Carbohydrate Research 346 (2011) 664–672
Contents lists available at ScienceDirect
Carbohydrate Research
journal homepage: www.elsevier.com/locate/carres
Converting fructose to 5-hydroxymethylfurfural: a quantum
mechanics/molecular mechanics study of the mechanism and energetics
Stavros Caratzoulas ⇑, Dionisios G. Vlachos
Catalysis Center for Energy Innovation and Department of Chemical Engineering, University of Delaware, Newark, DE 19716, USA
a r t i c l e
i n f o
Article history:
Received 11 October 2010
Received in revised form 14 January 2011
Accepted 26 January 2011
Available online 4 February 2011
Keywords:
Fructose dehydration mechanism
5-Hydroxymethylfurfural
QM/MM molecular dynamics
PM3
Free-energy calculations
a b s t r a c t
We studied the energetics of the closed-ring mechanism of the acid-catalysed dehydration of D-fructose
to 5-hydroxymethylfurfural (HMF) by carrying out canonical ensemble free-energy calculations using
bias-sampling, hybrid Quantum Mechanics/Molecular Mechanics Molecular Dynamics simulations with
explicit water solvent at 363 K. The quantum mechanical calculations are performed at the PM3 theory
level. We find that the reaction proceeds via intramolecular proton and hydride transfers. Solvent dynamics effects are analysed, and we show that the activation energy for the hydride transfers is due to reorganization of the polar solvent environment. We also find that in some instances intramolecular proton
transfer is facilitated by mediating water, whereas in others the presence of quantum mechanical water
has no effect. From a micro-kinetic point of view, we find that the rate-determining step of the reaction
involves a hydride transfer prior to the third dehydration step, requiring an activation free energy of
31.8 kcal/mol, and the respective rate is found in good agreement with reported experimental values
in zeolites. Thermodynamically, the reaction is exothermic by DF ¼ 20:5 kcal=mol.
Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction
The diminishing availability of fossil resources to produce energy and much needed chemical materials has spurred a burgeoning research activity to discover and develop technologies that
would involve renewable energy sources. Abundant biomass, as
the only carbon-containing, renewable, primary energy carrier,
promises to serve as a sustainable alternative that could supply
valuable intermediates to the chemical industry. In particular,
the class of carbohydrates—the prominent compound in biomass—possess a remarkable potential to act as a future resource.
Nature produces a vast amount of 170 billion tonnes of biomass
per year by photosynthesis, 75% of which can be assigned to the
class of carbohydrates. Surprisingly, only 3–4% of these compounds
are used in the food- and non-food sector.1 The economic viability
of biomass-based processes depends critically on selectivity, a
parameter that requires tight optimization. The many challenges
involved in such an endeavour stem from the fact that carbohydrates are highly functionalized molecules. Their high content in
oxygenated groups is a significant drawback for their conversion
to fuels. On the other hand, the high functionality they possess is
also an advantage, as the selective removal of some of these groups
and the modification of others can lead to various value-added
chemicals. The challenge is to develop cost-effective methods to
⇑ Corresponding author.
E-mail address: [email protected] (S. Caratzoulas).
