Lipscomb's Rule: Topology of Boranes
The overall bonding in boranes/higher boranes can be codified in a four-digit number, the so called styx number given by W. N. Lipscomb in 1963.
The significance of s, t, y and x are given below:
s = No. of 3c−2e B−H−B bonds
t = No. of 3c−2e B−B−B bonds
y = No. of 2c−2e B−B bonds and
x = No. of BH2 groups.
This four-digit coding system of bonding in boranes is also termed as topology of boranes.
Utility of Lipscomb's Rule
The number of atoms in a neutral boranes molecule is equal to twice the sum of s, t, y and x, that is,
No. of atoms in neutral boranes = 2(s + t + y + x)
The number of electron pairs involved in the bonding of the borane molecule is n plus the sum of the individual s t y x number, that is,
No. of electron pairs in a borane molecule = n + (s + t + y + x)
Here, n = number of B-atoms in boron clusters
Validity of Lipscomb's Rule
Various types of bonding in boranes can be understood by considering plane projections of their respective structures. The validity of Lipscomb's rule can be seen in all the boranes.
Examples:
Diborane (B2H6)
Total number of atoms = 2 + 6 = 8
Total number of valence electrons (VEs) = 3 × 2 + 6 = 12
s = No. of 3c-2e B–H–B bonds = 2
t = No. of 3c-2e B–B–B bonds = 0
y = No. of 2c-2e B–B bonds = 0
x = No. of BH2 groups = 2
Number of atoms in diborane = 2(s + t + y + x) = 2(2 + 0 + 0 + 2) = 2 × 4 = 8
So, the total number of atoms in B2H6 is 8.
No. of bond pairs in diborane molecule = n + (s + t + y + x) = 2 + (2 + 0 + 0 + 2) = 2 + 4 = 6
So, the total valence electrons in diborane is 12, that is, 6 electron pair
Thus, the four-digit coding system of bonding in B2H6 is (2002). The eight number of atoms and six electron pairs calculated by Lipscomb's rule in diborane validate this rule.
Hexaborane (B6H10)
Total number of atoms = 6 + 10 = 16
Total number of VEs = 3 × 6 + 10 = 28
s = No. of 3c-2e B–H–B bonds = 4
t = No. of 3c-2e B–B–B bonds = 2
y = No. of 2c-2e B–B bonds = 2
x = No. of BH2 groups = 0
Number of atoms in hexaborane (10) = 2(s + t + y + x) = 2(4 + 2 + 2 + 0) =2 × 8 = 16
So, the total number of atoms in B6H10 is 16
No. of electron pairs in this molecule = n + (s + t + y + x) = 6 + (4 + 2 + 2 + 0) = 6 + 8 = 14
So, the total VEs in this boron cluster is 28, that is, 14 electron pairs)
Thus, the four-digit coding system of bonding in B6H10 is (4220).
The 16 number of atoms and 14 electron pairs calculated by Lipscomb's rule in B6H10 indicate
the validity of this rule.
Limitations of Lipscomb's Topological Scheme
The topological scheme has its limitations. For the symmetrical closo-boranes and even for the large open cluster boranes, it becomes difficult if not impossible to write simple, satisfactory structures of this sort.
Example: B5H9 shown above the one structure shown is incompatible with the high symmetry (C4v) of the molecule. In this case, which is relatively simple, the difficulty is easily overcome by treating the structure shown as only one of four equivalent ones that together form a resonance hybrids. With increasing size and symmetry, however, this sort of approach becomes very cumbersome (because all canonical structures will not be equivalent) and it becomes desirable to employ an MO description, consistent with the full molecular symmetry and naturally incorporating delocalization.
Also read Wade's Rule