Transcript hybrid atomic orbitals

LCAO-molecular orbitals
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In MO Theory, atomic orbitals on the
constituent atoms are combined to form
bonding, non-bonding and anti-bonding
orbitals for the molecule
H2
MO configuration: ( 1s ) 2
He2
MO configuration: ( 1s )2 ( 1*s )2
Valence Bond (“hybridization”) theory
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Valence Bond (VB) theory is driven by the shape of the molecule (Chapter 10.7)
VB Theory begins with two steps:
 hybridization (combination of AOs on the same atom such that new AOs,
known as hybrid orbitals, are formed that POINT IN THE RIGHT
DIRECTION)
 hybrid orbitals and/or AOs on different atoms are combined to make sigma
bonds with electron density localized between the two bonding atoms
 Pi bonds are formed from unhybridized atomic p orbitals
Key differences between MO and VB theory:
 MO theory has electrons distributed over molecule
 VB theory localizes an electron pair between two atoms
 MO theory combines AOs on DIFFERENT atoms to make MOs (LCAO)
 VB theory combines AOs on the SAME atom to make hybridized atomic
orbitals (hybridization)
 In MO theory, the symmetry (or antisymmetry) must be retained in each
orbital.
 In VB theory, all orbitals must be looked at at once to see retention of the
molecule’s symmetry.
H—Be—H and sp hybridization
2p

2 p unhybridzed
2( sp )  
2s 
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In the method of hybrid orbitals, we “create” two hybrid atomic orbitals specifically designed to fit the
shape of the molecule, in this case linear, using atomic orbitals of an excited state Be atom!
Unused AOs are left behind as unhybridized atomic orbitals
The energy of the hybrid atomic orbitals are intermediate between those of the original constituent AO’s
The hybrid orbitals combine with other orbitals, atomic or hybrid, in the usual fashion, creating both
bonding and anti-bonding molecular orbitals, which are localized molecular orbitals
Be
2H
2px 2py
2px 2py
2 Be-H "antibonds"
sp hybrids
1s 1s
2 Be-H bonds
4
Hx2
Be
3
2p
1
1
2s
Energy
1s
2
1
BH3 and sp2 hybridization
2p
 
2 p unhybridzed
B
3H
2( sp 2 )   
2s 
2py
2py
3 B-H "antibonds"
sp2 hybrids
1s 1s 1s
3 B-H bonds
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BH3 is trigonal planar with three equal B—H bonds
To get this shape, we need to combine the 2s with two 2p
AO’s to generate three equivalent hybrid atomic orbitals
Combination with the H 1s leads to bonding and anti-bonding
molecular orbitals, which are localized molecular orbitals
pointing to the corners of a triangle
B
3H
2py
2py
3 B-H "antibonds"
sp2 hybrids
1s 1s 1s
3 B-H bonds
4
Hx3
B
3
2p
3
1
Energy
2s
1s
2
2
1
CH4 and sp3 hybridization
2p
  
no unhybridzed orbitals in 2nd shell
C
4H
2( sp )    
3
2s 
4 C-H "antibonds"
sp3 hybrids
1s 1s 1s 1s
4 C-H bonds
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CH4 is tetrahedral with four equal C—H bonds
To get this shape, we need to combine all the n=2 AO’s to
generate four equivalent hybrid atomic orbitals
Combination with the H 1s leads to bonding and anti-bonding
molecular orbitals, which are localized molecular orbitals
pointing to the corners of a tetrahedron
Compare to the LCAO model of CH4
4σ
3σ
4σ
2σ
3σ
1σ
2σ
2σ
1σ
1σ
VB theory is built on VSEPR shapes
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Recap: Molecular Geometry and Electron Group Geometry (Chapter 10)
Hybridization:
sp
sp2
sp2
VB theory is built on VSEPR shapes
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VB theory is useless beyond 4 electron groups!
Thus we need only consider 2, 3, and 4 electron groups from Chapter 10, section 7
Hybridization:
sp3
sp3
sp3
Summary of the VB (Hybrid AO) method
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The normal atomic orbitals have shapes that do not correspond to chemical bonds
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Atomic orbitals are essentially spherical
o Bonds are oriented towards the Terminal Atoms
1. Hybrid Atomic Orbitals (HAO) are mathematically valid mixtures of the
original atomic orbitals
2. They are “manufactured” by promoting electrons to the desired excited state
3. This energy has to be “paid” for – it is obtained by the bond energy that results
from good chemical bonds formed when the geometry “fits”
4. Remember that the method results in multiple equal – and hence degenerate –
HAO’s that differ only in their orientation
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Bonds can be formed from the “overlap” between any of the following:
1. HAO with HAO
2. HAO with AO
3. AO with AO
Two central atoms: ethane
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If we treat ethane by the VSEPR theory, we find that both
carbon atoms are tetrahedral
o The shape of the molecule is shown in the diagram: the
only additional information required is the conformation
which is adjusted to minimize contacts between the
atoms – this is known as the staggered conformation
o We can thus explain the bonding in ethane by using
sp3 hybrid orbitals on each carbon atom
o The H atoms bond using their 1s atomic orbitals
o In all there are 14 electrons or 7 electron pair bonds in the molecule
H H
H
C
H H
C
H
Ignore the “tail ends” of the HAO
Rotation…
Bonding in Ethane
Lewis structure (including all lone pairs)
VSEPR Geometry (including 3D)
Hybridization at central atoms
Double bonds: ethene
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If we treat ethane by the VSEPR theory, we find that both
carbon atoms are trigonal planar
The shape of the molecule is shown in the diagram: the
only additional information required is the conformation
which is planar. Why does this geometry occur?
We can explain the bonding in ethene by using
sp2 hybrid orbitals on each carbon atom, which leaves
one atomic p orbital unused on each C atom, while H atoms use their 1s atomic orbitals
In all there are 6 electron pair bonds in the molecule, 5 in σ orbitals, 1 in the π orbital
The sigma skeleton of ethene
The pi bond of ethene
Planarity in double bonds: ethene again
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We can now explain the origin of the
planar structure of ethene
o Only when the two CH2 fragments are co-planar
can there be efficient overlap between the
unhybridized p orbitals leading to the π bond
o As shown in the bottom diagram: if ethene is
rotated by 90° along the C—C bond, the atomic
p orbitals have zero net overlap
o Such an arrangement is know as an orthogonal
interaction of wavefunctions, and does not lead
to any net bonding
o Double bonds impose coplanar conformations
on the joining atoms
o This is true for all double-bonded molecules, and is a powerful confirmation of the
bonding theories that we have developed
o Note that a double bond is always the sum of a sigma + a pi bond
o Single bonds are always sigma bonds, so that in ethane, all the bonds are sigma
Bonding in Ethene
Lewis structure
VSEPR geometry
hybridization at central atom(s)
 bonding
 bonding
Bonding in Ethyne
Lewis structure
VSEPR geometry
hybridization at central atom(s)
 bonding
 bonding
Bonding in Formaldehyde
Lewis structure
VSEPR geometry
hybridization at central atom(s)
 bonding
 bonding
Bonding in Allene
(H2C=C=CH2)
Lewis Structure
VSEPR Geometry
Hybridization
σ bonding
π bonding