Angewandte
Chemie
effect on the rate of transition compared to the 3-position as it
is indeed the case. This observation in turn confirms the
conclusion on the non-ergodicity of the process hinted at in
our previous work.[6] That is, the dynamics are truly localized
in real space. The intergroup timescale differences also reflect
this locality, as the apparent nonlocal change of the ring size
actually has a very large local effect by significantly affecting
the angle of the central C-CO-C moiety.
Although it has been stressed that the dynamics leading to
disposal of the electronic energy is truly localized, an increase
in the total density of vibrational states on the lower surface
does slightly speed up the process. This effect is a consequence
of additional vibrational degrees of freedom acting as
acceptor modes in the lower electronic state. Comparison
between the rates of transition for molecules of different ring
sizes does not immediately reveal this aspect as the two other
effects discussed play a much larger role. This aspect is,
however, revealed by a comparison between the rates of
transition for 3-MeCP and 3-EtCP. The addition of an extra
CH2 group increases the density of vibrational states by
a factor of about 100 at an energy of 2 eV—approximately the
energy difference between the (n,3s) and (n,p*) states (see
the Supporting Information). However, this factor of 100 only
leads to a small decrease in the timescale for transitions from
5.79 ꢀ 0.16 ps to 5.16 ꢀ 0.17 ps—very different from the
behavior expected by application of theory in the statistical
limit.[11–14]
Figure 4. The vibrational frequency w and the energy difference DE
determine the intersection point between the two excited states. These
two parameters thereby determine how close the molecule can get to
the intersection point and, thus, the rate of nonadiabatic transition.
The enlarged region shows two possible pathways: one adiabatic
indicated by the dotted arrow and one nonadiabatic transition through
a conical intersection indicated by the dashed arrow.
allow the molecule to access a larger configurational space,
whereby it can more easily access the region near the very
important conical intersection crossing point[8] leading to
a faster nonadiabatic transition. Such a transition is illustrated
by the dashed arrow in Figure 4 as opposed to the adiabatic
dynamics indicated by the dotted arrow.
Herein, we have revealed some salient features of the
complex process of internal conversion. Most conclusions
derived from the observation that the dynamics leading to
a transition from one electronic state to another, and thereby
to the transformation of electronic energy into vibrational
energy, is inherently localized—only one or a few vibrational
modes play a significant role. Merely by small structural
variations, the vibrational frequency and the energy available
in the excited state can be affected thereby tuning the rate of
internal conversion over a range of more than an order of
magnitude. A lower frequency and a larger available energy
result in a faster process as the molecule can reach a config-
urational space in closer proximity of the crossing point
between the excited states. The total density of vibrational
states plays a smaller, secondary role as an increase in this
only leads to a very slight increase in the overall rate. In
contrast to the standard energy gap laws that neglect the
nuclear dependence on the electronic coupling,[12,13] our
results clearly show the effect of coherent nuclear motion
on these matrix elements.
The cause of the intergroup timescale differences is
primarily rooted in the energy difference factor, which is
apparent by comparison of the unsubstituted cycloketones.
The smaller, strained CB is able to relieve ring-strain in the
(n,3s) state through vibration in the ring-puckering mode,
whereas the five-membered ring of CP is less prone to such
motion. As calculated using equation of motion coupled-
cluster singles and doubles (EOM-CCSD), the energy differ-
ence in the (n,3s) state between the Franck–Condon and
equilibrium geometries is 0.32 eV for CB, whereas it is only
0.14 eV for CP (see the Supporting Information). The more
vibrationally congested (n,3s) absorption spectrum for CB
compared to CP further corroborates this difference.[9] The
even slower transition in cyclohexanone can be understood in
terms of the inverse relationship between ring size and
intensity of vibrational bands and, thus, release of angle strain
in the C-CO-C moiety.[10] The frequency factor, as caused by
different curvatures of the potential-energy surface illustrated
by the two examples in Figure 4, also contributes to the
intergroup timescale differences. The effect is clearly dem-
onstrated by the observed anti-correlation between the
vibrational frequency and the rate of transition for CB and
2-MeCP.
Received: October 11, 2012
Revised: December 31, 2012
Published online: January 16, 2013
The intragroup timescale differences can largely be
understood in terms of the frequency factor and how this is
affected by substitution. Alkyl substitution in the 2-position
leads to a significantly increased rate of transition, whereas
this is not the case for substitution in the 3-position as
observed when comparing 2-MeCP and 3-MeCP. The central
vibrational mode primarily involves motion in the C-CO-C
moiety, thus substitution in the 2-position should have a larger
Keywords: gas-phase reactions · kinetics · photophysics ·
time-resolved spectroscopy
.
Angew. Chem. Int. Ed. 2013, 52, 2247 –2250
ꢀ 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim