week 1 - intro to orbitals
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Beyond Lewis Structures
The building-block formalism of organic chemical structure, more
commonly called the "Lewis dot model," is a powerful schema for
organizing organic molecules and identifying similarities between them.
Coupled with the generalized stability trends, we can begin to reason fromthe seen to the unseen to make predictions about never-before-seen
chemical reactions. However, there are many observations that the Lewis
dot model cannot explain. Its explanatory power doesn't even come close
to its organizational strength. In fact, most stability trends find their origin
not in the Lewis dot model, but in a deeper theory of molecular structure:
molecular orbital theory. In this chapter, we'll develop a version of
molecular orbital theory useful for the student and everyday practitioner of
organic chemistry. Realize that we will notdisprove the Lewis dot model in
this chapter! Molecular orbital theory is meant to enhance, not replace the
Lewis dot model. Its organizational power still remains, and we will still rely
on the building-block formalism to make connections between analogous
structures in later discussions.
Before diving in to the details of molecular orbital theory, let's explore
some of the shortcomings of the Lewis dot model. What can't it explain,
and why is an additional theory necessary? Consider the process in Figure
1a, rotation about a carbon-carbon double bond. The Lewis dot model
stipulates that the four electrons in the double bond are shared betweenthe two carbon atoms, but it can't explain why rotation about the double
bond doesn't occur until the compound is heated to extremely high
temperatures. Molecular orbital theory reveals that carbon-carbon multiple
bonds cannot rotate without breaking.
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Figure 1.Observations that the Lewis dot model does not explain
adequately. (a) Rotation about double bonds does not occur at room
temperature, even though rotation around unhindered single bonds is rapid
at room temperature. (b) One-step substitution reactions result in an
inversion of configuration (two atoms appear to switch places) at the
electrophilic carbon. (c) Carbocations substituted with more carbon atoms
are more stable than less substituted cations.
The single-step SN2 reaction in Figure 1b has properties that are not
addressed by the Lewis dot model, too. Displacement of bromide by
hydroxide leads exclusively to an inversion of configuration at the central
carbon atom. This observation suggests a particular trajectory for hydroxide
as the substitution takes place, but the Lewis dot model offers no dominant
path. The spatial aspects of the reaction are best explained by molecular
orbital theory--in fact, simple steric considerations may argue against the
observed configuration of the product!Finally, Figure 1c shows the relative stability of two carbocations.
More substituted cations are more stable than those that are less
substituted, other things being equal. Yet, aside from the somewhat hand-
wavy explanation of steric hindrance due to flanking CH bonds, the Lewis
dot model cannot account for the exceptional stability of the left-hand (tert-
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butyl) cation. Orbital interactions, which find their theoretical basis in
molecular orbital theory, elegantly explain this ubiquitous observation.
To account for all of the observations in Figure 1, we need a model
that suggests the spatial positions and energies of electrons within a
molecule. Molecular orbital theory provides this information--in fact, anorbitalis just an electronic container with an associated energy value. In
the next section, we'll introduce the fundamentals of the orbital concept.
Throughout the following sections, keep in mind our goal of describing in
detail the electronic structure and reactivity of organic molecules.
***
Introduction to Orbitals
In this section, we'll begin to extend the Lewis model by expanding
our conception of the electron. While the Lewis dot model stipulates that
electrons sit, isolated, on or between atoms, the quantum mechanical truth
is far more interesting: electrons may be delocalized over large regions of
space, and even across several atoms! Belonging to each electron in a
molecule is a function called an orbital, which describes all of its properties
according to the principles of quantum mechanics.
Strictly speaking, an orbital is a function over all space that specifies
the probability of finding an electron at a given point.1Orbitals for atoms
and molecules take into account the positions of nuclei and other electrons
nearby. In practice, probability values rapidly approach zero at certaindistances from the nucleus. For this reason, we can focus only on a "slice"
of space, a container that encloses all of the points for which the probability
of finding the electron is larger than some cutoff value.2Organic chemists
most often think of orbitals in this way, as containers in which electrons are
likely to be found. A single orbital can contain up to two electrons of
different electronic spin. We typically refer to the different spins of the
electron as "spin up" and "spin down" or +1/2 and 1/2. To depict the
occupancy, energy, and shape of orbitals, chemists use orbital diagrams.
