Download Chapter 10 Chemical Bonding II

Chapter 10
Chemical
Bonding II
Valence Bond Theory

Valence Bond Theory: A quantum mechanical model which shows
how electron pairs are shared in a covalent bond.
◦ Bond forms between two atoms when the following conditions are
met:
◦ Covalent bonds are formed by overlap of atomic orbitals, each of
which contains one electron of opposite spin.
◦ Each of the bonded atoms maintains its own atomic orbitals, but the
electron pair in the overlapping orbitals is shared by both atoms.
◦ The greater the amount of overlap, the stronger the bond.
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Orbital Interaction




In some cases, atoms use “simple” atomic orbital (e.g., 1s, 2s, 2p, etc.) to
form bonds.
In other case, they use a “mixture” of simple atomic orbitals known as
“hybrid” atomic orbitals.
as two atoms approached, the partially filled or empty valence atomic
orbitals on the atoms would interact to form molecular orbitals
the molecular orbitals would be more stable than the separate atomic
orbitals because they would contain paired electrons shared by both
atoms
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Valence Bond Theory - Hybridization


one of the issues that arose was that the number of partially filled or
empty atomic orbital did not predict the number of bonds or orientation
of bonds
◦ C = 2s22px12py12pz0 would predict 2 or 3 bonds that are 90° apart, rather
than 4 bonds that are 109.5° apart
to adjust for these inconsistencies, it was postulated that the valence
atomic orbitals could hybridize before bonding took place
◦ one hybridization of C is to mix all the 2s and 2p orbitals to get 4
orbitals that point at the corners of a tetrahedron
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Valence Bond Theory Main Concepts
1.
2.
3.
the valence electrons in an atom reside in the quantum mechanical
atomic orbitals or hybrid orbitals
a chemical bond results when these atomic orbitals overlap and
there is a total of 2 electrons in the new molecular orbital
a) the electrons must be spin paired
the shape of the molecule is determined by the geometry of the
overlapping orbitals
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The Phase of an Orbital
•Orbitals are determined from mathematical wave functions.
•A wave function can have positive or negative values.
•As well as nodes where the wave function = 0
•The sign of the wave function is called its phase.
•When orbitals interact, their wave functions may be in phase (same sign)
or out of phase (opposite signs).
•This is important in bonding as will be examined in a later chapter.
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Types of Bonds

a sigma (s) bond results
when the bonding atomic
orbitals point along the axis
connecting the two bonding
nuclei
◦ either standard atomic
orbitals or hybrids
 s-to-s, p-to-p, hybrid-tohybrid, s-to-hybrid, etc.


a pi (p) bond results when the
bonding atomic orbitals are
parallel to each other and
perpendicular to the axis
connecting the two bonding
nuclei
◦ between unhybridized
parallel p orbitals
the interaction between parallel
orbitals is not as strong as
between orbitals that point at
each other; therefore s bonds
are stronger than p bonds
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Hybridization



some atoms hybridize their orbitals to maximize bonding
◦ hybridizing is mixing different types of orbitals to make a new set of
degenerate orbitals
◦ sp, sp2, sp3, sp3d, sp3d2
◦ more bonds = more full orbitals = more stability
better explain observed shapes of molecules
same type of atom can have different hybridization depending on the
compound
◦ C = sp, sp2, sp3
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Hybrid Orbitals


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H cannot hybridize!!
the number of standard atomic orbitals combined = the number of
hybrid orbitals formed
the number and type of standard atomic orbitals combined determines
the shape of the hybrid orbitals
the particular kind of hybridization that occurs is the one that yields
the lowest overall energy for the molecule
◦ in other words, you have to know the structure of the molecule
beforehand in order to predict the hybridization
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sp3 Hybridization of C
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3
sp


Hybridization
atom with 4 areas of electrons
◦ tetrahedral geometry
◦ 109.5° angles between hybrid orbitals
atom uses hybrid orbitals for all bonds and lone pairs
Ammonia Formation with sp3 N
H
s
H
sp3 •• sp3
C
N
H
s
H
H
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2
sp


atom with 3 areas of electrons
◦ trigonal planar system
 C = trigonal planar
 N = trigonal bent
 O = “linear”
◦ 120° bond angles
◦ flat
atom uses hybrid orbitals for s bonds
and lone pairs, uses nonhybridized p
orbital for p bond
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3-D representation of ethane (C2H4)
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Bond Rotation

because orbitals that form the s bond point along the internuclear axis,
rotation around that bond does not require breaking the interaction
between the orbitals

but the orbitals that form the p bond interact above and below the
internuclear axis, so rotation around the axis requires the breaking of
the interaction between the orbitals
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sp

atom with 2 areas of electrons
◦ linear shape
◦ 180° bond angle

atom uses hybrid orbitals for s bonds
or lone pairs, uses nonhybridized p
orbitals for p bonds
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3
sp d


