Hybridization and Molecular Orbital (MO) · PDF fileHybridization and Molecular Orbital (MO)...
Transcript of Hybridization and Molecular Orbital (MO) · PDF fileHybridization and Molecular Orbital (MO)...
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Hybridization and Molecular Orbital (MO)
Theory
Chapter 10
Historical Models
•Valence bond theory (VB) - a molecule arises from interaction of complete atoms, bound together through localized overlap of valence-shell atomic orbitals which retain their original character.
•Valence shell electron pair repulsion theory (VSEPR) – predicts molecular shapes based on valence electrons, lewis dot structures and electron repulsions.
•Molecular orbital theory (MO) – a molecule is formed by the overlap of atomic orbitals to form molecular orbitals, electrons are then distributed into MOs. A molecule is a collection of nuclei with the orbitals delocalized over the entire molecule.
•G.N.Lewis and I. Langmuir (~1920) laid out foundations•Ionic species were formed by electron transfer•Covalent molecules arise from electron sharing
Two Theories of BondingTwo Theories of Bonding
•• VALENCE BOND VALENCE BOND THEORYTHEORY —— LinusLinus PaulingPauling
•• valence electrons are valence electrons are localized between atoms (or localized between atoms (or are lone pairs).are lone pairs).
•• halfhalf--filled atomic filled atomic orbitalsorbitalsoverlap to form bonds.overlap to form bonds.
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Valence Bond (VB) Theory
• Covalent bonds are formed by the overlapoverlap of atomic orbitals.
• Atomic orbitals on the central atom can mix and exchange their character with other atoms in a molecule.– Process is called hybridizationhybridization.
� Hybrid Orbitals have the same shapes as predicted by VSEPR.
Valence Bond (VB) Theory
sp3d2Octahedral6
sp3dTrigonal
bipyramidal
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sp3Tetrahedral4
sp2Trigonal
planar
3
spLinear2
HybridizationElectronic
Geometry
Regions of High
Electron Density
Molecular Shapes and BondingMolecular Shapes and Bonding
• In the next sections we will use the following terminology:A = central atom
B = bonding pairs around central atom
U = lone pairs around central atom
• For example:AB3U designates that there are 3 bonding pairs and 1
lone pair around the central atom.
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Sigma Bond Formation by Sigma Bond Formation by Orbital OverlapOrbital Overlap
Two s Two s orbitalsorbitals
overlapoverlap
Sigma Bond FormationSigma Bond FormationSigma Bond Formation
Two s Two s
orbitalsorbitals
overlapoverlap
Two p Two p
orbitalsorbitals
overlapoverlap
Linear Electronic Geometry:AB2
Species (No Lone Pairs of Electrons on A)
• Some examples of molecules with this geometry are: BeCl
2, BeBr
2, BeI
2, HgCl
2, CdCl
2
• All of these examples are linear, nonpolarmolecules.
• Important exceptions occur when the two substituents are not the same!BeClBr or BeIBr will be linear and polar!
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Linear Electronic Geometry:AB2
Species (No Lone Pairs of Electrons on A)
Trigonal Planar Electronic Geometry: AB3 Species (No
Lone Pairs of Electrons on A)• Some examples of molecules with this geometry
are: BF3, BCl3
• All of these examples are trigonal planar, nonpolarmolecules.
• Important exceptions occur when the three substituents are not the same!BF2Cl or BCI2Br will be trigonal planar and polar!
Using VB TheoryUsing VB TheoryBonding in BFBonding in BF33
planar triangleplanar triangle
angle = 120angle = 120oo
F
F F
Boron configuration
↑↑↑↑↑↑↑↑↓↓↓↓↑↑↑↑↓↓↓↓
2p2s1s•• ••
••••
••
•• ••
••••
B
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Bonding in BF3Bonding in BFBonding in BF33
•• How to account for 3 bonds 120How to account for 3 bonds 120oo apart using a apart using a spherical s orbital and p spherical s orbital and p orbitalsorbitals that are 90that are 90oo apart?apart?
•• Pauling said to modify VB approach with Pauling said to modify VB approach with ORBITAL ORBITAL HYBRIDIZATIONHYBRIDIZATION
•• —— mix available mix available orbitalsorbitals to form a new set of to form a new set of orbitalsorbitals—— HYBRID ORBITALSHYBRID ORBITALS —— that will give the that will give the maximum overlap in the correct geometry. maximum overlap in the correct geometry.
