Chemistry and photochemistry of anthocyanins and related compounds: A thermodynamic and kinetic approach

Article abstract of DOI:10.3390/molecules21111502

Anthocyanins are identified by the respective flavylium cation, which is only one species of a multistate of different molecules reversibly interconverted by external inputs such as pH, light and temperature. The flavylium cation (acidic form) is involved

Full text of DOI:10.3390/molecules21111502

molecules
Article
Chemistry and Photochemistry of Anthocyanins and
Related Compounds: A Thermodynamic and
Kinetic Approach
Nuno Basílio * and Fernando Pina *
LAQV, REQUIMTE, Departamento de Química, Faculdade de Ciências e Tecnologia,
Universidade Nova de Lisboa, 2829-516 Caparica, Portugal
*
Correspondence: nuno.basilio@fct.unl.pt (N.B.); fp@fct.unl.pt (F.P.); Tel.: +351-212-948-355 (F.P.)
Academic Editors: Arturo San Feliciano and Celestino Santos-Buelga
Received: 28 September 2016; Accepted: 3 November 2016; Published: 10 November 2016
Abstract: Anthocyanins are identified by the respective flavylium cation, which is only one species of
a multistate of different molecules reversibly interconverted by external inputs such as pH, light and
temperature. The flavylium cation (acidic form) is involved in an apparent acid-base reaction, where
the basic species is the sum of quinoidal base, hemiketal and cis- and trans-chalcones, their relative
fraction depending on the substitution pattern of the flavylium cation. The full comprehension of
this complex system requires a thermodynamic and kinetic approach. The first consists in drawing
an energy level diagram where the relative positions of the different species are represented as a
function of pH. On the other hand, the kinetic approach allows measuring the rates of the reactions
that interconnect reversibly the multistate species. The kinetics is greatly dependent on the existence
or not of a high cis-trans isomerization barrier. In this work, the procedure to obtain the energy level
diagram and the rates of inter-conversion in the multistate in both cases (low or high isomerization
barrier) are described. Practical examples of this approach are presented to illustrate the theory, and
recently reported applications based on host–guest complexes are reviewed.
Keywords: anthocyanins; flavylium compounds; energy level diagram; multistate chemistry;
cyclodextrins; cucurbiturils
1
. Introduction
1
.1. The Flavylium-Based Multistate—A Brief History
The comprehension of the reversible multistate of chemical reactions involving 2-phenyl
benzopyrylium (flavylium cation) is a result of more than one century of research, since the first
synthesis of 4-methyl-7-hydroxyflavylium prepared by Büllow and Wagner [ ]. The most significant
1
flavylium-based multistates are anthocyanins. These natural compounds are generally extracted or
synthesized in acidic medium in the form of the red flavylium cation. Immediately after dissolution
of an anthocyanin (in the flavylium cation form) in water, a blue colour appears, but disappears
relatively fast to give a colourless solution. After the disappearance of the blue colour (or before),
the addition of some drops of concentrated acid restores the original red colour of the flavylium cation.
In order to explain this peculiar behaviour, many decades of research and the work of a large number
of scientists [
2,3] including two Nobel prizes, Richard Willstätter 1915 [4], and Richard Robinson, 1947,
were necessary [5].
Scheme 1 summarizes the four reversible chemical reactions that occur in anthocyanins and
related compounds, in a pH range from 1 to moderately acidic, exemplified for malvidin-3-glucoside
(oenin) [6].
Molecules 2016, 21, 1502; doi:10.3390/molecules21111502
www.mdpi.com/journal/molecules

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A
B
B
A
A
C
B
Scheme 1. Multistate of oenin in acid to moderately acid solutions.
Five different chemical species reversibly interconnected by four different chemical reactions
can be observed defining a multistate. Inspection of Scheme 1 shows that, according to Chatelier’s
principle, at lower pH values the multi-equilibrium is shifted towards the flavylium cation. This
generally occurs in very acidic solutions, for example at pH
≤
1 for anthocyanins. The multistate is
conveniently studied by means of direct pH jumps defined by the addition of base to equilibrated
solutions of flavylium cation. Reverse pH jumps should also be used and, in this case, the solutions are
previously equilibrated at higher pH values and acid is added. A direct pH jump triggers a succession
+
of reactions as reported in Scheme 1. The proton transfer that converts flavylium cation (AH ) in
quinoidal base (
A) occurs on a timescale of micro-seconds. Proton transfer can be followed using
temperature jumps [
flow equipment. The species AH and
subsequent kinetic processes (the fraction AH and
7
] or, in some favourable cases, flash photolysis, [
8
] but is too fast for the stopped
+
A
are in fast equilibrium and behave as a single one in the
+
a
A is dependent on the respective pK and pH
of the solution). In a much slower reaction, the flavylium cation is attacked by water in position 2
leading to the hemiketal ( ) (some years ago denominated pseudo-base). The rate of this reaction
has a characteristic pH dependence, because it decreases by increasing pH. Brouillard and Dubois [
B
2]
explained this behaviour during the seventies of the last century: quinoidal base is a kinetic product
motivated by the fact that this species does not hydrate in moderately acidic medium. In other words,
formation of
B (and the subsequent species Cc and Ct) takes place exclusively from the water attack
+
to AH . Consequently, higher pH values mean less flavylium cation available to react resulting in
a decrease of the respective disappearance rate. On the other hand, the species
cis-chalcone (Cc) by a ring opening that occurs in sub-seconds and, finally, Cc gives trans-chalcone
Ct) by isomerization, a process that could occur in a few seconds or hours and even days. It should
be noted that the cis-trans isomerism is referred to by the relative positions of the A and B rings
see Scheme 1). This terminology is more convenient than the E-Z isomerism (frequently used in
B is converted in
(
(
anthocyanins) for comparing 3-substituted with 3-H compounds because in the first case the cis isomer
corresponds E and in the last case to Z. In summary, in anthocyanins, three kinetic processes are well
separated in time, the first step is proton transfer, the second step is a succession of two reactions, then
hydration followed by tautomerization, being the former the rate limiting step. Noteworthy, at low
pHs, the hydration can be faster, but this “change of regime” is only observed in reverse pH jumps, or
from flash photolysis at sufficiently acidic solutions. Finally, the third step is the cis-trans isomerization
that defines the kinetic approach to study the system as will be described below.
1
.2. The Flavylium-Based Multistate
A very useful way to rationalize the chemistry of anthocyanins and related compounds is the
construction of an energy level diagram as the one shown in Scheme 2 for malvidin-3-glucoside (oenin).
The energy level diagram is easy to construct provided that the equilibrium constants of the four
chemical reactions have been previously calculated, see Appendix A [
9
]. According to Scheme 2, AH+
+
is the stable species at lower pH values. After a direct pH jump, for example to pH = 3.8, half of AH
and are formed and remain in this fraction during the successive kinetic steps. However,
pH value the most stable species and the system evolves to give in fast equilibrium with the minor
species Cc. Due to the fact that anthocyanins exhibit a high cis-trans isomerization barrier, at this point
A
B is at this
B

