Chapter 10Bonding and Molecular Structure: Orbital
Hybridization and Molecular Orbitals
Atoms are bonded together by electrons, but what is a bond?
A bond forms when two atomic orbitals overlap to make a molecule more stable than when there was no overlap
Bonds
The atomic orbitals constructively interfere to form molecular orbitals
1s(1) 1s(2) 1
Atom 1 Atom 2
Molecule
Nucleus 1 Nucleus 2
Wavefunction of the atoms combine to form wavefunctions for the molecule
Simple Molecular Orbitals
In LCAO, each AO is combined both in-phase and out-of-phase, corresponding to constructive and destructive interference.
The simplest atomic orbitals (AO’s) are the 1s orbitals, which are the ground state of hydrogen and helium
H forms bonds: H—H
He does not form bonds
The exact wavefunction of one-electron molecules such as H2
+ and He23+
, are known.
These exact wavefunctions can be approximated using linear combinations of atomic orbitals, LCAO
Constructive interference - Bonding orbital
Destrstructive interference - Anti bonding orbital Has a node between atoms
How do we explain this?
Energy Levels of LCAO-molecular orbitals
MO’s orbitals energy increases with # of nodes
The MO that forms when two 1s orbitals constructive interference have lower energy than those that destructively interfere.
MO energy levels are depicted using a correlation diagram which relates the energies of the MO’s relative to their constituent AO’s
Adding e’s to H2 a bond is formed (BO = 1)
Adding e’s to He2 no bond is lost (filling both the bonding and the antibonding MO leaves the “molecule” in a higher energy state (BO = 0), than free atoms)
H2
He2
21MO configuration: ( )s
2 * 21 1MO configuration: ( ) ( )s s
LCAO for the 2nd Period Elements
Ignore “core” orbitals in LCAO theory
22MO configuration: ( )s
The “dilithium” molecule can exist in very low-pressure vapours, whereas the normal state of lithium is the metallic solid
Lewis theory predict Li—Li, with only two bonding electrons in its valence
The net overlap of the 1s levels cancels out
The net overlap of the 2s wave functions leads to a single bond, the BO = 1
The Li—Li distance in Li2 is 159 pm; at this distance the degree of overlap of the 1s orbitals of Li is negligibly small
The assumption of “core” orbitals is thus valid
The next molecule to consider is Be2, and like He2 it should not exist.
LCAO from atomic p orbitals: σ-MO’s
For B2, with 6 valence e-, we need additional orbitals, made from next lowest atomic orbitals 2p
Here we must distinguish the orientation of the orbitals w.r.t. each other
Bond axis: z-axis for simple molecules,
consider pz orbital
p orbitals have a node at the nucleus,
out-of-phase MO will have an additional node, between the nuclei
Both MO’s are defined as σ = cylindrical
In-phase combination between two pz orbitals will have two nodes, at the nuclei but not between them.
- antibonding
- bonding
Since antibonding orbital has more nodes it is higher in energy
LCAO from atomic p orbitals: π-MO’s
Two orbitals remain at right angles to the bond axis on each atom, the px and the py
Side-on overlap which leads to a new kind of bond, the π-bond
The diagram shows the case for p x
It is called a π-orbital because from end-on it resembles an atomic p orbital
π orbitals contain a nodal plane throughout the molecule
The out-of-phase MO also has an additional node between the atoms, making it an antibonding MO
The pz orbital were higher in energy than px and py. Therefore, 2pz orbitals are higher in energy (less stable) than the two 2p orbitals which are equal in energy
Molecular OrbitalsAtomic orbitals will combine when:
1) Geometry makes it possible
Have the right shape
2) Are close in energy.
The degree of mixing depends on energy difference
3) If they have the right phase
Same phase – constructive interference
Opposite phase – destructive interference
Bond Order = [(# bonding e’s) – (# anti-bonding e’s)]/2
Correlation Diagram for the orbitals in the second period
X
2pz
X
2pz
The energy of the MO reflect that of the AO,s when atoms are aligned along the bond axis
Pz is higher than Px and Py
Similarly 2p is higher than 2p
Bonding behavior of the second period diatomic molecules can be predicted by filling the M.O.
The electron configurations of the diatomic molecules are analogous to the atom
Electrons fill in the order of MO energies from lowest to highest
(1s)2(1s*)2(2s)2(2s*)2(2p)4(2p)2(2p*)4(2p*)2
The complete energy level diagram
All the orbitals in the ground-state 2nd period elements have been considered
Bonding between these elements can be predicted by adding electrons to this orbital correlation energy level diagram
Li2 – bond order 1
Be2 - fills the σ2s* orbital, BO = 0
B2 - partially fills π2p levels, BO = 1
-2 e’s parallel i.e. paramagneticC2 - fills π2p, - BO = 2
- diamagnetic
O2 - partially fills π2p* levels, BO = 2
- paramagneticF2 - fills π2p* levels - BO = 1
Ne2 – fills σ2p*, BO = O, does not exist
N2 - fills σ2p - BO = 3 - diamangetic
Electron Configurations of diatomic molecules
You should be able to:
1. Write the MO electron configurations of each of these molecules
2. Write their Lewis Diagrams
3. Compare the predictions of Bond Order from the Lewis and the LCAO-MO descriptions
4. Compare the predictions of diamagnetism or paramagnetism from the LCAO-MO descriptions
Method of hybrid orbitalsFor molecules with more than 2 atoms, the LCAO method is computationally complex - done on a computer
Simplified molecular orbital method that retains the notion of a “chemical bond” rather than just a “net bond order” .