A simple orbital diagram is shown in Figure 2. Notice that the number ofelectrons, energy, and appearance of the orbital are all shown on the orbital
diagram. A horizontal line is drawn to indicate the position of the orbital on a
vertical energy scale. Half arrows up and down are drawn to show how
many electrons are in the orbital, and what their spins are. Often, the shape
of the orbital will be omitted or drawn in a separate picture of the molecule
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under study.
Figure 2.The three essential features of every orbital, with an
example of an orbital diagram.
Orbitals can take on either positive or negative values over space.
This seems at odds with our earlier definition of the orbital as a distribution
of probabilities: how can a probability be negative? We now need to
expand our previous definition: the magnitudeof the orbital is a probability,
and its sign refers to a property called phase. Phase is important when
orbitals combine or overlap, because they do so like waves, enhancing oneanother in some regions and canceling one another out in others. In
pictures of orbital shapes, positive and negative phases are indicated either
with different colors or with shading. In Figure 2, for example, we might
choose the unshaded area to represent a region of positive phase and the
shaded area to represent a region of negative phase. Our exact choice is
arbitrary, but it's important to keep in mind that the shaded and unshaded
regions are places where the signs of the orbital are different. We'll revisit
phase shortly, when we discuss how orbitals combine with one another.
Orbitals are special functions that apply to the electron. But where do
the functions themselves come from? What's the origin of the shapes and
energies of orbitals? We won't follow this line of inquiry too far, except to
say that the orbital belonging to an electron depends on the electron's
environment. Designations like "atomic" and "molecular orbitals" reflect the
environment of the electron. Atomic orbitals belong to electrons in atoms,
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molecular orbitals belong to electrons in molecules, et cetera. The nature of
the environment and a quantum mechanical relation called the Schrdinger
equation are used to solve for the form of the orbital. We'll largely treat the
shapes and energies of atomic orbitals as axiomatic--that is, we'll present
them without proof. Such proofs are generally reserved for physicalchemists...and organic chemists are glad to give them up!
Watch The Orbital Concept
Let's begin with a look at the atomic orbitals (AOs)that characterize
the first- and second-row elements. There are five that are important for
organic chemistry: the 1s, 2s, 2px, 2py, and 2pzatomic orbitals. Their
shapes and relative energies are shown on an orbital diagram in Figure 3.
At the center of each 2porbital, where the nucleus sits, we can identify a
node, where the phase of the orbital changes. At the node, the value of the
orbital is zero. These five orbitals form a sort of scaffold, into which we can
add electrons to characterize the organic atoms.
Figure 3.The atomic orbitals on an orbital energy diagram, with
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electronic configurations of the first- and second-row elements.
We use the term electron configurationto refer to how an atom's
electrons occupy the atomic orbitals. In the blue box in Figure 3.3, the
configurations of the first- and second-row elements are provided. The firstnumber in each orbital's name is its principal quantum number, a measure
of its energy (as principal quantum number goes up, energy does too). The
letters sandpindicate the orbital's subshell (an indicator of orbital shape
and energy). Finally, the superscripted 1's and 2's show the number of
electrons in each AO. Notice that electrons occupy the most stable orbitals
first, followed by more unstable orbitals. The three 2porbitals are all
degenerate--that is, they have the same energy. Degenerate orbitals are
filled one electron at a time, so that two electrons are not paired up until
they must be. Figure 4 illustrates how electrons fill the AOs of boron,
carbon, nitrogen, and oxygen. Notice that two electrons don't occupy the
same orbital until it's unavoidable. This method for filling orbitals with
electrons, which holds regardless of the type of orbital (atomic, molecular,
etc.) is called Hund's rule.
Figure 4. Orbital energy diagrams for B, C, N, and O atoms. Hund's
rule states that electrons should not be paired up until no other placement
is possible.
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Let's take a breather--what's the point of all this atomic orbital
mumbo-jumbo? With some notable exceptions, we won't deal directly with
the atomic orbitals once we've fully developed molecular orbital theory.
