Pincock and Pincock
1247
following, according to eq. [4], the higher values of kr for
the allyl ethers result in higher values of kt, and, conse-
quently, lower values for Φf = kf /kt, kf being essentially con-
stant for any given substituent X but independent of the
static (Φ ) or dynamic (τs) measurements of fluorescence can
f
be used although the latter is preferred because more reliable
experimental values can be obtained. The assumption used is
given in eqs. [4] and [5], where the changes in kt of the reac-
tive series only differ from those (ktM) of the model series 2
by kr . Therefore, subtraction of experimentally determinable
values (kt – ktM = kr) should reliably give kr. Because these
are exclusively properties of the excited singlet state, the kr
values obtained are independent of kir , the internal return
process.
alkyl group of the ether. The similar values of Φ for the
f
adamantyl ethers and the anisoles indicate that the kr values
for the adamantyl compounds do not make a large contribu-
tion to the kt of S1.
[4]
kt = kf + kic + kisc + kr
This method was applied quite successfully to obtain kr
values for the allyl ethers 4 in both cyclohexane and metha-
nol (3). From absorbance spectra (λmax, ⑀), fluorescence
spectra (λ0,0, ES1), and calculated kf values, good evidence
was provided that the sets 2 and 4 have very similar excited-
state properties for any given equivalently substituted pair in
either methanol or cyclohexane. The resulting kr values as a
function of substituents spanned almost two orders of mag-
nitude (108–1010 s–1), and for some cases (3- and 4-methoxy
and 3- and 4-methyl), were the dominant mode of decay of
S1. A plot of kr in methanol vs. kr in cyclohexane was linear
and the slope (0.96) indicated a parallel substituent effect in
the two solvents. This observation demonstrates that only
radical pair intermediates are being generated, ion pairs not
being possible in cyclohexane.
An examination of the kt (adamantyl ethers 1) and ktM
(anisoles 2) values in Table 1 indicates that the difference re-
quired to usefully apply eqs. [4] and [5] is hardly outside ex-
perimental error for most substitutents. Small positive values
are obtained in most cases, although a few are actually nega-
tive. This observation quantitatively demonstrates that the
adamantyl ethers have very small values of kr, the rate con-
stant of reaction, relative to the other modes of decay of the
excited singlet state (kic, kf, and kisc). The only noticeable
trend in the kr values is towards higher values for those com-
pounds 1j and 1k with cyano substitutents at C-3 and C-4,
respectively, more so in methanol than in cyclohexane, but
particularly for the 4-CN compound in methanol. This cor-
rectly accounts for the observation that the 4-cyano com-
pound gives a significant yield of the ion-derived product 10
in methanol. Unfortunately, overall, the changes in kr are too
small to attempt a quantitative substituent effect correlation.
Molecular orbital calculations
Excitation energies to S1 were calculated by TDDFT/6-
31G1(d) (20) using vertical excitations from the optimized
ground-state geometries calculated previously for both the
Φ = 0° and 90° conformer, again for the substituents shown
in Table 2. In all cases, as expected, the calculated oscillator
strength was lower for the 90° than the 0° conformer. More-
over, also in agreement with the UV absorption spectra, the
excitation energy was higher for the Φ = 90° geometry than
for the 0° geometry. Combined with the ground-state ener-
gies, the relative energies for the excited singlet state
(∆E(S1)) in Table 1 can be calculated indicating that, for all
substitutents, S1 for the 0° conformer is more stable than S1
for the 90° conformer. This observation supports the sugges-
tion that excitation of compounds 1 from S0 at Φ = 90° gives
S1 at 90°, which then relaxes by rapid rotation to give the
more stable conformer S1 at 0°. Fluorescence emission and
reaction should then occur from the 0° conformer.
Rate constants of reaction (kr) from the excited singlet
state of the adamantyl ethers 1
The quantum yield method, as described by eq. [1], for
obtaining rate constants for excited-state bond cleavage reac-
tions has a major defect. In all cases where experiments have
been designed to detect it, internal return of radical pair in-
termediates (kir in Scheme 1) has been observed (1). There-
fore, the efficiency of product formation that a quantum
yield measures does not give a reliable measure of kr . In ef-
fect, kir is a form of internal conversion, although not occur-
ring directly from S1. A knowledge of the fraction of this
internal return [kir /(kp + kir)], which is undoubtably depend-
ent on the substituent X, could be used to obtain correct val-
ues of kr, but this fraction is a difficult number to obtain
experimentally without a suitable probe. For instance, in the
cases examined for the allyl ethers (4a–4d) in both methanol
and cyclohexane, the importance of kir was demonstrated by
the fact that the quantum yield method (eq. [1]) gave signifi-
cantly lower values of kr than the unreactive model method
(eqs. [4] and [5]) (3), described in the following. With no
suitable probe for the adamantyl ethers 1, we decided not to
measure quantum yields of reaction.
The temperature dependence of the fluorescence method
The effect of temperature on photochemical reactions has
received far less attention than it deserves. However, recent
studies from the laboratories of Lewis (activation barriers to
E to Z isomerization in phenyl substituted alkenes) (25) and
Zachariasse (thermally activated internal conversion in amino
substitued aromatics) (26) have shown that the measurement
of fluorescence quantum yields and lifetimes and inter-
system crossing quantum yields over a wide temperature
range provides a valuable tool to obtain rate constants for
excited singlet state processes. Again, because the properties
measured are exclusively those of S1, the rate constants kr
obtained are independent of processes like kir or reaction
from T1. We have recently applied this approach to the
phototransposition reactions of substituted benzenes (27).
The simplest assumption used is presented in eq. [6],
which is the same as eq. [4] except that the reaction process
kr is considered to follow the Arrhenius expression. For
[5]
ktM = kf + kic + kisc
The unreactive model method
For the allyl ethers 4, we recently described an alternate
method of measuring kr for reactions of S1 that relies on
comparing a photochemically reactive compound with an
unreactive one that has identical excited-state properties (3).
We chose to compare compounds 4 with the anisoles 2,
which are, in comparison, photochemically inert. Either
© 2005 NRC Canada