Structure and Bonding Notes

N-Heterocyclic Carbenes (NHCs)

Both carbon atoms are tetrahedral.
Each carbon forms bonds to four other atoms.
Carbon atoms are sp^3 hybridized.
Two sp^3 hybrid atomic orbitals (AO) from neighboring carbon atoms overlap to form a C-C \sigma bond (and a vacant C-C \sigma^* bond).
Each remaining sp^3 hybrid AO overlaps with 3 x H 1s atomic orbitals to form C-H \sigma bonds (and vacant C-H \sigma^* bonds).
Hybridization is a tool for generating modified AOs that point to the atoms involved in bonding.
Knowing the shape of a molecule allows determination of how the orbitals are hybridized.
Rotation can occur about the C-C \sigma-bond.

Both carbon atoms are planar, forming bonds to three other atoms.
Carbons are sp^2 hybridized, created by combining the 2s and 2 x 2p orbitals, leaving an unchanged p orbital.
The sp^2 hybrid orbitals are planar and consist of 33% s and 67% p character.
Three equivalent sp^2 hybrid orbitals on each C overlap with three other orbitals.
One sp^2 hybrid orbital from each carbon forms C-C \sigma bond molecular orbitals (MOs).
Two H 1s AOs and two sp^2 hybrids form C-H \sigma bond MOs.
The two unused 2p orbitals combine to form a \pi bonding MO.
The skeleton comprises 5 \sigma bonds (one C-C, 4 x C-H) in the plane and a central \pi bond above and below the plane.
Rotation about the C-C axis is impossible because the p-orbitals would be orthogonal.

Acetylene is linear and contains a C-C triple bond.
Each carbon forms bonds to two other atoms.
Carbons are sp hybridized; the 2s and 1 x 2p orbitals combine to create 2 x sp hybrid orbitals that are linear (50% s, 50% p character), leaving two unchanged p orbitals that can overlap with p orbitals on another C to form \pi bonds.
Two equivalent sp hybrid orbitals on each C overlap with two other orbitals.
One sp hybrid orbital from each carbon forms a C-C \sigma bond MO.
1 x H 1s AO and an sp hybrid form a C-H \sigma bond MO.
The two unused 2p orbitals (orthogonal) on each C can combine to form \pi bonding MOs.
There are three C-C bonds: 1 x C-C \sigma bond and 2 x C-C \pi bonds.

Hydrocarbons are built from:
- Tetrahedral (sp^3)
- Trigonal planar (sp^2)
- Linear (sp) hybridized carbon atoms.
This procedure reveals the shapes of all C atoms, regardless of molecular complexity.
Counting single bonds (or atoms) bound to a particular carbon:
- If 2: C atom is linear (sp hybridized).
- If 3: C atom is trigonal (sp^2 hybridized).
- If 4: C atom is tetrahedral (sp^3 hybridized).

Hybridization is a property of atomic orbitals (AOs), not just carbon.
A tetrahedral arrangement of atoms around a central atom implies sp^3 hybridization.
Borohydride anion, methane, and ammonium cation have the same number of bonding electrons, are isoelectronic, and sp^3 hybridized; their charges differ due to increasing nuclear charge.
With 3 bonds around a central atom, the situation is more complex.
BH3 and CH3^+ are isoelectronic (6 electrons), but not NH_3 (8 electrons).
Place bonding or lone pairs into low energy hybridized orbitals (spX hybrids contain some s character); place empty or vacant orbitals in atomic orbitals (p orbitals in this case).

Organic molecules are dynamic; bond rotation is possible about single bonds (like C-C bonds) because rotation does not change the orbital overlap.
Rotation around a C=C of an alkene is restricted because it requires breaking the \pi-bond.
Bond rotation implies that, while the localized arrangement of atoms stays the same (e.g., each sp^3 hybridized C is tetrahedral), the molecule can adopt numerous overall shapes via bond rotation.
These shapes are known as conformations of a molecule.
No bonds are broken during interconverting conformations.

Alkanes with two or more carbon atoms can adopt various conformations by rotation around a C-C bond.
Ethane (C2H6) has infinite possible conformations, defined by the orientation of H atoms on adjacent C atoms; consider two extreme cases:
- Eclipsed conformation: 3 x C-H on adjacent C atoms are as close as possible (same plane).
- Staggered conformation: 3 x C-H on adjacent C atoms are as far apart as possible.
Rotation of the C-C bond by 60° from the staggered conformation changes the shape to the eclipsed conformation (often represented as Newman projections).