However, atomic orbitals are quite literally the building blocksof molecular
orbitals, which are our ultimate endgame. We'd like to understand theelectronic structures of molecules, but to do so, we need to recognize how
electrons are arranged in atoms. In particular, the molecular orbitals we
tend to care about are built from the valence atomic orbitals, an atom's
occupied orbitals with highest principal quantum number.3
Early in this section, we noted that the shape and energy of an
electron's orbital depends on the system of which it's a part. Atomic orbitals
pertain to atomic systems, molecular orbitals to molecular systems, etc. An
orbital is a solution to a problem that takes the system into account. Thus,
from first principles, we might imagine that molecular orbitals, the solutions
to molecular problems, are unrelated to atomic orbitals, the solutions to
atomic problems. Yet, remarkably, we find in practice that linear
combinations (weighted sums) of the atomicorbitals approximate solutions
to the problem of describing electrons in molecules. This approximation is
the cornerstone of the linear combinations of atomic orbitals-molecular
orbitals (LCAO-MO)method, which we'll explore in the context of
dihydrogen in the next section.
Watch The Atomic Orbitals
***
Molecular Orbitals of Dihydrogen
Our goal so far has been to describe the spatial positions and
energies of electrons in atoms and molecules, using the principles of
quantum mechanics as a foundation. Quantum mechanics sets up the
problem of determining an electron's orbital as a kind of physical
optimization problem: what spatial arrangement of electrons leads to the
most stable system? In the last section, we were introduced to the atomicorbitals, which are solutions for atomic systems of the first and second rows
of the periodic table. Thankfully, we do not need to start over at square one
to determine the orbitals of electrons in molecules! Molecular orbitals are
well approximated by linear combinations of the atomic orbitals associated
with the molecule's atoms.
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Keep our goal in mind throughout this section. We want to answer the
following questions:
Where are the electrons in a molecule located in space? What are
their energies?
We've already seen the containers that hold electrons in atoms--the
1s, 2s, and 2patomic orbitals. Molecular orbitals are constructed from
these building blocks, and have spatial and energetic properties that reflect
their construction from atomic orbitals. In fact, there are multiple ways to
carry out the process of building molecular orbitals, but we will adopt a
localized molecular orbital theoryapproach using the ideas of
hybridization and localized MOs. Localized MO theory breaks from the
"canonical" mold used by physical chemists, but will serve us well
throughout future discussions. Let's begin with a very simple case: the
molecular orbitals of the dihydrogen molecule, H2.
The hydrogen atom possesses a single electron in a 1satomic
orbital. When two hydrogen atoms come together, a molecule containing a
total of two electrons results (H2). Thus, we might imagine that only one
molecular orbital is needed to accommodate these two electrons. However,
this conclusion ignores the important fact that hydrogen's valence AO (1s)
is unfilled. Both the hydrogen atom and the dihydrogen molecule canaccept electrons. We could imagine giving one more electron to the
hydrogen atom to create the hydride anion, H. Then, we could combine
two Hatoms together to create the fantastical dianion, H22. Loading up
the valence atomic orbital of H with electrons shows us that we need two
molecular orbitals for the neutral H2molecule, even though the molecule
itself only possesses two electrons. H2can accept two additional electrons,
and we need a place to put those! In general, remembering that we need a
place to put any electrons that may enter the molecule, we can conclude
the following:
The total number of atomic orbitals possessed by all the atoms of a
molecule equals the molecule's total number of molecular orbitals.
Figure 5 below shows the molecular orbitals of dihydrogen at the
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center of an orbital energy diagram. The shapes of the molecular orbitals
are determined by quantum mechanical principles that we won't concern
ourselves with here. What we should notice is the relationship between
orbital shape and energy--notice that the MO with lobes of two different
phases (and a node in between) is higher in energy than the orbital lackingany sign changes. Mathematically, the higher-energy orbital is the result of
subtracting the two 1sAOs, and the lower-energy orbital is the result of
adding the two AOs. When we add two 1sorbitals of the same phase, they
reinforce one another in the region between the nuclei. When we add
orbitals of opposite phase, however (i.e., subtract two AOs of the same
phase), they tend to cancel one another out between the nuclei, and at
some point, a node results. Figure 5 is probably the simplest example of
the linear combinations of atomic orbitals-molecular orbitals (LCAO-MO)
method. The dotted lines from the atomic to the molecular orbitals indicate
contributions of the AOs to each MO.
Figure 5.A molecular orbital energy diagram for H2, with isolated H
atoms (and atomic orbitals) on the periphery and the molecule (and its
MOs) in the center.
Because the higher-energy orbital lacks electron density between the
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nuclei, we call that orbital antibonding. Antibonding orbitals have energies
that are higher than those of the isolated atoms. Bondingorbitals, on the
other hand, have enhanced electron density between the nuclei and lower
energies than the separated atoms. Bonding MOs involve constructive
overlapof AOs, overlap of two lobes of the same phase. Antibondingorbitals result from destructive overlap--when lobes of opposite phase
coincide in space.