0008-6215/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.carres.2011.01.029
control the functionality in the final product.2 In this context, furan
derivatives, such as 5-hydroxymethylfurfural (HMF), can be produced by the acid-catalysed dehydration of hexoses. HMF and its
2,5-disubstituted furan derivatives can replace key building-block
molecules, currently derived from petrochemicals, in the production of plastics and fine chemicals.3,4
The acid-catalysed dehydration of D-glucose and D-fructose to
HMF in aqueous media has received considerable attention over
the years and more so the last decade. The production of HMF from
glucose or fructose is typical for the selectivity and yield difficulties
one encounters in the conversion of highly functionalized sugars,
impeding high-volume production of HMF due to high costs. The
dehydration rate of glucose is about 40 times lower than that of
fructose, and much lower is the product yield. Kinetics studies by
Kuster and co-workers show that the initial glucose or fructose
concentration, the water concentration, the acidity of the aqueous
medium or the presence of weak-acid anions (functioning as base
catalysts) are all factors that influence the conversion of the sugars
to HMF, the HMF selectivity and the rate at which HMF degrades
by hydrolysis to levulinic and formic acids.5–7 At pH >3.9, no formation of HMF takes place, and at pH >2.7 no formation of levulinic
acid occurs.7 Water displacement (by polyethylene glycol or other
co-solvents) is also very beneficial to the formation of HMF from
fructose because it accelerates its formation and retards its hydrolysis.6 Kuster reports only low HMF selectivity in environmentally
benign solvents (water) and high selectivity in environmentally
questionable ones [dimethyl sulfoxide, (DMSO)];8 DMSO is also a
high-boiling point solvent and economic arguments can be made
S. Caratzoulas, D. G. Vlachos / Carbohydrate Research 346 (2011) 664–672
against its use, too. Nevertheless, the case of DMSO is intriguing, as
it has been suggested that DMSO preferentially stabilizes the furanoid tautomer of fructose (five-membered ring) to the pyranoid
form (six-membered ring), implying that the dehydration of fructofuranose is more HMF selective. Amarasekara et al. have carried
out mechanistic studies on the conversion of fructose to HMF in
pure DMSO solvent, and by establishing the presence of a key
intermediate, (4R,5R)-4-hydroxy-5-hydroxymethyl-4,5-dihydrofuran-2-carbaldehyde, have suggested that the DMSO catalyses the
reaction.9 Antal and Mok have performed the reaction in suband supercritical water and achieved only unsatisfactory yields of
HMF.10 Bicker et al. have used acetone–water mixtures as reaction
media under sub- and supercritical conditions and reported 77%
HMF selectivity and 99% fructose conversion. Interestingly, their
kinetics and NMR data suggest that the dehydration of fructose
to HMF seems to be most selective when the carbohydrate molecule is in its furanoid form. They have rationalized this finding
on the grounds that the acetone molecule is similar to DMSO, thus
suggesting that it favours the furanose tautomer.11 Román-Leshkov
et al. have used DMSO or poly(1-vinyl-2-pyrrolidinone) (PVP) as
‘phase modifiers’ in a biphasic process for the acid-catalysed conversion of fructose to HMF. By managing to suppress undesired
side reactions, they have achieved 80% HMF selectivity at 90% fructose conversion.12 It is unclear, however, how these modifiers function, from a mechanistic point of view.
Despite the significant progress that has been reported recently,
overcoming selectivity and yield difficulties related to the high
functionalization of sugars requires tight optimization, before
existing or even new processes become economically viable. This
requires extensive microkinetic modelling and thus understanding
of the fundamental chemistry, that is, of the reaction mechanisms
and rates.
In this article we focus on D-fructose and study the multistep
mechanism and energetics of the acid-catalysed dehydration reaction to form HMF. The higher selectivity and yield compared to the
direct dehydration of glucose as well as the development of new
catalysts13 for the efficient and cost-effective production of fructose from glucose by isomerization make it an important reaction
in the conversion of biomass to value-added chemicals. However,
accurate energetics for the selective dehydration of fructose, required for process optimization and to design appropriate catalysts
have not been reported.
Modelling the solvent explicitly (to account for solvation effects), and the reacting system Quantum Mechanically (at the
PM3 theory level) we employ hybrid Quantum Mechanics/Molecular Mechanics (QM/MM) Molecular Dynamics simulations to calculate, for the first time, reaction and activation free energies for every
elementary step of the reaction. Details about the calculations are
given in Section 2. This work also demonstrates that when investigating the mechanism of a reaction in solution it does not suffice to
consider only the changes in the quantum mechanical energy of
the reacting system, even if implicit or explicit solvent models
are employed—one must examine the free-energy changes along
the reaction coordinate monitoring the progress of the reaction.