The method of hybrid orbitals or sometimes valence bond theory
It is derived from molecular shape and used to define common bonding situations.
Ex) BeH2 with a central Be atom
BeH2 is linear by the VSEPR method, having two equal bonds
There are not two identical atomic orbitals on Be that allow us to define two equivalent bonds
These are obtained by combining the atomic 2s and 2p orbitals and hybridize them into two new hybrid atomic orbitals
Overlap of these new hybrid orbitals and the H 1s orbitals leads to the desired bonding orbitals
BeH2 and sp hybridization
Two hybrid atomic orbitals are made to fit the shape of the molecule, in this case linear, using atomic orbitals of an excited state Be atom!
unhybridzed2
2( )
p
sp
2
2
p
s
Be 2 H
sp hybrids
1s 1s
2 Be-H bonds
2 Be-H "antibonds"
2px 2py 2px 2py
Unused AO 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, creating both bonding and anti-bonding molecular orbitals, which are localized molecular orbitals
BH3 and sp2 hybridization unhybridzed
2
2
2( )
p
sp
2
2
p
s
B 3 H
sp2 hybrids1s 1s 1s
3 B-H bonds
3 B-H "antibonds"
2py 2py
BH3 is trigonal planar with three equal B—H bonds
To get this shape 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
CH4 and sp3 hybridizationno unhybridzed orbitals in 2nd shell
3
2( )sp
2
2
p
s
C 4 H
sp3 hybrids1s 1s 1s 1s
4 C-H bonds
4 C-H "antibonds"
CH4 is tetrahedral with 4 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
In 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
Hybrid AO’s and VSEPRA hybridization scheme exists for each member VSEPR shape families
Hybrid AO’s can be used both for bond pairs and for lone pairs
The hybridizations are:
Shape Family Hybridization No. of equivalent bondsLinear sp 2Trigonal planar sp2 3Tetrahedral sp3 4Trigonal bipyramidal sp3d 5Octahedral sp3d2 6
The hybrid atomic orbitals for the Trigonal bipyramidal and octahedral shapes will not be discussed further
For the first three shape families, the localized hybrid atomic orbitals description and a fully delocalized molecular orbital description are essentially equivalent
This method is used throughout most organic chemistry courses
H2O and sp3 hybridizationno unhybridzed orbitals in 2nd shell
3
2( )sp 2
2
p
s
H2O is bent and belongs to the tetrahedral family with 2 BP and 2 LP
The s and p orbitals combine sp3 hybrids
The 6 e’s from O, singly occupy 2 sp3 orbitals and doubly occupy the remaining 2 as LP’s
O 2 H
sp3 hybrids1s 1s
2 C-H
2 LP’s
The 2 sp3 orbitals combine with 2 1s orbital to form 2 C-H bonds
Two central atoms: ethane
C C
H
H
H
H
H
H
= H 1s = C sp3
VSEPR theory requires both carbon atoms to be tetrahedral
The shape of the molecule, its conformation, requires that contacts be minimized between the atoms – this is known as the staggered conformation
Bonding in ethane can be explained by using sp3 hybrid orbitals on each carbon atoms
The H atoms bond using their 1s atomic orbitals
In all there are 14 electrons or 7 electron pair bonds in the molecule
1 C-C sp3-sp3 single bond and 6 C-H sp3-s single bonds are formed
Double bonds: ethene
= H 1s = C sp2
2px2px
The sigma skeleton of ethene The pi manifold of ethene
Change perspective to show the π bond!
If we treat ethane by the VSEPR theory, we find that both carbon atoms are trigonal planar
The molecule is planar. Why ?
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
There are 6 e’ pair bonds in the molecule, 5 in σ orbitals, 1 in the π orbital
sp2-sp2 C-C bond, 1 px-px C-C bond , and 4 sp2-s C-H bonds
Planarity in double bonds: ethene againplanar structure of ethene can now be explained
When the two CH2 fragments are co-planar can there sufficient overlap between the unhybridized p orbitals leading to the π bond
If ethene is rotated by 90 along the C—C bond, the atomic p orbitals have zero net overlap
Double bonds impose coplanar conformations on the joining atoms
This is true for all double-bonded molecules, and is a powerful support for the bonding theories discussed
Note that a double bond is always the sum of a sigma + a pi bond
Single bonds are always sigma bonds, so that in ethane, all the bonds are sigma
Double bonds: ethyne
= H 1s
2px & 2py
The sigma skeleton of ethyne The pi manifold of ethyne
If we treat ethane by the VSEPR theory, we find that both carbon atoms are linear planar
The molecule is linear. Why ?