The simple example of dihydrogen from this section has introduced
us to the idea that molecular orbitals are built as weighted sums and
differences of atomic orbitals. In future discussions, we'll create molecular
orbital diagrams like Figure 5 using other types of atomic orbital building
blocks that sit on nearby atoms. Let's end this section with a quandary.
We've seen that molecular orbitals may be built from the 1s, 2s, and 2p
atomic orbitals. We've also seen that the 2porbitals are at right angles to
one another. The angles of the directional 2porbitals seem inconsistent
with the bond angles we saw in the section on molecular geometry. How
can we reconcile these two ideas, which seem to be at odds with one
another? We'll see how the idea of hybridizationsolves this problem in the
next section.
Watch Linear Combinations of Atomic Orbitals
***Atomic & Molecular Orbitals in Organic Molecules
Applying the LCAO-MO method of the last section to large organic
molecules produces complex, delocalized molecular orbitals. Such MOs tell
us little about how we should expect molecules to behave. Furthermore,
since delocalized MOs bear little resemblance to the lines and dots of
Lewis structures, it can be difficult to make connections between the two.
To get around this problem, we'd like an orbital theory that yields localized
MOs that look and "feel" like the elements of Lewis structures we already
know and love. In this section, we'll learn the six localized molecularorbitals that correspond directly to bonds and lone electron pairs in Lewis
structures. Our goal is to describe the shapes and energies of electron
sources and sinks in more detail, to paint a more vivid picture of electronic
structure in organic molecules.
At the end of the last section we confronted a quandary: is it possible
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to reconcile the geometry of the 2patomic orbitals (90 bond angles) with
the observed geometries of organic compounds (tetrahedral, trigonal
planar, and linear)? The answer is a resounding "yes," thanks to Linus
Pauling's concept of hybridization. To account for the observed
geometries of organic compounds, Pauling proposed that beforecombiningwith orbitals on other atoms, atomic orbitals can "hybridize" to produce a
new set of atomic orbitalsfor bonding. The process of "hybridization" is
essentially a kind of on-atom linear combination. We can take bits and
pieces from the different atomic orbitals to construct the hybrid atomic
orbitals. Don't worry about how exactly this is done--it's important just to
recognize the final result of hybridization, the three sets of hybrid AOs in
Figure 6.
Figure 6.The three sets of hybrid orbitals and their correspondinggeneralized building blocks.
The relative energies of the hybrid atomic orbitals are straightforward
to understand.4In the last section, we saw that the 2patomic orbitals are
higher in energy than the 2sorbital. Thus, we might expect hybrid orbitals
made of a greater percentage of 2pAOs to be higher in energy than those
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with less 2pcharacter. Experiments support this idea--the stability of
electrons held in hybrid AOs follows this trend:
(highest energy) 2p> sp3> sp2> sp> 2s(lowest energy)
Stated another way, hybrid AOs of greater scharacterare lower in
energy than those with less scharacter. Does this lower energy
automatically imply greater stability? No!The lower-energy hybrids are
stable when filled, but unstable without electrons. For this reason, cations
and other unsaturated species that possess empty hybrid orbitals are
usually unstable.
There is a profound link between the nature of an atom's building
block within a molecule and its hybridization. From Figure 6, notice that
hybridization depends on its geometry: tetrahedral atoms are sp3-
hybridized, trigonal planar atoms are sp2-hybridized, and linear atoms are
sp-hybridized.5Furthermore, the number of !bonds on an atom
corresponds to the number of AOs used to form its hybrids: 4 !bonds = 1 s
+ 3p= sp3, et cetera. Multiple bonds, as we will soon see, can be
understood as arising from interactions between unhybridized, leftover 2p
orbitals. For instance, sp2hybridization leaves behind one 2porbital for
multiple (") bonding. spHybridization leaves behind two 2porbitals for "
bonding. Examining the building blocks corresponding to thesehybridization states, we see one and two multiple bonds, respectively.
That's not a coincidence!The sp2and sphybrid orbital sets are shown in
Figure 7 with their leftover 2porbitals.
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Figure 7.Hybridization may leave behind unused 2porbitals, if less
than four !bonds are needed. Leftover 2porbitals may be used for "
(multiple) bonding or to hold nonbonding electrons.
