Lecture
#17 
Chapter 14 starting
with Section 2
(We'll return to Section 1 later)

CURMUDGEON
GENERAL'S WARNING. These "slides"
represent highlights from lecture and are neither
complete nor meant to replace lecture. It is
advised not to use
these as a reliable means to replace missed
lecture material. Do so at risk to healthy
academic performance in 09105. 

Lecture Outline (some material shown is
lookandlisten only) 
Quantum Theory of the Chemical Bond
Molecular orbitals (in "homonuclear diatomic
molecules"
Approximated by combinations of atomic
orbitals
Constructive and
destructive interference effects
Combining 1s atomic
orbitals to get molecular orbitals
"Sigma" bonding molecular
orbital
"Sigma" antibonding molecular
orbital
Combining 2p atomic orbitals
"Sigma" bonding molecular
orbital
"Sigma" antibonding molecular
orbital
"Pi" bonding molecular orbitals
"Pi" antibonding molecular
orbitals

This is a calculated solution for the constructive
interference result. 

If destructive interference represents the orbital in
which the electron happens to be found, the linear
combination results in a depeletion of electron density
between the positively charged protons. They repel each
other under these circumstances. 

This is the destructive interference combination of
1s atomic orbitals 

The total energy of the ground state of H_{2}^{+}
as a function of the distance between the protons. 

A schematic of the orbitals on separated protons
relative to "close" protons. The constructive
combination of atomic orbitals gives rise to a system
lower in energy than the isolated system and is a bonding
molecular orbital. 

Energy diagram and geometry for the sigma1s
(bonding) orbital construction.


Energy diagram and geometry for the sigma*1s
(antibonding) orbital construction


Energy diagram and geometry for the sigma2p_{x}
(bonding) orbital construction from the 2p atomic
orbitals originally directed along the bonding (x) axis. 

This (with luck) is an animation of the
computergenerated _{2p}
(or _{p}) bonding
molecular orbital showing how the symmetry about the bond
axis resembles that for the satomic orbital's symmetry
about the nucleus. Hence the label. 

Energy diagram and geometry for the sigma*2p
(antibonding) molecular orbital construction 

A reminder that, perpendicular to the bond axis in
the xdirection, there are 2p atomic orbitals in the
zdirection and in the ydirection. Just the 2p_{y}
orbitals on each atom are shown here. 

Energy diagram and geometry for the pi2p_{y}
(bonding) molecular orbital construction from the 2p
atomic orbitals originally pointing in the ydirection,
perpendicular to the bond axis and in the plane of the
illustration. Constructive interference occurs in the
region of overlap. (Recognize that there is an identical
pi bonding level, same energy, constructed in the
xdirection from the 2p_{z} atomic orbitals.) 

This is an animation of the computergenerated _{2p}
bonding molecular orbital showing how the symmetry about
the bond axis resembles that for the patomic orbital's
symmetry about the nucleus. Hence the label. 

Energy diagram and geometry for the pi*2p_{y}
(antibonding) molecular orbital construction from the 2p
atomic orbitals originally pointing in the ydirection,
perpendicular to the bond axis and in the plane of the
illustration. Destructive interference occurs here, in
contrast to what occurs for the bonding molecular
orbital. (Recognize that there is an identical pi*
antibonding level, same energy, constructed in the
zdirection from the 2p_{z} atomic orbitals.) 

Redefining how one calculates bond order within the
context of molecular orbital theory. 

The molecular orbital energy diagram for H_{2}^{}
and other isoelectronic species, all having bond order =
0.5. The electron configuration would be written as _{1s}^{2} ^{*}_{1s}^{2 }_{2s}^{2}
or, as in the current text, simply _{s}^{2}
^{*}_{s}^{2
}_{s}^{2}. 

Molecular orbital energy diagrams for 1, 2, 3, and 4
electrons systems. The correspondence between bond order
and bondlength and between bond order and bond energy is
shown for each molecular species. 

The molecular orbital energy diagram for Li_{2}
containing all six electrons. Since antibonding electrons
negate the effect of bonding electrons, the pair of * electrons cancels out the bonding
characteristics of the pair of electrons
and both pairs revert to the inner core 1s^{2}
configurations that we expect from simpler
considerations. The electron configuration could thus be
written as [He][He]_{2s}^{2}. 

The molecular orbital energy diagram for Be_{2}.
Since the number of antibonding electrons is equal to the
number of bonding electrons, there is no net bonding in
this molecule and it simply breaks back up into two Be
atoms. 

For "diboron", B_{2} we get a
somewhat surprising result out of the molecular orbital
energy diagram and the ensuing electron configuration.
The ninth and tenth electrons go into the lowest energy
available orbitals. These are the orbitals.
There are two of equal energy and Hund's rule forces us
to put one electron in each and with parallel spins. Thus
we have bond order = 1, a single bond, but it is not a
sigma bond. In fact, there is one electron in one
piorbital and another electron in a second piorbital
comprising this single bond. 

Molecular orbital energy diagram for the lower states
in molecular nitrogen, N_{2}. The lowest two
molecular orbitals return to 1s, inner core electrons on
each nitrogen atom. The next two pairs, with no net
bonding effect, become lone pairs that can be pictured as
being in 2s valence orbitals on each nitrogen. 

The valence molecular orbitals in nitrogen that give
rise to the triple bond, bond order = 3. 

Click the Detour sign to see an optional explanation
(several slides) of why the / sequence changes when O_{2}
and F_{2} are reached. Note, you do not
need to remember this reversal of sequence. For your
convenience in 09105, you can ignore it even if it seems
to apply. 

The electron configuration for all 14 electrons in N_{2}.
Three variations are shown on how to represent the inner
core, 1s^{2} electrons on each nitrogen atom.
Sometimes the two pi molecular orbitals are respresented
with a single ^{4} symbol. 

Comparison of ionization energies for atomic N and
molecular N_{2} to illustrate that the bonding
molecular orbital in the latter is more stable than the
atomic orbital from which it "originates". That
is, combining two N atoms leads to a more stable, bound
nitrogen molecule, releasing energy. 

The highest occupied molecular orbitals in molecular
oxygen. The bond order is 2, but is composed of a sigma
bond and one net electron in each of the two orbitals.
The molecule is paramagnetic due to the two parallel
electron spins. 

Comparison of ionization energies for atomic O and
molecular O_{2} to illustrate that the
antibonding molecular orbital in the latter is less
stable than the atomic orbital from which it
"originates". That is, electrons in the
antibonding orbitals "want" to release energy
by returning to atomic orbitals. 
