Page 97 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

76 as CH=O and NO decrease the negative potential (in fact it is positive for NO ) and
2
2
increase the distance from the double bond. This results in a weaker attraction to the
CHAPTER 1
approaching electrophile and reduced reactivity.
Chemical Bonding
and Molecular Structure
1.4.6. Relationships between Electron Density and Bond Order
We would expect there to be a relationship between the electron density among
nuclei and the bond length. There is a correlation between bond length and bond order.
Bonds get shorter as bond order increases. Pauling defined an empirical relationship
for bond order in terms of bond length for C–C, C=C, and C≡C bond lengths. 93 For
carbon, the parameter a is 0.3:
r −r

0
n = exp (1.26)
BOND
a
The concept of a bond order or bond index can be particularly useful in the description
of transition structures, where bonds are being broken and formed and the bond order
can provide a measure of the extent of reaction at different bonds. It has been suggested
that the parameter in the Pauling relationship (1.26) should be 0.6 for bond orders
< 1. 94
MO calculations can define bond order in terms of atomic populations. Mayer
developed a relationship for the bond order that is related to the Mulliken population
95
analysis :

B = PS PS (1.27)
AB )( ()
(∈A )∈B
Wiberg applied a similar expression to CNDO calculations, where S = 1, to give the
96
bond index, BI :

BI AB = P P () (1.28)
)(
(∈A )∈B
In these treatments, the sum of the bond order for the second-row elements closely
approximates the valence number, 4 for carbon, 3 for nitrogen, and 2 for oxygen. As
with the Mulliken population analysis, the Mayer-Wiberg bond orders are basis-set
dependent.
The NPA orbital method of Weinhold (Section 1.4.2) lends itself to a description
of the bond order. When the NPAs have occupancy near 2.0, they correspond to single
bonds, but when delocalization is present, the occupancy (and bond order) deviates,
reflecting the other contributing resonance structures. There have also been efforts to
define bond orders in the context of AIM. There is a nearly linear relationship between
the , and the bond length for the four characteristic bond orders for carbon 1, 1.5
c
(aromatic), 2, and 3. 97

93 L. Pauling, J. Am. Chem. Soc., 69, 542 (1947).
94
Ref. 30 in K. N. Houk, S. N. Gustafson, and K. A. Black, J. Am. Chem. Soc., 114, 8565 (1992).
95 I. Mayer, Chem. Phys. Lett., 97, 270 (1983).
96 K. B. Wiberg, Tetrahedron, 24, 1083 (1968).
97 ∗
R. F. W. Bader, T. T. Nguyen-Dang, and Y. Tal, Rep. Prog. Phys., 44, 893 (1981); For 6-31G values
see X. Fadera, M. A. Austen, and R. F. W. Bader, J. Phys. Chem. A, 103, 304 (1999).