Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 85
1. The Group 13 Elements
The elements of group 13 and 14 vary greatly in crustal abundance. The highest abundances are
of aluminum, carbon and silicon, as shown in the graph at right, which presents crystal abundances as
the logarithms of the abundances in parts-per-million by mass. Boron is found in nature primarily as
the hydrated oxide borax, Na 2 B4 O5 (OH)4 ⋅H2 O. Silicon and aluminum are present in thousands of
minearals, the silicates and the aluminosilicates. However, the only important ore for aluminum is
bauxite, which contains hydrated oxides such as Al2 O3 ⋅H2 O. Aluminum is recovered by the
electrochemical Hall-Héroult process, which is an extremely important industry in British Columbia
and Québec by virtue of the ready availability of hydroelectricity in those provinces. The Alcan
aluminum company is a Canadian-based world heavyweight in the aluminum industry. Carbon is
obtained largely in the impure form coke by pyrolysis of coal, but purer forms are obtained from
thermal decomposition of natural gas (carbon black). Silicon is obtained by coke reduction of sand (SiO2 ), and purified for
electronic purposes using the intermediate SiH4 (as discussed previously).
5.1.
Properties of the Group 13 elements
The elements at top of the group are hard or refractory network covalent materials, those at bottom are soft metals, as
reflected in their enthalpies of atomization and their melting points. Also, they are hard and soft in terms of their Lewis
acidity in the same order. The latter is correlated with polarizability of the atomic orbitals.
The First I.E. decreases down the group, but there is a minor hiccup at Gallium. Similarly, the electronegativities are do
not decrease smoothly: B 2.04; Al 1.61; Ga 1.81; In 1.78; Tl 2.04. The anomalous position of Gallium figures importantly in
the chemistry of this element, and is a consequence of the Scandide contraction. This is reflected in the electron
configuration of the element: it is the first in the group to have a set of filled d orbitals preceding the valence p orbitals. The
very poor shielding of the d electrons results in a higher-than-expected effective nuclear charge on the valence electrons of
Gallium, and hence its anomalous behaviour. We have already seen that Ga 2 H6 is more stable than the corresponding
aluminum hydride, and in some ways Gallium can act closer to boron than Aluminum does.
A similar effect is observed for Thallium, the first element in Group 13 to have a filled f orbital preceding the valence
orbitals. This is called the Lanthanide contraction. Another important factor, the primary influence of which is to greatly
stabilize the +1 oxidation state of Thallium compared to the group oxidation state of +3, is the inert-pair effect. This is
caused by the greater separation in the energy of the ns and np orbitals on going down the group. Tl3+ is in fact a strong
oxidizing agent (see the Frost diagram previously shown in section 4.3 of these notes.) These underlying energetics will limit
the ability of chemists to prepare analogous compounds down the group, e.g. such as in the preparation of multiple bonds for
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 86
the heavy elements, etc. This inert pair effect operates for all the heavy p-block
elements, whereas the scandide and lanthanide contractions lose their importance with
increasing group number (i.e. with the addition of more valence electrons within the psubshell.) A key question for any heavy p-element is as to whether the inert pair is
exercising a stereochemical influence on the structure. In some cases it does, in other it
seems not to.
Our chief focus will be on the element boron, and on attempts to prepare analogues
to boron among the heavier group 13 elements that are not part of the classical chemistry
of these elements.
5.2
Boron halides
The boron halides may be prepared by reaction of the elements (except the endoergic iodide). The preferred preparative
method for formation of BF3 , however, is:
B2O3 ( s ) + 3 CaF2 ( s) + 6 H2 SO4 ( l ) → 2 BF3 ( g ) + 3 [ H 3O][ HSO4 ] + 3 CaSO4 ( s )
This reaction is driven by the strong affinity of concentrated sulfuric acid for the water obtained by protonation of the solid
boric oxide, the HSAB affinity of boron for fluorine, and of course the gaseous nature of the product that allows it to be
removed from the reaction mixture and (typically) collected in a vacuum line where it is further purified.
The physical properties of the boron halides are presented in the following table:
For laboratory use, it is convenient to purchase these reactive compounds as solutions in donor solvents, most commonly in
ether. Their structures are trigonal planar and monomeric (they do not dimerized in the way the BH3 does.) As an example,
the structure of BBr3 is shown to the right of the table.
The bonding in these trihalides is interesting from two points of view. First, we need to explain that fact that they do not
self-dimerize, although they do form conventional ethane like structures in their adducts with stronger Lewis bases. Related
to this issue is the fact that the relative Lewis acid strength measured for the reaction:
isgivenby :
BF3 < BCl3 < BBr3
Second, we have so-far not considered MO diagrams for halogen derivatives of the elements, having always chosen either
hydrogen terminal atoms, or alkyl groups that can be approximated as pseudo s orbitals. The only exception has been where
we have deliberately chosen an oxygen terminal atom to form a multiple bond. On the whole, halogen compounds serve only
to complicate MO diagrams, because they carry with them so many “lone-pair”
electrons which are mostly unimportant for bonding, and serve only to clutter up the
MO diagrams. Thus it is important to be able to locate such orbitals for the purpose
of being able to ignore them. However, in many cases one formally lone-pair
orbital on each halogen interacts more strongly with the bonding MO’s, and thus
cannot be ignored from bonding situations. Such is the case for the boron halides.
First consider qualitatively what can happen to the MO diagram of BH3 , which
has an empty a 2 ” orbital corresponding to an unhybridized Boron p orbital. There
will be p orbitals on the halogens that can interact with this orbital to form π-type
bonds. The SAO for three p orbitals which are all perpendicular to the trigonal
plane lead to three combinations; one of these has a2 ” symmetry (note that the figure
in the book reproduced at right is mislabeled as a1 ”, which does not match the
SAO’s provided in the text’s appendices.) Only this orbital is of the correct
symmetry to overlap with the central p orbital. The other two remain non-bonding.
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
B
Page 87
X
To make this more understandable, we now
reconsider the MO diagram developed earlier
for trigonal planar BH3 . The original orbitals
2e ’
are indicated in black, and the additional orbitals
due to some of the halogen p functions are
2a2”
displayed in colour. The red lines indicate the
interaction that occurs with the a 2 ” orbitals –
2a1 ’
originally it was unhybridized from the boron
side of the interaction diagram. (This original
↑↓↑↓
situation is indicated by the dashed lines on the
↑↓
A2”
A2’
diagram.) Thus a bonding 1a 2 ” orbital, which is E’
E”
dominated by boron, is formed as well as an
(1a2 ”)
empty anti-bonding combination that is 2a”.
↑↓
Additionally there will be several new
1a2”
unhybridized MO’s (blue) that represent
genuine halogen lone-pair electrons. Note also
E’
that the new 1a 2 ” is a delocalized π-orbital.
Also, e” is an empty π-orbital by symmetry,
A1’
A1’
even though it is effectively a halogen lone-pair
function.
1e ’
The diagram at right is somewhat
simplified, in that it ignores mixing between the
original functions and those p-functions that are
1a1 ’
capable of mixing with the s-functions to form
new σ-MO’s. In fact, there is a complete duplication of the a 1 ’ and e’ MO’s using p orbitals; nonetheless the frontier orbitals
are exactly those that are shown here. You should compare these results with HyperChem AM1 calculations on BX3
molecules to convince yourself of this, and also to gain experience in recognizing the valuable interactions from among the
chaff.
We are now ready to consider the chief differences between BH3 and the BX3 halogen derivatives. First, the latter have
partial X–B π-bonds. What Lewis structures does this phenomenon correspond to? This should weaken their ability to be
Lewis acids. Thus the sequence of acid strength
BF3 < BCl3 < BBr3 is usually explained by postulating the strongest B–X
π-bonds to occur between the two second-period elements B and F, with weaker π-effects occurring for the heavier halogens.
Furthermore, the presence of these partial double bonds is sought to explain whey the monomers are stable, and dimers of
these boron halides are now know.
The boron halides are extremely versatile reagents.
Beside
undergoing many complex-formation reactions, they also undergo
protolysis with protic reagents to produce the esters of boric acid. A
display of typical reactions is provided in the diagram at right. Note that
while ethers give stable complexes, water and alcohols lead to
substitution via protolysis. Similary, while tertiary amines only give
complexes, primary and secondary amines react to give substitution
products. This “reactivity wheel” does not apply to BF3 , which resists
protolyis reactions under mild conditions. For example, a stable adduct
forms between BF3 and NH3 without metathesis occurring.
B(OH)3 is known as boric acid, and is a well-known starting
material in boron chemistry. It is weakly acidic, but this does not occur
via ionization of one of the OH groups to give [B(OH)2 O]- and H+.
Instead, boric acid acts as a Lewis acid towards the base H2 O. The
resulting adduct then ionizes partially to give the overall reaction:
dilutesolution

→ H 3O + + [ B (OH ) 4 ]−
B(OH ) 3 + 2 H 2O ←

Complex formation with anionic groups to provide [BX4 ]- species is
extremely common for the boron halides, and many such adducts have
remarkable stability. Thus for example the BF4 – ion can be handled even in aqueous solution.
Condensation of boric acids leads to polyborates, which form rings and cages based on six-membered B–O–B–O–
linkages. Such polymers are the basis for borate glass formation. Pure borate glasses are of little importance, but mixtures of
borates with normal glass leads to the borosilicate glasses, of which the most famous is the brand known as Pyrex.
Chemistry 3810 Lecture Notes
5.3
Dr. R. T. Boeré
Page 88
Boron nitride
The simplest boron-nitrogen compounds is boron nitride, BN, which is prepared from boric oxide and ammonia by the
reaction (at 1200 °C):
B2O3
+ 2 NH3
→ 2 BN
+ 3 H 2O
It provides an interesting illustration of the fact that BN is isoelectronic (and isolobal) with CC. Indeed, there are two
common forms of boron nitride that mimic the structures of elemental carbon in the forms of diamond and graphite. The
latter two structures were dealt with in detail in Chem 2810. Strictly speaking, the cubic BN form is the sphalerite structure.
