Ground (S0) and first excited singlet state
(S1) potential energy surfaces were calculated for a series
of six
symmetric carbocyanines as a function of the twisting angle (θ),
around a carbon−carbon bond of the
polymethine chain. The surfaces were computed using AM1
semiempirical quantum mechanical calculations.
Rotations around different bonds were considered in order to
determine the relevant rotation for isomerization,
that is, the rotation with the lowest activation energy for the
isolated molecule (E
0). For that rotation,
the
computed values of E
0 are in good agreement with
values extrapolated from experiments in solutions of
n-primary alcohols. The same holds for the computed
transition energies between both surfaces for the
thermodynamically stable N isomer (θ = 0°) and the P photoisomer
(θ = 180°). The effects of chain length
and pattern substitution of the indoline moiety on
E
0 were also analyzed for both surfaces.
The shape of the
potential surfaces referred as the Rullière's model holds in all
cases for at least one rotational coordinate.
The electrical dipole moment with respect to the center of
electrical charges was calculated as a function of
θ. The calculations show that the dipole moment remains almost
constant except in the vicinity of θ = 90°,
where a sudden increase with a sharp peak was obtained in both
surfaces. This gives a simple explanation
for the well-known experimental observation that the activation energy
on the excited state surface is
independent of solvent polarity, as the angle of the transition state
is smaller than 90°. On the other hand,
the transition state is at θ = 90° on the ground state, and a
polarity influence is predicted. An improvement
in the description of the experimental isomerization rate constants in
S0 is obtained for the two smallest
carbocyanines considered when polarity contributions are
included.