The hybrid atomic orbital sets will serve as our starting point for
thinking about the molecular orbitals of large organic compounds. Localized
molecular orbitals are built either from the hybrid AOs themselves, in
isolation (we call such molecular orbitals non-bonding), or from bonding
and antibonding combinations of the hybrids. At this stage, it's important to
realize that we can treat each !(single) bond in an organic compound like
we did the hydrogen atom, using hybrid orbitals in place of 1sorbitals. For
each !bond, there is a !bonding orbital, which holds the electrons of thebond, and a !* antibonding orbital, which reflects the ability of the bond to
break upon the addition of two more electrons. The bonding MO involves
constructive overlap of the hybrids, and the antibonding MO destructive
overlap. Figure 8 shows a simple orbital energy diagram for the carbon-
carbon !bond in ethane (C2H6).
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Figure 8.A simple orbital energy diagram for the CC bond of
ethane. The bond is associated with two molecular orbitals: a bonding !
orbital of low energy, and an antibonding !* orbital of high energy.
The !molecular orbital shows us where the electrons of the bond are
likely to be found in space. The energy of this orbital reflects the reactivityof the electrons in the bond as an electron source--a clean, intuitive idea.
But how should we interpret the empty antibonding orbital? What does an
antibonding orbital "mean" from the molecule's perspective? Put most
concretely: how does the nature of the !* orbital affect the bond's behavior
(structure and reactivity)? Spatially, the !* orbital shows us where incoming
electrons from a source are likely to go. Incoming electrons will tend to
approach the large lobes of the antibonding orbital. Like unfilled hybrid
AOs, antibonding MOs are most stable when high in energy. Summing up,
the nature of the !* orbital reflects the bond's potential as an electron sink!Since reactions require both an electron source and sink, we must keep the
importance of antibonding orbitals in mind when studying organic
reactivity--the sink is an essential piece of the puzzle.
!Bonding is advantageous for molecules because, as we can see
from Figure 8, the overall energy of electrons is lowered in the process. But
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!bonding also seems to present certain problems--for instance, how can
hybrids overlap to form multiple bonds? Using more than one hybrid orbital
to describe a multiple bond seems out of the question. Still, the 2porbitals
left behind on sp2- and sp-hybridized atoms don't look appropriately
positioned for orbital overlap. What gives? Evidently, the parallelarrangement of 2porbitals is good enough to establish a bond between
adjacent atoms. Figure 9 shows the idea for the simplest hydrocarbon that
contains a double bond, ethylene.
Figure 9.Multiple bonds are the result of "side on," parallel, or "-type
overlap of adjacent 2porbitals. Just as in the !bonding case, a bonding "
orbital and an antibonding "* orbital result from constructive and
destructive overlap.
Our spatial and energetic interpretations of the "and "* orbitals are
identical to those of the !and !* orbitals. To reiterate, the "orbital reflects
the potential of the double bond to serve as an electron source, and the "*
orbital reflects the potential of the double bond to serve as an electron sink.
Importantly however, the side-on overlap characteristic of "orbitals is
weaker than the head-on overlap involved in !bonding. As a result, "and
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"* MOs tend to be closer in energy to their atomic orbital building blocks
than !orbitals. Consequently, two important trends occur:
"Bonding MOs are higher in energy than !MOs.
"* Antibonding MOs are lower in energy than !* MOs.
Taken together, what do these trends suggest about the relative
reactivity of single and multiple bonds? In general, multiple bonds are more
reactive (both as sources andsinks) than single bonds. Electrons in "
bonds are higher in energy than electrons in !bonds; unfilled "* orbitals
are lower in energy than !* orbitals. In addition, we can see from Figures 8
and 9 that the spatial positions of "and !electrons differ. !Electron
density can be found along an axis connecting the atoms, while "electron
density is found above and below such an axis. In fact, "MOs possess a
node coinciding with the axis connecting their atoms.
Finally, we need to address nonbonding electrons and orbitals, which
are not involved in interactions with orbitals on adjacent atoms. In the
absence of resonance interactions, lone electron pairs can be found in
isolate hybrid AOs. We will refer to these as nmolecular orbitals (for
"nonbonding"). Figure 10 depicts three examples of n orbitals in common
compounds. Notice that each n orbital is characterized by a particular
hybridization, since the nMO is really just a hybrid atomic orbital. The norbital reflects the potential of the atom to serve as an electron source viaa
lone pair sitting on the atom.
