# sp 2 ```Molecular geometry (VSEPR)
The number of groups of electrons around
an atom determines the shape.
Each lone pair, single, double, or triple bond
counts as a group.
# groups
2
3
4
5
hybridization
sp
sp2
sp3
dsp3
Geometry of
the groups
Linear
Trigonal
planar
Tetrahedral Trigonal
bipyramid
Example 1
• CH4
• Four bonds =
H
H
C
Four groups
• Tetrahedral
H
H
Example 2
Two
lone pairs
O
Four groups of electrons.
H
H
Tetrahedral geometry for
groups.
Bent Molecule
Two
bonds
H
104o
O
H
Nature of Chemical Bonds
So far, we have the octet rule which tells us
how many bonds we can make. But how
do we understand the nature of the
bonds?
Three models for bonding: ionic, valence
bond, molecular orbitals.
Ionic Bonding
Requires very different electronegativities to
make the complete transfer of electrons worthwhile.
Not discussed further although it occurs in salts
of organic acids. For example sodium acetate.
Quantum or Wave Mechanics
• Albert Einstein: E = hn (energy is quantized)
– light has particle properties.
• Erwin Schr&ouml;dinger: wave equation
– wave function, : A solution to a set of equations that
depicts the energy of an electron in an atom.
– each wave function is associated with a unique set of
quantum numbers.
– each wave function represents a region of threedimensional space and is called an orbital.
–  2 is the probability of finding an electron at a given
point in space.
Quantum or Wave Mechanics
• Characteristics of a wave associated with
a moving particle. Wavelength is
designated by the symbol l .
Quantum or Wave Mechanics
• When we describe orbital interactions, we are referring
to interactions of waves. Waves interact
– constructively or
– destructively.
• When two waves overlap, if they are of the same sign
then they combine constructively, build-up. Opposite
sign overlap combines destructively, meaning they
cancel.
Shapes of Atomic s and p Orbitals
– All s orbitals have the
shape of a sphere with
the center of the
sphere at the nucleus.
– Figure 1.8 (a)
Calculated and (b)
cartoon
representations
showing an arbitrary
boundary surface
of the electron density.
Shapes of Atomic s and p Orbitals
– Three-dimensional representations of the 2px, 2py,
and 2pz atomic orbitals. Nodal planes are shaded.
Shapes of Atomic s and p
Orbitals
2px, 2py, and 2pz atomic orbitals.
Molecular Orbital Theory
• MO theory begins with the hypothesis that
– electrons in atoms exist in atomic orbitals
and
– electrons in molecules exist in molecular
orbitals.
Molecular Orbital Theory
• Rules:
– Combination of n atomic orbitals (mathematically
adding and subtracting wave functions) gives n MOs
(new wave functions).
– MOs are arranged in order of increasing energy.
– MO filling is governed by the same rules as for atomic
orbitals:
• Aufbau principle: fill beginning with lowest
energy orbital
• Pauli exclusion principle: no more than 2e- in a
MO
• Hund’s rule: when two or more MOs of
equivalent energy (degenerate) are available,
add 1e- to each before filling any one of them
with 2e-.
Molecular Orbital Theory
• MOs derived from combination by (a) addition and (b)
subtraction of two 1s atomic orbitals.
Covalent Bonding
• Bonding molecular orbital: A MO in which
electrons have a lower energy than they
would have in isolated atomic orbitals.
• Sigma (s) bonding molecular orbital: A MO
in which electron density is concentrated
between two nuclei along the axis joining
them and is cylindrically symmetrical.
Covalent Bonding
• A MO energy diagram for H2. (a) Ground
state and (b) lowest excited state.
Covalent Bonding
• Antibonding MO: A MO in which electrons
have a higher energy than they would in
isolated atomic orbitals.
VB: sp3 Hybridization of Atomic Orbitals
Energy
– The number of hybrid orbitals formed is equal to the
number of atomic orbitals combined.
– Elements of the 2nd period form three types of hybrid
orbitals, designated sp3, sp2, and sp.
– The mathematical combination of one 2s atomic
orbital and three 2p atomic orbitals forms four
equivalent sp3 hybrid orbitals.
2p
sp3
2s
sp 3 Hybridization, with electron population for
carbon to form four single bonds
VB: sp3 Hybridization of Atomic Orbitals
• sp3 Hybrid orbitals. (a) Computed and (b) cartoon threedimensional representations. (c) Four balloons of similar
size and shape tied together, will assume a tetrahedral
geometry.
VB: sp2 Hybridization of Atomic Orbitals
Energy
• The mathematical combination of one 2s atomic orbital
wave function and two 2p atomic orbital wave functions
forms three equivalent sp2 hybrid orbitals.
2p
2p
sp2
2s
sp 2 Hybridization, with electron
population for carbon to form double
bonds
VB: sp2 Hybridization of Atomic Orbitals
• Hybrid orbitals and a single 2p orbital on an sp2
hybridized atom.
