Valence bond theory: sticks
no more
Electrons are not simply dots
And bonds are not sticks
Learning objectives
 Describe principles of valence bond theory
 Predict hybridization of orbitals based on
Lewis dot structures and electronic
geometry
 Describe difference between sigma and pi
bonding
Taking it to the next level:
acknowledging orbitals
 VSEPR is quite successful in predicting
molecular shapes based on simplistic Lewis
dot approach and repulsion of charge
groups
 But orbital model has electrons occupying
atomic orbitals
 How do we reconcile the observed shapes
of molecules with the atomic orbital model?
Valence bond theory
 Valence bond theory is the simplest approach to an orbital
picture of covalent bonds
 Valence electrons occupy atomic orbitals (basic s, p, d, f or
hybridized versions of them)
 Covalent bond is formed by overlap of atomic orbitals
containing one electron from each atom
 Bonding orbitals contain two electrons paired
 Bonding electrons are localized between two atoms
 Lone pairs occupy single atomic orbitals, spins paired
 Bond strength is proportional to amount of orbital overlap
 Shape of molecule determined by geometry of overlapping
atomic orbitals
Overlap of two 1s orbitals in H2
 This is a visual representation of a
mathematical operation involving the wave
functions of each orbital
 Overlap of two 2p orbitals directed along the bond
axis (sigma bond)
 Overlap of p and s orbitals
Limits on qualitative approach
 Valence bond theory is a mathematical
model that yields bond lengths, bond
energies, and bond angles using the wave
functions of the bonding atoms
 Qualitative approach shows the overlap of
atomic orbitals and approximate geometry of
bonds that result
Problems with tetrahedral bonds
 In CH4 the bonds are
all equivalent and at
angles of 109.5°
 The 2p orbitals in C
are at 90° - far from
optimum for overlap
 The ground state
configuration is 2s22p2
 Reconcile these facts
with known structure
Hybridization: problem resolved
 The wave mechanics permits
mixing atomic orbitals to
produce “hybrid” orbitals
 Hybridization alters shape and
energy of original ao’s
 In case of C, two 2s and two 2p
are mixed to produce four
homogeneous sp3 hybrid orbitals
sp3 hybridization
 Formally, one 2s electron
is promoted to empty 2p
orbital (energy cost, repaid
on bond formation)
 The four basis orbitals are
then “hybridized” to yield
set of four sp3 hybrid
orbitals
 This is qualitative
explanation of a
mathematical operation in
wave mechanics
Tetrahedral directions and sp3
hybrids
 sp3 hybridization
produces four wave
functions that have
greater density along
the tetrahedral bonding
directions
 Improves overlap with
atomic orbitals on
bonded atoms
Valence bond picture of CH4
 Each C sp3 hybrid contains one electron
 Each H 1s contains one electron
Lone pairs occupy sp3 hybrid orbitals
 Valence bond picture of the tetrahedral electronic
geometry provides same results for molecules with
lone pairs
 Lone pairs occupy same sp3 hybrid orbitals as
bonding pairs
Do molecules with four charge
groups always use sp3 hybrids?
 H – S – H bond angle
is 92º
 Better result with S – H
bonds using 2p orbitals
rather than sp3 hybrids
(angle is 109.5º)
 Bonding orbitals more
“p-like”
 Lone pair electrons
more “s-like”
Notes on hybridization
 The total number of orbitals is unchanged before
and after
 Four ao’s (s + 3 x p) give four hybrid orbitals (4 x sp3)
 Three ao’s (s + 2 x p) give three sp2 hybrids
 Two ao’s (s + p) give two sp hybrids
 Electron capacity remains unchanged
 Unique hybridization scheme for each electronic
geometry (five total)
 Same hybridization scheme for given electronic
geometry
 Number of ao’s in hybridization scheme = number
of charge groups round central atom
sp hybridization for linear geometry
 One s and one p orbital
sp2 hybridization for trigonal planar
 One s and two p
orbitals
Sigma and pi bonding
 Sigma bonds (along
internuclear axes)
describe electronic
geometry
 “Surplus” p orbitals
overlap in parallel
arrangement above
and below internuclear
axis (pi bonds)
Comparison of pi and sigma bonding
 Pi bond
 Orbital overlap above
and below inter-nuclear
axis
 Sigma bond
 Orbital overlap along
inter-nuclear axis
 Sigma bond slightly
stronger than pi bond
Valence bond picture of ethylene
H2C=CH2
 Three sigma bonds
between C and 2 x H + C
 Six electrons around C
 Pi bond between C and C
 Two electrons around C
 Two + six = eight (full
octet)
 Contrast with Lewis model:
 Lewis: 4 dots shared
 Valence bond: sigma + pi
bonds
Valence bond picture of acetylene
HC≡CH
 Sigma bonds between C
and H (purple and blue)
and C and C (purple)
 4 electrons around C
 Two pi bonds between C
and C (red)
 4 electrons around C
 Four + four = eight
(complete octet)
Multiple bonds and implications for
structure
 Single bond allows rotation about C – C axis
 Double bond is rigid
Double bonds and geometrical
isomers
 Isomers: same atoms,
different forms
 CH2ClCH2Cl has just
one form
 CHClCHCl has two
isomers
Expanded octets:
Beyond coordination number 4
 Invoke empty d orbitals
(impossible for second row
elements)
 One d orbital for trigonal
bipyramidal sp3d
 Two d orbitals for octahedral
sp3d2
 Number of orbitals in
hybrid always equals
number of charge clouds
Trigonal bipyramid –sp3d
Octahedral –sp3d2
Shortcomings of valence bond
 The orbitals are restricted to atoms
 Bonds are limited to two atoms
 Cannot accommodate the concept of
delocalized electrons – bonds covering
more than two atoms
 Problems with magnetic and spectroscopic
properties
 Enter the LCAO: Linear Combination of
Atomic Orbitals (MO theory)