Also, the hexagonal form has one extremely important difference from graphite, in that in the latter the sheets tend to be
stacked over the center of the holes of the ring below. The difference observed for BN is readily attributed to the difference
in electronegativity of B and N, leading to significant ionic contributions to
bonding between Bδ+ and Nδ– .
The layered structure of hexagonal boron nitride has much shorter bonds
within the layers (1.45 Å) compared to the separation between the layers (3.33 Å).
Like graphite, this sheet structure is a slippery material that can be used as a
lubricant. But while the former is black and a good electrical conductor, BN is
colourless and an electrical insulator. The cubic form is adopted when BN is
heated under high pressure (2000 °C at 60 kbar). Like diamond, the sphalerite
form of BN is an extremely hard material that finds applications as an abrasive in
industrial applications. It is the second hardest of abrasive materials, second only
to diamond itself. The graph at right shows the correlation of hardness of the
material with the lattice enthalpy density. The point for C represents diamond, and
BN the sphalerite modification.
5.4.
Borazine, substituted borazines and borazine analogues
A very similar effect exists at the molecular level. Consider the planar ring compound borazine, shown as a model and
H
H
B
N
H
H
H
H
H
H
N
B
H
H
B
N
H
H
as a line diagram to keep track of the electrons. Borazine is often called "inorganic benzene", with which it is isoelectronic
and almost isostructural. Its physical properties are extremely similar to those of the unsaturated hydrocarbon. Borazine was
first made in 1926 by Alfred Stock (Germany).
5.4.1 Preparation of Borazines
Stock's original synthesis was the following reaction:
2 B2 H6 + 6 NH 3
→
3 (B2 H6 )(NH3 )2 →
2 B3 N3 H6 + 12 H2
There are now much better methods, as shown in the following reaction scheme.
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 89
H
Cl
H
3 NH4 Cl
+
140 - 150 °C
- 9 HCl
C6H 5Cl
3 BCl3
N
B
Cl
H
H
B
N
B
N
H
B
N
NaBH 4
N
B
Cl
B
H
N
H
H
H
CH 3MgBr
- 3 LiCl, 9 H 2
3 NH4Cl
+
Me
3 LiBH4
H
H
B
N
N
B
B
Me
N
Me
H
Also shown in this scheme is how the original compound can be derivatized by reaction with suitable nucleophiles. Thus
substituted borazines can be made in this manner. The other substitution pattern, i.e. at N, can also be achieved as follows:
Cl
Me
C6H5Cl 140 - 150 °C
3 CH 3NH2
+
3 BCl3
- 6 HCl
Toluene Me3 N
Cl3B-NH2CH3
Me
B
N
- Me 3 NHCl
N
B
B
Cl
N
Cl
Me
NaBH 4
H
Me
- NaCl, B2 H6
Me
B
N
Me
N
B
H
R
RLi
N
B
N
B
N
H
- LiCl
Me
B
B
R
N
Me
R
Me
Such substituted borazines have even closer resemblance in physical properties to the corresponding substituted benzene
compounds. However, the very way that they are made, i.e. by nucleophilic substitution at boron or nitrogen is a strong
indication that borazines have very different chemical reactivity than do the aromatic hydrocarbons. This can be seen more
closely by considering the following reactions of borazines.
5.4.2 Reactions of Borazine
(a) Polar addition reactions, HX, X = Cl, OH, OR etc.
H
H
H
H
H
B
N
N
B
B
N
H
HCl
Cl
B
H
N
H
N
B
H
B
H
N
(Benzene does not react with HCl at all.)
H
H
Cl
Cl
H
H
H
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 90
(b) Reaction with elemental bromine
H
H
H
H
B
N
B
H
H
N
Br 2
Br
B
H
N
Br
B
N
B
N
B
H
H
N
Br
H
Br
Br
H
Br
H
(Benzene undergoes aromatic substitution rather than addition.)
(c) Coordination complexes
H
H
H
B
N
B
N
B
N
H
H
Cr
C
H
Cr(0) carbonyl complexes
common to both ligands
Cr
C
C
O
O
C
O
C
C
O
O
O
These reactions suggest that there are both similarities and differences between boranzine and benzene. The formation
of “sandwich” complexes at Cr(0) strongly suggests the presence of a π-system in borazine, as does its odour which is
distinctive for aromatic carbon compounds. Yet the reactivity is very different. We need to consider the bonding in these
fascinating compounds in more detail to be able to understand the factors involved.
5.4.3 Bonding in borazine
Structure of borazine: flat hexagonal structure with equal B–N bond lengths:
Compare benzene:
We can easily calculate the molecular orbitals of borazine using the AM1 method. There are many orbitals, and our approach
is going to be that of ignoring the σ-skeleton entirely. The point group of borazine is D3h , and so the orbital labels used for
this compounds are drawn from that point group.
We contrast our result for borazine with that of benzene, for which the point group is D6h , so that the labels of the MO’s
in the diagram will be different. However, from topological sketches (taking a top view of the atomic p-orbitals), or from the
3D graphs taken from HyperChem, it is easy to recognize the similarity between the MO’s despite the difference in labeling
schemes (see detailed diagram on the next page.)
