Chapter 11
Covalent Bonding Theories
MO Theory
VSEPR
Before Einstein:
e-’s as discrete particles
(Lewis Dot Structures)
VB Theory
e-’s as waves
Orbitals as probabilities
(Quantum Mechanical
Model of Atoms)
All help with determining molecular shape.
Only MO theory can get at molecular energy.
Scientific models are approximations or simplifications of reality
VSEPR – predicts molecular shape by assuming that e- groups minimize repulsions,
and therefore occupy as much space as possible around a central atom
Does NOT explain: How molecular shapes arise from interactions of atomic orbitals
Knowledge of molecular shape – doesn’t help explain magnetic and spectral properties
of molecules (only an understanding of orbitals and
energy levels can do that)
More than 1 theory is needed to explain complex phenomena, such as covalent
bonding, and the resulting molecular shapes and behaviors:
• Valence bond (VB) theory – molecular shape due to interactions of atomic orbitals,
which results in new “hybrid” orbitals (sigma & pi bonding – two types of covalent bonds)
• Molecular orbital (MO) theory – deals with orbitals associate with the whole molecule
(molecular orbitals) to explain the energy and behavior of a molecule
Formation of Hybrid (VB theory) and Molecular Orbitals (MO theory)
Setting the stage for quantum weirdness: http://www.youtube.com/watch?v=VDmbdTtcoPM
Do electrons behave as particles or waves?
Electrons are matter – they take up space and have mass.
So far, we have been drawing e- dots (discrete units): This implies particles.
The Quantum Mechanical Model of Atoms: The behavior of e- is wave-like.
e- are hard to measure: Heisenberg Uncertainty Principle (position & velocity)
Atoms and molecules of the quantum mechanical model are hard to visualize.
Section 11.1: Valence Bond (VB) Theory
• Based on the quantum mechanical model of the atom (Chapter 7) – an atom has
certain allowed (discrete) quantities of energy due to the allowed frequencies of an
electron whose behavior is wavelike and whose exact location is impossible to know
• VB Theory – a covalent bond forms when orbitals of two atoms overlap and the
overlap region, which is between the nuclei, is occupied by a pair of electrons
VSEPR Theory
VB Theory
Section 11.1: Valence Bond (VB) Theory
• Central themes of VB Theory:
(1) The space formed by the overlapping orbitals has a maximum capacity of two e-’s
that must have opposite spins
(2) The greater the orbital overlap, the stronger (and more stable) the bond.
(Reason: Bond strength depends on attraction of the nuclei for the shared e-’s)
(3) When two atoms form a covalent bonds, there orbitals overlap to form a new hybrid
orbitals (which are not the original s-, p-, d- or f-orbitals, but some different shape)
Section 11.1: Valence Bond (VB) Theory
The extent of orbital overlap depends on the shapes and directions of the atomic orbitals
2 e-
s-orbitals are spherical  Orientation
during bonding does not matter
6 e-
In a bond involving p-, d-, and forbitals, the orbitals will be oriented
in a direction that maximizes overlap.
10 e-
F-orbitals: 7 orbitals, 2 e- in each
14 e-
(If oriented in a direction that does not
maximize overlap, the bond will be
weaker)
Section 11.1: Valence Bond (VB) Theory
Two points about formation of hybrid orbitals (called hybridization):
(1) # of hybrid orbitals formed = # of atomic orbitals mixed
(2) type of hybrid orbital formed depends on the types of atomic orbitals mixed
5 common types of hybridization: sp, sp2, sp3, sp3d, sp3d2
Section 11.1: Valence Bond (VB) Theory
sp hybridization = sp hybrid orbitals
(mix 1 s + 1 p orbital of the central atom = 2 hybrid orbitals)
Linear e- group arrangement
Example: BeCl2
Linear shape means that bonding orbitals must be oriented linearly.
