The Chemical Bond - Models for Bonding in Chemistry - page 55

the reverse being true for the remaining hydrides .Itis

apparent that the model parameter a H a X accounts in some way for
atom electronegativities within the bond. The bond energy parameter

ða H a X > 0 Þ

jbj
has the same order of magnitude of a 2 a 1 and, apart from LiH, regularly
increases from HeH þ to FH.

2.6 STEREOCHEMISTRY OF POLYATOMIC
MOLECULES

The structure in space of polyatomic molecules depends on the stereo-
chemistry of their chemical bonds through the principle of maximum
overlap (Magnasco, 2005).

2.6.1 The Molecular Orbital Model of Directed Valency

In the following, we shall use our model description of the chemical bond
to show that bonding is strongest for AOs maximizing the strength of the
exchange-overlap component of the bond energy. Making the usual
assumptions typical of elementary H

uckel theory including overlap, we €

shall show that the H uckel energy of the two-electron bond is minimized

for orbitals having maximum overlap.
Let b A be a directed orbital (atomic or hybrid) centred at the nucleus of
atomA andmaking an angle u with the interbond axis A-B directed along
z from A to B, and x B a spherical orbital on atom B a distance R apart.
Then, overlap S AB and bond integral b AB can be written as:

€

S AB ¼ S cos u; b AB ¼ b cos u ð 2 : 76 Þ

where S and b are integrals characteristic of the bond A-B, which depend
on R, but are independent of the orientation u .
The pseudosecular equation for the corresponding bond orbital f in a
one-electron H

€

uckel-type approximation including overlap can then be

written as:

¼

a A « ðb« S Þ cos u

0 ð 2 : 77 Þ

ðb« S Þ cos u B «

which expands to the quadratic equation in « :

S 2 cos 2 uÞ« 2 2 b S cos 2 uÞ«þða A a B b 2 cos 2 uÞ¼ ð 1 ða A þa B 0 ð 2 : 78 Þ