Borazine is described by the same type of bonding model as benzene, consisting of a σ skeleton of sp 2 hybrid orbitals
and a set of delocalized π orbitals. It is possible to write down the π orbitals using Hückel theory, and the orbital topologies
are the same as for benzene. However, in borazine they are not symmetrical, and the more electronegative N atoms have
larger coefficients for the bonding MO's, while the boron atoms have larger coefficients in the antibonding MO’s. After all,
there are fully 1.06 Pauling units difference in electronegativity between boron and nitrogen (huge, considering that the entire
range in electronegativity values across the whole periodic table is only 3.4 Pauling units!)
Such an unequal distribution of the π electron density reduces the ring π bonding, and renders borazine less aromatic
than benzene. This difference is reflected in the chemistry of borazine, which undergoes addition reactions, during which
electropositive substituents become attached to the nitrogen atoms, electronegative substituents to the boron, e.g. HCl.
Another key feature of the electronic structure of borazine is the much larger separation of the frontier orbitals, with the
HOMO-LUMO gap being twice as large as in benzene. This is the origin of the loss of aromaticity in borazine compared to
that of benzene. It also means that borazines are transparent to UV and visible radiation, whereas the benzene ring is an
important organic chromophore in the UV region of the spectrum.
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Occupied π-orbitals of borazine
1a”
1e”
Empty π*-orbitals of borazine
2 e”
and
and
2a”
Occupied π-orbitals of benzene:
1a 2u
1e1g
Empty π*-orbitals of benzene
2e2u
and
and
1b 1g
Page 91
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 92
5.4.4 Heavier-element borazine analogues
Borazine is an interesting example of a so-called III/V compound: in general, any combination of two elements from
Groups 13 and 15 are isolectronic to two Group 14 elements. The greatest interest in such substitution occurs among the
heavier elements among the elements themselves. Thus gallium arsenide, GaAs has for years been touted as a superior
alternative to elemental Si as the base semi-conductor for building microprocessors. The CRAY computer company, builder
of the famous “Supercomputers” has actually produced fuctioning computers using GaAs chips. From the vantage of the
year 2001, it does not seem, however, that the dominance of silicon for bulk fabrication of chips will soon be changed. On
the other hand, there are many specialty semi-conductor applications where III/V and even II/VI materials are useful, and
indeed essential.
This interest from materials science has served to re-ignite interest among chemists for III/V chemical compounds, and
thus the rather old chemistry of borazine has been dusted off in recent years. Prof. Phillip Power of the University of
California, Davis, has a strong research program directed at stabilizing heavier analogues to all elements from Groups 13, 14
and 15. Included among his papers are articles describing borazine analogues (i.e. six-membered rings, potentially aromatic
in nature) based on the combinations B/P, Al/N and Ga/P. In all cases, kinetic stabilization through large substituents on at
least one of the constituent elements is required. Some specific examples include the following (literature references below):
Borazine analogues
Cy
Mes
P
B
Mes
Me
B
P
Cy
Dip
N
Al
P
B
Dip
Mes 1
Me
N
P
Dip
Cy
P
Al
P
Ga
2
Mes*
Ter
Ph
3
Dip =
Pri
CH 3
3.
1.
Mes*
As
Al
P
Al
Ph
4
Mes*
Al
As
Ph
Mes*
Ter =
iPr
Cy =
Ph
Ph
As
Al
Ph
Mes*
4
Ph
Mes* =
H
H
H
H
1.
2.
Mes*
Al
P
Cy
Ph
Reference # in red
Mes =
CH 3
Ter
Ga
P
Al
Me
Ph
Ga
Substituent structures:
H 3C
Ter
Al
N
Cy
Cy
tBu
But
H
H
H
H
H
H
tBu
HVR Dias and PP Power, Angewandte Chemie, International Edition in English , 26 (1987) 1270 (B/P)
KM Waggoner, H Hope and PP Power, Angewandte Chemie, International Edition in English, 27 (1988) 1699
(Al/N)
H Hope, DC Pestana and PP Power, Angewandte Chemie, International Edition in English , 30 (1991) 691 (Ga/P)
RJ Wehmschulte and PP Power, J. Am. Chem. Soc., 118 (1996) 791 (Al/P and Al/As)
Structure of blue compound
(Mes*AlPPh)3
(Mes*AlAsPh)3
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 93
Of the indicated compounds, only the one coloured blue has a planar structure and shortened bonds (note that the X-ray
structure shows a second view without all the substituent atoms projected below which emphasizes the planarity of the ring;
calculations show that this element combination does lead to some aromatic resonance energy. The other examples are all
non-planar and behave as single-bonded compounds with a lone pair on the Group 15 element, and electron deficiency at the
group 13 element. We can understand this by thinking of the π-bonds in all III/V compounds as being dative π-bonds. As
shown in the following graphic, the lone pair on the Group 15 element can be donated into the empty p orbital on the Group
13 element (leading to double bonds, as in the B/P example), or they can remain on the Group 15 element (as for the Al/P):
Cy
Mes
P
B
⋅⋅
P:
Cy
Cy
Mes
Mes
B
Mes
P
B
:P
B
Cy
Mes
Mes*
B
P
Cy
Ph
Mes
⋅⋅
P:
P
B
P
Al
Cy
Ph
Mes*
Al
:P
Al
Ph
Mes*
In an MO context, one can think of all the variables that would favour such dative π-bond formation: compatibility of orbital
size and energy for the different element combinations; steric factors emphasizing the puckered structures, etc. Consistent
with this approach (e.g. if used for borazine itself) is the polar nature of the π-bonds that naturally result from such an
approach.
