Post on 09-Dec-2021
1
Section 2 (Chapter 3, M&T)
Chemical Bonding
Bonding Models
� We will look at three models of bonding:
� Lewis model
� Valence Bond model
� MO theory
Bonding Models (Lewis)
� Lewis model of bonding is simple: electrons are paired (where possible)
� Radical species have electrons left over after pairing
� In forming Lewis structures, atom symbols are drawn with their valence electrons (dots) and unpaired electrons are paired with those of other atoms to form covalent bonds
� Electrons are added as lone pairs and bonds around atoms to give each atom an octet. In certain cases, some atoms can have more than an octet of electrons, some less.
Bonding Models (Lewis)
� The Lewis model is useful for:
� Showing connectivity between atoms
� Showing lone pairs
� A starting point for valence bond
models and VSEPR theory
Lewis structures are not used to convey anything about the shape of a molecule/ion
Lewis Structures – Multiple Bonds
� In some cases (e.g. CO2, C2H2), multiple bonds
must exist in order to create an octet
� In some cases where multiple bonds exist, there
may be more than one possible structure. For
example, in carbonate ion, CO32-
� Structures which differ only in the placement of
electrons (position of atoms doesn’t change) are
called resonance structures. Resonance structures
increase the stability of an arrangement of atoms
Resonance Structures
� Each resonance structure contributes to the overall
bonding picture in a molecule or ion; none
individually is correct
� Bond lengths in CO32- are all found to be 129 pm.
C-O bond is ~ 143 pm and C=O ~ 116 pm
COO
O
COO
O
COO
O
2-2-2-
*correct Lewis structure also shows lone pairs
2
Formal Charge
• Formal charge is a comparison of the number
of electrons around an atom in a Lewis
structure with what you’d find for an isolated
atom of that element
• Formal charges can be used to assess different
resonance structures (to see which is most
favorable) and to provide a guess at a site’s
electron richness/poorness
Formal Charge = (group # of atom) - (# of electrons around atom in structure)
Formal charges are not actual charges, just a method of book keeping
Formal Charge
• In counting electrons, lone pairs count as two
electrons and bonds as one (only one of the
electrons in each bond is assumed to reside “on”
the atom)
• Consider the NCS- ion; which is most correct?
• Most “correct” structure has:
a. lowest formal charges and
b. most negative formal charge on most
electronegative element
N C S N C S N C S
- --
*again, correct Lewis structures also show lone pairs
Expanded Shells
� Many common organic compounds obey the
octet rule; however, many inorganic ones
incorporating heavier elements* (e.g. 3rd period)
may possess more than eight electrons (an
“expanded octet”)
� Examples include SF6, PCl5, PCl3
P
Cl
Cl
ClCl
ClBr
Cl
Cl
Cl S
F
FF F
F F..
. .
10e- 10e- 12e-
*possibly due to the availability of low lying, empty d-orbitals in these elements
Rem: correct Lewis
structures will also
show non-bonding
electrons
The Lewis structure that seems to agree best with experimental findings
is the one that has expanded octets and lowest formal charges
Less than an octet…� For group II and group III elements such as
Be (in BeF2) and B (in BF3), it is not possible
to obtain an octet without creating
unreasonable formal charges
� For these cases, experimental evidence seems
to indicate several possibilities are important
B
F
FF
••
••
••
••
•••• ••••
••
B
F
FF
-
••••
••••
••
••
+
••
••
••
••••
B
F
FF
••
••
•••• ••
•••• -
+
••
••
VSEPR Theory
� Valence Shell Electron-Pair Repulsion theory is
used to predict the shape of molecules based on
electron-pair repulsions
� Pairs of electrons include bonding pairs and
non-bonding pairs (lone pairs)
� Heirarchy of repulsions
� Lone pair-lone pair
� Lone pair-bonding pair
� Bonding pair-bonding pair
3
VSEPR Theory� The repulsions
that exist between electron pairs on the central atom dictates the arrangement of the other atoms
� The number of pairs of electrons around the central atom are sometimes called electron domains/stericnumber
