Mathematical Foundations - Models for Bonding in Chemistry - page 18

are atomic charges,and:

2 l S

q AB ¼ q BA ¼ ð 1 : 84 Þ

2

1 þ l þ 2 l S

overlap charges. The charges are normalized so that:

2

þ þ

2 2 l 4 l S

q A þ q B þ q AB þ q BA ¼

S ¼

2 ð 1 : 85 Þ

2

1 þ l þ 2 l

the total number of electrons in the bond orbital fð r Þ .

For a homopolar bond, l ¼ 1:

1 S

q A ¼ q B ¼ q AB ¼ q BA ¼ ð 1 : 86 Þ

1 þ S 1 þ S

so that for S 0, in the bond, the charge on the atoms is decreased,

electrons being transferred to the region between nuclei to an extent
described by q AB and q BA . This reduces internuclear repulsion and means
bonding.
For aheteropolarbond,

>

l = 1, andwedefinegross chargesonAandBas:

2 þ 2 l S

Q A ¼ q A þ q AB ¼ ð 1 : 87 Þ

2

1 þ l þ 2 l S

2

2 l þ 2 l S

Q B ¼ q B þ q BA ¼ ð 1 : 88 Þ

2

þ l þ

1 2 l S

and formal charges on A and B as:

2

l 1

d A ¼ 1 Q A ¼ ð 1 : 89 Þ

2

þ l þ

1 2 l S

2

l 1

d B ¼ 1 Q B ¼ ð 1 : 90 Þ

2

1 þ l þ 2 l S

If l > 1, d A ¼ d > 0, d B ¼d A ¼d < 0, and we have the dipole

A þ d B d (e.g. the LiH molecule).
In our model, an essential role will be assigned to the exchange-overlap
densities (MagnascoandMcWeeny, 1991;Magnasco, 2007, 2008, 2009a):

S x A ð S x B ð

x A ð r Þx B ð r Þ r Þ; x B ð r Þx A ð r Þ r Þ ð 1 : 91 Þ

which have the properties:
ð dr

ð dr

S x A ð S x B ð ½x A ð r Þx B ð r Þ r Þ ¼ 0 ; ½x B ð r Þx A ð r Þ r Þ ¼ 0 ð 1 : 92 Þ