5.5
The Higher Boron Hydrides and Polyhedral Borohydrides (BH-anions)
Since the initial discovery of diborane (in 1912, by Alfred Stock), there has been a steady stream of other boron hydrides
so that today the element that has the greatest diversity of EH compounds after the hydrocarbons is undoubtedly boron. But
after that statement, all similarity to the hydrocarbons stops. The structures of all boron hydrides defy the normal rules of
organic chemistry, and reflect the needs of such compounds to bond with a deficiency of electrons. The approach that nature
takes to this “problem” is to form clusters. Over 50 neutral boranes, Bn Hm , and an even higher number of boron hydride
anions, Bn Hm x– have been characterized. These can be classified by structure and stoichiometry into 5 classes as follows:
Closo-boranes (from Greek κλωβοσ, for cage) have complete closed polyhedral clusters of n boron atoms.
Nido-boranes (from Latin nidus, a nest) have non-closed structures in which the Bn cluster occupies n corners on an
(n + 1)-cornered polyhedron
Arachno-boranes (from Greek αραχνη, a spider’s web) have even more open cluster in which the B atoms occupy
n contiguous corners of an (n + 2)-cornered polyhedron
Hypho-boranes (from Greek υφη, a net) have the most open clusters in which the B atoms occupy n corners on an
(n + 3)-cornered polyhedron
Conjuncto-boranes (from Latin conjuncto, I join together) have structures formed by linking two or more of the
preceding type of cluster together.
In addition, there are hundreds of examples where one or more other element than boron has been introduced into or
attached to a borane cage, so that the boranes form the parents of a whole class of compounds. Recently some practical uses
of such molecules have also been developed. We will focus our discussion mostly on the first three classes of borane, the
closo, nido and arachno. Most importantly, the theories that have been developed for borane clusters have found wide
applicability to all other cluster structures, and since the early work on the these compounds in the 1960’s, an extensive array
of cluster compounds of the main group and the transition metals has emerged. Cluster Chemistry has become its own sub
discipline of sorts, with most of the modern applications being to cluster molecules and ions of transition metals that are
considered key model systems for the study of heterogeneous catalysis using these same metals. Several research groups in
Canada are active in cluster chemistry; perhaps the most well known is Dr. Arthur Carty who was for many years at the
University of Waterloo, and is now the president of the National Research Council of Canada.
We cannot deal with all the possible examples that are known, and there is not a great utility in doing so. We will
instead focus on the key organizational principles governing the recognized structures. We will also treat the bonding in
some key illustrative examples using a Molecular Orbital approach. Much of the original bonding theory was done with a
modified VB approach using the Longuet-Higgins approach first introduced by him while an undergraduate at Oxford to
explain the bonding in diborane. Now would be a good time to review what we said earlier about bonding in B2 H6 .
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 94
5.5.1 The three main classes of polyhedral boranes and borohydride anions
The following graphics serve to illustrate some examples of these interesting molecules, presenting first of all a
schematic explaining the interconversion between the structural types, and then representative examples with their IUPAC
names and their point groups. Obviously with such weird shapes, the use of point symmetry groups to label the structures is
essential.
The more closed the structure is, the more it approximates a cage structure of boron atoms, and in fact these closo cages are
found in a variety of allotropes of elemental boron as well as in some boron alloys. The more open the structure, the fewer
direct boron-boron bonds are drawn, and the more bridging hydrogen (two-coordinate hydrogen) atoms there are. However,
we will remember from our detailed consideration of the bonding in diborane that even in apparently bridging boranes, there
is a substantial element of direct boron-boron bonding present. It is the same here. In fact, no matter what the actual
structure (or where the artist chooses to draw “bonds” in these pictures) there is always a substantial amount of bonding
occurring at the dead center of the respective cluster structure. This special feature of cluster bonding is best illustrated using
delocalized MO bonding.
Note also in the top graphic the diagonal relationship between the boranes, with logical relationships connecting an ncloso with an (n – 1) arachno and an (n – 2) nido cluster. The significance of this relationship will be come clear soon. A
more comprehensive list of the possible boron cage structures, emphasizing just this diagonal link, will be presented a little
later after we have considered Wade’s rules.
