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306 Boron Hydrides

In Lipscomb’s method a boron hydride is considered to For a particular boron hydride formula B p H p+q there are
have one terminal hydrogen atom on every boron atom four structural unknowns, s, t, y, and x but only three
plus a number of “extra” hydrogen atoms. These “extra” equations. Therefore, a unique solution is not generally
hydrogen atoms may be bridging hydrogens or they may possible and there will be a family of solutions for each
be terminal hydrogen atoms on a boron atom in addition formula.
to the one terminal atom already assumed. The general For example, three styx solutions are possible for
formula for a boron hydride from this point of view is B 5 H 9 ,
B p H p+q , where there are p boron atoms each with its ter-
s t y x
minal hydrogen and q “extra” hydrogen atoms. The vari-
ables for the four kinds of bonding features are given by 41 2 0
the symbols, s, t, y, and x, where 32 1 1
23 0 2
s = number of three-center, boron-hydrogen-boron,
Solutions with negative values for s, t,or y are undefinable.
bridge bonds
A negative value of x would occur if there were fewer
t = number of three-center boron-boron-boron bonds
terminal hydrogen atoms than boron atoms, a situation
y = number of two-center, boron-boron bonds
observed in the unusual boron hydride B 20 H 16 .
x = number of terminal hydrogen atoms in excess of
A key to the different kinds of bonds in boron hydrides
one per boron atom
is given in Fig. 7. A structure for the 4, 1, 2, 0 styx solution
showing the disposition of all the kinds of bonds is
These variables can be related to the values of p and q
for a specific boron hydride formula by three equations of
H H
balance: H
B B
1. The total number of three-center bonds (s + t) equals
the number of boron atoms p. H H H
B
s + t = p B B
H
2. The total number of extra hydrogen atoms q equals H H
the number of boron-hydrogen-boron, three-center
bonds s plus the number of “extra” terminal hydrogen Normally, a number of different structures can be drawn
atoms x. for a specific boron hydride formula, and some selection is
necessary. The most favored structures incorporate some
s + x = q
symmetry and do not involve bond angles with excessive
3. Considering each boron-terminal hydrogen group p strain. Often, a number of equivalent but distinct struc-
to supply a pair of electrons for the other bonds in the tures that are satisfactory can be drawn for a particular
structure, there are p pairs of electrons available. One boron hydride. In these cases the positions of the atoms
pair is necessary for each boron-boron-boron, are the same but the disposition of the electrons, that is,
three-center bond t and for each boron-boron, the details of the bonding, are different. For example, the
two-center bond y. One electron (half a pair) is structure of B 5 H 9 given above can be oriented in four dif-
necessary for each boron-hydrogen-boron, bridge ferent directions.
bond s and for each “extra” terminal hydrogen x
beyond the one already assumed on each boron.
(Only one electron is necessary for bonds involving
hydrogen since the hydrogen atom itself brings in one
electron.)

s x
p = t + y + +
2 2
FIGURE 7 Bond types as drawn for boron hydride structures.
Now, since q = s + x, this equation can be simplified to (a) The bridging, boron-hydrogen-boron, three-center bond, (b)
the boron-boron-boron, three-center bond, (c) the boron-boron,
q
p = t + y + two-center bond, and (d) the terminal boron-hydrogen two-center
2 bond.