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10. Chemical Bonding II: Molecular Geometryand Hybridization of Atomic Orbitals
molecular shape
most molecules are 3-D objects
bond lengths and bond angles
Lewis structures convey no 3-D information
Valence Shell Electron Pair Repulsion model: VSEPR (“vesper”)
electron pairs repel each other =⇒ electron pairs tend to remain
as far apart as possible
lone pair – lone pair À lone pair – bond pair > bond pair – bond
pair
electrons are anchored to central atom, lie on a sphere: valence
shell
two pairs −−→ W 180◦−−→ linear
three pairs −−→ W 120◦−−→ trigonal planar
four pairs −−→ W 109.5◦−−→ tetrahedral
GChem I 10.1
electron-pair geometry
does not have to be equal to
molecular geometry
molecular geometry = geometry of the atomic nuclei bound to
the central atom: bond pairs
VSEPR notation: A = central atom, B = atom bonded to central
atom, E = lone pair on the central atom
Exercise: Determine the shape of PF5
procedure: (1) obtain Lewis structure; (2) write down VSEPR
notation; (3) determine electron-pair geometry; (4) determine
molecular geometry
(1) we have obtained the Lewis structure of PF5 previously
P....................................................
....................................................
....................................................
........................
........................
....
....................................................F····
··F ······
F ······
F ······F······
– Typeset by FoilTEX – 2
(2) VSEPR notation: AB5
GChem I 10.2
(3) electron-pair geometry: trigonal bipyramidal
(4) no lone pairs ⇒molecular geometry ≡ electron-pair geome-
try: trigonal bipyramidal
Exercise: Determine the shape of SF4
(1) Lewis structure
A = 1×6+4×7 = 34
N = 5×8 = 40
S = N − A = 40−34 = 6 =⇒ 3 bonds =⇒ S ↗ 8
S....................................................
....................................................
........................
........................
....
....................................................
··F······
F ······
F ······
F······
– Typeset by FoilTEX – 1
S has expanded valence
(2) VSEPR notation: AB4E
(3) electron-pair geometry: trigonal bipyramidal
(4) lone pair ⇒ molecular geometry 6≡ electron-pair geometry
molecular geometry: seesaw (sawhorse, distorted tetrahe-
dron)
GChem I 10.3
Exercise: Determine the shape of NF3
(1) Lewis structure
A = 1×5+3×7 = 26
N = 4×8 = 32
S = N − A = 32−26 = 6 =⇒ 3 bonds
N....................................................
....................................................
........
........
........
........
........
........
....
··
F ···· ··
F ······
F······
– Typeset by FoilTEX – 1
(2) VSEPR notation: AB3E
(3) electron-pair geometry: tetrahedral
(4) lone pair ⇒ molecular geometry 6≡ electron-pair geometry
molecular geometry: trigonal pyramidal
Exercise: Determine the shape of carbon suboxide C3O2
(1) Lewis structure
A = 2×6+3×4 = 24
GChem I 10.4
N = 5×8 = 40
S = N − A = 40−24 = 16 =⇒ 8 bonds
O ........................................................................................................··
··C ....................................................
.................................................... C ........................................................................................................ C ....................................................
.................................................... O····
– Typeset by FoilTEX – 1
(2) VSEPR notation for each carbon atom: AB2
(3) electron-pair geometry: linear
(4) no lone pairs ⇒molecular geometry ≡ electron-pair geome-
try
molecular geometry: linear
Exercise: Determine the shape of ozone O3
(1) Lewis structure
A = 3×6 = 18
N = 3×8 = 24
S = N − A = 24−18 = 6 =⇒ 3 bonds
O ........................................................................................................··
··O ....................................................··
O ······
O ....................................................·· ····
O ........................................................................................................
··O····
– Typeset by FoilTEX – 1
↔
O ........................................................................................................··
··O ....................................................··
O ······
O ....................................................·· ····
O ........................................................................................................
··O····
– Typeset by FoilTEX – 1
(2) VSEPR notation for the central oxygen atom: AB2E
GChem I 10.5
(3) electron-pair geometry: trigonal planar
(4) lone pair ⇒ molecular geometry 6≡ electron-pair geometry
molecular geometry: bent (angular)
expected bond angle: 120◦; experimental value: 117◦
polar molecules
polar covalent bond
example:
δ+H
δ−Cl
+−−−→d
measure of the charge separation (or polarity) is the dipole mo-
ment
µ=δ ·d
unit of dipole moment [µ] = Cm
too large, use the unit debye (D) for molecules
1 D = 3.34×10−30 Cm
experiments show that CO2 is nonpolar; however the molecule
has polar covalent bonds since the electronegativity of C is 2.5and that of O is 3.5
GChem I 10.6
why is carbon dioxide nonpolar??
consider the shape of the molecule
the Lewis structure is the same as that of CS2 (Set 9)
O····
C ............................................................................................................................................................