5.5.2 Wade's rules
Cage molecules which are deltahedra (i.e. built up of triangular faces) obey a structural classification called Wade's rules
(Prof. Kenneth Wade, Durham University, U.K.). These rules are as follows:
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 95
• Each building block in the deltahedron is a B–H fragment, bonding to other atoms through boron
• Count the total number of valence electrons, then subtract the 2e– in the B-H bond
• If a boron bears more than one H atom, include the 2e– in the second bond
• Count the resulting number of electrons, and divide by two to get the number of skeletal electron pairs
The skeletal electron pairs hold the cluster together, the cluster being considered to consist of x number of B-H units. In this
view, the bridging hydrogen atoms do not have a structural role; rather they are “pasted” onto the framework as best as they
can fit, and MO calculations bear out this viewpoint as being fairly accurate. If the rules seem arbitrary, they have the
advantage of being very effective.
Consider this example of applying the rules to a specific example, that of B4 H10 . Look back at the last page to reestablish the connectivity in this molecule. There are six terminal B–H bonds, one each on the central borons, two each on
the end borons. There are 4 bridging hydrogens along the sides of the cluster. Now we apply the rules in a systematic
manner. Each boron takes a single H atom in a B–H unit, whose electrons are considered to be firmly localized, and are
therefore subtracted from the cluster count. The remaining electrons are 7 pair. Hence there must be an assignable usage to
these electrons. First we must accommodate the remaining two terminal B–H bonds. Then there are four bridging H atoms
in 3c,2e bonds, thus four pairs of electrons. The seventh electron pair is used to create a formal B–B bond across the middle
of the structure.
The key parameter, however, remains the number of S.E.P., the electrons that are available in principle for cluster bonding.
Wade’s rules uses this paramter in conjunction with the molecular formu la to define the structural class of borane.
5.5.3. Classification of boron hydride deltahedra
Type
Closo
Nido
Arachno
Hypho
S. E. P.
n+1
n+2
n+3
n+4
Formula
[Bn Hn ]2–
Bn Hn+4
Bn Hn+6
Bn Hn+8
Examples
[B5 H5 ]2– to [B12 H12 ]2–
B2 H6 , B5 H9 , B6 H10
B4 H10 , B5 H11
No examples proven for BH species, but adducts exist
The structure of the closo species can be determined by building the smallest closed polygon with all triangular faces.
Note that the theory does not distinguish between electrons that do and those that do not bind H atoms. But in the closo form
there are not enough places to “stick” hydrogen atoms, so that these always carry a 2– charge. The remaining open structures
do provide room for hydrogen atoms, so that edge-forming or terminal H atoms are stuck on to mop up the excess negative
charge.
The diagonal relationship mentioned above is that the sequence
closo → nido → arachno
exists for clusters with the same number of skeletal electron pairs, and increment to one less boron atom, with
adjustment in electrons and hydrogen atoms as required. The full diagonal relationship is shown on the following diagram by
the diagonal linking lines. Your are strongly encouraged to write out a molecular formula for each of the structures below,
remembering that the larger circles are the boron atoms and the smaller are hydrogen. Remember that the closo forms are
dianionic, the rest neutral. You should also assign the point group of each structure. This is particularly important for the
high symmetry clusters. What is the point group of closo-[B6 H6 ]– ? What about for closo-[B12 H12 ]– ? This is a point group
you have very likely not encountered before, because there are no central atom molecules of the type EX n which have such a
high symmetry.
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 96
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 97
In case your solid-state analytic geometry is not quite as good as required, the following chart reminds you of the structures
and names of common deltahedra. These represent the basic building blocks of all cluster molecules.
5.5.4. An MO description of the bonding in [B 6H6]2–
This molecule has the shape of an octahedron, as shown at the right. The bonding scheme
we use employs a short-cut that is commonly used in borane cluster bonding schemes. We use
the Wade’s rule notion that the terminal B–H bonds are much more covalent, and hence more
stable, than any bridging or cluster-bonding orbitals. There are therefore a total of 6 electrons
from H, 18 from boron, plus two from the charge. From this total of 26 electrons, we subtract
the 12 that “belong” to the B–H terminal bonds, leaving 14 electrons to distribute in the
“frontier orbital” section of cluster MO’s. The shapes of these orbitals are simply sp hybrid
extension of the octahedral MO’s provided as SAO’s in Appendix 4 of the text, and you should
consult this helpful table in your analysis.
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 98
A helpful description of this approach that presents a bit more detail than Shriver-Atkins is provided by Housecraft and
Sharpe, and I reproduce their discussion below:
Symmetry allows us to separate the orbitals into radial and tangential components, with the sp hybrids being radial, and
the p orbitals tangential (i.e. along the surface of the deltahedron.) The treatment above only provides the bonding set of
orbitals. In all there are 18 combinations of the radial and tangential orbitals. Some of the resulting MO’s are purely
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 99
tangential, some are purely radial, and the rest are mixtures of the two. Now, let us construct an interaction diagram, using
not the single radial and two tangential orbitals, but the six and twelve that actually exist in the cluster. Then we get the
result in the diagram below. The fragment orbitals are the SAO’s provided by Shriver-Atkins for the octahedral point group.
Although spheres are shown for the radial orbital, it is important to realize that these can just as well be sp hybrids, so long as
they point along the radial direction. In fact, there are two sets of such orbitals, one point in, the other out (the B–H bonding
orbitals.