2. Methods
We study the energetics of the proposed mechanism by carrying out free-energy molecular dynamics calculations for each elementary step using a hybrid QM/MM Hamiltonian. The
calculations were carried out in explicit water solvent modelled
with the SPC/E molecular mechanics force field. As the mechanism
involves cleaving and forming of chemical bonds, the fructose molecule was treated quantum mechanically at the semi-empirical
PM3 theory level, as implemented in the AMBER 9 software package.14 Water molecules participating in the mechanism were also
665
included in the QM region and treated at the PM3 level. All the
simulations were carried out in the canonical ensemble at the
rather moderate temperature of T = 363 K. For the thermostat we
used Langevin dynamics with collision frequency 2 ps1. The integration time step in all the simulations was set to Dt ¼ 1 fs. The
ability of the PM3 method to model carbohydrate molecules was
more recently demonstrated by Wu et al. who employed it to study
the isomerization of fructose to glucose catalysed by a phosphoglucose isomerase.15 Pomata et al. have recently employed the SPC/E
water model to study the hydrogen bond network and dynamics
of fructose aqueous solutions up to 70 wt %.16
The free-energy calculations for every step of the mechanism
were carried out using bias sampling along a properly chosen reaction coordinate. For example, in an elementary step involving proton or hydride transfer, we define the reaction coordinate as the
distance between the transferring atom and the donor or acceptor
atoms. For the bias potential we used the parabolic form
V b ðnÞ ¼ ð1=2Þ kb ðn n0 Þ2 , where n is the reaction coordinate and
a function of the atomic coordinates of the system. For the bias
spring constant, kb, we used a range of values, depending on the
anticipated energy barriers for the various elementary steps of
the mechanism.
For each elementary step, profiling of the free-energy change
along a reaction coordinate entails a series of QM/MM MD simulations. These were performed according to the following protocol:
(i) preparation of the quantum mechanical system and solvation—on average the simulation box contained 650 water molecules; (ii) optimization to remove accidental overlaps between
atoms due to solvation; (iii) equilibration in the NpT ensemble
for 200 ps at p = 1 atm and T = 363 K to fix the density of the medium (i.e., the simulation box size); (iv) another round of equilibration in the NVT ensemble for 200 ps at T = 363 K; (v) discretization
of the reaction coordinate at a set of equidistant points fn0i gNi¼1
which define the centre of the bias potential V b ðnÞ and thus a sequence of N simulation ‘windows’ for biased sampling. In each simulation window, the system was propagated for 700 ps under the
bias Hamiltonian before switching over to the next one. Of the
700 ps of propagation time, 200 ps were used for equilibration
and 500 ps were used for the observation period, during which
we saved configurations every 10 fs for post-processing.
Care was exercised so that the bias energy at the centre of a
simulation window does not correspond to energy higher than
2–3 kBT of the neighbouring bias potential, where kB is Boltzmann’s
constant. Put differently, to ensure reversibility, the points fn0i gNi¼1
were chosen so that the domains of configuration space that were
sampled in neighbouring simulation windows overlap. This
requirement dictated the length increment between the points
n0i , which was never larger that 0.1 Å. For example, scanning along
strong C–H bonds with significant barriers to dissociation, required
a rather aggressive bias potential with kb ¼ 200 kcal=mol A2 . A
choice of Dn0 ¼ 0:1 A gives DV b ¼ 1 kcal=mol which at T ¼ 363 K
is equivalent to 1:4 kB T, ensuring that thermal fluctuations provide
the necessary overlap between neighbouring simulation windows.
In a simulation ‘window’, we can calculate the biased marginal
probability density, pb ðnÞ, in the reaction coordinate, n, that monitors the progress of the reaction in an elementary step, and from it
the biased free-energy change. The unbiased free-energy change
along n is given by DF ¼ kBTln pðnÞ , where pðnÞ is the unbiased marginal probability density. The latter is obtained from pb ðnÞ by the
formula pðnÞ ¼ pb ðnÞexp½ðV b ðnÞ f Þ=kB T, where f is the free energy
required to insert the bias potential V b into the system and depends on the simulation window. The free-energy profile for the
elementary step is subsequently constructed by combining the
unbiased probabilities across all simulation ‘windows’, using the
weighted-histogram analysis method.17,18 Upon locating the freeenergy barrier along a reaction coordinate, and in order to obtain
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S. Caratzoulas, D. G. Vlachos / Carbohydrate Research 346 (2011) 664–672
accurate activation energies, we performed further sampling in the
vicinity of the barrier, by adding simulation ‘windows’, and then
re-calculated the free-energy profile in the augmented sample
space. Typically, each simulation ‘window’ required about 5.5 h
of CPU time for equilibration and observation; and a full energy
profile for an elementary step required 25–30 ‘windows’.
