36
R. Papadakis / Chemical Physics 430 (2014) 29–39
value of the dipole moment difference will be
(
le
ꢀ
lg)w =
ꢀ11.4D ꢁ (le ꢀ g)s = ꢀ11.8D (where the index w denotes the bal-
l
anced value). This is very important since two different methods
for determining differences between excited and ground state di-
pole moment result in very close results. Furthermore taking into
account a general linear correlation in the whole glucose concen-
tration range (0 < Cglu 6 120 g/L) as shown in Fig. S11b gives
according to Eq. (3): (le
to the balanced dipole moment difference (le
as mentioned results prove that the use of the Van der Waals ra-
dius of 4, (5.01 Å) as the cavity radius ( ) in Eq. (6) is not mistaken.
ꢀ
l
)
g glu = ꢀ11.5D. This value is very close
ꢀ
l )
g w = ꢀ11.4D. The
a
This observation is supported by the fact that even small errors of
the cavity radius introduce higher errors to the determined
dipole moments through the term a
3. Unfortunately equation (6),
probably because of poor correlation of the MLCT energies of
4, measured in solvents of Table 1, resulted in a value of
Fig. 9. MLCT of 4 in different media, with respect to ionicity of 4. Calculated
differences between MLCT excited and ground state dipole moments through Eq.
(
le
ꢀ g)a ꢁ ꢀ22D. This value is smaller from the calculated dipole
l
(3): (a) (le
ꢀ lg)a = ꢀ32D, (b) (le ꢀ lg)b = ꢀ16.4D, and (c) (le ꢀ lg)c = ꢀ3D.
moment difference through Eq. (3) (ꢀ32D), though still higher as
compared to the one determined in glucose solutions. (Values
ꢀ22D and ꢀ32D were determined using Suppan’s and Saito’s
method respectively; see Supporting Information: Tables S1 and
S2 and Figs. S9–S11a). This discrepancy is anticipated since corre-
MLCT excited state and the ground state. Interestingly the values
obtained for 4 by means of the described methodology, in case of
the glucose solutions, are close to the ones obtained through an-
other method, the method of Suppan and Tsiamis [39]. This theory
allows the determination of ground and excited dipole moments of
solvatochromic compounds by using only absorption spectral data
[39,40]. That is very important for non-emitting compounds (for
instance compound 4). Eq. (6) is an extension of earlier Suppan’s
equation [41] containing only the first term which is the perma-
nent dipole interaction term. The second term represents the sta-
bilization difference of the ground state and excited state dipoles
lation coefficients (R) for correlations EMLCT vs [
EMLCT vs
u
(e
) ꢀ
u
(n2)] and
u
(n2), regarding EMLCT measured in solvents, were rather
low, whereas as mentioned EMLCT correlate excellently with
ET(30), rendering Saito’s method much more reliable in that case.
The as determined values of (le
methods are listed in Table S2 of Supporting Information.
ꢀ
lg) for 4, by means of different
4.5. Solvatochromic sensitivity of 4
(
lg and le respectively) [39]. Since the MLCT energy of 4 in glucose
solutions correlated very well with both polarity functions
and
(n2), Eq. (6) can give accurate results (Supporting Informa-
The fact that the ionicity of 4 differs depending on the medium,
can explain the observed alteration of the medium responsive
character of 4, as depicted in Fig. 9. In order to answer why such
alteration of the ionicity occurs, the analysis of contribution of dif-
ferent solvent polarity parameters on solvatochromism in neat sol-
vents, binary solvent mixtures, as well as in glucose solutions, is
needed. For that matter Linear Solvation Energy Relationships
(LSER’s) can be employed. [9,23,45–48] Herein the multiparamet-
ric equation of Koppel and Palm was used for different reasons.
First of all, in order to include the solvatochromic shifts measured
in glucose solutions in an LSER, one is obliged to know or to deter-
mine the values of the corresponding LSER parameters for each of
the examined glucose solutions. Unfortunately as also mentioned
in introduction, apart from Reichardt’s polarity scale of aqueous
glucose solutions (determined by Spange et al. [13]) refractive indi-
ces and static dielectric constants, no other solvent polarity param-
eters have been determined up to now. This decreases the number
of applicable LSER’s. Koppel–Palm equation in its extended form,
correlates a physicochemical quantity X with four parameters
[23,49] (see Eq. (8)). Two parameters describing non-specific sol-
u(e)
u
tion, Figs. S9 and S10). Ground and excited state dipoles are consid-
ered as collinear in case of 4. For the determination of both terms
of the biparametric linear equation (6), the value 5.01 Å was used
for the cavity radius (a). The latter is the Van der Waals radius of
4, determined as described in calculations part. This approach
has been applied in the past for the determination of ground and
excited state dipole moments when no other data concerning the
cavity term are available [42–43] (e.g. the density of the solute
[44]). Finally the scaling factor (4peo
ꢀ1
)
where eo is vacuum per-
mittivity, was used for SI units [41].
"
#
!
lg ꢂðl!g
ꢀ
l!eÞ
ð
le2
ꢀ
lg2
Þ
1
ECT
¼
ð
u
ðeÞ ꢀ
u
ðn2ÞÞ þ
u
ðn2Þ
4
peo
a3
a3
þ const:
where
2ðx ꢀ 1Þ
ð6Þ
ð7Þ
ute–solvent interactions, (one expressing polarization: Y(
e) where
u
ðxÞ ¼
2x þ 1
The dipole moment difference (le
obtained through Eq. (6) regarding the concentration range
0 < Cglu 6 320 g/L was (le g)s = ꢀ11.8 D (the index s denotes
the value obtained through Eq. (6)). It is obvious that (lg e)c =
3D < (lg e)s = 11.8D < (lg e)b = 16.4D. As mentioned MLCT
energies of 4 measured in glucose solutions correlate linearly to
polarity functions
) ꢀ
(n2) and (n2) in the whole concentra-
tion range 0 < Cglu 6 320 g/L. Thus it is not possible to obtain more
than one different values (le g) in the aforementioned concen-
e
is the static dielectric constant of a solvent, the other expressing
ꢀ
l
g) of 4 in glucose solutions
polarizability: P(n2) where n is the refractive index of a solvent)
then two more describing specific solute–solvent effects. The latter
two include both solvent Lewis acidity, expressed by parameter E
(values of E listed in Tables 1 and 2) and Lewis basicity expressed
by parameter B (to the best of the author’s knowledge no data for
this parameter are available for glucose solutions). Coefficients a1
to a4 represent the susceptibilities of physicochemical quantity X
to the four parameters of equation 8 and are determined through
linear regression. The most important solvent parameters to de-
scribe solvatochromism of pentacyanoferrate(II) complexes which
do not bear substituents giving rise to significant overall Lewis
acidity, are parameters describing dipolarity/polarizability of sol-
vents as well as solvents’ Lewis acidity. The latter is a general
ꢀ
l
ꢀ
l
ꢀ
l
ꢀ
l
u
(e
u
u
ꢀ
l
tration range. Nevertheless the value 11.8D is very well balanced
between the values obtained through application of Saito’s theory.
Since (le
ꢀ
l
g)c = ꢀ3D is valid in the range 0 < Cglu 6 120 g/L and
(le
ꢀ
l
g)b = ꢀ16.4D in the range 120 6 Cglu 6 320 g/L, the balanced