VB: sp Hybridization of Atomic Orbitals
Energy
• The mathematical combination of the 2s atomic orbital
and one 2p atomic orbital gives two equivalent sp hybrid
orbitals.
2p
2p
sp
2s
sp Hybridization, with electron
population for carbon to form
triple bonds
VB: sp Hybridization of Atomic Orbitals
• sp Hybrid orbitals and two 2p orbitals on an sp
hybridized atom.
Combining VB &amp; MO Theories
• VB theory views bonding as arising from electron pairs
localized between adjacent atoms. These pairs create
bonds.
• Further, organic chemists commonly use atomic orbitals
involved in three hybridization states of atoms (sp3, sp2,
and 2p) to create orbitals to match the experimentally
observed geometries.
• How do we make orbitals that contain electrons that
reside between adjacent atoms? For this, we turn back
to MO theory.
Combining VB &amp; MO Theories
• To create orbitals that are localized between adjacent
atoms, we add and subtract the atomic and hybrid
orbitals on the adjacent atoms, which are aligned to
overlap with each other.
• Consider methane, CH4. The sp3 hybrid orbitals of
carbon each point to a 1s orbital of hydrogen and,
therefore, we add and subtract these atomic orbitals
to create molecular orbitals.
• As with H2, one resulting MO is lower in energy than the
separated atomic orbitals, and is called a bonding s
orbital. The other is higher in energy and is antibonding.
Combining VB &amp; MO Theories
• Molecular orbital mixing diagram for creation of a C-C s
bond.
Combining VB &amp; MO Theories
• A double bond uses sp2 hybridization.
• Consider ethylene, C2H4. Carbon (and other secondperiod elements) use a combination of sp2 hybrid orbitals
and the unhybridized 2p orbital to form double bonds.
• Now the atomic and hybrid orbitals before mixing into
MOs.
Combining VB &amp; MO Theories
• MO mixing diagram for the creation of C-C p bond.
Present in double and triple bonds.
Combining VB &amp; MO Theories
• A carbon-carbon triple
bond consists of one s
bond formed by overlap of
sp hybrid orbitals and two
p bonds formed by the
overlap of parallel 2p
atomic orbitals.
Kinds of Hybridization
spn hybridization obtained by mixing the 2s
atomic orbital with n different 2p atomic
orbitals to yield (n+1) hybrids.
sp
geometry
VSEPR
groups
linear
2
Orbitals
Where
found
C
#
Pi bonds
2
C
sp2
trigonal
planar
3
sp3
tetrahedral
4
1
C
C
0
Hybrids are in black, colored orbitals are p orbitals not used in hybridization.
Example of how hybridization
determines geometry
Assign hybridization
CH2=C=CH2
sp2
Match up p
orbitals for pi
bonds
sp2
sp
H
H
C
C
C
H
H
Alkanes
Acyclic: CnH2n+2
Cyclic (one ring): CnH2n
Bicyclic (two rings) : CnH2n-2
Only single bonds, sp3 hybridization, close to
tetrahedral bond angles
Physical properties
• Boiling points
– Lower than other organic molecules of same
size.
– Lower attractive forces between molecules
than in alcohols.
methane
-164 oC
water
100 oC
hexane
68.7 oC
1-pentanol 137 oC
Intermolecular Forces
• Ionic Forces
• Hydrogen
Bonding
Dispersion
Forces:
due to fluctuating motionStrength
of the electrons
in a molecule. Motion in one molecule is correlated with that in
• other
Dipole
Dipole Forces
the
molecule.
• Dispersion Forces
Dispersion Forces and Molecular
Structure
Branching decreases surface area, reduces dispersion forces and, thus,
boiling point.
Molecular Structure and Heat of
Combustion
Difference in heats of
combustion indicates a
greater stability of branched
structures.
18.8 kJ
-5470.6
-5451.8
8CO2 + 9H2O
Isomerism and Naming
• Hexane
CH3CH2CH2CH2CH2CH3
2-methylpentane
CH3
CH3CH2CH2CHCH3
CycloAlkanes
Cl
1-chloro-3-methylcyclohexane
1,2-diisopropylcyclobutane
1-methyl-2-propylcyclopropane
Bicycloalkanes
Parent name: name of alkane with same number of carbons.
Number from bridgehead along largest bridge. If substituent choose
bridgehead to assign low number to substituent.
Size of bridges indicated by number of carbons in bridge.
Examples of numbering
1
Cl
2
5
6-chlorobicyclo[3.1.1]heptane
7
2,7-dimethylbicyclo[4.2.2]decane
Conformations
• Rotations about single bonds produce
different conformations.
60
Staggered Conformation.
Eclipsed Conformation.
Newman Projections
Staggered Conformation.
More stable!
Eclipsed Conformation.
Less stable.
Rotational Profile of ethane
CH3
CH3CH2CH2CHCH3
```