Section 11.1: Valence Bond (VB) Theory
VB Theory says: Mixing two nonequivalent orbitals (one s and one p) around a central
atom results in two equivalent sp hybrid orbitals that lie 180º apart
Be hybridization: 1s2, 2s2, 2p6 - NO e-’s in the p-orbitals of Be before it bonds
The 2s2, 2p6 orbitals of Be form the hybrid orbital.
Section 11.1: Valence Bond (VB) Theory
sp hybrid orbital shape: one small and one large lobe
The 2s2, 2p6 orbitals of Be form the hybrid orbital.
Section 11.1: Valence Bond (VB) Theory
sp hybrid orbital orientation during bonding: e- density extended in bonding direction,
which minimizes repulsion between e- occupying other orbitals of the atom
Bonding orbitals – Be: 2s2-2p6 hybrid + 1 of the three 2 p orbitals of Cl
Cl: 1s2, 2s2, 2p6, 3s2, 3p5
Note: The 2s2 orbital of Be shares 1 e- with each Cl 3p5
Non-bonding 3p5 orbitals of Cl remain unchanged
Section 11.1: Valence Bond (VB) Theory
sp3 hybridization – sp3 hybrid orbitals
(mix 1 s + 3 p orbitals of the central atom = 4 hybrid orbitals)
tetrahedral e- group arrangement
CH4
NH3
H2O
Section 11.1: Valence Bond (VB) Theory
sp3d hybridization – sp3d hybrid orbitals
(mix 1 s + 3 p + 1 d orbitals of the central atom = 5 hybrid orbitals)
trigonal bipyramidal e- group arrangement
*For elements of Period (Row) 3 and higher: d-orbitals are included (can break octet rule)
Section 11.1: Valence Bond (VB) Theory
sp2 hybridization – sp2 hybrid orbitals
(mix 1 s + 2 p orbitals of the central atom = 3 hybrid orbitals)
trigonal planar e- group arrangement
Bonding orbitals – Be: 1s2, 2s2
Cl: 1s2, 2s2, 2p6, 3s2, 3p5
(Note: The 2s2 orbital of Be shares 1 e- with each Cl 3p5 – 1 of the three 2 p orbitals)
Section 11.1: Valence Bond (VB) Theory
sp3d2 hybridization – sp3d2 hybrid orbitals
(mix 1 s + 3 p + 2 d orbitals of the central atom = 6 hybrid orbitals)
octahedral e- group arrangement
Section 11.1: Valence Bond (VB) Theory
Summary
Section 11.1: Valence Bond (VB) Theory
When neither VB nor VSEPR theory apply
In hydrides: When Group 6A (and sometimes 5A) elements are the central atom.
H2S –
VSEPR: tetrahedral geometry (ideal = 109.5º)
VB theory: 4 sp3 hybrid orbitals formed
Reality: Bond angle is 92º.
p-orbitals are unhybridized.
Real factors influence molecular shape:
Bond length
Atomic size
Electron-electron repulsions
Long bonds between H and S result in less ecrowding and, therefore, less e- repulsion.
So, do not need hybrid orbitals to minimize
repulsion.
Section 11.1: Valence Bond (VB) Theory
In-class problems: 11.8, 11.10, 11.12
Optional Homework problems: 11.7, 11.9, 11.11, 11.19
Section 11.2: Modes of Orbital Overlap (σ and π bonds)
The σ bond – End-to-end overlap
All single bonds are σ bonds.
Highest e- density is along the bond axis.
Section 11.2: Modes of Orbital Overlap (σ and π bonds)
The π bond – Side-to-side overlap
All double bonds = 1 σ bond + 1 π bond
Two regions of e- density in a π – 1 above and 1 below the σ bond axis (holds 2 e-).
Significance? Explains how double (& triple) bonds form without e- repulsion.
Section 11.2: Modes of Orbital Overlap (σ and π bonds)
Triple bonds = 1 σ bond + 2 π bond
Section 11.2: Modes of Orbital Overlap (σ and π bonds)
Bond strength of single, double, and triple bonds
End-to-end overlap of σ bonds is more extensive than side-to-side π bond overlap.