Building the MO scheme for B6H62-
tangential
radial
2t1u
eg
radial
(6 orbitals)
eg
t1g
t1g
t2u
t2u
tangential
t1u
(12 orbitals)
t1u
t2g
1t1u
a1g
a1g
t2g
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 100
There are indeed 7 bonding combinations, and hence 11 antibonding combinations, and we note that this is exactly what
is needed to accommodate 14 cluster electrons to completely fill up the t2g HOMO of the cluster. Note also that once again
the text gets one of their labels wrong. The diagram shown below here is a correction to the one provided by Shriver-Atkins
who mislabel the antibonding t1g orbital as t2g . The topologically correct MO sketches were produced using ISIS-Draw, and
are based on the fragment orbitals shown on the interaction diagram on the previous page.
ENERGY LEVEL DIAGRAM
2–
TOPOLOGICAL ORBITAL SKETCHES for [B6H6]
We can also treat the bonding in this complex molecule using HyperChem (AM1
method). In addition to the 18 MO’s shown above, there are a further 12 dealing
with bonding and antibonding components of the six B–H orbitals. In the fully
delocalized MO method, there is not clean separation between the two types of
orbitals. However, one can recognize the six lowest MO’s as predominantly B–H
bonding. Also, many of the orbitals sketched above are recognizable in the AM
output. This is an exercise all students in this class need to do. Notice the very
striking agreement with the correct electron population. If a calculation is done
with an overall 2– charge, electrons fill completely the t2g level and leave the antibonding orbitals empty. The order of the empty orbitals is, however, different.
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
5.5.5. Structural evidence for borane clusters
Most of the evidence for the structures of the borane clusters comes from X-ray
diffraction. However, it is always desirable to obtain evidence for structure in
solution. A convenient way to do this for the borane clusters is to use 11 B NMR. The
spectrum of the nido cluster [B11 H14 ]– is shown in the picture at the right. The three
distinct types of boron sites are readily distinguished in a 1:5:5 ration, despite the
otherwise featureless spectrum (protons have been decoupled to prevent obscuring of
the weaker signals.)
In addition to this structural evidence, NMR studies have also shown that many
borane hydride structures are fluxional in solution at or near room temperature.
The spectrum shown at right is highly stylized. In actual practice, the boron
NMR lines are much broader than what is shown in the sketch, a limiting feature on
the usefulness of 11 B NMR, caused by the nuclear quadrupole of boron. The original
spectrum corresponding to this graphic is worth considering. Below that we present
some general information of the NMR of boron hydrides, along with a second example.
The spectrum of [B11 H14 ]– in both
pictures has been broadband-proton
decoupled, to simplify the spectrum of
these closely overlapping lines. There
is no further coupling information
buried under the broad lines; the
breadth is caused by rapid relaxation
of the magnetization of the boron
nucleus. However, the main influence
on the width of the lines is from the
symmetry of the boron; the more
symmetrical, the sharper the lines.
Thus in the sample spectra shown
in Fig 6-11 at right, the boron spectrum of the BH4 – is incredible
sharp, showing no quadrupole line broadening. This is because
the boron nucleus is at the center of a tetrahedron, and the
quadrupole moment reduces to a shielding scalar.
The 11 B nmr patterns shown at right tell us how many
terminal H atoms there are attached to boron. The bridging
hydrogens are generally not resolve, and may even not show up
at all in the 1 H NMR spectrum. They may contribute something
to the breadth of the 11 B lines, however. It is important to
emphasize that many of these boranes are expected to be
fluxional in solution, and this means that the solution phase
structure may well appear to be of higher symmetry than the
solid-state structure determined by X-ray crystallography.
The second specific example shown belongs to that of the
non-deuterated B10 H14 molecule.
The structure with the
numbering scheme used to label the boron atoms in the NMR is
shown below. The inset spectrum is from the monoiodinated
derivative B10 H13 I. The NMR of this compound clearly shows
that the iodine has substituted a hydrogen atom on the #2 boron
atom.
Page 101
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 102
5.5.6 Reactions of boranes and borohydrides
The main reaction types that all boron hydride cage compounds undergo can be placed under four categories.
1. Lewis base cleavage
Remember that boron hydrides are Lewis bases. Thus diborane B2 H6 reacts with tertiary amines in a symmetric cleavage
reaction (remember that primary and secondary amines react in an unsymmetrical cleavage reaction.)
H
H
H
B
B
H
H
H
H
H
H
•N
•
H
H
H
B N
H
H
H
Consider the reaction of ammonia with a robust higher boron hydride. The reaction occurs along with the breaking of
some B–B bonds, but not all the bonds. Hence these reactions can be rationalized, but not easily predicted.
2. Deprotonation using strong bases
Deprotonation occurs with less nucleophilic bases, and is the dominant reaction for larger boron hydrides, which tend to
have more acidic bridging hydrogen atoms. The origin of this greater acidity is thought to be the greater delocalization
of the negative charge of the resulting anion. Thus trimethylamine, a weak Brønsted base, reacts with B10 H14 in a
deprotonation rather than a cluster-fragmenting reaction:
B10 H14 + N (CH 3 ) 3 → [ HN (CH3 )3 ]+ [B10 H13 ]−
Deprotonation occurs preferentially at the edges of molecules, where the hydrogen nuclei experience weaker bridge
bonding rather than the stronger terminal bonds.
