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Clusters and catenation in p-block
Allotropes of carbon
Allotropes of boron
Part of one layer of the infinite lattice of αrhombohedral boron, showing the B12 icosohedral
building blocks that are covalently linked to give a
rigid infinite lattice
CM 2312
The construction of the B84-unit, the main building block of the
infinite β-rhombohedral boron. (a) In the centre of the unit is a
B12-icosohedron, and (b) to each of these twelve, another boron
atom is covalently bonded. (c) A B60-cage is the outer ‘skin’ of
the B84-unit. (d) The final B84-unit can be described in terms of
covalently bonded sub-units {B12}{B12}{B60}.
Clusters and Catenation
1
Isoelectronic species:
Molecules, ions or molecular fragments that possess the same number of valence and core
electrons are said to be isoelectronic. However, this term is often used to refer to species that simply
possess the same number of valence electrons.
Example: BN is isoelectronic with CC
The structure of layered, hexagonal boron
Nitride, note that the atoms are in register
between layers
The sphalerite structure
of boron nitride
B-N analogues of hydrocarbons
−
H
H
H
H
H
B
H
+
H
H
H
C
H
H
N
H
8 valence electron series
CM 2312
Clusters and Catenation
2
BONDING IN BORANES
B2H6:
The boron atom in BH3 possesses a vacant 2p atomic orbital that readily accepts a
pair of electrons from a Lewis base (L:). In the absence of a Lewis base, BH3 will
dimerise by the donation of a pair of B-H bonding electrons from one molecule into the
empty 2p orbital of the other. The two bonding electrons are now shared between
three atoms and a H-B-H bridge is formed.
:L
H
L = 2e- donor
B
LBH3
H
H
BH3
H
H
dimerisation
B
H
B
H
H
H
H
H
B
H
B
H
H
H
Number of atoms in bonding contact in B2H6 = 8
∴ need 8 x 2 = 16e if all bonds are 2e/2 centre
Number of valence electrons = (2 x 3) + (6 x 1) = 12
∴ all bonding contacts between pairs of atoms are not 2e/2 centre
Polyhedral Boranes
e.g. closo-[B6H6]2[B6H6]2- is an octahedral (Oh) cluster of 6 boron atoms, each of which is bonded to a terminal
hydrogen atom.
2H/B
B
H
B
B
A prototype for the consideration of bonding in boron cages
CM 2312
Clusters and Catenation
3
Unit used for bonding in polyhedral borane clusters
z
x
sp hybridised x 6
H
H
B
SALC → a1g + eg + t1u = 6 orbitals
B
px, py x 6 → t1g + t1u + t2g + t2u
B
= 12 orbitals
y
Molecular orbital scheme for a B6 cluster in Oh point symmetry
t1u
eg
B-B
Anti-bonding
Relative energy
t1g
LUMO
Thus, a B6 cluster possesses 7
strongly bonding orbitals.
Therefore, [B6H6]2− is stable
as a 2− anion.
t2u
This is a general result.
HOMO
t2g
t1u
B-B
Bonding
BnHn (n = 6 to 12) clusters
possess (n + 1) bonding orbitals
and are stable as [BnHn]2-.
a1g
The seven bonding orbital combinations of [B6H6]2−
CM 2312
Clusters and Catenation
4
[BnHn]2- clusters have a deltahedral boron cage, i.e. the polyhedra possess only
triangular faces, and each boron atom is bonded to a terminal H atom.
CM 2312
Clusters and Catenation
5
The cage structure of the boron hydrides (boranes), their
carbon-substituted relatives (carboranes), many clusters of the
p-block elements (and many d-transition metal clusters)
follows from:
The relationship of the number of
vertices to the number of electron pairs
involved in the cage skeleton:
Boranes
Type
Formula
Skeletal
Examples
electron pairs
Closo
[BnHn]2-
n+1
[B6H6]2-, [B12H12]2-
Nido
[BnHn+4]
n+2
[B5H9], [B6H10]
Arachno
[BnHn+6]
n+3
[B4H10], [B5H11]
Closo
CM 2312
Nido
Clusters and Catenation
Arachno
6
Relationship between closo, nido and arachno B-H
structures
1.