σ bonds are stronger than π bonds.
Based on this, is this statement True or False:
Double bonds in ethylene are twice as strong as single bonds in ethane, and
triple bonds in acetylene are three times as strong as single bonds in ethane.
Other factors: lone pair repulsions, bond polarities, etc affect overlap and strength
Section 11.2: Modes of Orbital Overlap (σ and π bonds)
A final note on σ and π bonds – Rotation of one part of molecule around another
σ bonds allow free rotation, π bonds do not.
Significance? It is the reason that cis- and transforms of molecules exist distinctly, rather than as
resonance hybrids.
Section 11.2: Modes of Orbital Overlap (σ and π bonds)
Problems: 11.20, 11.21
Optional Homework Problem: 11.23
Section 11.3: Molecular Orbital (MO) Theory
Moving from e-’s localized around atoms to
e-’s delocalized around entire molecule
VB and MO theories both based on the quantum mechanical model of the atom.
VB Theory
MO Theory
Hard to visualize
Molecule = atoms bound together
through localized overlap of
valence orbitals
Molecule = a collection of nuclei with
e- orbitals delocalized over
entire molecule
Recall: Resonance forms of
molecules are hybrids or averages.
A molecule has different molecular orbitals with a given energy and shape
Different energy levels within a molecule
Microwave
X-rays
E-’s ejected
Can break chemical bonds
(i.e. DNA molecules = cancer)
e-’s in the molecule
excited into higher
energy orbitals
Molecules
rotate (i.e. H2O
molecule friction)
http://www.wag.caltech.edu/home/jang/genchem/infrared.htm
Photons in the IR region cause vibrations in the molecule.
Lowest energy,
most stable econfiguration
Formation of Molecular Orbitals
Two orbital types: Bonding orbitals and Antibonding orbitals
Setting the stage for quantum weirdness: http://www.youtube.com/watch?v=VDmbdTtcoPM
Do electrons behave as particles or waves?
Electrons are matter – they take up space and have mass.
So far, we have been drawing e- dots (discrete units): This implies particles.
The Quantum Mechanical Model of Atoms: The behavior of e- is wave-like.
e- are hard to measure: Heisenberg Uncertainty Principle (position & velocity)
Atoms and molecules of the quantum mechanical model are hard to visualize.
Formation of Molecular Orbitals
Two orbital types: Bonding orbitals and Antibonding orbitals
Combine (add or subtract) the atomic orbitals of nearby atoms to form MO’s.
When 2 H atoms are bonded,
their electrons can interact in 2 ways.
Wave interferences
Electrons as waves:
Bonding MO:
• Amplitudes add
• Region of high edensity between nuclei
Antibonding MO:
• Amplitudes subtract
• Region of zero edensity between nuclei
Energy of Molecular Orbitals
Two orbital types: Bonding orbitals and Antibonding orbitals
The bonding MO is lower in energy and the antibonding MO is higher in energy than
the original AO’s (atomic orbitals) that combined to form them.
Bonding MO: Why lower energy? e-s spread between two nuclei rather than one
 e- repulsions reduced
 e-’s shield the nuclei from each other
= more stable than separate atoms
Recall: Bond Energies from Chapter 9
Bonded H2
more stable
Non-bonded H’s
less stable
Energy of Molecular Orbitals
Two orbital types: Bonding orbitals and Antibonding orbitals
The bonding MO is lower in energy and the antibonding MO is higher in energy than
the original AO’s (atomic orbitals) that combined to form them.
Antibonding MO: Why higher energy? e-s outside internuclear region
 e- repulsions not reduced
 e-’s do not shield the nuclei from each other (inc nucleus-nucleus
repulsion)
= less stable than separate atoms
Shape of Molecular Orbitals
Two orbital types: Bonding orbitals and Antibonding orbitals
For H2 gas, bonding MO and antibonding MO are sigma (σ) MOs.
