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A:B+A :B =A:B +A :B
Δ
E > 0
(47)
H-S S-H H-H S-S
[H = harder, S = softer]
Gazquez et al. [58] showed that the feasibility of the above reaction
may be studied in terms of the energy change in a simple quadratic model
as follows:
ΔE = NΔμ
− (1/2)
N
2
∆η
(48)
(approximated up to second order of energy change)
where
N
is the number of electrons, and Δμ and ∆η are the changes
between the reactants and products. If μ were constant, then ΔE would
decrease if ∆η were positive.
For a very small amount of electron transfer (∆N) from base to acid
during the acid-base adduct formation, it is better to use the following
equation:
Δ
E
= (∂
E
/∂
N
)
v
∆
N
+ (1/2) (∂
2
E
∂
N
2
)
v
(∆
N
)
2
(49)
Now, we obtain
Δ
E
= Δ
Nμ
− (1/2) η ∆
N
2
(50)
This hard-soft classifi cation is based on the relative hardness of the
interacting species. Feasibility of a reaction can be explained by a funda-
mental rule of nature. Pearson fi rst studied that a reaction proceeds to the
direction that produced the hardest molecule. Thus, apart from the cel-
ebrated HSAB principle, Pearson proposed “there is a rule in nature that
every system tries to be as hard as possible” a rule of thumb known as the
principle of maximum hardness (PMH) [59].
1.2.15 THE FUKUI FUNCTION
Parr and Yang [60] connected DFT with the frontier orbital theory of
chemical reactivity of Fukui. Although electronegativity and hardness are
global properties of the system, the electron transfer between two mol-
ecules involves the electron transfer from a definite filled orbitals on the
donor orbital, usually the highest-occupied molecular orbital, HOMO to
an empty acceptor orbital usually the lowest unoccupied molecular orbital,
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