Molecules 2016, 21, 1502
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of the kinetics, a pseudo-equilibrium can be considered, a transient sate involving all species except
Ct. The system reaches the equilibrium by formation of a small fraction of Ct, a process that takes a
few hours.
Scheme 2. Energy-level diagram for malvidin-3-glucoside (Oenin), obtained according to the procedure
shown in Appendix A [9]. The rate of the tautomerization reaction is faster than the values reported
due to the acid and basic catalysis [3] (not included in the Scheme).
One interesting characteristic of the flavylium based multistates is the great dependence of the
relative energy levels of the different species according to the nature and position of the substituents
0
in the flavylium core. For example, in 4 ,7-dihydroxyflavylium, the species Ct has a lower energy
and
B and Cc are not detected at the equilibrium. They are transient species necessary to convert
+
AH into Ct, during the kinetic steps [
9
]. Conversely, in the case of 4-methyl-7-hydroxyflavylium, the
+
equilibrium in water is established exclusively between AH and A.
The reactions reported in Scheme 1 can be written in Equations (1)–(4):
Proton transfer
+
+
AH + H O ꢀ A + H O Ka
(1)
(2)
(3)
(4)
2
3
Hydration
+
+
AH + 2H O ꢀ B + H O Kh
2
3
Tautomerization
Isomerization
B ꢀ Cc Kt
Cc ꢀ Ct Kt
In spite of the complexity of the multi-equilibria, the flavylium multistate system can be simplified
+
considering a single acid-base reaction involving the species AH and a conjugate base CB defined as
the sum of the other species A, B, Cc and Ct, Equation (5),
+
+
AH + H O ꢀ CB + H O K0a
(5)
2
3
with [CB] = [A] + [B] + [Cc] + [Ct].
The equilibrium constant of Equation (5) relates with the equilibrium constants in Scheme 1
according to Equation (6).
K0a = Ka + K + K Kt + K KtK
(6)
h
h
h
i
The pseudo-equilibrium is similarly given by Equations (7) and (8).
+
ˆ
+
AH + H O ꢀ CB + H O Kˆa
(7)
2
3
ˆ
with [CB ] = [A] + [B] + [Cc].

Molecules 2016, 21, 1502
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The apparent equilibrium constant of Equation (7) relates with the equilibrium constants in
Scheme 1 according to Equation (8).
Kˆa = Ka + K + K Kt
(8)
h
h
The kinetic processes following a direct pH jump (for the multistate systems exhibiting high
cis-trans isomerization barrier as anthocyanins) are summarized in Equations (9)–(11) [10].
+
Equation (9) regards the first kinetic step that converts AH into
A. This equation and the
subsequent have been deduced taking into account the reversibility. In other words, the observed rate
constant in such a case is the sum of the direct and reverse rate constants.
+
k = ka + k−a[H ]
(9)
1
Considering the second process, the rate determining step is the hydration and thus the direct
+
rate constant should be multiplied by the mole fraction of AH , XAH+, (from the acid base equilibrium
with
A) and the reverse rate constant by the mole fraction of
B
available, X , (from the tautomerization
B
equilibrium with Cc)
+
[
+
H ]
1
+
+
k2 = XAH
+
k + X k [H ] =
kh +
k
[H ]
(10)
h
B −h
−h
[
H ] + Ka
1 + Kt
When there is a high cis-trans isomerization barrier, the system reaches a pseudo equilibrium
+
where all the species AH
, A, B and Cc can be considered in (pseudo)equilibrium, because their
interconversion is much faster than the isomerization, that in anthocyanins takes a few hours. In the
kinetics of this last step, the direct rate constant k should be multiplied by the mole fraction of Cc, XCc
,
i
involved in the pseudo-equilibrium available to isomerize. See Appendix B for the deduction of the
mole fractions at the equilibrium and pseudo-equilibrium [9].
K Kt
h
k = X k + k
=
ki + k
(11)
2
Cc
i
−i
−i
+
[
H ] + Ka + K + K Kt
h h
In many other flavylium networks, the cis-trans isomerization barrier is very small, the
pseudo-equilibrium is not formed and steps 2 and 3 described above are transformed into one step
+
(
Scheme 3). Assuming that the equilibrium between AH and
A
as well
B
and Cc is reached during
the kinetic process, the following Equation (12) can be deduced, again from simple reasoning without
use of more complex mathematical deductions [10].
+
[
H ]
+
K Ktk + k [H ]
+
h
i
−i
[
H ]+Ka
k4 =
(12)
+
Ktki
[
H ] + k
h
−
Equilibrium
Equilibrium
Ka
Kt
kh
k
i
AH+
Cc
A
B
Ct
H+
k H
+
k-i
-h
Scheme 3. Flavylium network for compounds with small isomerization barrier:
A/ B/Cc are
AH+ and
in fast equilibrium.

Molecules 2016, 21, 1502
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2
. Results and Discussion
2
.1. Low cis-trans Isomerization Barrier
The equilibrium between AH+ and
A
, Equation (1), is illustrated for the compound shown in
Scheme 4 and Figure 1a. The absorption spectra were taken immediately after the pH jump before
+
significant disappearance of AH /A.
OH
O
O
O
HO
O+
Scheme 4. Compound 1.
2
.5
1
2
pK =4.2
2
1.5
1
pK' =2.85
a
a
0
.8
1
1.5
A
0.4
A
1
0.5
0
0
.5
0
0
0
2
4
6
pH
0.5
0
2
4
6
pH
0
2
50
350
450
550
300
400
500
600
700
Wavelength (nm)
Wavelength (nm)
(
a)
(b)
Figure 1.
(a) Absorption spectra of compound 1 taken immediately (circa 1 min) after a direct pH jump;
(
b) the same at the equilibrium.
The spectral variations are typical of anthocyanins and related compounds bearing hydroxyl
substituents, showing isosbestic points and the absorption of the quinoidal base red shifted in
comparison with flavylium cation. The measured pK
a
= 4.2 is the same of the analogous compound
0
7-hydroxy-4 -methoxyflavylium [11]. In Figure 1b, the absorption spectra of the same solutions at the
equilibrium are presented, Equation (5). In this case, the flavylium cation is involved in a single acid
base equilibrium with CB (basically Ct and a minor contribution from Cc and being negligible).
A
,
B
The characteristic absorption spectrum of Ct appears blue shifted and the isosbestic points confirm
that the system at the equilibrium is equivalent to a single acid base reaction with acid-base constant
0
0
equal to pK a = 2.85, which compares with 3.0 for 7-hydroxy-4 -methoxyflavylium [11].
0
Compound
1
, similarly to 7-hydroxy-4 -methoxyflavylium, does not have a high cis-trans
isomerization barrier and by consequence from the situation reported in Figure 1a to the one in
Figure 1b, only one kinetic process is observed, as shown in Figure 2a. Representation of the rate
constants as in Figure 2a for different pH values can be fitted with Equation (12), see Figure 2b and
Table 1.