The unbiased expectation of a dynamical variable, say K, as a
function of the reaction coordinate (i.e., the unbiased conditional
expectation) is calculated by
R
hKiðnÞ ¼
dqKðqÞdðn nðqÞÞeðV b ðnÞf Þ=kB T eHb =kB T
R
dqdðn nðqÞÞeðV b ðnÞf Þ=kB T eHb =kB T
ð1Þ
where q collectively denotes the coordinates of the atoms in the
system and Hb is the Hamiltonian of the biased system.
3. Results and discussion
3.1. Mechanism and energetics
In the following, we label the fructose carbon atoms according
to the convention depicted in Figure 1; to the oxygen atoms of
the OH groups we assign the same label as the carbon atom to
which they are attached, viz., the oxygen atom on the anomeric
carbon (C2) is labelled O2, etc.
We are investigating the energetics of the closed-ring mechanism of the acid-catalysed dehydration, whereby the fructofuranose ring remains intact. According to Antal and Mok,10,19 the
preponderance data from chemical kinetics studies favour the
closed-ring over the open-ring mechanism. Recent gas-phase electronic structure calculations of the acid-catalysed dehydration of
xylose and glucose show that open-ring pathways to HMF are very
unlikely as they involve very high activation barriers.20
The outcome of the QM/MM MD studies presented in this paper
is the mechanism that we show in Figure 2. In the following we
analyse its energetics.
3.1.1. Protonation and first dehydration
We model the acid catalyst by protonating the OH groups of the
fructose ring. Protonation of each of the three OH groups was considered separately and the free-energy change for the formation of
the respective oxonium ion was calculated. As a free proton cannot
exist in solution, in Figure 3a we show the free-energy change for
the transfer of a proton from a hydronium, H3O+, to a fructose-ring
OH as a function of the distance between the proton and the
accepting oxygen atom. In this calculation the QM region consisted
of the fructose molecule and the hydronium ion. We find that the
protonation is an activated process, requiring activation free energy, DF z ; of 17:7 kB T (12.8 kcal/mol) for the OH on C2, 20.1 kBT
Figure 1. Atom labelling convention for fructose.
(14.5 kcal/mol) for the one on C3 and 18.9 kBT (13.6 kcal/mol) for
that on C4. All three curves have a global minimum at 1.75 Å,
which corresponds to the formation of a hydrogen bond between
the OH group and the approaching hydronium ion. The reactions
are endergonic, with that of the C2–OH being less so by about
4 kcal/mol. So, from a kinetic point of view, protonation of either
one of the three ring OH groups is equally likely, with the protonation of the C2–OH being slightly favoured from a thermodynamic
point of view.
Qian et al. have carried out Car–Parrinello MD simulations for
the dehydration of D-glucose and D-xylose at 500 K. They have proposed that the protonation of the OH group is probably the ratelimiting step.21 They predicate that conclusion on the observation
that in the course of the MD trajectory (5 ps long), the proton,
which was initially attached to one of the ring OH groups, transferred back to a water molecule in less that 100 fs, that is, quite
rapidly. Transfer of the proton back to a water molecule is not unlikely, according to our calculations, as the barrier to de-protonation is in the range of 8–10 kBT at 363 K, with the upper bound
corresponding to the C2–OH profile (see Fig. 3a). However, we find
that the Classical Transition-State Theory (CLTST) lifetime of the
protonated state is significantly longer in the case of D-fructose:
3 ns at 363 K, and 100 ps at the elevated temperature of
500 K; if one includes friction corrections, these numbers should
go up.22,23 (Although for hydrogen transfer quantum mechanical
corrections are important, at this point we content ourselves with
the classical estimates as the reaction temperatures under consideration are high.24) As we shall see in the following, we do not find
the protonation to be the rate-determining step of the acid-catalysed dehydration of fructose.
The free-energy change for the removal of the protonated OH is
shown in Figure 3b, for each of the three OH groups. The potential
of mean force (pmf) is graphed as a function of the length of the
cleaving bond.
