p orbitals yields two degenerate orbitals that are hybrids of the two orbitals.
  • sp hybrid orbitals have two lobes, like a p orbital.
  • One lobe is larger and more rounded.

Position of sp Orbitals

• The two degenerate orbitals align themselves 180^{\circ} from each other.
• Consistent with the linear geometry of Be compounds and VSEPR.

sp^2 Hybridization: Boron

• Similar model for boron leads to three degenerate sp^2 hybrid orbitals.

sp^3 Hybridization: Carbon

• With carbon, we get four degenerate sp^3 hybrid orbitals.

Hybrid Orbital Description of Water

• Water has tetrahedral electron domain geometry.
• Four electron domains—two bonding, two nonbonding.
• Bond angles for sp^3 hybridization are 109.5^{\circ}.
• Measured bond angle is 104.9^{\circ}. Nonbonding electron pairs repel, compressing the bond angles.

Hybrid Orbital Summary

• When electron-domain geometry is known, hybridization can describe bonding of atoms:
  1. Draw the Lewis structure of the molecule or ion.
  2. Use VSEPR to determine the electron-domain geometry around the central atom.
  3. Specify the hybrid orbitals needed to accommodate these electron pairs based on their geometric arrangement (Table 9.4).

Hypervalent Molecules

• Central atoms have more than an octet.
• Valence-bond model uses d orbitals to make more than four bonds (works for period 3 and below).
• Application of hybridization to these molecules is not feasible; a more detailed bonding view is needed.

Multiple Bonds

• In a covalent bond, electron density is concentrated along the internuclear axis (sigma bond).
• Multiple covalent bonds use a second type of bond resulting from overlap between hybridized p orbitals perpendicular to the internuclear axis (pi bond).
  • Sigma: along the internuclear axis.
  • Pi: perpendicular to the internuclear axis.

Sigma and Pi Bonds

• Sigma bonds:
  • Head-to-head overlap.
  • Cylindrical symmetry of electron density along the internuclear axis.
• Pi bonds:
  • Sideways overlap.
  • Electron density above and below the internuclear axis.

Bonding in Molecules

• Single bonds are always sigma bonds.
• Multiple bonds have one sigma bond; all other bonds are pi bonds.

Localized or Delocalized Electrons

• Bonding electrons specifically shared between two atoms are localized electrons.
• In some molecules, all electrons cannot be described that way (resonance structures).
• Electrons shared by multiple atoms are delocalized electrons.

Benzene Resonance Structures

• Benzene has alternating single and double bonds and a p orbital on each C atom.
• Delocalized pi bonds form using one electron from each p orbital.

Molecular Orbitals

• Magnetic and spectral properties are not explained by VSEPR or hybridization.
• Molecular Orbital (MO) Theory addresses these shortcomings; bonding is continuous over the whole molecule.
• Molecular orbitals have properties like atomic orbitals:
  • Maximum of two electrons per orbital
  • Electrons in the same orbital have opposite spin
  • Definite energy of orbitals
  • Wave function-based

Molecular Orbital Theory

• Molecular orbitals represent the entire molecule, not a single atom.
• Whenever two atomic orbitals overlap, two molecular orbitals are formed: one bonding, one antibonding.
• Bonding orbitals are constructive combinations of atomic orbitals.
• Antibonding orbitals are destructive combinations of atomic orbitals with a nodal plane where electron density equals zero.

Molecular Orbitals

• Bonding orbitals form when electron density is added (constructive combination - sigma bonding molecular orbitals).
• Antibonding orbitals form when electron density cancels (destructive combination - sigma antibonding molecular orbitals).
• Example: formation of the hydrogen molecule from two hydrogen atoms.

MO Diagram and Bond Orders

• An energy-level diagram, or MO diagram, shows how orbitals from atoms combine to form molecular orbitals.
• Lowest energy orbitals are filled first.
• In H_2, two electrons go into the bonding molecular orbital.
• Stability of the bond is related to the bond order.

Can He_2 Form? Use MO Diagram and Bond Order to Decide

• Bond order equals 0 in He_2.
• Therefore, He_2 does not exist using MO theory.

Molecular-Orbital Description of Period 2 Diatomic Molecules

1. The number of MOs formed equals the number of AOs combined.
2. AOs effectively combine with AOs of similar energy.
3. The effectiveness with which two AOs combine is proportional to their overlap.
4. Each MO can accommodate at most two electrons with opposite spin (Pauli exclusion principle).
5. When MOs of the same energy (degenerate) are populated, one electron enters each orbital (same spin) before pairing (Hund’s rules).

MOs, Bonding, and Core Electrons

• N_2 occurs at high temperatures.
• Lewis structure: N≡N
• N_2 exists using MO theory.
• Core electrons don’t play a major part in bonding and should be excluded in an MO diagram.

MOs from 2p Atomic Orbitals

• Like s orbitals, p orbitals also undergo overlap, resulting in direct or sideways overlap.
• Like s orbitals, bonding and antibonding MOs form.
• Like s orbitals, nodes exist in antibonding orbitals.

MO Diagrams for the Second Period p-Block Elements

• Sigma orbitals form from s and p atomic orbitals.
• Pi orbitals form from p atomic orbitals.
• Direct overlap is stronger, hence energy raising and lowering effect is greater for sigma orbitals.

s and p Orbital Interactions

• In some cases, s orbitals can interact with sigma orbitals more than pi orbitals.
• This raises the energy of the σ{2p} orbital and lowers the energy of the σ{2s} orbital.
• The π_{2p} are degenerate orbitals.

MO Diagrams and Magnetism

• Diamagnetism results from all electrons in every orbital being spin-paired; substances are weakly repelled by a magnetic field (e.g., nitrogen).
• Paramagnetism results from the presence of one or more unpaired electrons in an orbital.
• Oxygen is paramagnetic; liquid oxygen sticks to the poles of a magnet.
• The MO diagram was adjusted to account for orbital interactions.

Paramagnetism of Oxygen

• Lewis structures would not predict that O_2 is paramagnetic.
• The adjusted MO diagram clearly shows that O_2 is paramagnetic.
• Lewis and MO agree: Both show a double bond (bond order = 2).

Heteronuclear Diatomic Molecules

• Diatomic molecules can consist of atoms from different elements.
• MO diagram reflects differences; atomic orbitals have different energy, changing interactions slightly.
• More electronegative atom has orbitals lower in energy, so bonding orbitals will more resemble them in energy.