Chapter 11: Theories of Covalent Bonding

Merged flashcards from Chapter 11 of Chemistry: The Molecular Nature of Matter and Change.

Valence bond theory (VB theory)

A model that relates molecular shapes to orbital shapes through orbital overlap and hybridization

• Covalent bonds form in constructively interfering orbital overlaps, where electrons reside

• Overlapping regions are bound by the Pauli exclusion principle, with opposing spins

• Orbitals are reoriented to maximize overlap and strength, seen in p and d orbitals’ shapes

• Orbitals hybridize and form new hybrid orbitals to account for new behavior and properties

Hybridization

The formation of new hybrid orbitals from the combination of different valence orbitals, where:

• The number of orbitals formed is equal to the number of orbitals mixed

• The types of orbitals formed varies with the types of orbitals mixed

• The shape and orientation of hybrid orbitals maximizes its overlap between its composites

• The resultant orbitals have an energy level between the original composites

Serves best as a mathematical concept rather than a literal translation

sp Hybridization

The creation of new sp orbitals from electrons in an s orbital with a p orbital for linear shapes, through:

1. An electron from an s orbital being promoted to a higher-energy p orbital

2. The now-separate s and p orbitals hybridizing (mixing) to form new, half-filled sp orbitals

   • The unused p orbitals remain empty and in place

3. The presentation of these new orbitals to other atoms, now correctly shaped and available

sp² Hybridization

The creation of new sp² orbitals from electrons in s and p orbitals, explaining trigonal planar shapes

• For atoms that bond with three other atoms, an s electron is promoted to a higher-energy p orbital alongside another half-filled p orbital, creating three hybridized sp² orbitals to bond

• For molecules that need a lone pair, an entire s pair and two half-filled p orbitals are hybridized into three sp² orbitals (with one fully paired)

• Unused p orbitals remain empty and in place

sp³ Hybridization

The creation of new sp³ orbitals from electrons in s and p orbitals, explaining tetrahedral shapes

• For atoms that bond with four other atoms, an s electron is promoted to a higher-energy p orbital alongside two half-filled p orbitals, creating four hybridized sp³ orbitals to bond

• For atoms that require one or two lone pairs, an entire s pair alongside three p orbitals (one of which may be complete) is hybridized into four sp³ orbitals (with one or two fully paired)

sp³d Hybridization

The creation of new sp³d orbitals from electrons in s and p orbitals utilizing a d orbital as another promotion level, explaining trigonal bipyramidal shapes

• For atoms that bond with five other atoms, an s electron is promoted to a higher-energy d orbital above three half-filled p orbitals, creating five hybridized sp³d orbitals to bond

• For molecules that require a lone pair, a full p orbital promotes an electron to a higher-energy d orbital, allowing for a full s orbital and any remaining full p orbitals to be hybridized into five sp³d orbitals

sp³d² Hybridization

The creation of new sp³d² orbitals from electrons in s and p orbitals, utilizing 2 d orbitals as promotion levels to explain octahedral shapes

• For atoms that bond with six other atoms, two full lone pairs from the s and p levels each promote one electron to a d orbital, which then has all orbitals hybridize into sp³d² orbitals to bond

• For square pyramidal and square planar molecules, lone pairs also exist in these sp³d² orbitals after promotion

Draw the Lewis structure and determine the electron group arrangement and shape. Then, determine the hybrid orbital type from the specified arrangement.

How do I determine the type of hybrid orbitals present in a molecule?

Large nonmetal hydrides (like H₂S) due to longer bonds, and molecules with expanded valence shells due to d orbital instability.

Which two categories of molecules have limitations when examining them under VB theory?

Sigma bond (σ bond)

A bond formed by the end-to-end overlap of orbitals, with highest density along the bond axis

• Includes all single bonds

Pi bond (π bond)

A bond formed by the side-to-side overlap of orbitals, increasing electron density between two nuclei

• Includes the bonds formed after a single σ bond, such as double and triple bonds

• Has two equally-occupied lobes of electron density, above and below the σ bond axis

• Utilizes the unhybridized p orbitals, but is weaker due to less overlap

Free rotation

This is permitted in σ bonds due to overlap not being affected

Restricted rotation

This occurs in π bonds (if trying to rotate just one atom) due to overlap being reduced

• Results in the creation of distinct isomeric structures for certain molecules

Molecular orbital theory (MO theory)

A model of bonding to explain each molecule’s properties through the use of delocalized electrons in molecular orbitals of given energies and shapes that extend over the whole molecule

• Creates a number of bonding and antibonding orbitals equal to the number of atomic orbitals

Bonding molecular orbital (bonding MO)

This is formed through the overlap of two electron clouds, increasing density between nuclei

• Acts through the amplification of two atomic orbital wave functions, adding two functions

• Lower in energy due to density spread between nuclei across larger volumes, lowering repulsions for a more stable state

• Always coexists with an antibonding MO

Antibonding molecular orbital (antibonding MO)

This is seen in nodes, or regions of zero electron density between the nuclei

• Acts through the cancellation of two atomic orbital wave functions, subtracting one function

• Higher in energy due to greater nuclear repulsions and a lack of separating electrons via a node, lowering stability

• Always coexists with a bonding MO

Sigma molecular orbital (σ MO)

A molecular orbital that is cylindrically symmetrical about the nuclei, formed through similar energy and orientation

• Denoted by a σ with a subscript listing the derived atomic orbital, such as σ_1s

• Antibonding molecular orbitals are denoted with a star, such a σ^*_1s

Molecular orbital diagram (MO diagram)

A diagram showing the atomic orbitals that compose each MO, following normal diagram rules

• Fills lower-energy bonding before higher-energy antibonding forms

• Each level is written in parentheses; for H₂, this is (σ_1s)²

Molecular orbital bond order (MO bond order)

Calculated by taking:

• ½ (number of bonding electrons - number of antibonding electrons)

  • Greater than 0 indicates more stability and formation, increasing with strength

  • Equal to 0 indicates no difference in stability, resulting in no formation

• Correlates with greater bond energy and shorter bond length

Homonuclear diatomic molecule

A molecule composed of two identical atoms; these only use outer atomic orbitals to determine molecular orbitals

Pi molecular orbital (π MO)

A molecular orbital formed through the side combination of two p orbitals with orientations perpendicular to the internuclear axis

• Noted in pairs like π_2p and π^*_2p

• Expected to have a σ_2p < π_2p < π^*_2p < σ^*_2p energy order for the smaller O₂, F₂ and Ne₂

• Expected to have a π_2p < σ_2p < π^*_2p < σ^*_2p energy order for the larger B₂, C₂, and N₂ due to sp mixing raising the energy of the σ_2p and σ^*_2p orbitals

sp Mixing

This occurs for the larger homonuclear diatomic molecules B₂, C₂, and N₂, with energies being lowered on the σ_2s and σ^*_2s and raised on the σ_2p and σ^*_2p orbitals due to less repulsion

• Deviates from the expected non-mixing of two orbitals for normally large energy differences, as seen in O₂, F₂, and Ne₂

• Results in molecular bond energy being listed as π_2p < σ_2p < π^*_2p < σ^*_2p

Magnetism

This can be observed in a molecular orbital diagram, determining if any unpaired electrons are present in a molecular orbital while avoiding the shortcomings of Lewis structures

Heteronuclear diatomic molecules

These have asymmetric MO diagrams due to unequal atomic energies and nuclear charges, with greater charges resulting in more stable forms

Nonbonding molecular orbital (nonbonding MO)

A molecular orbital that is not involved in bonding, with the same energy as the isolated orbital

• Seen with the two filled pairs in F not interacting with H in HF