Coupling reaction of the quinonediimine with the phenolic or naphtholic couplers.
Coupling reaction rate constant =k
k=( kb・T／h ) { exp ( ΔrS°++／R ) } { exp ( ーΔrH°++／RT ) }
ΔrH°++ ≈ E₀ーRT The order of reaction is omitted.
E₀ is the activation energy of the coupling reaction,
and the coupling reaction rate increases due to the decrease of E₀.
⊿Etotal=ーqr・qs ／ Rmitted. rs ＋2(Cmｒr・ Cnｓs・⊿β)² ／(E*nrーE*ms)
(the second term) (the third term) (the first term is omitted)
(coulomb term) (electron transfer interaction term)
where
E*nr is the energy level of the coupler anion's HOMO,
E*ms is the energy level of quinonediimine's LUMO,
Cmrr is the molecular orbital coefficient of HOMO on the coupler active point carbon,
Cnss is the molecular orbital coefficient of LUMO on the quinonediimine reaction point nitrogen,
Δβ is the stabilization energy due to the formation of CN bond.
It's equivalent to the amount of change in the resonance integral.
Although the absolute value of electron transfer interaction | ⊿Etotal | between HOMO and LUMO is not directly related to the reaction rate,
the relevant relation might be inferred.
The coupling reaction between HOMO and LUMO mentioned above
is a case in which the relevant relation can be inferred.
Therefore, due to the decrease of absolute value of electron transfer interaction, the activation energy (E₀) increases and the coupling reaction rate constant decreases to slow down the coupling reaction rate.
The reason why I use absolute value is that ⊿Etotal is usually a negative value.
In the following, the magnitude of the electron transfer interaction ⊿Etotal
is discussed with absolute value.
The reaction in which a covalent bond (sigma bond) is formed due to the reaction of a weak acid with a weak base can be explained by the dominance of the electron transfer interaction term of the third term.
It is advantage to decrease the differince between En*r and Em*s.
Decrease of the denominator can increase the absolute value of ⊿Etotal
which is a negative value.
Electron transfer interactions form bond and become energetically stable,
a low value in the energy level is achieved.
It's important to decrease the difference between E*nr and E*ms
within a range where the desorption rate is not the rate-determining.