Removal of the protonated OH that is attached to the C2 carbon
can take place in a facile manner, with an activation free energy of
just 8.3 kBT (or 6 kcal/mol) and results in the formation of a stable
intermediate, (30 ). The first dehydration is mildly exergonic with
DF ¼ 3:1 kB T (2.2 kcal/mol). The water break-off is followed
by charge transfer from the ring oxygen, O5, to the C2 carbon
and the formation of a double bond between them, of average
length 1.25 Å. Because of the sp2 hybridization of the C2 carbon,
the O5–C2 and C1–O1 bonds assume a co-planar conformation.
The effects of solvations are significant; they are analysed in Section 3.2.
In comparison, initiation of the reaction by removal of the (protonated) OH on the C3 carbon is less likely, as the free-energy barrier is equal to 43 kBT (or 31 kcal/mol), which implies that the
CLTST rate constant is 10-6 s1, viz., slower by fifteen orders of
magnitude. Removal of the OH on C4 has a lower activation free
energy, about 34 kBT (or 24.5 kcal/mol), but still an order of magnitude greater than the free-energy barrier for removal of the OH on
C2 (8.3 kBT). Further dehydration of the resulting intermediate results in either ring opening or fragmentation and formation of very
energetic free radicals. This is a parasitic pathway, but one that is
surely initiated much slower (by twelve orders of magnitude) than
the productive one.
3.1.2. Second dehydration
The second dehydration involves three sequential, elementary
steps: (a) hydride transfer from C1 to C2, (30 ?4); (b) proton transfer from O1 to O3 to form an oxonium ion, (4?5); and (c) dehydration, (5?6).
The proton transfer from O1 to O3 is not feasible without prior
hydride transfer (step (a)). Scanning along the nascent O3–H bond
produces a potential of mean force with a very high barrier of over
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S. Caratzoulas, D. G. Vlachos / Carbohydrate Research 346 (2011) 664–672
H
H
HO
OH
O
H
HO
HO
H+
OH
OH
H H
+OH
2
H
HO
O
- H2O
H
HO
H H
HO
H
O+
H
OH
OH
HO
+OH
O
H
OH
H
O
O
+
HO
O
H
O
H
H
H
2
-H2O
H
H
HO+
O
O+ H
HO
H
H
6
+OH
5
HO
H
O
HO
H
HO
O
H
4
HO
OH
OH
3
H
3'
C+
H H
2
HO
H
HO
H
HO
OH
H H
1
H
HO
OH
O
H
H
H
8
7
HO
HO
O
O
H2+O
H
H
H
HO
O
O+
- H2O
O
O
- H+
H
H
H
8'
9
H
H
10
Figure 2. Reaction mechanism for the dehydration of fructose to HMF. Unstable species are shown within square brackets.
80 kB T (58 kcal/mol) (shown in Fig. S1 of the Supplementary data
scan failed to identify the formation of a stable intermediate, which
is reflected in the lack of a local minimum in the pmf at short
distances.
The necessary hydride transfer (30 ?4) is not a fast one. The corresponding potential of mean force, shown in Figure 4a, has
DF z ¼ 35 kBT (25 kcal/mol)—a significant activation energy to make
the transfer a slow process but not high enough to render it unlikely,
especially at elevated temperatures. The hydride transfer is electronically favoured, as we find that in the 30 ?4 transition the unbiased expectation of the quantum mechanical energy of the reacting
QM ¼ 16:1 kB T (or 11.6 kcal/mol).
system drops, with DE
Considering, however, the free energy of the system, we see that this
step requires DF ¼ þ19:6 kB T (14.1 kcal/mol).
In the intermediate that forms, the C1–O1 bond length is shortened and fluctuates about the typical double bond length of 1.25 Å,
while the C2–O5 double bond is elongated and fluctuates about the
mean value of 1.4 Å, a consequence of the C2 carbon’s acquiring
more of an sp3 character. Upon transferring to the C2 carbon, the
hydride may be syn- or anti-coplanar to the OH group of the C3 carbon (or equivalently, the C2–C1 and C3–O3 bonds may be anti- or
syn-coplanar). Structure optimization at the PM3 level, in the presence of explicit solvent, shows that the two conformations are isoenergetic. Furthermore, we have found that there are no
differences between the respective free-energy profiles for the
transfer of the hydride to ‘syn’ or ‘anti’ geometry.
