Solvent Effect on Sensitized Photooxygenation
and presence of dihydropyrazine derivatives,23 afforded
the same value as that obtained by time-resolved experi-
ments.
In eq 3, the bulk/steric term is described by the
Hildebrand parameter, FH. The parameter π1 corresponds
to the index of polarizability, accounts for the ease of
moving or polarizing the electron cloud, and is obtained
from the ratio between polarizability volume and molec-
ular volume. The hydrogen bond acceptor basicity (HBA)
involves covalent, ꢀb, and electrostatic, q-, terms. Simi-
larly, hydrogen-bond donor acidity (HBD) includes cova-
lent, ꢀa, and electrostatic, q+, terms.29,31
Data in Table 1 show that the total quenching rate
constant for reaction of DMD with singlet oxygen in-
creases by more than 2 orders of magnitude when the
solvent is changed from hexafluoro-2-propanol to N,N-
dimethylacetamide. Similarly, MPD rate constants in-
crease by about a factor of 30 on changing from trifluo-
roethanol to tributyl phosphate. Also, we found for all
solvents that the total rate constants for MPD are near
to 1 order of magnitude larger than those for DMD. As
expected, these results show that dihydropyrazines be-
have similarly to related olefins and reactivities toward
singlet oxygen depend on both dihydropyrazine structure
and solvent properties. However, solvent effects are
larger than those for diolefins5 and cannot be associated
only with changes in macroscopic properties such as
dielectric constant, suggesting the existence of specific
solute-solvent interactions. We have previously demon-
strated that in these cases it is useful to use linear
solvent free-energy relationships to correlate experimen-
tal rate constants with solvent properties.15-19
The coefficients of the LSER and TLSER equations (eqs
2 and 3) obtained by multilinear correlation analysis for
dependence of kT on solvent parameters are given in
Table 2 and are based on purely statistical criteria.
Current criteria used for derivation of the correlation
equations include the following: (a) Descriptor coef-
ficients accepted in the correlation equation are those
that have a significance level g0.95 [large t-statistic,
P(two-tail) < 0.05]. (b) The VIF statigraph,32 a measure
of parameter orthogonality that indicates independence
of the parameters, is defined by VIF ) 1/(1 - R2), where
R is the correlation coefficient for that particular param-
eter in terms of the other parameters. For a given
parameter, the closer VIF is to unity, the less cross-
correlation there is with the other parameters. When VIF
is too large, the least significant variable is eliminated.
We accept a low variable collinearity (VIF < 5). (c) The
correlation coefficient, R, is equal to or higher than 0.90
(variance, R2 > 0.80). (d) The sample size is as large as
possible; N must be at least three times the number of
independent parameters included in the correlation
equation. In summary, the sample size, N, the product
correlation coefficient, R, the standard deviation, SD, and
the Fisher index of equation reliability, F, indicate the
quality of the overall correlation equation. The reliability
of each term is indicated by the t-statistic (t-stat) and
the variance inflation factor (VIF). Good quality is
indicated by large N, F, and t-stat values; small SD
values; and R and VIF close to 1.
Results in Table 2 show that not all descriptors are
important. Descriptor coefficients accepted in the cor-
relation equation were those that have a significance
level g0.95. For this reason FH and π* parameters were
not included in the LSER correlation for DMD and MPD,
respectively. According to the LSER coefficients in Table
2, kT values for DMD increase in solvents with the largest
capacities to stabilize charges and dipoles and decrease
in strong HBD solvents. Furthermore, for MPD rate
constants increase in HBA solvents with high cohesive
energy and decrease in strong HBD solvents. Similarly,
in TLSER equations, only q- and q+ were included for
DMD and ꢀb, q+, and FH for MPD.
Therefore, to obtain insights on solvent effects on
interactions of singlet oxygen with dihydropyrazines, we
analyze the quenching rate constant dependence on
microscopic solvent parameters by using the semiempiri-
cal solvatochromic equation (LSER) of Kamlet et al. (eq
2).12,24
2
log k ) log ko + sπ* + dδ + aR + bâ + hFH (2)
where π* accounts for polarizabilities and dipolarities of
solvents;25-27 δ is a correction term for polarizability; R
is related to the hydrogen-bond donor solvent ability; â
indicates solvent capability as a hydrogen-bond acceptor;
and FH is the Hildebrand parameter, which corresponds
to the square root of solvent cohesive density and is a
measure of disruption of solvent-solvent interactions in
creating a cavity.12,28 Also, we analyzed the dependence
of kT on solvent by using a theoretical set of correlation
parameters determined solely from computational meth-
ods.14,29,30 The theoretical linear solvation relationship
(TLSER) descriptors have been developed to give optimal
correlation with LSER descriptors.14,29 The generalized
TLSER equation proposed by Famini et al.14,29 (eq 3) can
be used to analyze dependence of reaction rates on
solvent properties.
2
log k ) log ko + sπ1 + bꢀb + cq- + dꢀa + eq+ + hFH
Results of TLSER analyses accord with those obtained
with LSER equations, showing that for DMD kT increases
in HBA solvents and decreases in HBD solvents, and for
MPD the rate constant increases in HBA solvents with
high cohesive energy and decreases in HBD solvents.
Ch em ica l Rea ction of O2(1∆g) w ith Dih yd r op yr a -
zin es. Irradiation of aerated solutions of DMD or MPD
in the presence of TPP or RB, at the wavelength for which
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