Theories of Covalent Bonding

Valence Bond Theory

Overlap between partially filled atomic orbitals

• Single electrons from each orbital combine together to form an electron pair

  • Covalent bonding: + charge (nuclei) attracted to - charge (electron)

• The bigger the overlap (until equilibrium distance is reached) the stronger the bond

  • More concentration of the negative charges

Example: Covalent Bonding H₂

• Start: atomic orbitals have a great distance of separation

  • Potential energy decreases as the molecules move closer together

• End: maximum overlap of orbitals

  • Complete overlap is not possible, but the more overlap there is, the stronger the bond

Sigma Bonds

Electron density is concentrated in the region along the internuclear axis

• Sigma = single bond

Pi bonds

Electron density is concentrated in the region above and below the internuclear axis

• Along this axis = a node

• Node = area where there is absolutely zero chance of finding e- on internuclear axis

Water

2py and 2pz orbital from O and two 1s orbitals from H

• According to valence bond theory, the angle between the bonds should be 90° (b/c of x, y, z planes)

• Water is an exception b/c it has tetrahedral geometry (109.5° angles)

Hybridization

Wavefunctions/orbitals combine together on a single atom to give a new set of orbitals with different orientation and shape

• Linear combination of atomic orbitals = hybrid orbitals

• Hybrid orbitals = only when atoms are bound together in a molecule

• The # of hybrid orbitals must be equal to the # of atomic orbitals

• All hybrid orbitals form sigma bonds

• All unhybridized orbitals form pi bonds

sp Hybridization

Linear combination of s and p orbitals

• s and p: two atomic orbitals → 2 hybridized sp orbitals

• Situated along the same axis (can be x, y, or z)

• Situated between the s and p orbitals (same energy level)

sp² Hybridization

• One s and two p orbitals

• Combine to make 3 hybridized sp² orbitals

• Trigonal planar geometry (120°)

• Situated between s and p orbitals (same energy level)

• Each e- occupies one of the sp² orbitals

sp³ hybridization

• One s and three p orbitals

• Combine to make 4 hybridized sp³ orbitals

• No unhybridized orbitals

  • Came in with a full s orbital and two e- occupying p_x and p_y; ended with one e- occupying each sp³ orbital

Hybridization on Atoms

Count the # of lone pairs and adjacent atoms

• #2: sp hybridization; one s and one p

• #3: sp² hybridization; one s and two p orbitals

• #4: sp³ hybridization; one s and three p orbitals

• #5: sp³d hybridization; one s, three p and one d orbitals

• #6: sp³d² hybridization; one s, three p and two d orbitals

Hybridization and Shapes

This is the electron geometry

• sp: linear

• sp²: trigonal planar

• sp³: tetrahedral

• sp³d: trigonal bipyramidal

• sp³d²: octahedral

VSEPR and Hybridization

Steps:

1. Molecular formula

2. Lewis structure

3. Electron geometry (consider lone pairs + adjacent atoms)

4. Molecular shape

Molecular Geometry (VSEPR)

Molecular geometry (shape) determined using the electron geometry

• Same as e- geometry if no lone pairs on the central atom

• If no lone pairs → shape is determined by placement of the atoms only

• Influence of the lone pairs on molecular shape

Double Bond

• The hybridized orbitals form sigma bonds (head to head interaction)

• The unhybridized orbitals for pi bonds (side to side interaction)

  • Sit perpendicular to the sigma bonds

Triple Bond

• Two unhybridized p orbitals → two pi bonds

• Ex: if there’s a hybridized sp on the x axis, there will be two pi bonds from p_z and p_y

Hybridization and Resonance

Resonance hybrid: delocalization of pi bond

• System of 3 p orbitals with overlap between them

• All of these orbitals form ONE pi bonding pair

• This pi bond is delocalized between the C and one O, and the C and the other O

Roatation

• Around a single bond = works

• Around a double bond = does not work

  • B/c of the overlap of the p lobes above and below the internuclear axis

  • Rotating the double bond will cause rupture of the pi bond

Conjugation and Rotation Restriction

Conjugation = p orbital on three or more adjacent atoms can overlap

• Each C is sp2 with one unhybridized p orbital

• p orbitals on adjacent atoms: the pi bond is delocalized

Constructive and Destructive Interactions

• Valence bond theory: overlap between atomic and hybrid orbitals

• Atomic orbitals: wavefunctions, solutions of Schrodinger equation

• Combining orbitals together: constructive and destructive interactions between the wavefunctions

Molecular Orbitals

Linear combinations of atomic orbitals

• Constructive = bonding orbital

• Destructive = antibonding orbital

Sigma Molecular Orbitals

Combination between two s orbitals → resulting orbital is sigma

• Constructive: 𝜎_s

• Destructive: 𝜎*_s

Molecular Orbitals and Bond Order

Bond order = (# of e- on bonding orbitals - # of e- on antibonding orbitals)/2