.................................................... O····
– Typeset by FoilTEX – 1
VSEPR notation: AB2 =⇒ molecular geometry = linear
O····
C ............................................................................................................................................................
.................................................... O····
– Typeset by FoilTEX – 1
δ− 2δ+ δ−
+� -
µ=0
dipole moment of a molecule depends on the shape of the mol-
ecule
water molecule: O: EN = 3.5, H: EN =2.1
polar bonds exist in H2O
shape of H2O
(1) Lewis structure
A = 2×1+1×6 = 8
N = 2×2+1×8 = 12
S = N − A = 12−8 = 4 =⇒ 2 bonds
GChem I 10.7
H .................................................... O ....................................................····
H
– Typeset by FoilTEX – 1
(2) VSEPR notation: AB2E2
(3) electron-pair geometry: tetrahedral
(4) lone pairs ⇒ molecular geometry 6≡ electron-pair geometry
molecular geometry: bent (angular)
bond angle: 104◦
H .................................................... O ....................................................····
H
O
HH
– Typeset by FoilTEX – 1
2δ−
δ+δ+ +@@@I
+���� 6
µ6=0
net dipole moment µ= 1.94 D
molecules of the type ABn are NOT polar if all terminal atoms B
are the same.
Examples:
CH4 AB4 nonpolar
CH3Cl AB4 polar
GChem I 10.8
different theories of the chemical bond
Lewis: simple; relies on electron pairs =⇒ problems: O2, odd-
electron species, resonance
VSEPR: predicts molecular shape; relies on electron pairs
Quantum Mechanics
valence-bond theory: covalent bond = overlap of atomic or-
bitals
H2
H2S
provides information on bond energies: 1s-1s overlap is stronger
than 1s-3p overlap
C [He]
2s 2p
=⇒ simplest hydrocarbon CH2 with bond angle of 90◦
! CH2 does not exist!
simplest hydrocarbon: methane CH4
???
excited-state
GChem I 10.9
C [He]
2s 2p
promotion: 2s → 2p
problem: 2s nondirectional, 2p at right angles
Lewis structure of methane
C H
H
H
H
....................................................
....................................................
....................................................
........
........
........
........
........
........
....
– Typeset by FoilTEX – 1
VSEPR: AB4 =⇒ tetrahedral (electron-pair and molecular geom-
etry) =⇒ bond angle 109.5◦ 6= 90◦
???
we cannot solve the Schrödinger equation to obtain an exact,
analytical expression for the molecular wave function ψ
atomic orbitals −→ approximation of ψ for multielectron atoms
this approximation does not work well for molecules; find a bet-
ter approximation:
hybridization
GChem I 10.10
2s +3×2p = 4sp3 hybrid orbitals
ammonia NH3
Lewis
N H
H
H ....................................................
....................................................
....................................................··
– Typeset by FoilTEX – 1
VSEPR: AB3E =⇒ electron-pair geometry: tetrahedral (molecular
geometry: trigonal pyramidal) =⇒ hybrid: sp3
2p2s
⟩−→ sp3
N
H
H
H
GChem I 10.11
water H2O
Lewis
H .................................................... O ....................................................····
H
– Typeset by FoilTEX – 1
VSEPR: AB2E2 =⇒ electron-pair geometry: tetrahedral (molecu-
lar geometry: bent) =⇒ hybrid: sp3
2p2s
⟩−→ sp3
O
H
H
BF3 AB3
electron-pair geometry: trigonal planar
3 sp2 hybrid orbital + 1 p orbital
BeCl2 AB2
electron-pair geometry: linear
GChem I 10.12
2 sp hybrid orbital + 2 p orbital
ethene (ethylene) C2H4
Lewis
C
H
H
C
H
H
C
H
H
....................................................
........
........
........
........
........
........
....
....................................................
.................................................... C
H
H
....................................................
........
........
........
........
........
........
....
