Hydrolysis of 1,8- and 2,3-naphthalic anhydrides and the mechanism of cyclization of 1,8-naphthalic acid in aqueous solutions

Article abstract of DOI:10.1039/b104148g

Naphthalene-1,8-dicarboxylic acid, 1,8-Acid, cyclizes spontaneously in acidic aqueous solution to naphthalene-1,8-dicarboxylic anhydride, 1,8-An, and here we Present an ab initio study of the reaction pathway. The effect of pH on the hydrolysis of 1,8-An was analysed and compared with the hydrolysis of naphthalene-2,3-dicarboxylic anhydride, 2,3-An, to naphthalene-2,3-dicarboxylic acid, 2,3-Acid. The values of the pK_a's of 1,8-Acid and 2,3-Acid were ca. 3.5 and 3.0, for monoanion formation, pK_a1, and 5.5 and 5.0 for dianion formation, pK_a2, respectively. Fluorimetric titration demonstrated that the diprotonated 2,3-Acid. AH₂, was further protonated to yield AH₃⁺. The pH-rate constant profile for 2,3-An hydrolysis showed a water reaction between pH's 1.0 and 6.0 and a base catalysed hydrolysis above pH 7.0. Under no condition was 2,3-An formed from 2,3-Acid. The pH dependent decomposition kinetics of 1,8-An is complex and, below pH 6.0, the pH-rate constant profile was fitted by assuming that both AH₂ and AH₃⁺ are in equilibrium with 1,8-An. The values of the equilibrium constants for 1,8-An formation from AH₂ and AH₃⁺ were ca. 4 and 100 in dilute and concentrated acid, respectively. Ab initio calculations for a possible reaction pathway connecting the undissociated 1,8-Acid to 1,8-An show a transition state where an intramolecular proton transfer is concerted with oxygen alignment towards the carbonyl centre. The planar intermediate is then dehydrated yielding a complex between water and 1,8-An.

Full text of DOI:10.1039/b104148g

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Hydrolysis of 1,8- and 2,3-naphthalic† anhydrides and the
mechanism of cyclization of 1,8-naphthalic acid in aqueous
solutions‡
2
Teresa C. Barros,§a Santiago Yunes,b Guilherme Menegon,a Faruk Nome,b
Hernan Chaimovich,a Mario J. Politi,a Luis G. Diasa and Iolanda M. Cuccovia*a
a Departamento de Bioquímica, Instituto de Química, Universidade de São Paulo, Brazil
b Departamento de Química, Universidade Federal de Santa Catarina, Florianópolis, Brazil
Received (in Cambridge, UK) 4th May 2001, Accepted 21st September 2001
First published as an Advance Article on the web 24th October 2001
Naphthalene-1,8-dicarboxylic acid, 1,8-Acid, cyclizes spontaneously in acidic aqueous solution to naphthalene-
1,8-dicarboxylic anhydride, 1,8-An, and here we present an ab initio study of the reaction pathway. The effect of
pH on the hydrolysis of 1,8-An was analysed and compared with the hydrolysis of naphthalene-2, 3-dicarboxylic
anhydride, 2,3-An, to naphthalene-2,3-dicarboxylic acid, 2,3-Acid. The values of the pKa’s of 1,8-Acid and 2,3-Acid
were ca. 3.5 and 3.0, for monoanion formation, pKa1, and 5.5 and 5.0 for dianion formation, pKa2, respectively.
ϩ
Fluorimetric titration demonstrated that the diprotonated 2,3-Acid, AH2, was further protonated to yield AH3 . The
pH–rate constant profile for 2,3-An hydrolysis showed a water reaction between pH’s 1.0 and 6.0 and a base catalysed
hydrolysis above pH 7.0. Under no condition was 2,3-An formed from 2,3-Acid. The pH dependent decomposition
kinetics of 1,8-An is complex and, below pH 6.0, the pH–rate constant profile was fitted by assuming that both
AH2 and AH3ϩ are in equilibrium with 1,8-An. The values of the equilibrium constants for 1,8-An formation
from AH2 and AH3ϩ were ca. 4 and 100 in dilute and concentrated acid, respectively. Ab initio calculations
for a possible reaction pathway connecting the undissociated 1,8-Acid to 1,8-An show a transition state
where an intramolecular proton transfer is concerted with oxygen alignment towards the carbonyl
centre. The planar intermediate is then dehydrated yielding a complex between water and 1,8-An.
thalic acid derivatives.3 Due the importance of modelling
Introduction
peptide cleavage by using simple organic compounds we studied
Carboxylic anhydrides hydrolyse in water and the reaction can
the hydrolysis of 2,3- and N-butyl-1,8-naphthalimides.4 Alk-
be acid or base catalysed.1–6 In aqueous solution even mono-
aline hydrolysis of N-butyl-1,8-naphthalimide includes ring
carboxylic acids readily equilibrate with the corresponding
opening yielding naphthalamic acid which, at low pH, cyclizes
anhydride, although the equilibrium strongly favours the acid.7,8
to the naphthalene-1,8-dicarboxylic anhydride, 1,8-An.4 The
The equilibrium constants for anhydride formation, KE
=
alkaline hydrolysis of N-butyl-2,3-naphthalimide, however,
yields naphthalamic acid, which does not cyclize in acid.4 The
analysis of imide hydrolysis in this system would be simplified
by understanding the mechanism of 1,8-An formation from
naphthalene-1,8-dicarboxylic acid, 1,8-Acid.4,5
k1/kϪ1 = [anhydride]/[dicarboxylic acid] [eqn. (1)], have been
determined in several cases.9–12
(1)
Here we present the study of the equilibrium reaction
between naphthalene-1,8-dicarboxylic acid and its anhydride in
aqueous acid, the alkaline hydrolysis of 1,8-An, and compare
these data with the hydrolysis of naphthalene-2,3-dicarboxylic
anhydride (Scheme 1).
The values of KE vary from 10Ϫ7 to 25 depending on the
structure of the diacid. The unionized acid is the kinetically
active species in anhydride formation.12
The hydrolysis of cyclic anhydrides has been studied in
aqueous media and in water–solvent mixtures. There are several
correlations between rates and nature of the acid, size and con-
figuration of the anhydride ring for both mono- and bi-cyclic
anhydrides.13
The model system most extensively used to analyse particular
aspects of enzymatic catalysis covalently incorporate reactants
into the same molecule, modelling bimolecular reactions in an
intramolecular system.2 Relative accelerations, obtained by
comparisons of the second and first order rate constants can
reach values as large as 1013 in model systems based upon naph-
† The IUPAC name for naphthalic acid is napthalenedicarboxylic acid.
‡ Electronic supplementary information (ESI) available: tables contain-
ing the values of the rate constants. See http://www.rsc.org/suppdata/
p2/b1/b104148g/
§ Present address: Instituto de Ciências da Saúde, Universidade
Paulista, UNIP, Bauru, São Paulo, Brazil.
Scheme 1
2342
J. Chem. Soc., Perkin Trans. 2, 2001, 2342–2350
This journal is © The Royal Society of Chemistry 2001
DOI: 10.1039/b104148g

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1,8-Acid is 15%. Hence in this pH region the anhydride–acid
equilibrium needs to be considered.
Experimental
Materials
Spectrometric titrations. The pKa1 and pKa2 of 2,3-Acid
Naphthalene-1,8-dicarboxylic anhydride, 1,8-An (Aldrich),
was purified by sublimation. Naphthalene-2,3-dicarboxylic
anhydride, 2,3-An, was synthesised and purified using standard
procedures.14 Naphthalene-2,3-dicarboxylic acid, 2,3-Acid
(Aldrich), was used as received. Naphthalene-1,8-dicarboxylic
acid, 1,8-Acid, was prepared by adding 0.03 M NaOH to a
water suspension of 1,8-An (0.01 M) and maintaining the
sample at 50 ЊC for 5 h. At the end of the reaction absorbance
measurements (at 343 nm) assured total absence of the
anhydride (see below).
(Scheme 2) were determined from the absorbance (255 nm)
All reagents were PA grade or better and organic solvents
were distilled. All aqueous solutions and buffers were prepared
in freshly glass-bi-distilled water.
Methods
Absorbance spectra (UV–visible) and kinetic measurements
were obtained on a Hewlett-Packard HP8452A spectrophoto-
meter equipped with a thermostatted water-jacketed cell
holder (Microquímica MQBTZ99-20), or a Beckman DU-7
spectrophotometer equipped with a Peltier block. Fluorescence
measurements were made on a Hitachi F-2000 spectrofluoro-
meter. pH was measured with a Beckman model Φ71 pH meter.
The electrode was calibrated against standard buffers, in a
thermostatted stirred vessel, at the appropriate temperature
( 0.1 ЊC). The pH of the buffers was adjusted with NaOH.
Titration of the 2,3-Acid and 1,8-Acid were made on a Radio-
meter PHM 82 Standard pH Meter equipped with a glass
electrode calibrated with standard buffers at 30 ЊC.
Scheme 2
measured at several pH’s, by adding 0.025 mL of 1 × 10Ϫ3
methanolic solution of the 2,3-Acid to 2.5 mL of 0.10 M buffer.
The buffers used were borate, phosphate and citrate from pH 9
to 2.5 and HCl at lower pH’s.
M
The values of pKa0, pKa1 and pKa2 of 2,3-Acid were deter-
mined from the variation of the uncorrected fluorescence emis-
sion intensities at 378 nm using the excitation wavelength fixed
at 300 nm. pKa1 of 1,8-Acid was determined using emission
intensities at 420 nm and excitation wavelength at 300 nm.
Excitation and emission slits were fixed to a 10 nm bandpass
width. Fluorescence rectangular quartz cells of 1 cm optical
pathlength were used with a 90Њ excitation–emission geometry.
A methanolic solution, 0.025 mL, of 2,3-Acid 1 × 10Ϫ3 M was
added to 2.5 mL of buffer giving a final concentration 1 × 10Ϫ5
M. For 1,8-Acid, a 1 × 10Ϫ3 M solution in NaOH pH 11 was
used.
The values of pKa1 and pKa2 of 1,8-Acid (Scheme 2) were
obtained by absorbance measurements (320 nm) at several pH’s
in 1.0 cm optical pathlength quartz cells. 1,8-Acid (0.05 mL,
0.01 M) was added to 2.5 mL of 0.10 M buffer yielding a final
concentration of 2 × 10Ϫ4 M of 1,8-Acid.
Kinetics
The kinetics of hydrolysis and cyclization of the substrates were
followed at 343 nm for 1,8-An (ε = 12900 MϪ1 cmϪ1) and 365 nm
for 2,3-An (ε = 3600 MϪ1 cmϪ1) in a quartz cell of 1 cm optical
path. The reaction was initiated by adding 20 µL of a stock
solution of the substrates prepared in acetonitrile to 2.0 ml of
buffer. The final concentration of substrate was 1.0 × 10Ϫ5
M
for the reactions performed at 30 ЊC and 1.7 × 10Ϫ5 M at 50 ЊC.
The buffers used were borate (pH 9.0 to 10.0), phosphate
(pH 6.4 to 8.0), citrate (pH 2.2 to 6.0) and HCl for pH’s lower
than 2.0, where the H0 scale was used.15 The buffer concen-
trations are detailed in the tables and figure legends. The
absorbance values were stored directly on a microcomputer and
analysed using the HP 8452 kinetics software. Data analysis
demonstrated first order behaviour for, at least, 4–5 half-
lives. Reported rate constants are averages of, at least, three
independent determinations differing by no more than 5%.
Since absorbance or fluorescence values were obtained within
ca. 20 seconds of 1,8-Acid addition to the buffered solution
no correction on the pKa values regarding the anhydride–acid
equilibrium was necessary.
pKa determinations
All determinations were made at 30 ЊC.
Computational procedures
Potentiometric titrations. The 2,3-Acid was titrated with HCl
using 50 mL of a 0.001 M solution of 2,3-Acid made alkaline
with NaOH to pH 11.0, with or without NaCl, under a N2
atmosphere. Titrating HCl (0.0667 M) was added to the solu-
tion with a Hamilton microsyringe. 1,8-Acid was titrated poten-
tiometrically with HCl (0.0667 M) under N2 using an aliquot of
5.0 mL of a 0.01 M solution of 1,8-Acid (pH 12.0) diluted to
50 mL. The initial pH in this solution is near 11.0. Since the
pKa2 of 1,8-Acid is near 5.5, and at this pH the 1,8-Acid does
not cyclize (see below), it is not necessary to consider the
anhydride–acid equilibrium.
Ab initio calculations. The potential energy surface for the
formation of 1,8-An was studied by ab initio quantum chemical
methods. The gas-phase geometries of reactant, products,
intermediate and transition states were fully optimised at the
Hartree–Fock (HF) level of theory using the standard 6-31G*
basis set. Electron correlation energy was included by single-
point calculations at second-order Møller–Plesset perturbation
theory (MP2), using the same basis set. The characteristics of
all stationary points were evaluated by calculations of vibration
harmonic frequencies at the HF/6-31G* level. Vibrational har-
monic frequencies were obtained from second-order analytical
energy derivatives. Assuming ideal behaviour, partition func-
tions (translational, rotational, vibrational and electronic) and
thermodynamic properties (referring to the standard state of
The potentiometric titration of 1,8-Acid at pH’s lower than
4.0 were completed in ca. 15 min. On this time scale, the max-
imum calculated amount of 1,8-An formed upon cyclization of
J. Chem. Soc., Perkin Trans. 2, 2001, 2342–2350
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Table 1 pKa’s of naphthalic acids and phthalic acids
Compound
1,8-Acid
Method
Salt or buffer
pKa0
pKa1
pKa2
Potentiometric
Potentiometric
Potentiometric
Spectrophotometric
Fluorescence
0
3.63
3.52
3.54
3.50
3.56
3.49
3.27
3.33
3.05
2.80
2.80
2.89
3.54
3.51
5.53
5.38
5.44
5.40
NaCl 0.02 M
NaCl 0.10 M
Buffer 0.1 M
Buffer 0.02 M
Buffer 0.05 M
0
NaCl 0.02 M
NaCl 0.10 M
Buffer 0.1 M
Buffer 0.1 M
Fluorescence
2,3-Acid
Potentiometric
Potentiometric
Potentiometric
Spectrophotometric
Fluorescence
5.28
5.09
5.00
5.00
4.90
5.51
4.60
4.82
Ϫ0.30
o-Phthalic acida
m-Phthalic acida
p-Phthalic acida
a Ref. 28.
1 mol LϪ1 and 298 K) were calculated by employing standard
statistical mechanical theory.16 Low frequency modes were
subtracted from enthalpic and entropic contributions.
(3)
(4)
Reaction coordinate points were determined using the
intrinsic reaction coordinate (IRC) approach, also at the HF/6-
31G* level, using the method of Gonzales and Schlegel.17,18
Solvation free energies (related to the transfer of the solute
molecule from the 1 mol LϪ1 vapour to 1 mol LϪ1 aqueous
solution at 298 K) were calculated at the MP2/6-31G* level by
using the polarized-continuum model (PCM) and standard
atomic radii, at the gas-phase determined geometries.19,20
Addition of the energetic and entropic contributions to the
MP2/6-31G*//HF/6-31G* electronic energies gave the gas-
phase free energies. Aqueous-phase free energies were obtained
from further addition of solvation (PCM) contributions.
The values of the molar extinction coefficients εAH , εAH and
2
εA, corresponding to diprotonated, AH2, monoprotonated,
AH, and dianionic species, A, respectively, are presented in the
legend of Fig. 1.
The values of pKa1 and pKa2 of 1,8-Acid and 2,3-Acid,
estimated by spectral measurements (Table 1) are, within the
experimental error, similar to those determined by potentio-
metric titration and in the same range of pKa’s of derivatives of
phthalic acid, Table 1.22
Photophysical properties of 1,8-Acid and 2,3-Acid have been
described.23 pKa values of both 1,8-Acid and 2,3-Acid were
determined by changes in fluorescence emission yields with pH
and are included in Table 1.
Since 2,3-Acid does not cyclize even at very low pH, the
fluorescence emission of 2,3-Acid was determined at high acid-
ities and another pKa was apparent (Fig. 1C). The pKa in the H0
region, pKa0, was attributed to the protonation of 2,3-AcidH2,
AH2, leading to 2,3-AcidH3ϩ, AH3ϩ (Scheme 3), as described in
eqn. (5).