In Figure 4b we show free-energy profiles for the subsequent
proton transfer (4?5) in four cases: (i) in the conformation where
the C3–O3 and C2–C1 bonds anti-coplanar; (ii) in the syn-coplanar
conformation; (iii) in the syn-coplanar conformation with a bridging water molecule in the QM region (to facilitate proton transfer);
and (iv) in the syn-coplanar arrangement with two bridging water
molecules in the QM region. They are all graphed as functions of
the O3–H separation, namely, the length of the nascent bond. In
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S. Caratzoulas, D. G. Vlachos / Carbohydrate Research 346 (2011) 664–672
20
20
C2--OH
C3--OH
C4--OH
15
C2--O2
C3--O3
C4--O4
10
ΔF/kBT
ΔF/kBT
0
10
5
-10
-20
0
-30
1
1.2
1.4
1.6
1.8
2
2.2
rxn coordinate (Å)
-40
1
2
3
4
5
6
rxn coordinate (Å)
Figure 3. Protonation and first dehydration free energies. (a) Free-energy profiles for the protonation of the ring OH groups of D-fructose. The reaction coordinate is the
separation between the transferring proton and the acceptor oxygen atom; the reaction proceeds from right to left. (b) Free-energy profiles for the first dehydration, for each
of the three OH groups on the ring of D-fructose. The reaction coordinate is the cleaving bond. (Free energies reported in thermal units, kBT, at T = 363 K.)
cases (iii) and (iv), the extra water molecules were treated quantum mechanically.
Without bridging water, the rates of proton transfer are comparable in the ‘syn’ and ‘anti’ conformations. In the syn-coplanar
geometry (curve (ii) in Fig. 4b), the energy barrier is 42.2 kBT
(30.5 kcal/mol). In the anti-coplanar arrangement, the barrier is
equal to 41.5 kBT (29.9 kcal/mol) (curve (i) in Fig. 4b). Both curves
have a local minimum (deeper in the case of the ‘syn’ geometry) at
1.8 Å, which corresponds to the formation of an intramolecular
hydrogen bond between the acceptor OH on C3 and the donating
one on C1. With respect to the reaction free energies, we find
DF anti ¼ 23:8 kB T and DF syn ¼ 30:2 kB T.
It is not uncommon for proton-transfer reactions of this type to
be facilitated by mediating water molecules. To investigate such a
possibility, we have included a water molecule in the QM region
and allowed it to move freely (viz., unrestrained) within a domain
defined by the intersection of two spheres: one centred about the
O1 oxygen and a second centred about the O3 oxygen. The spheres
have the same radius of 3.2 Å and soft, harmonic boundaries
2
jðr r0 Þ2 =2, with r0 ¼ 3:2 Å and j ¼ 100 kcal=ðmol Å Þ. (The radius of the spheres was chosen on the basis of the first coordination shell of hydrogen-bonded water molecules.) The relevant
free-energy profile for proton transfer in the ‘syn’ geometry is curve
(iii) in Figure 4b. Clearly, the water-assisted proton transfer results
in an activation free-energy drop 18.4 kBT (13.3 kcal/mol), bringing
the barrier down to DF z ¼ 23:8 kB T (17.2 kcal/mol). It also makes
the transfer thermodynamically more favourable, with
DF ¼ 12 kB T (8.7 kcal/mol). Note that the water molecule also stabilizes the state at 1.8 Å in which the transferring proton is
shared between the donating O1 oxygen, the accepting O3 oxygen
and the bridging water molecule via hydrogen bonds.
We repeated this calculation in the presence of two extra water
molecules in the QM region. Remarkably, we find that the activation free energy climbs back up to higher values, as shown by curve
(iv) in Figure 4b, with DF z ¼ 36:4 kB T (26.3 kcal/mol).