sp hybrid orbitals on each carbon atom, which leaves two atomic p orbitals unused on each C atom, while H atoms use their 1s atomic orbitals
There are 5 e’ pair bonds in the molecule, 3 in σ orbitals, 2 in the π orbital
sp-sp C-C bond, 2 p-p C-C bonds , and 2 sp-s C-H bonds
= C sp
C
H
H
O
Bonding in FormaldehydeLewis structure VSEPR geometry
bonding
OCH
H
:.. sp2sp2
= H 1s
= C sp2
2py2py
LP
LP
bonding
Flat
Triangular
1 sp2-sp2 C-C bond
2 sp2-s C-H bonds
2 sp2 LP’s
1 py-py C-C bond
Bonding in OzoneLewis structure VSEPR geometry
Bent
: :
::::
: :
::
::
sp2sp2
sp3sp3
sp2 sp2 sp3-sp2 bond
sp2-sp2 bond
3 sp2 LP’s
3 sp3 LP’s
p-p bond
Resonance
..OO
O..:
..
:
:
-1
+1
O
OO
:..
..
..:
:-1
+1
O
O
O-1/2 -1/2
+1
Localized electrons !
Bonding in Ozone Revisited
sp2sp2
sp2sp2
sp2 sp2
sp2-sp2 bonds
5 sp2 LP’s
p-p bond
1 p LP
: :
: :::
:::
: :
:
All Oxygen atoms can be considered to be sp2 hybridized instead
There are 4 p electrons
All 3 p orbitals combine to form 3 MO’s, therefore the LP in a p orbital and a BP in a two centre bonding orbital is not strictly speaking correct.
MO’ s of Ozone
3p
O-O-O
bondingorbital
non-bondingorbital
anti-bondingorbital
Three centre bonding orbital
LP’s
Resonance, Delocalization & Conjugation
CCCCA chain of alternating single and double bonds resonance allows the bonds to to be interchanged.
CCCC
sp2 sp2 sp2 sp2
The real situation is an average between them
All the carbons are considered to be sp2
hybridized.
The chain does not have to contain only carbon any atom that can involve at least 3 electrons in bonding will work as long as it can be sp2 hybridized, ex) N
For a chain of N carbons that are conjugated, there are N p orbitals that form N M.O.’s, where the first N/2 are occupied. The MO will increase in energy with incresing nodes.
Ex N = 4Linear molecule
# nodes
0
1
2
3
B’ing
B’ing
A. B’ing
A. B’ing
E
P orbitals
CCCC
Bonding in trans-1,3-butadieneLewis structure VSEPR geometry
bonding
bonding
C H
H
CCCH
H HHC
H
H
C
CC
H
H
H
H
sp2
sp2
sp2
Electrons are delocalized
sp2
4 MO’s with 0, 1, 2 and 3 nodes:
+ - + - a-bonding+ - - + a-bonding+ + - - bonding+ + + + bonding
Bonding in benzeneLewis structure
VSEPR geometry
bonding
C
CC
C
CC
H
H
H
H
H
H
H
H
H
6 sp2-s C-H bonds
6 sp2-sp2 C-C bonds
3 p-p C-C bonds
Bond order for C-C bonds is 1.5
p orbitals overlap
Electrons are delocalized
H
H
H
H
H
H
MO’s of Benzene
The 6 p orbital form 6 MO with 0,1,2 and 3 nodes
The MO’s with 0 and 1 node are bonding orbitals and are occupied
These represent 6 centered bonding orbitals
6 p
anti-bondingorbitals
bondingorbitals
# nodes
0
1
2
3
Bonding in Allene
bonding
bonding
Lewis structure
C H
H
CCH
H
VSEPR geometry
C
H
H
CC
H
H
4 sp2-s C-H bonds
2 sp2-sp C-C bonds
2 p-p C-C bonds
orbitals are perpendiculardo not overlap
e’s not delocalized
C-C B.O. = 2
sp2 sp sp2
Bonding in large molecules
sp3
sp3
sp3
sp3
sp3
sp2
sp2
sp3-sp3 S-C bond
s-sp3 H -S bond
2 s-sp3 H-C bonds
sp3-sp3 C-N bond
s-sp3 H-C bonds
2 s-sp3 N-H bonds
1 sp3 LP
sp3-sp2 C-C bond sp3-sp3 C-C bond
sp2-sp2 O-C bond
p-p O-C bond
sp2-sp3 C-O bond
s-sp3 H-O bond
2 sp2 LP’s
2 sp3 LP’s
Concepts from Chapter 10
MOLECULAR ORBITALS
LCAO theory
Correlation diagrams
Bonding, nonbonding and antibonding interactions
Calculating bond order using MO theory
hybridization (sp, sp2 and sp3 orbitals)
Sigma (σ) vs. pi (π) bonds
Composition of single, double and triple bonds
Resonance according to MO theory