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1
.6
.2
.8
.4
0
1
.2
0
.002
.001
0
1
0
0
20
40
60
80
100
A
Time (min)
0
0
0
1
2
3
4
5
6
7
8
250
350
450
550
Wavelength (nm)
pH
(
a)
(b)
−
3
−1
Figure 2.
(
a
) Spectral variations after a direct pH jump 1–5.5; kobs = 1
×
10
s
; (
b
) Representation of
the pH dependent rate constants of the kinetic process to reach the equilibrium after a direct pH jump.
Fitting was achieved by means of Equation (12) for the parameters reported in Table 1.
Table 1. Parameters obtained from Figure 1 to Figure 2.
0
−1
−1
−1
)
pK a
.85
pKa
K Ktk (M·s
)
Ktk /k (M)
k
(s
)
kh (s
0.018
h
i
i
−h
−5
−i
3.6 × 10−
7
2 × 10
2.7 × 10
−4
2
4.2
According to Table 1, and Figures 1 and 2, the following relationship between the equilibrium
−
2.85
−4.2
.
constants is known Ka + K + K Kt + K KtK = 10
, Ka = 10
The relations of the constants are not enough to calculate all the constants and further experiments
should be done.
h
h
h
i
2
.2. A Little Help from Photochemistry
When the trans-chalcone is the major species of the conjugated base, CB, there is the possibility
of using light to create a perturbation in the system and follow the associated kinetic processes.
The procedure is shown in Scheme 5. Excitation of the trans-chalcone gives rise to the cis isomer. This
last species could give backward the trans-chalcone or forward flavylium cation/quinoidal base via
tautomerization and dehydration (step 1). The light irradiation is thus accompanied by the appearance
of the coloured species flavylium cation and/or quinoidal base depending on pH and pK of the
a
system. In a second process (step 2), the system equilibrates and this kinetic step is equivalent to a
direct pH jump to the pH of the irradiation.
Ct*
1
b
hν
Cc kt
kh
+
B
AH (pH=pK h)
ki
k-t
+
k [H ]
k-i
-h
1a
1c
AH+ (pH=pKa)
A
Ct
2
AH+ (pH=1)
Scheme 5. Representation of the photochemical process in flavylium multistates.

Molecules 2016, 21, 1502
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In previous work, the quantum yields as a function of pH were used to obtain the relations
between rate and equilibrium constants in order to find an independent set of equations to resolve the
system [12]. In this work, we report for the first time an alternative method, which is easier and more
precise than the quantum yields.
2
.3. Flash Photolysis in Flavylium Systems
Some years ago, we reported a simple and inexpensive flash photolysis apparatus built with
a flash camera and a spectrophotometer in time drive [13]. Currently, a system of optical fibbers is
used. The time scale of the experiments is a few seconds, the most convenient timeframe to follow
the kinetics of step 1, in Scheme 5. Figure 3a shows the absorption traces monitored at 372 nm and
at 475 nm after the flash pulse. These wavelengths correspond to the absorption maximum of Ct and
+
AH /A, respectively. The observed rate constant (equal at both wavelengths) is the sum of the forward
and backward rates, accounting to two parallel reactions that are responsible for the disappearance of
+
Cc to give Ct (backward reaction) and AH /A (forward reaction).
1.2
0
.15
0
0.8
(Y-X)/Y
0
0.4
Y
X
-
-
0.06
0.12
0
-
1
0
1
2
3
4
5
2
3
4
5
6
7
Time (s)
pH
(
a)
(b)
Figure 3.
(
a
) Flash photolysis traces after a light flash at pH = 4.04.; (
b
) Ratio (Y
−
X)/Y corresponding
to the efficiency of the back reaction as a function of pH. A global fitting was carried out using the data
from Figures 1–3.
The absorbance variations of Figure 3a observed immediately after the flash pulse clearly show
a bleaching of the Ct absorption at 372 nm, because the molar absorption coefficient of Ct is higher
+
than Cc at this wavelength. Immediately after the flash, no AH /A is formed. The amplitude Y is
proportional to the amount of Ct that disappeared to give Cc. However, at this pH, a fraction of
Ct (Y
−
X) is recovered. This result indicates a low cis-trans isomerization barrier and that in less
than 2 seconds part of Cc goes back to Ct. Simultaneously, the fraction X of Ct lost is the one that is
responsible for the formation of AH /A observed at 457 nm. Representation of the efficiency of the
+
backward process ηCt = (Y − X)/Y is reported in Figure 3b. According to Figure 3b, there is a change
of the kinetic regime around pH 4.5. This behaviour was already observed for the quantum yield
pH dependence. At lower pH values, the hydration that is dependent on the proton concentration
becomes faster than tautomerization (change of regime) [14]. The kinetics after the change of regime
(
lower pH values) can be accounted for by Equation (13). The equilibration between
B
and Cc does
+
not occur because once
B
is formed it immediately disappears to give AH /A (i.e., the tautomerization
is the rate limiting step).
H
+
OH
−
kf lash(low pH) = k + k−t + k [H ] + k [OH ]
(13)
i
−t
−t

Molecules 2016, 21, 1502
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where the terms kH and k
OH
refer to the acid and basic catalysis of the tautomerization, respectively.
−
t
−t
For the present compound, the basic catalysis is not significant at this pH range and k is much
i
H
+
higher than k allowing the simplification of this equation (k + k−t + k [H ]).
−
i
i
−t
The efficiency of Ct recovery is thus given by Equation (14)
ki
η
=
(14)
Ct
H
+
ki + k−t + k [H ]
−t
At higher pH values, the process is controlled by the hydration reaction, and so there is time
to establish the equilibrium between and Cc. By consequence, the disappearance of and Cc is
multiplied by the respective mole fractions X , and X , and the same holds for the flavylium cation
B
B
B
Cc
+
which must be multiplied by XAH+, Equation (15), because AH and A are in fast equilibrium.
+
kf lash(high pH)
=
X k [H ] + X
+
k + X k
B −h
AH
h
Cc
K
i
+
+
(15)
[
H ]
[H ]
t
=
k
+
kh +
ki
+
1
+Kt −h
[H ]+Ka
1+Kt
The efficiency of the Ct recovery is thus given by Equation (16).
Kt
ki
1
+Kt
η
=
(16)
Ct
+
+
[
1
H ]
[H ]
K
t
k
+
kh +
ki
1+Kt
+Kt −h
+
[H ]+Ka
A global fitting of Equations (14) and (16), Figure 3b together with the data from Table 1 allow
calculating all the equilibrium (Table 2) and rate (Table 3) constants of the multistate and drawing the
respective energy level diagram, Scheme 6.
Table 2. Equilibrium constants for compound 1.
0
−1
pK a
pKa
K (M
h
)
Kt
Ki
5.6 × 10−
7
1.9 × 103
2
.85
4.2
1.3
Table 3. Rate constants for compound 1.
kh (s 1)
−
k
(M·s
−1
)
kt (s
0.57
−1
)
k
(s
−1
)
ki (s
−1
)
k
−1
(s )
−h
−t
−i
3.2 × 104
2.7 × 10
−4
0
.018
0.45
0.5
O
OH
O
O
HO
O
+
AH+ (pH=6.2)
AH+ (pH=4.2)
Cc
B
A
3
5.2 kJ mole-1
Ct
3
5.3 kJ mole-1
2
3.9 kJ mole-1
AH+ (pH=1.0)
AH+ (pH=0)
1
7.9 kJ mole-1
Scheme 6. Energy level diagram of compound 1.

Molecules 2016, 21, 1502
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2
.4. High cis-trans Isomerization Barrier
The kinetics of flavylium multistates exhibiting a high cis-trans isomerization barrier, as observed
in anthocyanins, requires a different kinetic treatment and the compounds do not need to be
photochromic to access all kinetic and thermodynamic constants. Because the isomerization step
is very slow, it is possible to obtain a transient state (pseudo-equilibrium) which behaves like the
equilibrium but the apparent acid-base constant Kˆa is equal to K
a
+ K + K K
h
t
. The constants K
a
,
h
0
K
ˆa = K
a
+ K (1 + K
t
) and K
a
t
= K
h
a t t
i
+ K (1 + K + K K ) lead to a system of three equations of four
h
unknowns. Calculation of K
through reverse pH jumps, see below, allows solving the system and
obtaining all the equilibrium constants, allowing the construction of the energy level diagram.
The model compound (Scheme 7) is used to illustrate the procedure for the compounds bearing
2
high cis-trans isomerization barrier. A communication regarding its dual photochromism was recently
reported [15]. In this work, the experimental data necessary to calculate the rate and equilibrium
constants as well as the energy level diagram of this multistate were taken from the appendix of this
work [15]. Figure 4 shows the pH-dependent spectral variation immediately after the pH jumps (a)
and at the equilibrium (b).
Scheme 7. Compound 2.
0
.8
.4
0
pK'a = 2.2
0
.8
.4
0
0
A
0
0
2
4
6
pH
250
300
350
400
450
500
550
600
Wavelength (nm)
(
a)
(b)
Figure 4.
(a) Spectral variations immediately after a direct pH jump for compound 2; (b) the same at
the equilibrium. With permission from RSC from ref. [15].
The flavylium multistates possessing a high cis-trans isomerization barrier have a great advantage,
because the three kinetic processes occur in very different time scales and can be treated separately,
see Equations (10) and (11) of the introduction. The calculation of the rate constants can be achieved
by following the kinetics of the direct and reverse pH jumps. In Figure 5a, the kinetics of the second
process taking place upon a direct pH jump is shown. The quinoidal base in equilibrium with
flavylium cation formed during the mixing time of the base disappears in some seconds to give the
pseudo-equilibrium state. At this pH (4.9), the hydration is the rate determining step, meaning that as
soon as
B is formed, it equilibrates with Cc. In Figure 5b, the rate constants of this step are plotted as a
function of pH and were fitted by Equation (10).

Molecules 2016, 21, 1502
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(
a)
(b)
Figure 5.
(a) Spectral variations observed upon a direct pH jump from 1 to 4.9; (b) pH dependence of
the kinetic process controlled by the hydration reaction followed by stopped flow: (
•
) direct pH jumps;
= 4.6; k = 0.3 s 1; k = 75 M
−
−1 −1 ◦
·
s
. ( ) reverse
Fitting was achieved with Equation (10) for pK
pH jumps, fitting was achieved with Equation (17) which is coincident with Equation (10) within
experimental error due to the low value of K = 0.05, see below. With permission of RSC from ref. [15].
a
h
−h
t
−
1
The fitting of Equation (10) allows obtaining the value of k = 0.3 s (K
a
was already calculated
. At this point, it is clear that the equilibrium
t
is a key constant that is needed to calculate all the equilibrium and rate constants, see below.
h
−
1
−1
s
from Figure 4a) and the ratio k h/(1 + K
t
) = 71.4 M
·
−
constant K
2
.5. Reverse pH Jumps
The reverse pH jumps to study the flavylium systems were introduced by McClelland and
co-workers [ 16 17]. It consists of two steps: (i) the first one to reach the equilibrium (or pseudo
3, ,
equilibrium) after a direct pH jump, (from the flavylium cation); (ii) the second one back to the
flavylium cation by addition of acid and the respective spectral variations collected using a stopped
flow equipment (Figure 6).
-1
Cc
k1=8.5 s
-1
k2=0.25 s
0.2
B
A
0.1
0
0
0.5
1
1.5
2
Time (s)
0
250
350
450
550
Wavelength (nm)
0
Figure 6. Spectral variations upon a reverse pH jump of the compound 4 ,7-dihydroxy-3-
−
6
methoxyflavylium 7.5
from RSC, ref. [15].
×
10 M, from equilibrated solutions at pH = 6 to 1, K = 0.05. With permission
t
At higher proton concentration, the hydration becomes faster than tautomerization and by
consequence the flavylium cation absorption increases according to two kinetic processes. The first
+
one corresponds to the conversion of
B
into AH and the second and slower to the conversion of Cc

Molecules 2016, 21, 1502
11 of 25
into more AH+ via
B. Equations (17) and (18) account for these two steps. Moreover, the ratio of the
amplitudes of the slowest and faster exponentials is equal to Kt = [Cc]/[B].
+
[
+
H ]
+
kreverse1
=
kh + k [H ]
(17)
−h
[
H ] + Ka
kreverse2 = k−t
The accuracy of this method is very dependent on the fraction of
in the present model compound, the fraction of Cc is very small (K
(18)
B
and Cc. In anthocyanins and
= 0.05) and several experiments
t
should be carried out to give some statistical meaning to the constant. In principle, the pH dependence
of the hydration rate constants obtained from direct pH jumps, Equation (10), is different from the
one obtained from reverse pH jumps, Equation (17). In the present compound, they are practically
coincident due to the very small value of Kt, see Figure 6.
At this point, all the equilibrium constants can be calculated. Regarding the rate constants k h is
−
obtained from Equation (10) and/or Equation (17) and k from the equilibrium constant K . The same
h
h
for k−t Equation (18) and kt from Kt.
Going back to the direct pH jumps, the last step to attain the equilibrium is the formation of Ct
through a much slower process, Figure 7.
Figure 7. Spectral variations regarding the slowest step to attain the equilibrium, which is controlled by
the cis-trans isomerization. The increase in the rate for pH > 6 take place from the ionized species and
was not used in this calculation, which restrains to the moderately acidic pH range. With permission
from RSC reference [15].
In the pH region up to pH = 6, the fitting in the inset is achieved with Equation (11) allowing
calculation of the remaining rate constants k and k . A final control should be made, to assure the
i
−i
coherence of the constants, see Tables 4 and 5.
0
Table 4. Equilibrium constants of the compound 4 ,7-dihydroxy-3-methoxyflavylium.
0
pKˆa
−1
pKa
.2
pKa
K /M
Kt
Ki
h
4 × 10−
3
2
2.37
4.6
0.05
10.4
Estimated error 10%.

Molecules 2016, 21, 1502
12 of 25
0
Table 5. Rate constants of the compound 4 ,7-dihydroxy-3-methoxyflavylium.
−
1
−1·s−1
−1
−1
−1
−1
s
k s
k
M
kt s
k
s
ki s
k
h
−h
−t
−i
1.25 × 10−
Estimated error 15%.
2
2.3 × 10−4
2.2 × 10
−5
0
.3
75
0.25
Comparing the energy level diagram of compounds
the most dramatic effect is the much higher energy level of species
in position 3 by a methoxy, a model compound of anthocyanins, stabilizes the species
1
and
2
, respectively Schemes 6 and 8,
and Cc, in the former. Substitution
in agreement
B
B
with the observed behaviour of anthocyanins. In Scheme 8, the energy level diagram and the respective
kinetic patterns are shown for the two types of kinetics. Considering a direct pH jump, in both cases
the proton transfer is the faster reaction, leading to an acid base equilibrium between flavylium cation
and quinoidal base. These two species behave in the subsequent kinetic steps as a single one. In other
words, disappear simultaneously and maintain the fraction AH+
/
A
equal to [H ]/K
+
. When there is a
a
low isomerization barrier, the equilibrium is reached through a single step, which presents a bell shape
variation with pH, Scheme 9. Conversely, in the presence of a high barrier, two kinetic steps could be
identified, the hydration (followed by fast tautomerization) and the slower isomerization, Scheme 10.
Scheme 8. Energy level diagram of compound 2.
Hydra on
1st step (μs)
B
AH+
pH=6
Cc
AH+
Ct
A
pH=4
pH jump
AH+
pH=1
Scheme 9. Energy level diagram of a system with low cis-trans isomerization barrier. During the mixing
+
time, an equilibrium between AH and
A is established and the kinetics towards the equilibrium is
constituted by a single step.

Molecules 2016, 21, 1502
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Scheme 10. Energy level diagram of a system possessing high cis-trans isomerization barrier. During the
+
mixing time, an equilibrium between AH and
A is established. The second step (green) is controlled
by the hydration reaction, and the third and slower (blue) by the isomerization.
2
.6. Applications
2
.6.1. Host–Guest Interaction with a Flavylium Based Multistate
The co-pigmentation is a very important issue in the expression of the colour in plants [18].
In spite of co-pigmentation being a complex process, it is possible to conceive a simple model to
account for the basic physical chemical processes that are associated with it. In this context, host–guest
complexes involving cucurbit[7]uril (CB7) and β-cyclodextrins (β-CD), Scheme 11, are interesting
examples to give some clues regarding co-pigmentation interactions in vivo.
Scheme 11. Structures of cucurbit[7]uril and β-cyclodextrin.
Considering an energy level diagram of a flavylium-based multistate, the mole fraction
distribution of the adducts would change as a function of the magnitude of the association constant
and this is reflected in the relative changes in the diagram. Let us consider two species of the multistate
with equilibrium constant Keq, assuming a 1:1 interaction, and an association constant Kass (Scheme 12).
In the example of Scheme 12a, the species X is slightly more stable than the species Y. If the
association with Y is much more efficient than with X, there is inversion of the stability and the
complex with Y becomes more stable than the one with X. However, if X is much more stable than
Y, Scheme 12b, unless the association with Y is very much stable than with X the inversion does not
take place.
In conclusion, for the multistate species, that in the absence of the host have a high energy level
(
their mole fraction distribution at the equilibrium is very small), difficultly would become significant
upon host–guest interaction.

Molecules 2016, 21, 1502
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Y
0
ΔG (2)=-RTlnK
0
ass(Y)
ΔG (1)=-RTlnK q
e
0
Y
ΔG (1)=-RTlnK q
e
X
Y@Host
X
0
0
ΔG (2)=-RTlnK
ΔG (3)=-RTlnK
ass(Y)
ass(X
0
X@Host
ΔG (4)
0
ΔG (3)=-RTlnK
ass(X
0
Y@Host
ΔG (4)
X@Host
(
a)
(b)
Scheme 12.
(
a
) Energy level diagram regarding the equilibrium Y
ꢀ
X, with X slightly stable than Y.
Inversion of stability occurs upon interaction with the host; (
b) The association constants are the same
as A, but X is much more stable than Y. Inversion of stability does not take place.
2
.6.2. Cucurbit[7]uril
Cucurbit[n]urils are recognized for their ability to complex positively charged molecules with
high affinity and thus it was not surprising to find that flavylium cations form inclusion complexes
with CB7. The stability of the complexes with several flavylium derivatives (Scheme 13 and Table 6)
was investigated by absorption and/or emission spectroscopy while their structural properties were
1
elucidated by H-NMR [19]. All compounds were found to form 1:1 complexes with this host and the
5
−1
6
−1
association constants vary between K = 2.7
×
10 M for compound 6 and K = 8.0
×
10 M for 8.
The results suggest that hydrophobicity, dimension and the nature of the substituent affect the stability
for CB7.
Scheme 13. Flavylium derivatives employed as guest molecules to form inclusion complexes with
cucurbit[7]uril.
Table 6. Association constants (K) for the formation of host–guest complexes between flavylium cations
and cucurbit[7]uril at pH 1. The estimated error is below 10%.
−
K/M
1
Flavylium
6
5
5
5
6
6
6
Compound 3
Compound 4
Compound 5
Compound 6
Compound 7
Compound 8
Compound 9
2.1 × 10
5.1 × 10
5.5 × 10
2.7 × 10
5.1 × 10
8.0 × 10
5.0 × 10
The nature and position of the substituents in the flavylium core have only a moderate influence
on the stability of the complexes. On the other hand, the inclusion mode seems to be strongly dictated