– Typeset by FoilTEX – 1
each C: AB3
electron-pair geometry: trigonal planar
=⇒ hybrid: sp2 + 1 p
σ-bond: overlap on the internuclear axis
for ethene: 1s − (1)sp2 and (1)sp2 − (1)sp2
π-bond: overlap off the internuclear axis
weaker than a σ-bond
for ethene: p −p
double bond = σ-bond + π-bond
GChem I 10.13
stronger than a single bond (σ-bond), but not twice as strong
shape of a molecule: determined by σ-bond framework
rotation about a double bond is severely restricted
ethyne (acetylene) C2H2
Lewis
CH .................................................... ............................................................................................................................................................ C H....................................................
– Typeset by FoilTEX – 1
each C: AB2
electron-pair geometry: linear
=⇒ hybrid: sp + 2 p
triple bond: 1 σ-bond + 2 π-bonds
still no explanation why O2 is paramagnetic
fourth description of chemical bond:
molecular-orbital theory (MO)
use wave functions or orbitals that belong to the entire molecule
H2molecule: 1s + 1s↗ σ∗
1s antibonding
↘ σ1s bonding
GChem I 10.14
a bonding molecular orbital has lower energy than the atomic
orbitals from which it was formed
lower energy =⇒ greater stability
bonding orbital: electron density greatest between the two nu-
clei
formation of bonding orbital: constructive interference
an antibonding molecular orbital has higher energy than the
atomic orbitals from which it was formed
higher energy =⇒ lower stability
antibonding orbital: electron density goes to zero between the
two nuclei
formation of bonding orbital: destructive interference
sigma molecular orbital: electron density is concentrated on the
internuclear axis, cylindrical symmetry
Molecular Electron Configuration (molecular-orbital diagram)
1. The number of molecular orbitals formed = number of atomic
orbitals combined
2. The more stable the bonding orbital, the less stable the cor-
responding antibonding orbital
GChem I 10.15
3. Aufbau principle (filling of MOs proceeds from low to high en-
ergies)
4. Pauli exclusion principle (at most two electrons per MO, op-
posite spins)
5. Hund’s rule (when MOs of identical energy are available,
electrons occupy those orbitals singly if possible and have
the same spin orientation)
6. Number of electrons in MOs = total number of electrons on
the bonding atoms
bond order = 12 (# of electrons in bonding MOs − # of electrons
in antibonding MOs)
a molecule is stable if the bond order is greater than zero
First and Second Period Homonuclear Diatomic Molecules
hydrogen molecule H2
atomic hydrogen H 1s1 =⇒ H2 two electrons
molecular electron configuration of H2: (σ1s)2
bond order = 12(2−0) = 1
helium molecule He2
He 1s2 =⇒ He2 four electrons
GChem I 10.16
molecular electron configuration of He2: (σ1s)2(σ∗1s)2
bond order = 12(2−2) = 0
the helium dimer does not exist
lithium dimer Li2
Li 1s22s1 =⇒ Li2 six electrons
molecular electron configuration of Li2: (σ1s)2(σ∗1s)2(σ2s)2
bond order = 12(2+2−2) = 1
stable diamagnetic molecule; found in vapor phase
beryllium dimer Be2
Be 1s22s2 =⇒ Be2 eight electrons
molecular electron configuration of Be2: (σ1s)2(σ∗1s)2(σ2s)2(σ∗
2s)2
bond order = 12(2+2−2−2) = 0
beryllium dimer is unstable
boron dimer B2
B 1s22s22p1 =⇒ B2 ten electrons
p-orbitals come into play
GChem I 10.17
σ2p ,σ∗2p 1×
π2p ,π∗2p 2×
molecular-orbital energy level diagram
molecular electron configuration of B2: (σ1s)2(σ∗1s)2(σ2s)2(σ∗
2s)2(π2p)2
(σ1s)2(σ∗1s)2(σ2s)2(σ∗
2s)2(π2py)1(π2pz
)1
bond order = 12(2+2+2−2−2) = 1
stable paramagnetic molecule
molecular-orbital diagrams for 2nd period homonuclear diatomic
molecules
oxygen molecule
O2: (σ1s)2(σ∗1s)2(σ2s)2(σ∗
2s)2(σ2px)2(π2py
)2(π2pz)2(π∗
2py)1(π∗
2pz)1
bond order = 12(2+2+2+2+2−2−2−2) = 2
stable paramagnetic molecule
molecular orbital theory explains the magnetic properties of
the oxygen molecule and other diatomic molecules and ions
GChem I 10.18