So, vicinal water accelerates the proton transfer by participating
in the reaction, but more of it has the same adverse effect as not
having any at all. This behaviour appears to be in agreement with
Kuster’s observations that water displacement (by polyethylene
glycol or other co-solvents) can accelerate the formation of HMF
from D-fructose.6
In Figure 4c we show the potential of mean force for the second
dehydration (5?6) as a function of the C3–O3 bond length. The
activation free energy is equal to 34.3 kBT (24.7 kcal/mol). The local
minimum at 2.5 Å corresponds to the formation of a hydrogen
bond between the departing water molecule and the OH group
on the C4 carbon. Removal of the second water requires
DF ¼ 24:4 kB T (17.6 kcal/mol). We should note that for this step
z 70 kB T, indicating how solvation, and in parwe calculate DE
QM
ticular entropic effects, reduce the size of the barrier.
The species 6 is unstable, and once the second water molecule
has broken off the ring, a spontaneous hydride transfer from the
C4 to the C3 carbon (6?7) occurs, releasing 50.0 kBT (36.1 kcal/
mol) of free energy. (This was calculated by carrying out free-energy calculations for the reverse reaction 7?6, viz, hydride transfer
from the C3 to the C4 carbon.) Thus, the C3 carbon retains its sp3
character, whereas the C4 acquires sp2 hybridization.
To study this spontaneous hydride transfer further, we ran a
series of QM/MM MD trajectories with the H atom constrained to
stay on the C4 carbon after the water removal from C3. Within a
few hundred femptoseconds—and following a charge transfer from
the C1 to the C3 carbon—the HCO moiety (formyl group) broke off
the C2 carbon of the ring. The reason for this very rapid H- transfer
is that the second dehydration creates a partial electron deficit on
the C3 carbon. The H- transfer from the C4 carbon to C3 replenishes
this deficit, while, in turn, the electron deficit on C4 is covered by
the non-bonding electrons of O4. If, instead, we constrain the H
atom to remain on C4, then electronic density transfers from C2
to C3, weakening the C2–C1 bond and the HCO break-off ensues.
We thus infer that the second dehydration is followed by two,
very fast and probably competing processes. One involves hydride
transfer from a neighbouring carbon atom to the one that has just
lost an OH group. The other involves re-distribution of the electronic density, entailing partial fragmentation and thus decreased
selectivity in the conversion of D-fructose to HMF.
3.1.3. Third dehydration and proton release
The third dehydration involves the following elementary steps:
(a) hydride transfer to C4 to restore its sp3 hybridization, (7?8);
(b) proton transfer from C3 to O4 to form an oxonium ion,
(8?80 ); and (c) the actual water break-off from C4, (80 ?9).
The proton transfer to the O4 oxygen cannot take place without
prior hydride transfer to C4—an already familiar situation from the
second dehydration step. The relevant free-energy profile is shown
in Figure S2 in the Supplementary data. A hydride transfer from C3
to C4 is not a consideration, on account of what we have just
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S. Caratzoulas, D. G. Vlachos / Carbohydrate Research 346 (2011) 664–672
40
50
(i) C2-C1 and C3-O3 bonds anti-coplanar
(ii) C2-C1 and C3-O3 bonds syn-coplanar
(iii) "syn" geometry w/ H2O bridge
-
H transfer from C1 to C2
40
30
(iv) "syn" geometry w/ two H2O in bridge
ΔF/kT
ΔF/kT
30
20
(ii)
(iv)
20
(i)
10
10
(iii)
0
0
1
1.5
2
0
2.5
1
2
3
4
5
rxn coordinate (Å)
rxn coordinate (Å)
10
ΔF/kT
0
-10
-20
1
1.5
2
2.5
3
3.5
4
4.5
rxn coordinate (Å)
Figure 4. Second dehydration free energies. (a) Potential of mean force for hydride transfer from the C1 carbon atom to the C2. The reaction is monitored by the separation
between the transferring hydride and the acceptor carbon atom C3 and proceeds from right to left. (b) Potential of mean force for proton transfer from the O1 oxygen atom to
the O3. The reaction coordinate is the separation between the transferring proton and the acceptor oxygen atom (O3) and the direction of reaction is from right to left. We
graph the free-energy profiles for four cases: (i) C3–O3 and C2–C1 bonds are anti-coplanar; (ii) C3–O3 and C2–C1 bonds are syn-coplanar; (iii) syn-coplanar conformation with
one mediating water molecule in the QM region; and (iv) syn-coplanar geometry with two mediating water molecules in the QM region. (c) Potential of mean force for the
second dehydration. The reaction coordinate is the cleaving C3–O3 bond. (Free energies reported in thermal units, kBT, at T = 363 K.)