Closo → nido
e.g. [B6H6]2- → [B5H9]
[B6H6]2-
- 2 e−
[B6H6]
- BH
[B5H5]
+ 4H
14 skeletal electrons
(7 pairs)
lose one electron pair
12 skeletal electrons
(6 pairs)
lose one vertex
10 skeletal electrons
(5 pairs)
added to cage bridging between
pairs of boron atoms
[B5H9]
14 skeletal electrons
(7 pairs)
Thus each H atom added (beyond the terminal B-H bonds) brings one electron to
the skeletal (B-H/B-B) cage.
CM 2312
Clusters and Catenation
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2.
Closo → arachno
e.g. [B6H6]2- → [B4H10]
[B6H6]2-
- 2 e−
[B6H6]
- 2BH
14 skeletal electrons
(7 pairs)
lose one electron pair
12 skeletal electrons
(6 pairs)
lose two vertices,
each with one pair of electrons
[B4H4]
+ 6H
[B4H10]
8 skeletal electrons
(4 pairs)
6 electrons added to skeleton
14 skeletal electrons
(7 pairs)
(n + 3) arachno structure based on closo minus two vertices
H
B
H
H
H
H
B
B
B
H
H
H
H
H
4 of the 6 hydrogen atoms bridge across B . . . . B edges
and two form terminal B-H bonds
CM 2312
Clusters and Catenation
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A set of guidelines may be followed in order to predict the
structure of a borane cluster.
1.
2.
3.
4.
5.
6.
7.
How many [B-H] units are there?
How many additional H atoms are there?
How many valence electrons are available for cluster bonding?
What is the parent deltahedron?
After each [B-H] unit has been accommodated at a skeletal vertex, are there
any vertices vacant in the parent deltahedron? What class is the cluster?
Additional H atoms are placed either around the B-B edges of an open face
of the cluster or in extra terminal positions, usually if a boron atom is of
particularly low connectivity.
In arachno structures vacant vertices are usually adjacent. Cluster
symmetry is generally kept as high as possible.
Why do bridging hydrogen atoms occupy sites around the open faces of a cluster?
The open face of a cluster is generated by removing one, or more, vertices from a deltahedral cluster.
Considering MO theory, the loss of a vertex leaves a region of electron density focused around an open
face, hence protons will readily interact with the open face. This leads to B-H-B bridges around the open
face.
Bonding cluster MO
2-
derived from [B6H6]
H 1s
AO
Example 1. B10H14
CM 2312
Clusters and Catenation
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Example 2. [B6H9]-
Example 3. [B12H12]2-
Example 4. C2B4H6
CM 2312
Clusters and Catenation
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ISOELECTRONIC SPECIES
Molecules, ions or molecular fragments that possess the same number of valence and core
electrons are said to be isoelectronic. However, this term is often used to refer to species that
simply possess the same number of valence electrons.
With respect to the number of valence electrons available the following fragments are
isoelectronic with each other:
{BH-}, {CH}, {CMe}, {NH+}
e.g. Carboranes
The Isolobal Principle
It is possible to convert a borane into a carborane cluster by replacing a {BH−} by a {CH} unit
because both fragments possess the same frontier orbital properties. The two sets of MOs have the
same symmetry characteristics, are of approximately the same energy, and contain the same number
of electrons, 3, available for cluster bonding. The {BH−} and {CH} fragments are said to be
isolobal. The principle can be extended to include a range of atoms and molecular fragments all of
which exhibit similar frontier orbitals. Series of isolobal p-block fragments are:
(a)
{BH−}, {BR−}, {CH}, {CR}, {NR+}; (where R is a one electron donor e.g.
alkyl, aryl, halogen atom)
Contribute 3 orbitals and 3 electrons for skeletal bonding
(b)
{BR}, {AlR}, {GaR}, {GeR+}, {SR3+}; (where R is a one electron donor e.g.
alkyl, aryl, halogen atom)
Contribute 3 orbitals and 2 electrons for skeletal bonding
(c)
{BH}, {Ge}, {Sn}, {N+}, {Bi+}, {Se2+}; (where each bare atom carries an
exo-lone pair of electrons.
Contribute 3 orbitals and 2 electrons for skeletal bonding
CM 2312
Clusters and Catenation
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Zintl Ions
A Zintl phase, MnEx, is formed between a very electropositive metal (M) and a less
electropositive metal E), e.g. between a Group 1 metal such as Na and a heavy p-block metal such as
Tl. Early syntheses involved dissolving the p-block metal in liquid ammonia containing Na. Current
syntheses use special chelating ligands.
Syntheses
The structures of the Group 14 anionic clusters [E4]2- (tetrahedron, [E5]2- (trigonal bipyramid),
[E9]2- (tricapped trigonal prism) and [E9]4-(monocapped square antiprism)
CM 2312
Clusters and Catenation
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[Ge4]4-
[Sn5]2-
[Ge9]2-
2Bi
Bi
Bi
Bi
[Bi4]2-
CM 2312
2+
Isoelectronic
species
Se
Se
Se
Se
D4h
[Se4]
Clusters and Catenation
2+
13
Reactions of Boron Clusters
The syntheses of boron clusters involve cage expansion, cage coupling, cage fusion and the
introduction of heteroatoms.
1. Closo hydroborate dianions - reactivity similar to aromatic organic molecules
[B12H11(CO)]2+ 1,7-(CO)2B12H10
[B12H11R]2-
+ 1,10-(CO)2B12H10
CO in presence
RCl with
AlCl3
water
soluble
salts
of H
H2O
+
[B12H12-xXx]2-
X2
x = 1 to 12
X = Cl, Br or I
2-
[B12H12]
Hydride
Electrochemical
oxidation
in MeCN
[B24H23]3-
No reaction
The reactivity and stability depends on cluster size and the counter-ion. Ag2[B6H6] detonates upon
heating, but Cs2[B6H6] is thermally stable. [B10H10]2- and [B12H12]2- are hydrolytically stable in
aqueous acidic and basic solutions.
Substitution is electrophilic
Resistant to chemical oxidation
All sites are structurally equivalent
CM 2312
Clusters and Catenation
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2. Neutral nido boranes: e.g. B5H9
1-RB5H8
isomerise
5 B(OR)3 + 12 H2
2-RB5H8
RCl with
AlCl3
M[B5H8] + H2
ROH
NaH or KH
deprotonation
1
o
Cl2, T > 0 C
1,2-Cl2B5H7
with Lewis
isomerise
5
2
4
3
nido-B5H9
acid
o
C2H2, 500 C
X2, X = Br or I
2,3 (or 2,4)Cl2B5H7
carborane formation
closo-C2B3H5 + closo-C2B4H6
+ closo-C2B5H7
isomerise
2-XB5H8
1-XB5H8
Electrophilic and nucleophilic attack
Electrophilic attack at apex followed by conversion to basal isomer
Deprotonation at bridge
3. Neutral arachno boranes: e.g. B4H10
4B(OH)3 + 11H2
H2O
2-BrB4H9 + HBr
Br2 at -15 oC
4
2
3
NaH or KH
M[B4H9] + H2
1
arachno-B4H10
CO or PF3
C2H2 100 oC
1-(CO)B4H8 or
1-(PF3)B4H8
+ H2
closo-C2B3H5 + closo-C2B4H6
+ closo-C2B5H7
Nucleophilic attack
Deprotonation at bridge
HYDROLYSIS: closo < nido < arachno
CM 2312
Clusters and Catenation
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