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atom with 5 areas of electrons around it
◦ trigonal bipyramid shape
◦ See-Saw, T-Shape, Linear
◦ 120° & 90° bond angles
use empty d orbitals from valence shell
d orbitals can be used to make p bonds
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3
2
sp d

atom with 6 areas of electrons around it
◦ octahedral shape
◦ Square Pyramid, Square Planar
◦ 90° bond angles
use empty d orbitals from valence shell

d orbitals can be used to make p bonds

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Predicting Hybridization and Bonding Scheme
1)
2)
3)
4)
5)
Start by drawing the Lewis Structure
Use VSEPR Theory to predict the electron group geometry around
each central atom
Use Table 10.3 to select the hybridization scheme that matches the
electron group geometry
Sketch the atomic and hybrid orbitals on the atoms in the molecule,
showing overlap of the appropriate orbitals
Label the bonds as s or p
# of e- groups around
central atom
2
Hybrid orbitals used
3
sp2
4
sp3
5
sp3d
6
sp3d2
Orientation of Hybrid
Orbitals
sp
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Examples:
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
Predict the Hybridization and Bonding Scheme of All the Atoms in
Then sketch a σ framework and a π framework
••
•O
•
••
N

CH3CHO

CH2NH

H3BO3
••
Cl ••
••
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Problems with Valence Bond Theory


VB theory predicts many properties better than Lewis Theory
◦ bonding schemes, bond strengths, bond lengths, bond rigidity
however, there are still many properties of molecules it doesn’t predict
perfectly
◦ magnetic behavior of O2
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Molecular Orbital Theory


in MO theory, we apply Schrödinger’s wave equation to the molecule to
calculate a set of molecular orbitals
◦ in practice, the equation solution is estimated
◦ we start with good guesses from our experience as to what the orbital
should look like
◦ then test and tweak the estimate until the energy of the orbital is
minimized
in this treatment, the electrons belong to the whole molecule – so the
orbitals belong to the whole molecule
◦ unlike VB Theory where the atomic orbitals still exist in the molecule
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LCAO
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
the simplest guess starts with the atomic orbitals of the atoms adding
together to make molecular orbitals – this is called the Linear
Combination of Atomic Orbitals method
◦ weighted sum
because the orbitals are wave functions, the waves can combine either
constructively or destructively
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Molecular Orbitals


when the wave functions combine constructively, the resulting molecular
orbital has less energy than the original atomic orbitals – it is called a
Bonding Molecular Orbital
◦ s, p
◦ most of the electron density between the nuclei
when the wave functions combine destructively, the resulting molecular
orbital has more energy than the original atomic orbitals – it is called a
Antibonding Molecular Orbital
◦ s*, p*
◦ most of the electron density outside the nuclei
◦ nodes between nuclei
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Molecular Orbital Theory


Electrons in bonding MOs are stabilizing
◦ Lower energy than the atomic orbitals
Electrons in anti-bonding MOs are destabilizing
◦ Higher in energy than atomic orbitals
◦ Electron density located outside the internuclear axis
◦ Electrons in anti-bonding orbitals cancel stability gained by
electrons in bonding orbitals
H2
s bonding MO
HOMO
s* Antibonding MO
LUMO
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MO and Properties


Bond Order = difference between number of electrons in bonding and
antibonding orbitals
◦ only need to consider valence electrons
◦ may be a fraction
◦ higher bond order = stronger and shorter bonds
◦ if bond order = 0, then bond is unstable compared to individual
atoms - no bond will form.
A substance will be paramagnetic if its MO diagram has unpaired
electrons
◦ if all electrons paired it is diamagnetic
# Bond Elec. - # Antibond Elec.
Bond Order 
2
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Molecular Orbital Theory: The
Hydrogen Molecule
Bond Order =
2-0
=1
2
What would happen if two helium atoms tried to form a
bond by overlapping their two 1s orbitals?
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

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The bonding picture is essentially
the same as for the hydrogen
molecule, except that each helium
atom
brings two electrons to the
molecular orbitals. There would be
four electrons to fill into our
molecular
orbital diagram and that would
force us to fill in the bonding
sigma MO and the anti-bonding
sigma-star MO.
The bond order calculation equals
zero, as expected for a diatomic
helium molecule.
Bond order =
2-2
=0
2
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Lithium
Atomic
Orbitals
Dilithium, Li2
Molecular
Orbitals
Lithium
Atomic
Orbitals
s*
2s
2s
s
BO = ½(4-2) = 1
Any fill energy level will
generate filled bonding and
antibonding MO’s;
therefore only need to
consider valence shell
s*
1s
1s
s
Since more electrons are in
bonding orbitals than are in antibonding
orbitals, net bonding interaction
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Examples

What would the MO pictures of H2+, H2-
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