Bonding in BFBonding in BF33
rearrange electronshydridize orbs.
unused porbital
three sp2
hybrid orbitals
2p2s
•• The three hybrid The three hybrid orbitalsorbitals are made are made
from 1 s orbital and 2 p from 1 s orbital and 2 p orbitalsorbitals →→→→→→→→ 3 sp3 sp22
hybrids.hybrids.
Bonding in BF3Bonding in BFBonding in BF33
•• Now we have 3, halfNow we have 3, half--filled HYBRID filled HYBRID orbitalsorbitals
that can be used to form Bthat can be used to form B--F sigma bonds.F sigma bonds.
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Trigonal Planar Electronic Geometry: AB3 Species (No Lone
Pairs of Electrons on A)
BFBF33, Planar , Planar TrigonalTrigonal
Tetrahedral Electronic Geometry: AB
4Species (No Lone Pairs of
Electrons on A)
• Some examples of molecules with this geometry are: CH
4, CF
4, CCl
4, SiH
4, SiF
4
• All of these examples are tetrahedral, nonpolarmolecules.
• Important exceptions occur when the four substituents are not the same!CF3Cl or CH2CI2 will be tetrahedral and polar!
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Tetrahedral Electronic Geometry: AB4 Species (No Lone Pairs of
Electrons on A)
Bonding in CHBonding in CH44How do we account for 4 How do we account for 4
CC——H sigma bonds 109H sigma bonds 109oo
apart? apart?
Need to use 4 atomic Need to use 4 atomic orbitalsorbitals
—— s, s, ppxx, , ppyy, and , and ppzz —— to to
form 4 new hybrid form 4 new hybrid orbitalsorbitals
pointing in the correct pointing in the correct
direction.direction.
109o109o
4 C atom orbitals
hybridize to form
four equivalent sp3
hybrid atomic
orbitals.
4 C atom 4 C atom orbitalsorbitals
hybridize to form hybridize to form
four equivalent spfour equivalent sp33
hybrid atomic hybrid atomic
orbitalsorbitals..
Bonding in a Tetrahedron Bonding in a Tetrahedron ——Formation of Hybrid Atomic Formation of Hybrid Atomic
OrbitalsOrbitals
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Tetrahedral Electronic Geometry: AB
4Species (No Lone Pairs of
Electrons on A)
Bonding in CHBonding in CH44
Figure 10.6Figure 10.6
Tetrahedral Electronic Geometry: AB4
Species (No Lone Pairs of Electrons on A)
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Tetrahedral Electronic Geometry: AB3U Species (One Lone Pair of
Electrons on A)• Some examples of molecules with this geometry
are: NH3, NF3, PH3, PCl3, AsH3
• These molecules are our first examples of central atoms with lone pairs of electrons.Thus, the electronic and molecular geometries are
different.
All three substituents are the same but molecule is polarpolar.
• NH3 and NF3 are trigonal pyramidal, polar molecules.
Steps in predicting the hybrid orbitals used by an atom in bonding:
1. Draw the Lewis structure
2. Determine the electron pair geometry using the VSEPR model
3. Specify the hybrid orbitals needed to accommodate the electron pairs in the
geometric arrangement
NH3
1. Lewis structure
2. VSEPR indicates tetrahedral geometry
with one non-bonding pair of electrons
(structure itself will be trigonal pyramidal)
3. Tetrahedral arrangement indicates four
equivalent electron orbitals
Tetrahedral Electronic Geometry: AB2U2 Species (Two Lone Pairs of
Electrons on A)
• Some examples of molecules with this geometry are: H2O, OF2, H2S
• These molecules are our first examples of central atoms with two lone pairs of electrons.Thus, the electronic and molecular geometries are different.
Both substituents are the same but molecule is polarpolar.
• Molecules are angular, bent, or V-shaped and polar.
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Orbital HybridizationFigure 10.5
Orbital HybridizationOrbital HybridizationFigure 10.5Figure 10.5
BONDSBONDS SHAPESHAPE HYBRID REMAINHYBRID REMAIN
22 linearlinear spsp 2 2 pp’’ss
33 trigonaltrigonal spsp22 1 p1 pplanarplanar
44 tetrahedral sptetrahedral sp33 nonenone
Compounds Containing Double Bonds
Valence Bond Theory (Hybridization)
C atom has four electrons.
Three electrons from each C atom are in sp2
hybrids.