Molecules 2016, 21, 1502
15 of 25
by the substituents. For compounds
3
and
4
, the B ring is specifically included within the host cavity
1
while, in the cases of
5
and
6, the H-NMR experiments suggest an unspecific dynamic behaviour with
the CB7 shuttling quickly between the AC and B rings. This behaviour was more pronounced and,
thus, more evident in the case of because, for , despite evidence of dynamic shuttling, the B ring
seems to be favoured and more populated.
In the case of the amino-substituted compounds (
6
5
7, 8 and 9), these groups were shown to dictate
the structure of inclusion complexes. The partially positive character of the nitrogen atom of these
groups, due to electronic delocalization, allows attractive ion–dipole interaction with the carbonyl
oxygen atoms of the host, resulting in favoured inclusion of the B ring in the case of 8. On the
other hand, for the diethylamino substituent it was found that independently of his position (A or B
ring), evidence for deep inclusion of this group in the CB7 cavity was found in both cases probably
due to its optimal packing coefficient of 55% [20]. Nevertheless, it is worth mentioning that, for 9,
the experimental results suggest the existence of dynamic behaviour with the host shuttling between
the diethylamino and the A and C ring motifs.
The high affinity of CB7 for the flavylium cation can be leveraged to increase the stability of this
coloured species in less acidic conditions. In the case of the trihydroxy derivative
6
, a shift in the
0
pK
a
from 3.1 to 4.3 in the presence of 0.3 mM of CB7 was observed [21]. This results can be easily
rationalized by taking into account the energy diagram of Scheme 12 and arise from the preferential
stabilization of the flavylium cation in comparison with neutral species. Our attempts for colour
stabilization were more impressive in the case of 7-hydroxyflavylium
3 [22]. For this compound,
0
a pK
a
shift from 2.3 to 4.8 was observed for 1 mM of host. This can be ascribed, mainly, to higher
comparatively with (K is almost one order of magnitude higher) and also to
affinity of CB7 for
3
6
higher concentrations of host employed in the last example. More interesting (and unpredicted) was
the fact that amongst the neutral species, CB7 also showed selectivity for the coloured quinoidal base.
Thus, increasing the concentration of host to a solution of
uncoloured trans-chalcone) drives the equilibrium towards the formation of quinoidal base (Figure 8a).
Likely, when CB7 is added to a solution of at pH 4, the equilibrium is driven to the regeneration of
3 equilibrated at pH 6 (mainly composed by
3
the flavylium cation (Figure 8b), demonstrating the ability of this host to selectively bind and stabilize
the coloured species of the multistate.
0
.8
.4
0
0.8
A
A
0
0.4
0
250
350
450
550
250
350
450
550
Wavelength (nm)
Wavelength (nm)
(
a)
(b)
Figure 8. Equilibrated spectra of compound
concentrations of CB7 (up to 2.5 mM) at pH 6 (
reference [22].
3
(7-hydroxyflavylium) in the presence of different
); and pH 4 ( ). With permission from ACS
a
b
The potential of CB7 to stabilize the flavylium species was also investigated by Bohne and
0
0
0
a
= 3.0) is completely stabilized at
Quina, who have showed that 3 ,4 ,7-trimethoxyflavylium (pK
pH = 5.5 in the presence of low concentrations of CB7 (0.12 mM) [23]. The authors found evidences for

Molecules 2016, 21, 1502
16 of 25
the formation of 2:1 host–guest complexes that can be responsible for this remarkable stabilization
0
(
it requires a pK a > 7.0 to keep the mole fraction of flavylium higher than 97% at this pH).
2
.6.3. 6,8 Rearrangement
The 6,8 rearrangement was previously described by Jurd and Andersen, in acidic pH values [24,25].
More recently, it was extended to the other species of the multistate [26].
The 6,8 rearrangement consists of the formation of a flavylium cation having a substituent
in position 8 that migrates to position 6 and vice-versa, see Scheme 14. In order to observe this
isomerization, the flavylium cation should possess a hydroxyl in position 5 and the substituents in
position 6 and 8 should be different. This is the reason why 6,8 rearrangements are not observed in
anthocyanins monoglucoside and deoxyanthocyanins, (like luteolinidin), because both positions 6 and
8
are substituted by H.
Scheme 14. Key step of the 6,8 rearrangement in flavylium multistates.
The 6,8 rearrangement in the case of the compound (or )-bromo apigeninidin at the equilibrium,
6
8
pH = 1.0, leads to circa 50% of each isomer [26]. It was possible to separate both isomers by HPLC and
extend the study to the other species of the multistate. An alternative method to isolate (transiently)
1
isomer
6
is through selective binding with CB7 [27]. As demonstrated by H-NMR experiments
(
Figure 9), in the presence of CB7 at pH = 1.0 the 6,8 rearrangement equilibrium is completely
displaced toward the formation of isomer owing to its selective binding and making it possible to
isolate this species from the initial mixture with a rate constant kobs = 1.3
Addition of 1-aminoadamantane which presents a much higher association constant with CB7
6
−
5
−1
s Figure 9b.
×
10
1
4
−1
) [28] leads to the releasing of pure AH . This one slowly reverts back to
6
+
(
5
K
ass = 2
×
10
M
0% mixture of the equilibrium (d) coincident with (a).
AH+ AH+
Isomer 6 + isomer 8
6
8
AH+
6
Isola on AH+
100%
6
≈
B r
Discrimina on
AH+ AH+
6
8
Isomer 6 + isomer 8
Figure 9. 1H-NMR spectra of the compound 6-bromo apigeninidin and its isomer
equilibrium pH = 1.0; ( ) at the equilibrium after addition of cucurbit[7]uril; ( ) immediately after
addition of 1-aminoadamantane (AD) (d) Equilibration of (c) which is coincident with (a).
8 (a) at the
b
c

Molecules 2016, 21, 1502
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2
.6.4. β-Cyclodextrin Interaction
While CB7 is efficient to selectively recognize the flavylium cation, the
β-cyclodextrin binds
preferentially the trans-chalcone.
0
In Scheme 15, the interaction of β-cyclodextrin with the multistate of 4 ,7-dihydroxyflavylium is
shown [29]. The interaction of
constants with the quinoidal base and trans-chalcone are respectively 100 M and 2.1
In the absence of the host, the flavylium cation is in an acid-base equilibrium with trans-chalcone (87%)
and quinoidal base (13%), hemiketal and cis-chalcone could not be detected at the equilibrium. In the
β-cyclodextrin with flavylium cation is negligible while the association
−
1
3
−1
×
10 M .
presence of β-cyclodextrin 9 mMn these fractions change to 99% and 1%, respectively. The energy
level diagram is once more very useful to visualize the system, Scheme 15.
Ct*
AH+(pH=6.0)
AH+(pH=4.0)
Forward
Cc
B
hν
3
4.2 kJmol-1
Backward
A
+
AH (pH=3.6
+
)
Ct
A-CD
2.8 kJmol-1
AH (pH=2.8)
2
Ct-CD
1
6.0 kJmol-1
2
0.5
7.7 kJmol-1
kJmol-1
1
1
0.3 kJmol-1
AH+
(pH=0)
0
Scheme 15. Energy level diagram of 4 ,7-dihydroxyflavylium in the absence (black color) and presence
of β-cyclodextrin 9 mM (red color). With permission of ACS from reference [29].
Irradiation of the trans-chalcone inside the host leads to the flavylium cation that does not interact
and is removed from the cavity (Scheme 16). The system is reversible and defines a photochromic
system showing great potential to be applied in the fields of photo-responsive host–guest complexes
and self-assembled soft materials.
0
Scheme 16. Emptying the β-cyclodextrin cavity from 4 ,7-dihydroxyflavylium by the action of light.
The formation inclusion complexes between (2-hydroxypropyl)-
dracoflavylium (4 ,7-dihydroxy-5-methoxyflavylium), a natural pigment extracted from a resin
β
-cyclodextrin and
0
(
Dragon’s blood) appearing in the injury parts of the tree Dracaena Draco, was investigated in a
0
subsequent work [30]. Similarly to 4 ,7-dihydroxyflavylium, the multistate of dracoflavylium at low
acidic pH values is composed by quinoidal base and trans-chalcone species. However, in this case,
the former species predominate (63%). The high fraction of colored quinoidal base at the equilibrium
reduces the contrast of the photochromic system and, consequently, his potential applications.
This problem was overcome by taking advantage of the preferential affinity of β-cyclodextrin to
complex the trans-chalcone and as a result its fraction increases from 37% to 87% at the expense of the
quinoidal base. This allowed an improvement in the performance of this photochromic system based
on water-soluble natural products (Figure 10).