Results
The values of pKa1 and pKa2, of 1,8-Acid and 2,3-Acid (Scheme
2), calculated from potentiometric titration curves,21 with
and without NaCl are presented in Table 1. NaCl produced a
moderate decrease in the pKa’s of both diacids (Table 1).
The values of pKa1 and pKa2 of 2,3-Acid and 1,8-Acid were
also determined by UV spectra (Fig. 1). The data in Figs. 1A
and 1B were fitted using eqn. (2). AbsT and CT are the absorb-
(2)
(5)
The fluorescence decrease at high HCl concentration was not
due to quenching of the AH2 fluorescence by chloride ion, but
rather a significant decrease in quantum yield due to the form-
ation of AH3ϩ species.23 The fluorescence of the 2,3-Acid in 5.0
M HCl decreases 95% compared with that in pH 2.0, while the
addition of 5.0 M NaCl to 2,3-Acid at pH 2.0 leads to only a
30% decrease in the fluorescence intensity.
ance and the total concentration of the diacid, and pKa1 and
pKa2 refer to the dissociation constants of the diacid, Ka1 and
Ka2 (Scheme 3), as defined by eqns. (3) and (4).
The values of the relative fluorescence intensity, F, versus pH
were adjusted using eqn. (6) where CT is the total 2,3-Acid
concentration, ꢀAH3, ꢀAH2, ꢀAH, and ꢀA are adjustable
parameters (presented in the legend of Fig. 1C) proportional to
the molar absorption coefficient at the excitation wavelength
and the emission yield for the 2,3-Acid species.
The calculated values of the three pKa’s of 2,3-Acid are
presented in Table 1.
The hydrolysis of 2,3-An was studied over a wide pH range.
The observed rate constant, kψ, for 2,3-An hydrolysis does not
Scheme 3
(6)
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Fig. 1 pH effect on the absorbance or fluorescence of: (A) 2,3-Acid: the concentration of 2,3-Acid was 1 × 10Ϫ4 M and the solid line was calculated
using εA = 1190 MϪ1 cmϪ1; εAH = 1950 MϪ1 cmϪ1; εAH = 1360 MϪ1 cmϪ1 in eqn. (2). (B) 1,8-Acid: the concentration of 1,8-Acid was 2 × 10Ϫ4 M and the
2
solid line was calculated using eqn. (2) and the following parameters: εA = 1000 MϪ1 cmϪ1; εAH = 1850 MϪ1 cmϪ1; εAH = 2500 MϪ1 cmϪ1. (C) 2,3-Acid:
2
the sample was excited at 300 nm and the fluorescence measured at 378 nm. The solid line was calculated using eqn. (6) and ꢀAH3 = 100; ꢀAH2 =
3400; ꢀAH = 2600 and ꢀA = 475. The concentration of 2,3-Acid was 1 × 10Ϫ5 M, buffers 0.1 M and the temperature 30 ЊC.
Table 2 Rate and equilibrium constants for the reactions of hydrolysis
of 2,3-An and 1,8-Ana
1,8-An
2,3-An
Parameters
30 ЊC
50 ЊC
30 ЊC
kH/MϪ1 sϪ1
1.2 × 10Ϫ4
1.13 × 10Ϫ3
3.20 × 103
kOH/MϪ1 sϪ1
1.3 × 103
9.9 × 103
k
Ϫ1/sϪ1; kϪ2/sϪ1
5.0 × 10Ϫ5
3.30 × 10Ϫ4
3.90 × 10Ϫ3
1.35 × 10Ϫ3
2.45 (Ϫ0.39)
3.55 × 10Ϫ4 (3.45)
2.8 × 10Ϫ3
k2/sϪ1
8.0 × 10Ϫ4
k1/sϪ1
1.5 × 10Ϫ4
Ka0 (pK0)
Ka1 (pKa1)
Ka2 (pKa2)
KE0
2.45 (Ϫ0.39)
2.51 × 10Ϫ4 (3.6)
3.16 × 10Ϫ6 (5.5)
115.5
4.25
KE1
3.0
a Values obtained from adjusting experimental data to kinetic and
equilibrium equations (see text).
Fig. 2 pH effect on observed rate constant of hydrolysis of 2,3-An at
30 ЊC. The line was obtained using eqn. (7) and the parameters used are
in Table 2.
vary from pH 0.0 to 7.0 (Fig. 2), increasing sharply with pH in
alkali. The slope of the linear log kψ–pH function was 1.0 above
pH 7.0 (not shown) and the kψ–pH pattern can be attributed to
the water attack on 2,3-An up to pH 7.0 and OHϪ catalysed
hydrolysis in alkali.24,25 The data of Fig. 2 were adjusted using
eqn. (7), where kϪ1 is the first order rate constant for water
attack on anhydride and kOH is the second order rate constant
for OHϪ attack. The values of the rate constants are presented
in Table 2.
The spectra of 2,3-Acid, product of the hydrolysis of 2,3-An,
remained unchanged, even for 5 days at 50 ЊC in HCl 5.0 M
(not shown), implying that if any 2,3-An is formed under these
conditions, the equilibrium strongly favours the 2,3-Acid.
The kψ–pH dependence for 1,8-An hydrolysis is complex,
consisting of an acid catalysed region at pH’s lower than 1.0, a
well defined plateau between pH 1.2 and 2.4, a pH dependent
kψ = kϪ1 ϩ kOH[OH]
(7)
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Fig. 3 Observed rate constant for the hydrolysis of 1,8-An and
attainment of equilibrium between 1,8-An and 1,8-Acid as a function
of pH–H0. At 30 ЊC (0.02 M buffer) the rate constants were obtained
starting with: (a) 1,8-An for hydrolysis (above pH 6.0) and equilibrium
(below pH 6.0) (O) and (b) 1,8-Acid (᭹). At 50 ЊC (0.1 M buffer) rate
constants for both hydrolysis (above pH 6.0) and equilibrium
attainment were obtained starting the reaction with 1,8-An (∆). The pH
scale at [Hϩ] > 1.0 M is given in H0. The lines were obtained using eqns.