One electron in each C atom remains in an unhybridized p orbital
2s 2p three sp2 hybrids 2p
C ↑↓ ↑ ↑ ⇒ ↑ ↑ ↑ ↑
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Compounds Containing Double Bonds
• The single 2p orbital is perpendicular to the trigonal planar sp2 lobes.The fourth electron is in the p orbital.
Side view of sp2 hybrid
with p orbital included.
Compounds Containing Double Bonds
• An sp2 hybridized C atom has this shape.Remember there will be one electron in each of the three
lobes.
Top view of
an sp2 hybrid
Compounds Containing Double Bonds
• The portion of the double bond formed from the head-on overlap of the sp2 hybrids is designated as a σ bond.
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Sometimes it is not necessary for all the valence electron orbitals to hybridize. For
example, ethylene has the following structure:
The bonds between C and H
are all sigma bonds between
sp2 hybridized C atoms and
the s-orbitals of Hydrogen.
The double bond between the
two C atoms consists of a
sigma bond (where the
electron pair is located
between the atoms) and a pi
bond (where the electron pair
occupies the space above
and below the sigma bond.
σσ and and ππ Bonding inBonding in CHCH22OO
Compounds Containing Triple Bonds
• Ethyne or acetylene, C2H2, is the simplest triple bond containing organic compound.
• Compound must have a triple bond to obey octet rule.
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Compounds Containing Triple Bonds
Lewis Dot Formula
C C HHCH HC··
······
·· orCH HC·
·······
··
VSEPR Theory suggests regions of high
electron density are 180o apart.
Compounds Containing Triple Bonds
Valence Bond Theory (Hybridization)
Carbon has 4 electrons.
Two of the electrons are in sp hybrids.
Two electrons remain in unhybridized p orbitals.
2s 2p two sp hybrids 2p
C [He] ↑↓ ↑ ↑ ⇒ ↑ ↑ ↑ ↑
σσ and and ππ Bonding inBonding in CC22HH22
Figure 10.12Figure 10.12
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Compounds Containing Triple Bonds
A σ bond results from the head-on overlap of two sp hybrid orbitals.
Compounds Containing Triple Bonds
• The unhybridized p orbitals form two π bonds.� Note that a triple bond consists of one σ and
two π bonds.
Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,
and AB2U3� Some examples of molecules with this geometry
are: PF5, AsF5, PCl5, etc.
• These molecules are examples of central atoms with five bonding pairs of electrons.The electronic and molecular geometries are the same.
• Molecules are trigonal bipyramidal and nonpolarwhen all five substituents are the same.If the five substituents are not the same polarpolar molecules
can result, AsF4Cl is an example.
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Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,
and AB2U3Valence Bond Theory (Hybridization)
4s 4p 4d
As [Ar] 3d10 ↑↓ ↑ ↑ ↑ ___ ___ ___ ___ ___
⇓five sp3 d hybrids 4d
↑ ↑ ↑ ↑ ↑ ___ ___ ___ ___ ___
Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2, and
AB2U3
• If lone pairs are incorporated into the trigonal bipyramidal structure, there are three possible new shapes.
1. One lone pair - Seesaw shape
2. Two lone pairs - T-shape
3. Three lone pairs – linear
• The lone pairs occupy equatorial positions because they are 120o
from two bonding pairs and 90o from the other two bonding pairs.
– Results in decreased repulsions compared to lone pair in axial position.
Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,
and AB2U3
• AB4U molecules have:1. trigonal bipyramid electronic geometry
2. seesaw shaped molecular geometry
3. and are polar
• One example of an AB4U molecule is
SF4
• Hybridization of S atom is sp3d.
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Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,
and AB2U3
Molecular Geometry
H
C
HH
H
Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,
and AB2U3• AB3U2 molecules have:
1. trigonal bipyramid electronic geometry
2. T-shaped molecular geometry
3. and are polar
• One example of an AB3U2 molecule is
IF3
• Hybridization of I atom is sp3d.
Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,
and AB2U3Molecular Geometry
H
C
HH
H
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Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,
and AB2U3• AB2U3 molecules have:
1.trigonal bipyramid electronic geometry
2.linear molecular geometry
3.and are nonpolar
• One example of an AB3U2 molecule isXeF2
• Hybridization of Xe atom is sp3d.
Trigonal Bipyramidal Electronic Geometry: AB5, AB4U, AB3U2,
and AB2U3Molecular Geometry
H
C
HH
H
Octahedral Electronic Geometry: AB6, AB5U, and AB4U2
• AB5U molecules have:1.octahedral electronic geometry
2.Square pyramidal molecular geometry
3.and are polar.
• One example of an AB4U molecule is
IF5
• Hybridization of I atom is sp3d2.
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Octahedral Electronic Geometry: AB6, AB5U, and AB4U2
Molecular Geometry
H
C
HH
H
Octahedral Electronic Geometry: AB6, AB5U, and AB4U2
• AB4U2 molecules have:1.octahedral electronic geometry
2.square planar molecular geometry
3.and are nonpolar.
• One example of an AB4U2 molecule is
XeF4
• Hybridization of Xe atom is sp3d2.
Octahedral Electronic Geometry: AB6, AB5U, and AB4U2
Molecular Geometry Polarity
H
C
HH
H
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Summary of Electronic & Molecular Geometries
•• MOLECULAR MOLECULAR ORBITAL THEORYORBITAL THEORY ——Robert Mullikan (1896Robert Mullikan (1896--1986)1986)
•• valence electrons are valence electrons are delocalizeddelocalized
•• valence electrons are in valence electrons are in orbitalsorbitals (called molecular (called molecular orbitalsorbitals) spread over ) spread over entire molecule.entire molecule.
Two Theories of BondingTwo Theories of Bonding
Review of Atomic Orbitals - s, p and d
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The Need for MO
�VSEPR and VB theory are good to explain the molecular shape.
�BUT they did not explain the magnetic or spectral properties of molecules.
�Molecular orbital theory is needed.
Homonuclear Diatomic Molecules: Molecular Orbital (MO) Theory
�MOs are derived from a linear combination (addition and subtraction) of atomic orbitals represented as wavefunctions of nearby atoms to form molecular orbitals.
•There are two possible combinations
•Adding two atomic orbitals forms a bonding MO.
•Subtracting two atomic orbitals forms an antibondingMO.
•Basic Tenant –•The number of atomic orbitals contributed equals the number of molecular orbitals generated.
Electron Wave Functions – Wave-Particle DualityLinear Combination of Wavefunctions – Ψ
Ψ(1) + Ψ (2)
Ψ(1) + Ψ (2)
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If we look at H2, we see that each hydrogen atom has a 1s atomic orbital
that is half-filled. Remembering that orbitals are mathematical functions,
they can combine by adding or subtracting to give two new combinations
which we call molecular orbitals.
Homonuclear Diatomic MoleculesMolecular Orbital TheoryIn Phase / Out of Phase Overlap
σσσσ
HHHHaaaaHHHHbbbb
σσσσ****
Ψ(1) + Ψ (2)
Ψ(1) − Ψ (2)
The energy of the H2 molecule with the two electrons in the bonding
orbital is lower by 435 kJ/mole than the combined energy of the two
separate H-atoms.
On the other hand, the energy of the H2 molecule with two electrons in
the antibonding orbital is higher than two separate H-atoms. To show the
relative energies we use diagrams like this:
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Homonuclear Diatomic Molecules: Molecular Orbital Theory
σ label implies rotation of MO about internuclearaxis (z axis) generates no phase change
*label implies a nodal plane between the nuclei which is orthogonal to the z axis
π label implies rotation of orbital about internuclear axis generates a phase change
In the H2 molecule, the bonding and anti-bonding orbitals are
called sigma orbitals ( σ )
Sigma Orbital: A bonding molecular orbital with cylindrical symmetry about
an internuclear axis.
When atomic orbitals are combined to give molecular orbitals, the
number of molecular orbitals formed equals the number of atomic orbitals
used.
A molecular orbital (like an atomic orbital) can contain no more than two
electrons (Pauli Exclusion Principle), and are filled starting with the
lowest energy orbital first.
In general, the energy difference between a bonding and anti-bonding
orbital pair becomes larger as the overlap of the atomic orbitals increase.
Example: H2 molecule
Each hydrogen atom contributes one electron. These go in the bonding
molecular orbital because we fill the lowest energy orbital first.
Electrons fill MOs by standard rules - aufbau, pauli, etc.
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σ*1s
σ1s
Bond Order / Electron Configurationfor H2 Molecule
φΗ1 φΗ1
Ψbσ1s
Ψaσ∗1s -Bond Order (B.O.)B.O. = 1/2 (Nb - Na)Nb = bonding electronsNa = antibonding electrons
-Molecular electron configurations - analogous to atomic configurations
- H2 = σ21s
Example: He2 molecule
Not observed because there is no energy benefit to bonding these two atoms
together.