Molecules 2016, 21, 1502
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(
a)
(b)
−
5
Figure 10.
(
a
) Spectral variations upon irradiation at 366 nm of dracoflavylium (2
×
10 M) at pH = 4.1
;
−
2
(b
) the same at pH = 3.1 in the presence of the HCD (1.6
×
10 M) illustrating the higher photochromic
contrast observed in the presence of the host molecule. With permission from RSC, reference [30].
Direct evidence for the inclusion of a trans-chalcone (of the multistate system based on
-(2-hydroxyethoxy)-7-hydroxyflavylium) in the β-cyclodextrin cavity was obtained from induced
0
4
circular dichroism spectra, Figure 11 and Scheme 17 [31].
5
5
4
4
3
-
1
3
2
1
0
Kass=1700 M
2
1
0
0
0.002
0.004
[β-cyclodextrin]
2
60
340
420
500
580
Wavelength (nm)
0
Figure 11. Circular dichroism spectra of the compound 4 -(2-hydroxyethoxy)-7-Hydroxyflavylium in
the presence of increasing concentrations of
reference [31].
β-cyclodextrin at pH = 4.8. With permission from Elsevier,
a
b
0
Scheme 17.
(
a
) 4 -(2-hydroxyethoxy)-7-hydroxyflavylium and (
b) possible structure of the respective
trans-chalcone in the presence of β-cyclodextrin.

Molecules 2016, 21, 1502
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In Figure 11, the CD spectra as a function of
β-cyclodextrin is shown. This type of signal is
due to the induced circular dichroism (ICD) that occurs when a chiral transparent compound causes
a structural perturbation or a coupling of the transition moments with achiral UV-Vis absorbing
molecules [32]. The ICD is therefore a very powerful technique to investigate inclusion phenomena in
multistate systems because only complexed species show ICD signals while the uncomplexed ones are
silent. Owing to this advantage, it can be used to demonstrate (or discard) selective complexation and
to measure association constants without perturbation from the other components of the system [33].
3
. Experimental Section
3
.1. General
All reactants and solvents obtained from commercial suppliers were used without further
purification. The solutions were prepared in Millipore water (Millipore, Madrid, Spain). The pH
of the solutions was adjusted by addition of HCl, NaOH or universal buffer of Theorell and
Stenhagen [34] and the pH was measured in a Radiometer Copenhagen PHM240 pH/ion meter
(Copenhagen, Denmark). UV-Vis absorption spectra were recorded in a Varian-Cary 100 Bio or 5000
spectrophotometer (Palo Alto, CA, USA). NMR experiments were run on a Bruker AMX 400 instrument
1
13
(
Billerica, MA, USA) operating at 400 MHz ( H) and 101 MHz ( C).
3
.2. Flash Photolysis
Flash photolysis experiments were performed on a Varian Cary 5000 spectrophotometer with a
Harrick fiber-mate attached to a 4-way cuvette holder (Ocean Optics, Dunedin, FL, USA) to perform
light excitation perpendicular to the analyzing beam (sample compartment protected from daylight by
black cardboard and black tape). As a pulsed white light source, a commercially available Achiever
630AF camera flash, placed in close contact with the sample holder, was used (time resolution of
ca. 0.05 s) [13].
3
.3. Synthesis
0
4
-Hydroxyacetophenone (1.41 g, 10 mmol) was treated with one equivalent of
2-[2-(2-chloroethoxy)ethoxy]ethanol, three equivalents of potassium carbonate and a catalytic
amount of potassium iodide in 10 mL acetonitrile and stirred under reflux overnight. After cooling to
room temperature, the solution was filtered and the filtrate was concentrated by rotary evaporation.
The residue was treated with water and extracted with dichloromethane. The organic layer was dried
over anhydrous sodium sulfate. After evaporation of the solvent, the product was purified by flash
column chromatography on silica gel with gradient elution starting with ethyl acetate:hexane 1:1 and
increasing the polarity to ethyl acetate:hexane 4:1. The product was isolated as uncolored oil in 60%
yield (1.6 g). The identity of the desired 1-(4-[2-(2-(2-hydroxyethoxy)ethoxy)ethoxy]phenyl)ethanone
1
1
by H-NMR spectroscopy. H-NMR (400 MHz, Chloroform-d)
δ
7.9396 (d, J = 8.6 Hz, 2H), 6.9682
(
(
d, J = 8.6 Hz, 2H), 4.2084 (d, J = 4.4 Hz, 2H), 3.8967 (t, J = 4.7 Hz, 2H), 3.7720–3.6876 (m, 6H), 3.6283
t, J = 4.3 Hz, 2H), 2.5602 (s, 3H).
A solution of 1-(4-[2-(2-(2-hydroxyethoxy)ethoxy)ethoxy]phenyl)ethanone (268 mg, 1 mmol) with
one equivalent of 2,4-dihydroxybenzaldehyde (138 mg) in a mixture of glacial acetic acid/concentrated
sulfuric acid (2 mL:0.5 mL) was stirred overnight at room temperature. Ethyl acetate was added to
the red solution and a precipitate was formed. This precipitate was dissolved in methanol acidified
with HCl and precipitated with diethyl ether. The dark orange solid was filtered, washed several times
1
with diethyl ether and dried under vacuum. Yield: 120 mg, 28%. H-NMR (400 MHz, Methanol-d
4
+
DCl)
δ 9.1597 (d, J = 8.7 Hz, 1H), 8.5104 (d, J = 8.7 Hz, 2H), 8.4002 (d, J = 8.7 Hz, 1H), 8.2044 (d,
J = 8.9 Hz, 1H), 7.5690 (br, 1H), 7.4588 (dd, J = 8.9, 2.1 Hz, 1H), 7.3141 (d, J = 8.7 Hz, 2H), 4.3823
(
(
t, J = 4.4 Hz, 2H), 3.9484 (t, J = 4.4 Hz, 2H), 3.7920–3.7343 (m, 2H), 3.7220–3.6604 (m, 6H), 3.5966
t, J = 4.8 Hz, 2H). 13C-NMR (101 MHz, Methanol-d + DCl)
173.43, 170.60, 167.71, 160.56, 155.06,
δ
4