(18), (23) and (25) and the parameters used are in Table 2.
region between pH 2.5 and 4.5, a water catalysed region and a
OHϪ catalysed reaction above pH 7.0 (Fig. 3).
Below pH 4.5 the values of kψ increase to a plateau with an
apparent pK, pKap, near 4.0 at 30 and 50 ЊC. The values for kψ,
below pH 4.5, were the same whether the reaction was started
by addition of 1,8-Acid or 1,8-An (Fig. 3), demonstrating that
kψ, in this pH region, is related to the rate of diacid–anhydride
equilibrium attainment.
The quantitative analysis of the kinetic data presented in Fig.
3 required the analysis of the diacid–anhydride equilibrium.
The marked spectral difference between 1,8-Acid and 1,8-An,
as observed upon 1,8-An hydrolysis at pH 7.5 (Fig. 4A), allowed
the determination of the anhydride concentration at equi-
librium as a function of pH at 340 nm where only the anhydride
absorbs. The absorbance at equilibrium, AET, was determined at
50 ЊC (Fig. 4B).
The final absorbance obtained using 1,8-An as substrate at
pH’s higher than 6.0 does not change with pH, consistent with
near quantitative hydrolysis of 1,8-An to 1,8-Acid in this pH
range. Furthermore no absorbance change is detected at pH
higher than 7.0 when 1,8-Acid is used as substrate, strongly
suggesting that the dissociated ionic forms of the diacid do not
cyclize.
At pH’s lower than 4.5 the equilibrium absorbance increases
becoming constant between pH 2.0 and 0. As the acid concen-
tration increases the absorbance increases again reaching a
value consistent with near quantitative anhydride formation
(Fig. 4B). As expected, the values of AET at several pH’s were
identical using either 1,8-Acid or 1,8-An to initiate the reaction.
From data of Fig. 4B it can be supposed that there are
two equilibrium phenomena, involving differently protonated
species, one between pH 4.5 and 0.0 and another below pH
0.0. One of the simplest forms to rationalise these results
follows. Between pH 0 and 4.5 equilibrium is established, as
described for several related systems,12 between the anhydride
and AH2. At [Hϩ] > 1.0 M equilibrium is established between
the anhydride and the protonated form of 1,8-AcidH2,
1,8-AcidH3ϩ (Scheme 3).
Fig. 4 (A) Hydrolysis of 1,8-An followed by UV spectra at pH 7.5,
50 ЊC. Spectra were obtained after intervals of 45 seconds, (——)
initial spectrum of 1,8-An and (—ؒ—ؒ—) final spectra of 1,8-Acid.
(B) Absorbances at 340 nm, after attainment of equilibrium between
1,8-An and 1,8-Acid at 50 ЊC, HCl pH 2.5. Scale of pH at values lower
than zero is in H0. The solid line was obtained using eqn. (16).
Here, as previously shown in related systems, the mono-
protonated form of 1,8-Acid, AH, does not cyclize to the
anhydride.9,12
Considering, as described repeatedly,2 that [H2O] is constant,
KE0 and KE1 can be defined as shown in eqns. (8) and (9).
(8)
(9)
The absorbance at the equilibrium at each pH, AET, (Fig. 4B)
was related to eqns. (8) and (9) and Scheme 3 as follows. AT,
is taken as the absorbance corresponding to quantitative
anhydride formation. 1,8-Acid does not absorb at 340 nm;
hence, at any pH absorbance is related only to anhydride con-
centration. The absorbance contribution from the anhydride
produced from AH3ϩ, in the absence of any other ionic species,
is defined as AE1, and that from AH2 as AE2. Since the ratio of
ϩ
1,8-AcidH2 and 1,8-AcidH3 changes with acidity, the value
ϩ
of AET will be the sum of the molar fraction of 1,8-AcidH3
(α) and 1,8-AcidH2 (β) multiplied by AE1 and AE2, respectively
[eqn. (10)].
In fact protonation of both cyclic anhydrides and dicarboxy-
lic acids were proposed decades ago.26,27 The variation of AET
with pH was analysed by assuming that formation of 1,8-An
can occur from 1,8-AcidH3 and from the neutral 1,8-AcidH2
and can be described by the equilibrium constants KE0 and KE1,
AET = αAE1 ϩ βAE2
(10)
ϩ
Eqn. (13) can be derived, given the definitions in eqns.
(11) and (12), where the subscript E refers to equilibrium
concentrations.
respectively (Scheme 3).
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Table 3 Thermodynamic parameters of the equilibrium between 1,8-Acida and 1,8-An and comparison with the same reaction using DMPAcid
and DMPAn
Reagent
Product
∆H/kJ molϪ1
∆S/J molϪ1 KϪ1
∆Gb/kJ molϪ1
1,8-Acid
DMPAcid
1,8-An
DMPAn
10.1 1.9
16.51c
42.8 5.8
37.8c
Ϫ3.72 × 0.02
4.3b, c
a Thermodynamic parameters at pH 2.5 for the reaction of cyclization of 1,8-Acid to 1,8-An were calculated from measured equilibrium constants at
several temperatures using: ∆G = ϪRTln Keq; ln Keq = ∆S/R Ϫ (∆H/R) × 1/T ; R = 8.317 J KϪ1 molϪ1 b ∆G was calculated for Keq at 50 ЊC. c The ∆G
value for the cyclization reaction of DMPAcid to anhydride at 50 ЊC was calculated from literature data11 for comparison.