σ*1s
σ1s
Bond Order / Electron Configurationfor He2 Molecule
φΗ1 φΗ1
Ψbσ1s
Ψaσ∗1s -Bond Order (B.O.)B.O. = 1/2 (Nb - Na)Nb = bonding electronsNa = antibonding electrons
-Molecular electron configurations - analogous to atomic configurations
- H2 = σ21s σ∗21s
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MO of He2
+
σ*1s
σ1s
Energy
He2+ bond order = ??
MO Diagram for He2+ and H2
-
MO of H2
-
H2- bond order = ??
AO of He
AO of He+
AO of
H-
AO of H
σ*1s
σ1s
Summary Data for First Row Homo - Diatomics
----022He2
2301.08½12He2+
4580.74102H2
2691.06½01H2+
Bond Energy (kJ/mol)
Bond length (Å)
Bond Order
Antibond. e-
Bonding e-Molecule
σ*1s
σ1s
Orbital Interaction for Li2 MoleculeLi atom - 1s22s1
σ2s
σ*2s
1s
2s Bond order for Li2?
Molecular electronconfiguration?
Be2?
Li2+?
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σ*1s
σ1s
Orbital Interaction for Li2 MoleculeLi atom - 1s22s1
σ2s
σ*2s
1s
2s Bond order for Li2 = ½(4-2) = 1σ21s σ∗21sσ22s
Be2 = ½(4-4) = 0σ21s σ∗21sσ22s σ∗22s
Li2+ = ½(3-2) = ½
σ21s σ∗21sσ12s
MO of He2
+
σ*1s
σ1s
AO of He+
1s
Energy
He2+ bond order = 1/2
AO of He
1s
MO Diagram for He2+ and H2
-
MO of H2
-
σ*1s
σ1s
AO of H
1s
H2- bond order = 1/2
AO of H-
1s
We can also form bonding orbitals using other atomic orbitals. For
example, we can combine two p orbitals to form a sigma bond:
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Using p orbitals a second type of orbital called a π orbital can also be formed. These exist above and below the internuclear axis. We see πbonds used for the second bond of a double bond or the second and
third of a triple bond. π bonds limit rotation of the atoms in space.
Relative MO Energy Levels for Period 2
Homonuclear Diatomic Molecules
MO energy levels for
O2, F2, and Ne2
MO energy levels for
B2, C2, and N2
No 2s-2p repulsion Effect of 2s-2p
repulsion
Homonuclear Diatomic Molecules Molecular Orbital Theory - p Orbital Set
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O2 molecule is an example
with sigma and pi bonds
forming between atoms. MO
theory predicts that oxygen
will be paramagnetic.
Molecular Oxygen (O2)
Using the following MO Diagram
σ21s σ∗21sσ22s σ∗22sπ42p π∗22p
BO = ½(8-4)= 2
Orbital Energies for Second Row Homodiatomics
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VBT describes O2 as a double bond (O=O), however experimentindicates the molecule is paramagnetic.
MOT describes the bonding and accounts for the paramagnetism.
Paramagnetic= > 1 unpaired electronDiamagnetic = 0 unpaired electrons
Experimental Data for Homodinuclear Diatomics Li to F
D11591.41F2
P24981.21O2
D39451.10N2
D26071.24C2
P12971.59B2
--0----Be2
D11102.67Li2
Magnetic Info
Bond Order
Bond Diss. Enthalpy (kJ/mol)
Bond Length (Å)
Diatomic
Energy
MO of
HF
AO of H
1s
σ
2px 2py
σ∗
AO of F
2p
Two non-bonding orbitals
are the lone pairs on F
seen in The Lewis structure
for HF
Note the H1Sis less stable
than the F2P
The MO Diagram for HF
Note: 2s non-bondingorbital (F) not shown
Energy
The MO Diagram
for NO
2s
AO’s of
N
2p
σσσσ*2s
σσσσ2s
2sAO’s of
O
2p
ππππ2pxy
σσσσ2pz
ππππ*2pxy
σσσσ*2pz
PARAMAGNETIC
1 unpaired e-
Note AO’s of the more
electronegative O are
More stable than those
of N
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Heteronuclear Diatomic Molecules - CO
Homonuclear Diatomic Molecules Review of Bonding Types
sigma - σ
pi - π delta - δ