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expressions:
zz
(X)
χ
aa
(X) =
χ
P
2
(cos
β
)
,
(7)
zz
(Y)
χ
aa
(Y) =
χ
P
2
(cos
β
)
,
(8)
in which
is the instantaneous angle between
a
axis and the XY internu-
clear axis
z
and
β
is the second Legendre coefficient. Substitution of
Eqs. 7 and 8 into Eqs. 5 and 6 leads to the following expressions for
P
2
(cos
β
)
δ
p
,
the fractions of an electronic charge transferred from B to X and from X to Y,
respectively, when B
δ
i
and
···
XY is formed:
0
(Y)
χ
A
(Y)
χ
-
χ
aa
(Y)
χ
A
(Y)
-1
δ
P
=
P
2
(cos
β
)
(9)
-
χ
aa
(X)
χ
A
(X)
χ
0
(X)
χ
A
(X)
χ
0
(Y)
χ
A
(Y)
+
χ
aa
(Y)
χ
A
(Y)
-1
δ
i
=
+
P
2
(cos
β
)
.
(10)
Hence, the inter- and intramolecular electron transfer
δ
i
e
and
δ
p
e
can be de-
termined once the value of
P
2
(cos
) is available. It has been possible to make
good estimates of the last quantity for members of each of the series B
β
···
Cl
2
,
B
···
BrCl, B
···
Br
2
and B
···
ICl as follows. By making the reasonable assump-
δ
i
= 0 in the weak complexes Ar
···
···
tion that
BrCl [57] and Ar
ICl [93], the
β
av
=cos
-1
cos
2
β
1
/
2
= 6.4
◦
and 5.4
◦
, respectively, and
values
δ
p
= 0.0035(6)
and 0.0054(1), respectively, are determined. The very small values of
δ
p
jus-
δ
i
= 0 initially. All other complexes B
···
tify,aposteriori,theassumption
BrCl
and B
···
ICl considered are much more strongly bound than Ar
···
BrCl and
av
(in the range of 5.0(5)
◦
and 4.0(5)
◦
, respectively) were assumed. Moreover,
Ar
···
ICl, respectively, and so smaller values of
β
P
2
(cos
β
)
is close to
unity even for the Ar complexes and changes so slowly as
β
av
deceases that
any errors incurred by such assumptions are negligible. A similar treatment
was employed for B
···
Br
2
and B
···
Cl
2
complexes using OC
···
Br
2
[87] and
OC
···
Cl
2
[39] as the complexes appropriate to the weak limit having
δ
i
=0,
in the absence of experimental knowledge of linear complexes Ar
···
Br
2
and
Ar
···
Cl
2
.Hence,valuesof
δ
i
and
δ
p
have been determined for the four se-
ries B
XY, where B is N
2
,CO,C
2
H
2
,C
2
H
4
,PH
3
,H
2
S, HCN, H
2
OandNH
3
and XY is Cl
2
,Br
2
, BrCl and ICl. Some systematic trends are evident in
···
δ
i
and
δ
p
.
i
against the first ionisation potential
I
B
of
the Lewis base B for each of the three series B
Figure 20 displays plots of
δ
···
Cl
2
,B
···
BrCl [55] and
B
ICl [178]. Each set of points can be fitted reasonably well by a function
δ
i
=
A
exp(-
aI
B
). This function is shown by a continuous line in each case.
The points for the series B
···
···
Br
2
lieveryclosetothosefortheB
···
BrCl series
and are omitted for clarity.
Figure 20 demonstrates that there is a family relationship among the
curves and that the smaller the energy required to remove the most loosely
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