Chapter 9, continued
Hybrid orbitals & multiple bonding
Consider the ethylene molecule
H
H
C
H
C
H
the observed H-C-H and H-C-C bond angles are 1200 in
ethylene ; what type of hybridization does this suggest for
the C atoms?
what happens to the unhybridized 2p orbital on each C?
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Now consider the bonding in acetylene, C2H2:
H
C
C
H
Experimental evidence indicates that the H-C-C bond
angles are 180o in acetylene; what hybridization scheme
does this suggest for the carbon atoms?
Again, what happens to unhybridized 2p orbitals on the
carbons?
Bonds with e- density concentrated along the internuclear
axis are called sigma () bonds
e.g., overlap of 2 s-type AOs, 2 p-type AOs, or s - p overlap
along the internuclear axis
also, overlap of sp, sp2, or sp3 hybrid with an unhybridized
AO along the internuclear axis
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Bonds which result from overlap of p-type AOs oriented
perpendicularly to the internuclear axis are called pi ()
bonds
 bonds result from sideways overlap of unhybridized ptype AOs
e- density is above and below the internuclear axis
e.g., how many  and  bonds in C2H4? C2H2?
e.g., the Lewis structure for glycine is
H O
H2N C C O H
H
What are the bond angles and hybridizations of the C, O,
and N atoms?
How many  and  bonds are there in this structure?
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Delocalized bonding
Consider the ethylene molecule, C2H4:The  bonding
in C2H4 is said to be localized between the C atoms
What about molecules with 3 or more atoms which can 
bond (i.e., have unhybridized p-orbitals)?
e.g., NO3-, CO32-, C6H6 : all have resonance forms
 bonding in molecules with resonance forms can't be
accurately described as localized
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Why? e.g., C6H6 (benzene):
what is the hybridization of the C atoms in C6H6? what are
the bond angles?
In C6H6, all C-C bonds are of equal length, and are
intermediate between C-C (single) and C=C (double) bonds
how to explain this?
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Each C atom is using sp2 hybrid orbitals:
the  orbitals of C6H6 are formed by the overlap of the
'leftover' 2p orbitals of each C:
We envision the 2p e- of the carbons as being shared
among all 6 C atoms, i.e., the 3  bonds are 'smeared out'
over all 6 C
this is delocalized  bonding
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other representations of benzene:
General conclusions about VB theory and orbital
hybridization
 bonds are localized between the atoms which are
sharing the ethe set of hybrid orbitals used to form  bonds is
determined by the observed geometry of the molecule
when atoms share > 1 e- pair, the additional pairs are
in  bonds
e- in  bonds that extend over > 2 atoms are said to be
delocalized
The VB model is a model of a molecule as composed
of individual atoms
Overlap of AOs on each atom leads to bond
formation
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Molecular orbitals
VB theory relates AOs and Lewis structures
hybrid orbitals help explain observed geometries
VB theory does not explain an extremely important feature
of molecules, namely, the fact that they can absorb and
emit radiation
recall: the allowed energy states of e- in atoms (i.e., n, l, ml)
are called atomic orbitals
we combine AOs to form molecular orbitals (MOs), in
which e- can exist in discrete energy states in molecules
in this model, the atoms themselves are not important
– only the properties of the molecule are relevant
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MOs and AOs have many of the same properties, e.g.,
MOs can hold a maximum of 2 e- (with opposite spin)
When 2 AOs are combined, 2 MOs result
e.g., consider the H2 molecule: how many ways can
combine 2 1s orbitals?
1s: lower E than separated 1s atomic orbitals; bonding
MO (high e- density between nuclei)
*1s: higher E than 1s AOs; antibonding MO (no e- density
between nuclei)
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draw as a MO diagram:
follow Hund's rule in filling the MOs
Notice that, when we combined 2-s type AOs we obtained
2 -type MOs
the total number of orbitals is
conserved, i.e., we combine n
AOs and obtain n MOs
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e.g., draw the MO diagram for the He2
molecule and the He2+ ion
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Bond order
Measure of stability of a covalent bond
Bond Order = 1/2 (# of bonding e- # of antibonding e-)
Bond order = 1 represents single bond
Bond order =2 “
“ double bond, etc.
e.g., find the bond orders of H2, He2, and He2+
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MOs for homonuclear 2nd period diatomics
Rules to live by:
# of MOs formed = # of AOs combined
AOs combine with other AOs of similar energy (e.g. 2s
with 2s, 2p with 2p etc)
Each MO can hold 2 e- with spins paired
Hund's rule is used in filling MOs
We will be concerned with valence electrons only
when constructing MO diagrams
Consider the Li and Be atoms
note that the 2s AO on one atom interacts only with
the 2s AO on the other atom
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Draw the MO diagrams and find the bond orders of Li2
and Be2
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MOs from 2p AOs: B2 - F2
in the above cases: only -type MOs formed (why?)
recall: 3 p-type AOs (px, py, pz)
p-type AOs which overlap along the internuclear axis
(usually 2pz) form  and * MOs
p-type AOs which overlap perpendicular to the
internuclear axis (2px, 2py) form and* MOs
General MO diagram for second-row diatomics
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In constructing the above diagram we assume no
interaction between the 2s AO on one atom and the 2p
AO on the other
These in fact do interact with one another
The closer together the 2s and 2p energy levels in the
atoms, the stronger the interaction
The 2s-2p energy gap increases moving across the
second period
For oxygen - neon, the 2s-2p gap is large enough that
there isn’t a strong 2s-2p interaction
For O2 – Ne2: 2p MO > 2p MO
For boron-nitrogen, the 2s-2p gap is small enough
that there is a strong 2s-2p interaction
For B2 – N2: 2p MO > 2p MO
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Moral of the story: start with ordering
2s, 2s*, 2p, 2p, 2p*, 2p* for B2-N2 (strong interaction)
For O2 – Ne2, switch 2p, 2p (weak interaction):
2s, 2s*, 2p, 2p, 2p*, 2p*
E.g., write MO configurations for B2, C2, N2, O2, and F2
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E.g., Find the bond orders for these molecules
How can MO theory explain magnetism in molecules?
How does the molecular orbital theory explain molecular
spectra?
Problems du Jour
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List the members of the following series in order of
increasing bond length: N2+, N2, N2-
Give the molecular orbital configuration for the following
cations:
C2+
Ne22+
Indicate whether addition of an electron would increase or
decrease the stability of these species.
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