.
shown in Table 2. The pKw values used for the calculation of
[OHϪ] at 30 and 50 ЊC were 13.833 and 13.2617 respectively.28
The value of kϪ1 was determined at the pH independent region,
between pH 5.5 and 6.0, Table 2.
(11)
Between pH 1.0 and 5.0, where the concentration of
anhydride at equilibrium is measurable, the observed rate con-
stant reflects the kinetic process for attainment of equilibrium
between the diacid and the anhydride. Assuming that AH2 is the
kinetically active species in this range of pH the reaction rate
is given by eqn. (19) where k1 is the rate constant for AH2
cyclization.
(12)
(13)
ϩ
[AH2]E = [AH3ϩ]T Ϫ [AH3
]
E
Using eqns. (8), (9) and (13), eqns. (14)–(16) can be derived.
(19)
(14)
In this pH range the total acid concentration, [1,8-Acid]T, is
given by eqn. (20).
ϩ
(15)
[Acid]T = [AH] ϩ [AH2] ϩ [AH3
]
(20)
Using eqns. (3), (5) and (20), eqn. (21) can be derived.
The experimental AET–pH dependence (Fig. 4B) was ana-
[Acid]T = [AH2](1 ϩ Ka1/[Hϩ] ϩ [Hϩ]/Ka0)
(21)
lysed using eqn. (16) and the best fit values, at 50 ЊC, were Ka0
=
2.45 (pKa0 = Ϫ0.39), Ka1 = 3.55 × 10Ϫ4, (pKa1 = 3.45), KE0 = 115.5
and KE1 = 4.25 (Table 2). The value of pKa1 calculated from the
fit of the equilibrium data with eqn. (16) is very similar to that
determined by titration a 30 ЊC (Table 1). The value of pKa0
(Table 2) obtained by fitting the equilibrium data between 1,8-
An and 1,8-Acid using eqn. (16) is identical to that determined
for 2,3-Acid by fluorescence titration (Table 1).
Eqns. (19) and (21) give rise to eqn. (22) and kψ for equi-
librium cyclization from AH2, the predominant active species
between pH 5 and 2, is given by eqn. (23).9
(22)
(23)
(16)
ϩ
At pH’s lower than 2.0 the ionic form AH3 contributes
to the equilibrium anhydride formation. The reaction in this
acidity range can be characterised by the equilibrium between
The effect of temperature on KE1 was determined at pH 2.5,
where essentially all the 1,8-Acid is in the AH2 form. The values
of ∆S and ∆H, calculated from the linear plots of ln KE1 vs.
1/T , are shown in Table 3.
After the determination of the equilibrium constants for
anhydride formation and pKa’s of 1,8-Acid (Fig. 3) the pH
effect on the rate constants of 1,8-An decomposition can be
analysed quantitatively.
ϩ
AH3 and 1,8-An and an acid catalysed reaction, kH, for the
ϩ
cyclization of AH3 (see Fig. 3). The reaction rate is given by
eqn. (24), where k2 and kϪ2 are the rate constants for formation
and decomposition of 1,8-An from AH3ϩ, respectively.
v = kH [Hϩ] [AH3ϩ] ϩ k2[AH3ϩ] Ϫ kϪ2[An]
(24)
At pH’s higher than 7, the predominant reaction is the alk-
aline hydrolysis of 1,8-An. The reaction rate, v, in this region
and the observed rate constant, kψ, are given by eqns. (17) and
(18), where kOH is the second order rate constant for OHϪ
ϩ
The plot of kψ vs. aH , at values of H0 lower than Ϫ1, is linear
and from the slope of the plot the value of kH was obtained.
From the pertinent acid–base dissociation equilibria it can be
shown that eqn. (25) is true.
v = kψ[1,8-An]
(17)
(18)
(25)
kψ = kOH[OHϪ] ϩ kϪ1
attack on the anhydride and kϪ1 is the rate constant of water
attack on the anhydride.
The plot of log kψ vs. pH, from pH 7.0 to 9.0, was linear with
a slope of 1.0 at 50 and 30 ЊC and the calculated value of kOH is
The kψ vs. pH profiles of Fig. 3, at 30 and 50 ЊC, were
adjusted using eqns. (18), (23) and (25). Between pH 1.0 and 5.0
the only adjustable parameter was k1. Below pH 1.0 both k2 and
k
Ϫ2 were varied to fit the experimental data to eqn. (25). As an
J. Chem. Soc., Perkin Trans. 2, 2001, 2342–2350 2347

View Article Online
0.2 M HCl, additional acid catalysis was not observed.9 The kψ
vs. pH profile for the dimethylmaleic acid reaction is similar to
that obtained here with 1,8-An from pH 1.0 to 6.0. Maleic acid
derivatives cyclize only upon protonation of both carboxylic
groups.9
Spontaneous formation of 1,8-An from 1,8-Acid has been
suggested previously.29,30 We have shown that in the pH 2.0–
5.0 region the equilibrium formation of 1,8-An can be
adequately described by cyclization of AH2. Below pH 1.0 the
values of 1,8-Acid cyclization rate constants increased sharply
ϩ
with aH
.
The pH dependence of kψ for the anhydride–acid equilibrium
was adequately fitted with the equilibria presented in Scheme 3.