Figure 10.Nonbonding n orbitals in common organic molecules.
Most commonly, n orbitals are just hybrid atomic orbitals.
Building blocks bearing fewer than 8 total electrons must possess an
empty nonbonding MO, which we call an aorbital (for "atomic"). What are
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the atomic orbital constituents of aMOs? Empty hybrid AOs present an
energetic problem: they're low in energy and thus tend to be unstable when
lacking electrons. To get around this problem, molecules without geometric
constraints adopt geometries that allow them to leave high-energy 2p
orbitals unfilled. Thus, in the vast majority of cases, aorbitals are justempty atomic 2porbitals. When you spot a building block with 6 or fewer
total electrons, take note that an empty aorbital is present on the atom!
This MO reflects the potential of the atom itself to serve as an electron sink.
Empty aorbitals are typically the lowest energy (and most unstable) unfilled
orbitals one finds in organic compounds. This fact is unsurprising when we
consider that building blocks bearing aorbitals lack an octet of electrons.
Figure 11 provides two examples of empty aorbitals: the typical a= 2p
case, and a case in which the empty orbital must be a hybrid AO (based on
the geometry of the building block, which demands sp2hybridization).
Figure 11.Empty atomic, aorbitals in organic molecules. aMOs are
most commonly just 2patomic orbitals; however, geometric constraints
may force a hybrid AO to be empty. Notice that both cationic building blocks
have 6 total electrons.
With the aorbital, we've reached the sixth and last of the localized
MO classes. Figure 12 provides a summary of the orbital shapes of the six
classes and the structural elements to which they correspond. These
shapes both confirm our intuition and suggest some intriguing new ideas.On the confirmatory side, notice that electron sources tend to be
concentrated between nuclei, where the Lewis model suggests we should
find electrons. More interestingly, the !* electron sink is primarily located
outside of the space between the nuclei. Incoming electrons will most likely
approach the outskirts of a bond, not between the atoms. Trigonal planar
atoms lacking an octet of electrons (thus bearing an aMO) will be
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approached by electrons perpendicular to the molecular plane. Consider
the "MOs--notice that they depend on a parallel alignment of 2porbitals.
Rotation away from the parallel alignment ruins "-type overlap, so double
bonds must remain planar. All kinds of interesting spatial ideas come to
light!
Figure 12.Shape and occupancy of the six classes of localized
molecular orbitals. The filled orbitals reflect the potential of the structure as
an electron source; the empty orbitals reflect the structure's potential as an
electron sink.
The relative energetics of these six classes are also extremely
important to keep in mind. These form a kind of stability trend that allows us
to quickly pinpoint the most reactive sources and sinks within a molecule.
We touched on this trend in Figure 13, but it's worth bringing up again here,
now that we've seen the shapes of the localized MOs. Figure 14 depicts
the most common relative energies of the localized MOs. Based on Figure
14, we should expect n orbitals to be the most reactive sources and a
orbitals to be the most reactive sinks. By identifying the localized MOs
present in a molecule and using Figure 14 to predict their relative energies,
we can predict how molecules will behave in a very powerful, general way.
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Figure 14.Typical relative energies of the localized molecular
orbitals. To drive the point home once more, low-energy unfilled orbitals
and high-energy filled orbitals are reactive.
Watch Localized Molecular Orbital Theory***
Effects of Electronegativity & Charge
Figures 12 and 14 lay out the shapes and relative energies of the six
classes of localized MOs. But a simple problem reveals that those figures
don't tell us the whole story. Consider Figure 15 below, which depicts a
good nucleophile (thiolate anion) in the presence of a compound containing
C=O and C=N bonds. Based on ideas from the last section, the "* orbitals
of the C=O and C=N bonds should be the electrophile's best electron sinks.
Can we predict which of the two sinks is better?
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Figure 15.Two possible courses of action: thiolate can add either to
the C=O or C=N bonds. Can we used localized MO theory to predict which
of the two "* orbitals is more reactive?
We can, if we first recognize that the identity of the atoms that make
up the two double bonds are different. Where we see a nitrogen in one
double bond, an oxygen sits in the other. We need to understand how atom
type affects the shapes and energies of molecular orbitals. Even more
specifically, we need to understand the relationship between
electronegativityand the properties of orbitals. How does electronegativity
affect the energies of the atomic orbitals? How are orbital shapes
influenced by electronegativity?