Molecules 2016, 21, 1502
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134.09, 133.48, 122.72, 120.44, 117.59, 113.63, 103.72, 73.66, 71.82, 71.44, 70.45, 69.69, 62.20. Elemental
analysis (%) calcd for C H O . Cl. 1.5H O (Mr = 433.88): C 58.13, H 6.04; Found: C 58.34, H 5.48.
21
23
6
2
4
. Conclusions
The fact that anthocyanins follow the same multistate of chemical reactions of other flavylium
derivatives, independent of whether they of a natural or synthetic origin, is a fortunate situation.
The achievements from the study of these flavylium-based systems contribute to a better understanding
of anthocyanins, which are the most significant compounds of the family. The interaction of
flavylium compounds with cyclodextrins and cucurbiturils contributes to the understanding of the
co-pigmentation phenomenon and may help in defining strategies to stabilize color in anthocyanins.
Moreover, many synthetic flavylium compounds and also some natural ones, having the trans-chalcone
as the major species at moderately acid solutions, are photochromic, allowing the obtainment of a
panoply of color responses under light irradiation.
Acknowledgments:
This work was supported by the Associated Laboratory for Sustainable
Chemistry-Clean Processes and Technologies-LAQV. The latter is financed by national funds from
FCT/MEC (UID/QUI/50006/2013) and co-financed by the ERDF under the PT2020 Partnership Agreement
(
POCI-01-0145-FEDER-007265). The NMR equipment is part of The National NMR Facility, supported by
the Portuguese FCT (RECI/BBB-BQB/0230/2012). N.B. gratefully acknowledges a postdoctoral grant from
FCT/MEC (SFRH/BPD/84805/2012).
Author Contributions: Nuno Basílio and Fernando Pina conceived and designed the experiments; Nuno Basílio
performed the experiments and synthesized compound 1; Nuno Basílio and Fernando Pina analyzed the data;
Fernando Pina wrote the paper.
Conflicts of Interest: The authors declare no conflicts of interest.
Appendix A
Considering an equilibrium between two species A and B, Scheme A1, with equilibrium constant
◦
K: the standard Gibbs free energy
absolute temperature ( K) [9].
∆
G is defined by Equation (A1), where R is the gas constant T the
◦
K
A
B
Scheme A1. Equilibrium between A and B.
o
∆
G = −RTlnK
(A1)
◦
If the equilibrium constant is K = 1,
∆
G = 0, and the energy level of both species in Scheme A1
is equal. If the equilibrium constant is K = 10,
G = +11.4 kJ·mol as illustrated in Scheme A2.
◦
−1 ◦
5.7 kJ mol at 25 C and K = 0.01 leads to
∆
G =
−
·
◦
−1
∆
Scheme A2. Energy level diagram for a hypothetical equilibrium between two species A (reference)
and B.

Molecules 2016, 21, 1502
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◦
Due to the fact that the values of ∆G are relative, it is more convenient for the next developments
to maintain the energy level of B as the reference state, Scheme A3.
Scheme A3. Energy level diagram for a hypothetical equilibrium between two species A and B (reference)
.
When the equilibrium is dependent on pH, as is the case of the proton transfer and hydration
reactions in the flavylium network of chemical reactions, Scheme A4, a similar reasoning can be made
considering that for each pH value there is an apparent equilibrium constant (which are different for
different pH values).
K
A
B + H+
Scheme A4. pH dependent equilibrium between A and B.
K
H ]
A
Kap =
=
(A2)
(A3)
+
+
[
[AH ]
K
o
∆
G = −RTln
[
= −RTlnK − 2.303RTpH
+
H ]
When pH = pKa ∆G = 0 and by consequence
◦
RTlnK = −2.303RTpKa
(A4)
(A5)
and Equation (A3) can be rearranged to Equation (A5)
o
∆
G = −2.303RTpKa − 2.303RTpH
◦
According to Equation (A5), it is possible to calculate ∆G for each pH value. In particular, if pH
◦
−1
is one unit higher than pK
a
,
∆
G increases by 5.7 kJ mol and one unit lower decreased by the same
·
amount, Scheme A5.
Scheme A5. Energy level diagram for a hypothetical acid-base equilibrium between two species A
and B.

Molecules 2016, 21, 1502
22 of 25
At this point, we have all the tools to apply these ideas to the flavylium network of chemical
◦
−1
kJ mol . A scale in pH values
reactions. Taking pH = 0 as reference,
∆
G would be equal to
−
5.7pK
a
·
can be constructed. In the case of the hemiketal (B) formation the procedure is identical. Final Cc
◦
can be positioned from
B
taking into account that
∆
G =
−
t
RTlnK and Ct form Cc considering that
◦
∆
G = −RTlnK , see Scheme A6.
i
Scheme A6. Energy level diagram for a hypothetical flavylium multistate.
Appendix B
The following set of equations account for the different equilibria in which anthocyanins and
related compounds are involved [9].
+
+
AH + H O ꢀ A + H O Ka
(B1)
2
3
+
+
AH + 2H O ꢀ B + H O Kh
(B2)
(B3)
(B4)
2
3
B ꢀ Cc Kt
Cc ꢀ Ct Kt
+
Considering now the equilibrium between AH and the remaining “basic species”,
+
+
AH + H O ꢀ CB + H O K0a
(B5)
(B6)
(B7)
2
3
where [CB] = [A] + [B] + [Cc] + [Ct]
+
{
[A] + [B] + [Cc] + [Ct]} [H ]
K0a =
+
[
AH ]
Using Equations (B1)–(B4)
K0a = Ka + K + K Kt + K KtK
(B8)
h
h
h
i
The total concentration C can be written as in Equation (B9)
0
ꢀ
ꢁ
Ka
Kh
K Kt
K KtK
[H ]
+
+
h
h
i
C = [AH ] + [A] + [B] + [Cc] + [Ct] = [AH ] 1 +
+
+
+
(B9)
0
+
+
+
+
[
H ] [H ] [H ]
ꢀ
ꢁ
K0a
+
C = [AH ] 1 +
(B10)
0
+
[
H ]

Molecules 2016, 21, 1502
23 of 25
+
From Equation (B10), the mole fraction of AH is obtained
AH+]
C0
[H ]
+
[
χ
AH+
=
=
(B11)
+
[H ] + K0a
Using the equilibrium constant of Equation (B1)
+
[
A]
Ka[AH ]
Ka
χ =
=
=
(B12)
(B13)
A
+
+
C0
[H ]C0
[H ] + K0a
by an identical procedure the mole fraction of the other species are also obtained.
Kh
K Kt
[H ] + K0a
K KtK
[H ] + K0a
h
h
i
χ =
B
; χCc
=
;
χ
=
Ct
+
+
+
[
H ] + K0a
The mole fraction distribution of several species as a function of pH can be calculated from
−
4
−3
t
i
10 M; K = 0.1; K = 3
Equations (B11)–(B13) (Figure B1). A simulation for K
a
= 10 M; K = 2
×
h
0
−3
(K a = 2.9 × 10 ).
−
4
Figure B1. Mole fraction distribution for the following set of equilibrium constants K = 10 M;
a
−
3
0
−3
K = 2 × 10 M; Kt = 0.1; K = 3 (K a = 2.9 × 10 ).
h
i
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Sample Availability: Samples of the compounds 1 and 2 are available from the authors.
©
2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC-BY) license (http://creativecommons.org/licenses/by/4.0/).