It should be noted that the equilibrium constant for anhydride
formation determined experimentally is identical, within
experimental error, to that calculated from the rate constants
presented in Table 2 in the pH 1–5 range. This calculation was
made possible since the rate constant for water attack on
anhydride, kϪ1, was obtained experimentally (Table 2). Such a
comparison was not possible at the higher acidity range since
the rate constant for the water attack on the anhydride, kϪ2, may
contain a term in protonated water. Furthermore the error
in the estimation of the equilibrium constant at high acidity,
KE0, is much larger, since there is essentially total conversion of
1,8-Acid to 1,8-An.
Fig. 5 Structure of the possible reactant A (1,8-Acid), transition states
B and D, intermediate C and products E (1,8-An ϩ H2O) in the
cyclization reaction. The naphthalic ring atoms are not shown for a
better structure visualisation.
There is extensive literature concerning hydrolysis of
anhydrides in aqueous acid.27,30–33 The effect of high acid con-
centration (0.5–4 M) on reaction rate is dependent on the
structure of the anhydride.31 Perchloric acid in dioxan–water
(60 : 40) increases the hydrolysis rate of glutaric, homophthalic
and camphoric anhydrides but inhibits the hydrolysis of maleic
and phthalic anhydrides. Univalent salts retard the acid
hydrolysis of these cyclic anhydrides. Therefore, for both mono-
and bi-cyclic anhydrides there is a relationship between sensi-
tivity to acid, size and configuration of the anhydride ring.
However, flexibility of the anhydride ring systems does not
affect the sensitivity to acid, e.g., camphoric anhydride has a
rigid structure, but nonetheless, its hydrolysis is acid-catalysed.
Bunton et al. suggested that the acid hydrolysis occurs by an
A-2 mechanism involving protonation of an oxygen atom and
nucleophilic attack upon the carbonyl carbon atom.31
Fig. 6 Relative MP2/6-31G*//HF/6-31G* activation energies for the
gas phase (᭿) and solution (᭹) for the cyclization reaction of 1,8-Acid.
Leisten, in a cryoscopic study of the equilibrium between
cyclic anhydrides and diacid in 100% sulfuric acid, suggests that
there is an equilibrium between the anhydride and the pro-
tonated form of the diacid.26 This suggestion is in agreement
with the protonation proposed in this work for 1,8-Acid below
pH 1.0
initial estimate we assumed that kϪ1 = kϪ2. The best fit values for
the rate and equilibrium constants are presented in Table 2.
The study of the potential energy surface for the formation
of 1,8-An from 1,8-Acid, AH2 form, led us to the following
Anhydride formation from carboxylic acids is a general
phenomenon. The equilibrium constant between mono-
carboxylic acids and its anhydrides lies strongly toward the
acid. Acetic acid, for example, at the boiling point, contains
only ca. 0.03% of the anhydride.7,8,12 For dicarboxylic acids the
equilibrium constant for anhydride formation, KE, varies from
25 to 1 × 10Ϫ5 depending on structure.12 Apparently, high KE
values for anhydride formation are related mainly to strong
non-bonded interactions in the diacid that are relieved in the
cyclic anhydride.12
reaction scheme: 1,8-Acid
TS1
Intermediate
TS2
1,8-An ϩ H2O. The fully optimised structures are shown in Fig.
5 and the free energy profiles for the reaction in the gas phase
and aqueous solution are presented in Fig. 6. The reaction has
two distinguishable steps.
(1) An intramolecular proton transfer concerted with oxygen
alignment (O2, Fig. 5) towards the carbonyl centre form-
ing transition state 1 (TS1) and then a neutral and planar
intermediate (minima in the potential energy surface), with a
tetragonal sp3 carbon (C1).
Dicarboxylic anhydrides also form in solution upon mono-
ester hydrolysis. Monoesters of dicarboxylic acids hydrolyse by
intramolecular nucleophilic attack by the carboxylate ion upon
the ester carbonyl yielding anhydrides.34–37 Linear correlations
between the rate constant for diacid cyclization and ∆pK
(pKa1 Ϫ pKa2), have been described. The ∆pK of a diacid is
largely determined by the existence of an intramolecular hydro-
gen bonded species in the monoanion. In a study of pKa of 1,2
dicarboxylic acids attached to rigid skeletons intramolecular
hydrogen bonding increases with the distance between the car-
boxy groups. The stronger intramolecular hydrogen bonding
occurs in the monoanion in solution when the carboxy group is
spaced so that an essentially linear bond of about 2.45 Å lying
(2) The second step is dehydration, through transition state
2 (TS2), yielding a complex between water and 1,8-An. Both
transition states were characterised by a single imaginary fre-
quency and IRC calculations pointed to the expected previous
and forward minima structures in the reaction pathway.
Discussion
The pH effect on the observed rate constants for anhydride
solvolysis, kψ, has been studied in few cases.