Cylindrical about an imaginary line that runs through the two nuclei.
Notation: bonding MO for H2: σ1s
antibonding MO for H2: σ1s*
Filling MOs with Electrons
Two orbital types: Bonding orbitals and Antibonding orbitals
Aufbau Principle (Chap8): Electrons fill
shells in order of Increasing energy
Formation of H2 for two H atoms
Magnesium (Mg)
Pauli Exclusion Principle (Chap8): MO fits two e- with opposite spin.
Hund’s Rule (Chap8): Orbitals of equal energy half filled, with spins parallel, before
any of them is completely filled
Bond Order and MO Theory: You can predict - Will a molecule form? Will it react?
In Lewis dot structure-land: Bond order = # e- pairs per linkage between atoms
In MO theory-land: Bond order = ½ (# e- in bonding MO – # e- in antibonding MO)
Bond order > 0: The molecular species is stable relative to separate atoms.
(*The higher the BO, the stronger the bond.)
Bond order = 0: No net stability (not likely that the molecule will form)
Does the H2 form? Does the He2 form?
Homonuclear Diatomic Molecules
Molecules made of two atoms of the same element.
Period 1: H2 (not He2)
Period 2: N2, O2, others
Which molecules form?
Period 2, s-block elements: 1s2, 2s2 – only valence orbital interact enough
to form molecular orbitals
Be2?
Energy
Li2?
AO
MO
AO
Homonuclear Diatomic Molecules
Period 2, p-block elements: 1s2, 2s2 2p6 – only valence orbital interact enough
to form molecular orbitals
Things get more complicated……p-orbitals overlap in two ways:
(1) end-to-end: σ2p, σ2p*
(2) side-to-side: π2p, π2p*
Homonuclear Diatomic Molecules
Period 2, p-block elements: 1s2, 2s2 2p6 – only valence orbital interact enough
to form molecular orbitals
Similar to s-orbitals:
Bonding MO:
e- density b/w nuclei
Antibonding MO:
e- density outside nuclei
Homonuclear Diatomic Molecules
Period 2, p-block elements: 1s2, 2s2 2p6 –valence orbital form molecular orbitals
End-to-end overlap – σ MOs: more stable.
Side-to-side overlap – π MOs: less stable
Homonuclear Diatomic Molecules
Period 2, p-block elements: 1s2, 2s2 2p6 - The difference b/w O,F,Ne and B,C,N
O,F,Ne – small atoms
• Strong repulsions b/w
p-orbitals  Energy
of p-orbitals increase
• ∆Energy b/w p- and s-orbitals large
= no mixing of orbital types
B,C,N – larger atoms (= more space)
• Repulsions b/w p-orbitals not so
strong
• ∆Energy b/w p- and s-orbitals small
• Mixing occurs
Period 2, p-block elements: 1s2, 2s2 2p6 - The difference b/w O,F,Ne and B,C,N
Result of mixing:
σ2s energy lowered
σ2p energy raised
Bonds and Molecular Properties
Paramagnetic ≠ Magnetic
Attracted by the magnetic field
but does not remain magnetic
once it leaves the field.
VSEPR vs MO
Note: VSEPR predicts the O2
has no unpaired electrons. MO
theory says it does.
Observation: Liquid O2 sticks
to a magnet
http://www.youtube.com/watch?v=yJs5ENtilIo
Heteornuclear Diatomic Molecules
Molecules made of two atoms of different elements.
MOs are assymetrical due to unequal energies of the AOs of different atoms.
Example 1: HF
Why is AO of F lower than AO of H?
H 1s interacts only with F’s 2p (not 2s)
And only 1 of the 3 2p orbitals interacts.
Result: 1σ and 1σ*
Other p’s unchanged – nonbonding MOs
O2
F2
Ne2
B2
C2
N2
CH4 versus CH2
CO2 versus CO4