As we move from left to right across the periodic table, orbital
energies decrease. Rather intuitively, more electronegative atoms are
associated with lower energy orbitals. Another way of saying this is that
more electronegative atoms are more electrophilic, or that they tend to be
associated with more electrophilic orbitals. Put yet another way, more
electronegative atoms make worsenucleophiles (electron sources).
Whereas carbanions are extremely nucleophilic (electron-donating)
molecules, fluoride anion is hardly nucleophilic at all. Applying this idea to
the problem in Figure 15, we can predict that the "* orbital associated withthe C=O bond ("*CO) is lower in energy than the "* orbital associated with
the C=N bond ("*CO). Since this orbital is unfilled, the C=O bond ought to
be more reactive than the C=N bond.6
Molecular orbitals may involve identical atom types that differ only in
their charge. Thus, to finally complete our understanding of the effects of
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molecular structure on orbital energy and shape, we need to learn how
charge influences orbitals. Think of charge as a specialized case of
electronegativity, making use of the classic maxim that "opposite charges
attract and like charges repel." Positive charge on an atom boosts its
electronegativity over its neutral counterpart--positively charged atoms holdelectrons more tightly than neutral atoms (opposites attract). Negative
charge has the opposite effect, and lowers the electronegativity of the atom
relative to its neutral counterpart (like charges repel). Consider the example
in Figure 16.
Figure 16.Which of the two C=N double bonds ought to be more
reactive under these conditions?
Since positive charge increases electronegativity, we can think about
the positively charged nitrogen atom in the same way we thought about
oxygen in the first example from this section. It's more electronegative than
neutral nitrogen, so the energy of its "* orbital is lower. Consequently, the
C=N+double bond ought to be more reactive than the C=N double bond.
Organic chemists confirm predictions like these on a daily basis with
experiments!
Electronegativity's effects on orbital shape are intuitive to understandas well. Polarized MOs are built using atomic orbitals from atoms of very
different electronegativity, and consist of lobes of different sizes on each
atom. As we might expect, filled orbitals tend to have large lobes on
electronegative atoms, since electrons tend to spend their time around
atoms that are hungry for them. Unfilled orbitals, on the other hand, tend to
have larger lobes on less electronegative atoms. We will revisit this idea
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when we discuss frontier molecular orbital theory and the fundamentals of
reactivity.
For now, it's most important for us to understand how
electronegativity affects orbital energies. Our intuitive ideas about
electronegativity map nicely onto orbital energy ideas: electronegativeatoms possess low orbital energies and thus stabilize electrons. Treating
charge as a kind of electronegativity booster or restrictor, we can treat
charged atoms using this same idea. Armed with this principle, we can
easily compare the electronic viability of two possible reaction pathways,
even if the pathways in question differ only in the charge or element type of
the atoms involved.
1. Orbitals are interchangeably called "wavefunctions." We'll use the term
"orbital" whenever possible, but you should be aware that these two termsare often used interchangeably.
2. Because we think of orbital shapes as containers for electrons, we
commonly say that an electron is "in" an orbital.
3. For example, in Figure 3.4 the valence AOs are the 2slevel and all three
2plevels.
4. See the subsection addressing hybridization in the "Generalized Stability
Trends" section.
5. This relationship between geometry and hybridization always holds true.
However, it's important to remember that "geometry dictates hybridization,
not the other way around." (Scott Denmark) Hybridization follows from
geometry, and not necessarily from the apparent bonding network of the
atom.
Benzyne is a classic example of this idea: the triple bond of benzyne
suggests sphybridization for the two atoms involved; however, geometry
demands that they be at least approximately sp2-hybridized. The triple
bond of benzyne more closely resembles an sp2-hybridized diradical than a"classical" triple bond.
6. It's important to recognize this thought process as highly context
dependent. Say we treated the organic compound in Figure 15 with an acid
(HA) instead. Acids are electrophilic species, so we're interested in the
organic compound as a nucleophile. Comparing the norbitals on oxygen
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and nitrogen, we can conclude that the norbital on less electronegative
nitrogen is higherin energy than the norbital associated with oxygen.
Thus, nitrogen should be the better nucleophile (or base) in this context.
For every reaction you encounter, ask yourself which of the startingmaterials are nucleophiles (electron sources) and electrophiles (electron
sinks). As these examples show, mixing up these concepts can have
damaging effects on predictive ability.
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