The much stronger base methyl lithium is required to deprotonate the smaller nido cluster B5 H9 .
Now remember that we are talking about boron hydrides, yet they act as acids. The smaller hydrides are indeed
hydridic, and especially the anionic ones. But large boron hydrides are robust molecules with sufficiently robust
bonding that they become very much like hydrocarbons, and the hydrogen atoms are somewhat positively charged. All
of this reflects on the stability of larger boron hydride clusters, and this stability can only be understood in terms of the
electron delocalization that occurs in these clusters.
3. Cluster building reactions
Boranes react with anionic boron hydrides to build larger clusters. An example of such a reaction is:
5 K [ B9 H 14 ] + 2 B5 H 9
→ 5 K [B11 H 14 ] + 9 H 2
This type of reaction has been used extensively to build large boron hydride clusters.
4. Electrophilic substitution reactions
Remarkably, boron hydrides undergo electrophilic substiution reactions, the same kind of reactions that aromatic
hydrocarbons undergo. Thus hydrogen atoms can be replaced by halogens (e.g. iodine, see the example in section 5.5.5)
or alkyl groups under typical Friedel-Crafts conditions. This reactivity again reflects the importance of delocalized
bonding in BH clusters. Replacement of preferentially the terminal boron hydrides occurs, rather than the bridging
atoms. For example, the alkylation of B5 H9 occurs as follows:
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 103
5.5.7 Heteroboranes
Anionic boron hydrides are excellent ligands for metals, and many derivatives of
especially the transition metals are known. These are bonded through bridging
hydrogen atoms. Of more interest to cluster compounds are metallaboranes where
metals are incorporated into the cluster structure with boron-metal bonds. There are
many examples of this type. One example that illustrates the latter type of cluster is the
closo-[B11 (AlCH3 )H11 ]2– , a direct analogue with a heavier Group 13 element, but that
requires an alkyl group on aluminum to be stable. This cluster is shown in the picture at
right, and can be made by the reaction:
2 [ B11 H13 ]
+ Al2 Me6 → 2 [ B11 H11 AlMe ]
+ 4CH 4
The picture of the structure clearly shows the relationship of this cluster to the closo[B12 H12 ]2– . It turns out that a vast number of mixed boron-element cluster compounds,
and even clusters with no boron at all, have structures that are rationalized by the
application of Wade’s rules. One of the most extensive series of such mixed boron
element clusters are the carboranes. This substitution is based on the isolobal
relationship between a H–B group and a H–C group, but since this is a Group 14
element, there is one more positive charge. Hence CH replaces [BH]– , and you will
immediately see that this has important implications in that anionic boron hydrides can
become neutral carboranes. Thus two carbon substitution of any closo borane anion
results in a neutral closo carborane. The isolobal relationship is illustrated by:
2−
2−
The preparation of one such cluster will serve to illustrate the general principles. First nido-B10 H14 is activated by reaction
with the Lewis base SEt 2 , which displaces bridging hydrogens to form arachno-B10 H12 (SEt 2 )2 . This reactive cluster adds one
equivalent of acetylene to form1,2-closo-[B10 C2 H12 ], which is now a neutral molecule. Heating of this compound in the
absence of oxygen forms at about 500°C the re-arranged isomer 1,7-closo-[B10 C2 H12 ], and further heating to an astounding
700°C further isomerizes the structure to the 1,12-closo-[B10 C2 H12 ] isomer. Survival of molecules at such extreme
temperatures is an indication of remarkable and unusual chemical stability. Structures are shown below.
1,2-closo-[B 10 C2 H12 ]
1,7-closo-[B 10 C2 H12 ]
1,12-closo-[B 10 C2 H12 ]
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 104
One of the most interesting applications of these carboranes is a result, oddly enough, of converting them back to anionic
structures. Thus 1,2-closo-[B10 C2 H12 ], despite its high thermal stability, can be partially fragmented by a combination of the
strong bases ethoxide and sodium hydride. The deprotonated compound has the formula Na 2 [B9 C2 H11 ]. The structure of this
compound is shown below in a view that emphasizes the empty orbitals along the rim of five boron and carbon atoms. It is
isolobal to the extremely important cyclopendadienide anion, perhaps the single most important ligand for organometallic
complexes of the metals, being used with transition, main group, and f-elements. [B9 C2 H11 ]2– is a dianion, and for certain
metal ions, it forms stronger bonds than the monoanioic [C5 H5 ]– is capable of.
Even small-ring carbon-boron anionic rings can act as powerful donor ligands to transition metals. For example the
highly negative [B3 C2 H5 ]4– ring has a high tendency to form “multidecker sandwich complexes” with late transition metals
such as cobalt and nickel. The structure of the ring, and two mixed-sandwich complexes of metals are shown. The
hydrocarbon [C5 H5 ]– of lower charge must be placed at the outsides of the sandwich, else the charge cannot be fully
compensated. But in the central layers, the carborane ring readily bonds to two electron deficient metal ions.