The value of kψ for decomposition of maleic anhydride
derivatives in aqueous solution is pH dependent between
pH 3.0 and 5.0 and, since the reactions were followed only up to
2348
J. Chem. Soc., Perkin Trans. 2, 2001, 2342–2350

View Article Online
in the intersection of the two planes of the carboxy groups is
formed. The carboxy groups should be attached to a carbon
skeleton such that no change in conformation of the carbon
skeleton is allowed, but the carboxy group may rotate.22
The pKa1/pKa2 ratios of 1,8- and 2,3-Acid were ca. 1.6, imply-
ing an intramolecular bonding of the same effectiveness. How-
ever, 1,8-Acid cyclizes at pH’s below 4.0 while the 2,3-Acid does
not cyclize, to a measurable extent, even at 50 ЊC and 6.0 M
HCl. The cyclization of 2,3-Acid cannot be observed using our
methods, probably because the equilibrium strongly favours the
acid. Hence, the correlation between ∆pK and anhydride for-
mation does not hold for the comparison between 2,3-Acid and
1,8-Acid. In fact, although correlations between ∆pK and rates
of anhydride formation do exist in a limited series of diacids,
they cannot hold for all diacids.38 In order for a diacid to exhibit
a high ∆pK its geometry should allow the formation of an
internal hydrogen bond of about 2.40 Å with little change in
molecular strain on going from the open chain to the cyclic
form. If, on the other hand, the hydrogen bond in the mono-
anion is formed at the expense of a large increase in strain, the
∆pK of the diacid may be small. Thus, an important require-
ment for fast cyclization, apart from the existence of steric
strain in the diacid, appears to be that the carboxy groups are as
closely situated as possible.12
reactants in the gas phase and obtained good agreement with
relative rate constants measured in solution. No such series of
rate constants is available for the present system. Nonetheless,
the calculated mechanism (Figs. 5 and 6) is a possible pathway
for the 1,8-Acid cyclization reaction and shows the same
proximity and strain features present in the reaction studies of
Bruice and Lightstone40 which account for reaction rate
enhancements.
Hawkins’11 studies of the hydrolysis of phthalic, PTAn,
and 3,6-dimethylphthalic, DMPAn, anhydrides show that in
aqueous acid DMPAn is in equilibrium with 3,6-
dimethylphthalic acid, DMPAcid, while PTAn is quantitatively
hydrolysed to phthalic acid, PTAcid, and the equilibrium con-
stant cannot be measured. In water PTAn hydrolyses ca. 8 times
faster than DMPAn and the cyclization step is ca. 6 times faster
for DMPAcid. The slower hydrolysis rate of DMPAn is prob-
ably not due to steric hindrance towards water attack, but to the
relief of steric strain by the methyl groups of DMPAcid, when
compared with the corresponding anhydride. Comparison of
the thermodynamic parameters for the cyclization reaction for
1,8-Acid and DMPAcid (Table 3) shows that the difference in
equilibrium constants reflects differences in the enthalpy term
for the equilibrium and not an entropic difference as has been
suggested in related systems.40
It has been suggested that strain is released in the intra-
molecular diacid to anhydride conversion.34 As seen from the
calculated structures (see Fig. 5), 1,8-Acid is a rigid and highly
strained system, where each carboxy group lies in an opposite
side of the aromatic ring plane. On the other hand, the 1,8-An is
a rigid but planar structure, without any carboxy interaction
resulting in strain.10,12,13 It was suggested previously that the
carboxy group proximity is also determinant in anhydride
formation.12,35–38 Here, and in other bridged cyclic anhydrides
where the equilibrium constant for anhydride formation is rela-
tively high, 3 carbon atoms and the anhydride bonds, forming a
6-membered ring, separate both carboxy groups.13,39 The dis-
tance between the attacking oxygen (O2) and electrophilic car-
bon (C1) is just 2.76 Å in the 1,8-Acid, reaching 2.27 Å in TS1
(Fig. 5). As in similar dicarboxylic acids, strain release and car-
boxy group proximity are the major factors governing the rate
of anhydride formation from 1,8-Acid. The structures 1,8-Acid
(see Fig. 5, A) and TS1 (B) are quite different and the pathway
could include a previous proton transfer from one oxygen to the
other in the same carboxy group. Additional calculations would
be necessary to fully investigate this putative step. We can
assume, however, that this step may be unimportant kinetically.
If such a transfer is not a barrierless process, it would have a
smaller energy barrier than a hydrogen transfer between differ-
ent carboxy groups and, because of short transfer distance,
hydrogen tunnelling effects would be present.
Conclusions
Reversible 1,8-An formation from 1,8-Acid was observed in
acidified aqueous solution below pH 5.0 while the decom-
position of 2,3-An leads to quantitative formation of 2,3-Acid.
The undissociated 1,8-Acid, AH2, as well as the protonated
form, AH3ϩ, were the kinetically reactive species. The values of
the equilibrium constant for 1,8-An formation of ca. 4 and 100,
ϩ
respectively, for the AH2 and AH3 forms, indicated that
protonation stabilizes the anhydride relative to the dicarboxylic
acid. Ab initio calculations demonstrated that the pathway
for anhydride formation includes a rate determining intra-
molecular proton transfer concerted with oxygen alignment
towards the carbonyl centre.
Acknowledgements
The authors are grateful to the Brazilian Agencies FAPESP,
CNPq, and CAPES for financial support. This work is part of
the MSc dissertation of T.C.B, IQUSP (1991) and of the PhD
thesis of S.Y., UFSC (1996). T.C.B. was a CAPES graduate
fellow and S.Y. was a CNPq and CAPES fellow. G.M. and
L.G.D. are graduate and post-doctoral fellows from FAPESP.
The authors thank Dr Jorge Masini, IQUSP, for his helpful
suggestions and for his computational advice in the calculation
of potentiometric pKa’s of the diacids and Professor C. A.
Bunton, UCSB, USA, for advice and helpful suggestions with
the manuscript.
The mechanism here proposed for the cyclization of the
diprotonated 1,8-Acid is similar to those described where the
reaction of a neutral diacid proceeds towards an intramolecular
carboxylate attack upon the other carboxy function with final
anhydride formation.35–38
References
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was not to theoretically obtain the value of the experimental
rate constants. Using a simplified model (PCM) to describe
solvation effects does not account for specific solvent–solute
interactions (e.g. hydrogen bonds) that are certainly important
in this particular reaction in aqueous solution. Theoretical
calculations for cyclization involving a number of explicit water
molecules, although possible, was not the subject of our present
interest.
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