Pauling bond order
The degree or order of bonding between two atoms cannot only be determined
through analysis of the molecular wavefunction, but also through using the
bond distance/bond order correlation established by Linus Pauling. This
empirical scheme is particularly useful for comparing calculated
and experimentally determined data, but also has some value as a "post factum"
analysis method. The approach is based on the assumption that bond orders
vary exponentially with bond distances. This can be expressed in a straightforward
manner with equation (1):
nx = no EXP((ro - rx)/c)
In equation (1) the bond order nx of a bond of length rx
is a function of a reference bond of length ro, whose bond order is
defined as no. The constant c determines, how steeply the bond orders
change with bond distances. Very frequently the reference bond distance is that
of a single bond with no=1.0.
The original equation suggested by Pauling for single and double bonds uses
a value of c = 0.3 (black line). For the analysis of bond orders in transition states
this value leads to bond orders which are too small. For these structures
a value of c = 0.6 appears to be more appropriate (blue line).
The calculation of bond orders n for ground state molecules will be demonstrated using
ethylene, butadiene, and benzene as example. The following structural data have been
calculated for these systems at the Becke3LYP/6-31G(d) level of theory (distances in pm):
The double bond in ethylene is used here as the reference systems for bonds with
bond order 2 at a bond length of 133.09 pm. Using Paulings original expression (c = 0.3)
the bond orders in butadiene amount to 1.937 (C1-C2) and 1.312 (C2 - C3), and to 1.607
for benzene. It is clear from this example, that the calculated bond orders always
depend on the chosen reference system!
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last changes: 29.01.2005, HZ
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