� Each of the following count as one electron domain:� Single bond
� Double bond
� Triple bond
� Lone pair
Effect of Lone Pairs
Increasing the numbers of lone pairs
around the central atom increases the
degree of repulsion experienced by the
bonding pairs
The net effect is a closing of the H-X-H
bond angle
This effect is seen in other geometries also
Notice that while these molecules have differentmolecular geometries, they all have the same
electron domain geometries (tetrahedral)
tetrahedral
MolecularGeometry
trigonalpyramid
bent
A B
bonding pairnon-bondingpair
5-Coordinate (Trigonal bipyramid)
� The trigonal bipyramidal
geometry involves two kinds of
environments (axial and
equatorial)
� Introducing a lone pair into this
geometry creates two possibilities
� Heirarchy of repulsions (angle):
90o>>120o>180o
strongrepulsion
weakrepulsion
ClF3 Geometry
Two lone pairs on a trigonal bipyramidal EDG
6 total 90o
repulsions in each
1x lp-lp3 x lp-bp2 x bp-bp
4 x lp-bp2 x bp-bp
the difference
strongest repulsionleast favorable angle
Effect of Multiple Bonds
� Multiple bonds confine a
greater amount of electron
density between two atoms
than do single bonds. Their
effect on geometries is similar
to lone pairs (though not as
strong)
•Multiple bonds
•Larger groups
Electronegativity and Size Effects
� Observed bond angles in molecules are
influenced by both the size and
electronegativity of atoms
� The influence of size and electronegativity
depends on the position of the atom in the
molecule (central or peripheral)
4
Periodic Electronegativity Trends
Electronegativity trend
Increases L ���� R
Decreases top ���� bottom
These electronegativities
are derived from bond-
dissociation enthalpies
(Pauling)
Periodic Electronegativity Trends
� Figure (previous slide) shows Pauling electronegativities, χχχχP, but the trend is the same as for Mulliken (χχχχM) values
� Bond dissociation enthalpy, D:
H2(g) ���� 2H(g) DH2 = 432 kJ.mol-1
Cl2(g) ���� 2Cl(g) DCl2 = 240 kJ.mol-1
½(DH2 + DCl2) = 336 kJ.mol-1
• Pauling electronegativity is related to the difference in the
average of the homonuclear bond dissociation enthalpies and
the value for the heteronuclear (experimental) bond enthalpy
� HCl(g) ���� H(g) + Cl(g) DHCl = 428 kJ.mol-1
Experimental bonddissociation energy
Averaging would describea situation where thebonding electrons are
equally shared
Difference results from unequal sharing of electrons in H-Cl bond
Electronegativity and Size Effects
� Peripheral atoms
� The greater the size of the outer atom, the larger the
bond angle
� The greater the electronegativity of the outer atom, the
smaller the bond angle
� Most times, these effects are cooperative
F is smaller and more electronegative than Cl
Bond angle as a function of outer
atom electronegativity
Effect of size/electronegativity of outer atom
Electronegativity and Size Effects
� Where the electronegativity or size of the
central atom is concerned,
� Bond angle increases as the electronegativity of
the central atom increases
� Decreases as the size of the central atom
increases
FN
FF
FP
FF F
AsF
FF
SbF
F
. . . . . . . .
102.2o 97.8o 96.2o 87.3o
For group 5 elements electronegativity: N > P > As > Sb
Bond angle as a function of center
atom electronegativity
5
Polar Molecules
� Bonds between non-identical atoms (heteronuclearbonds) will often involve unequal sharing of electrons
� The situation is one of relative electron deficiency (Q+) at one end and electron excess (Q-) at the other (a dipolar bond) – an electric dipole
� The extent of the polarity of a bond is expressed in units of the dipole moment, m
µµµµ = Q ×××× r
� Where Q is the apparent charge (C) of each atom separated by a distance, r (in m).
� The dipole moment is a measure of the charge separation (bigger the disparity in charge at each end, bigger the dipole moment)
Polar Molecules
� Entire molecules may be polar as a consequence
of their polar bonds
� Molecules with polar bonds may be non-polar as
a consequence of their symmetry
� Sometimes the electronegativity of the atoms
involved makes prediction of the dipole difficult
HN
HH
HO
H FN
FF
. . . ... ..
1.47D 1.85D 0.23D
Valence Bond Theory (A bonding model that
uses combinations of valence atomic orbitals to
explain shapes)
� Consider a H2O molecule. If we try to explain the
bonds of this molecule as overlap of valence atomic
orbitals of H (1s) and O (2s, 2p), we cannot get a
picture that describes a 104.5o H-O-H bond angle
Valence Bond Theory
� One way of describing a bonding picture in
polyatomic molecules is through valence
bond theory (a localized bonding model)
� This model describes the σσσσ-bonding
framework of polyatomic molecules through
overlap of hybrid orbitals
� Orbital hybridization: mixing of atomic
orbitals
Hybrid orbital: orbital that is created by mixing two or more atomic orbitals
Hybrid Orbitals
� Directional hybrid orbitals are obtained by
mixing characters of different atomic orbitals
of similar energies
� Use sp hybrid orbitals to describe bonding in
linear molecules like BeCl2(g)
Two linear combinations
of valence atomic orbitals
sp Hybrid Orbital Scheme
� In this scheme, there are two different combinations
of the 2s orbital and the 2px orbital of Be, yielding
two different sp hybrid orbitals
� First combination adds the 2px orbital to the 2s
orbital. The overlap region where the phases (signs)
are similar is reinforced, producing a bigger function
here. Where the signs are opposite, the lobe becomes
smaller (cancellation)
)(2
122_ xpshybridsp ϕϕϕ +=
A coefficient which describes the contribution of each orbital to the hybrid
6
sp Hybrid Orbital Scheme
� The second combination involves the “subtraction” of
the 2px orbital from the 2s orbital – this implies
overlap of the 2px-orbital drawn pointing in the
opposite direction
� This hybrid is degenerate (same energy) with the one
discussed on the previous slide
)(2
122_ xpshybridsp ϕϕϕ −=
Orbital Energy Diagram
Atomic orbitals Hybrid orbitals
Singly occupied hybrid orbitals can overlap
with other singly occupied hybrid orbitals
sp2 Hybridization
� For trigonal planar molecular geometries,
there must be a hybrid orbital picture that
describes three equivalent orbitals available
for overlap with the orbitals (atomic or hybrid)
of other atoms
� sp2 hybrids involves mixing of an s and two p
orbitals. There are three combinations
considered
sp2 Hybridization
yx
yx
x
ppshybridsp
ppshybridsp
pshybridsp
222_
222_
22_
2
1
6
1
3
1
2
1
6
1
3
1
3
2
3
1
2
2
2
ϕϕϕϕ
ϕϕϕϕ
ϕϕϕ
−−=
+−=
+=
Coefficients which describe the
contribution of each atomic orbital
to the hybrid orbital The combination of “n” atomic
orbitals will yield “n” hybrid orbitals
Bonding in BH3
� Each bond is described by the overlap of a
H 1s orbital with a sp2 hybrid orbital of B
� The bonds in this picture are 2c, 2e- bonds
sp3 Hybridization
� For tetrahedral molecules, we need a scheme
that involves four equivalent hybrid orbitals
(s, px, py, pz)
( )
( )
( )
( )zyx
zyx
zyx
zyx
pppshybridsp
pppshybridsp
pppshybridsp
pppshybridsp
2222_
2222_
2222_
2222_
2
1
2
1
2
1
2
1
3
3
3
3
ϕϕϕϕϕ
ϕϕϕϕϕ
ϕϕϕϕϕ
ϕϕϕϕϕ
+−−=
−+−=
−−+=
+++=
7
NH3 Hybrid Orbital Picture
NHH
H
..
N
H
H
H
N-atom uses sp3-hybrid orbitals
H-atoms use 1s-atomic orbitals
Use sp3-hybrid orbitals to describe atoms having four electron domains
Other Hybridization Schemes
� Other orbital hybridization schemes
should involve different combinations
of atomic obitals
� Examples:
� sp3d: trigonal bipyramidal
� sp3d2: square-base pyramid
� sp3d2 : octahedral
5-coordinate
6-coordinate
Molecules having multiple bonds
� Ethene, C2H4; ask the questions
� What is the central atom?
� What is the geometry (electron domain) around
the central atom?
� What orbital hybridization scheme will enable
this geometry?
� Are there orbitals left over? Which? How are
they involved?
C C
H
HH
H
Unhybridized pz orbitals are
available for ππππ-bond formation
overlap yields π-bond
A Quick Discussion of Bond Symmetry
� Sigma bonding symmetry implies that the orbital
overlap picture which described the bond is
symmetric with respect to a 180o rotation about
the internuclear axis
Symmetric ���� no sign change
Sign change for 180o rotation: ππππ-bond
Hydrogen Cyanide, HCN
� Same questions:
� What is the central atom?
� What is the geometry (electron domain)
around the central atom?
� What orbital hybridization scheme will
enable this geometry?
� Are there orbitals left over? Which?
How do they become involved?
8
Hs-Csp overlap
Csp-Nsp overlap
2 unhybridized p-orbitalsper atom, available for
formation of 2 π-bonds
What is the other sp-orbital on nitrogen for?
Boron Trifluoride, BF3
� Central atom
� e- domain geometry
� Orbital hybridization scheme (do for F also)
� Unperturbed orbitals – what do they do?
•BF3 is trigonal planar
•Requires sp2 hybrid orbitals for boron
•Fluorine could have sp3 or sp2
•Empty pz-orbital on boron can accept
lone pair from an adjacent F-atom to
form a ππππ-bond