discussed regarding the second dehydration. Thereby, there are
only two alternatives available to us: hydride transfer from C5 to
C4; or simultaneous H- transfer from C3 to C4 and from C2 to C3,
which would force the ring oxygen, O5, to partake in electron sharing with its non-bonding electrons and which would result in an
electronic configuration that does not weaken the C2–C1 bond.
The coordinated H- transfer from C3 to C4 and from C2 to C3
does indeed result in a stable intermediate without fragmentation
products. However, the activation free energy for this elementary
reaction is 68 kBT (49 kcal/mol), which precludes the possibility
of measuring any conversion on a laboratory time scale, even at
elevated temperatures; the relevant free-energy profile is shown
in Figure S3 in the Supplementary data.
Nevertheless, hydride transfer from the C5 carbon to the C4
(7?8) is a viable alternative with DF z ¼ 44:0 kB T (31.8 kcal/mol)
(see Fig. 5a). It results in a stable intermediate with the C5 carbon
being double-bonded to the O5 oxygen. This is a significant activation energy at T = 363 K, but not so much for temperatures in the
range between 393 and 450 K, which are typical reaction temperatures for the conversion of D-fructose to HMF. This step requires
DF ¼ 30:3 kB T (21.9 kcal/mol).
Subsequent capturing of a C3-hydrogen by the OH group on the
C4 carbon, 8?80 , requires 32.0 kBT (23.1 kcal/mol) of activation energy. The relevant potential of mean force is graphed in Figure 5b
as a function of the distance between the transferring hydrogen
and the acceptor oxygen. As expected, the H capture by the O4
atom is endothermic with DF ¼ 12:8 kB T (9.2 kcal/mol), as the
C–H bond is stronger than the O–H bond. We have investigated
whether a bridging water molecule can facilitate the H transfer
from C3 to O4 and found that the free-energy barrier for such a
process is more than twice as high [75.0 kBT (54.1 kcal/mol)].
The resulting intermediate, 80 , is unstable. As soon as the proton
is captured by the O4 oxygen, the C4–O4 bond cleaves and the
incipient water molecule spontaneously departs (80 ?9). Thus,
the third dehydration is non-activated and quite exothermic,
releasing 70:0 kB T (50.5 kcal/mol) of free energy (see Fig. 5c).
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S. Caratzoulas, D. G. Vlachos / Carbohydrate Research 346 (2011) 664–672
40
30
ΔF/kT
ΔF/kT
30
20
10
20
10
0
0
1
2
1.5
1
2.5
2
1.5
rxn coordinate (Å)
2.5
3
rxn coordinate (Å)
20
70
60
15
40
ΔF/kT
ΔF/kT
50
30
20
10
5
10
0
1
1.5
2
2.5
3
3.5
4
4.5
rxn coordinate (Å)
5
0
1
1.5
2
2.5
3
rxn coordinate (Å)
Figure 5. Third dehydration and proton release free energies. (a) Free-energy profile for H-transfer from the C5 carbon to C4. The reaction coordinate is the distance between
the transferring H atom and the acceptor carbon (C4) and the direction of reaction is from right to left. (b) Free energy profile for H transfer from the C3 carbon to the O4
oxygen atom and water formation. The reaction coordinate is the separation between the transferring H atom and the acceptor oxygen O4. (c) Free-energy profile for the third
dehydration. The reaction coordinate is the breaking bond. The process is non-activated and very exothermic. (d) Free-energy profile for proton transfer from the HMF
molecule to a solvent water molecule. (Free energies reported in thermal units, kB T, at T = 363 K.)
Proton (i.e., catalyst) release from HMF back to the solvent is an
activated process, with DF z ¼ 15 kB T (10.8 kcal/mol) and DF ¼
4:3 kB T (3.1 kcal/mol). The relevant pmf is shown in Figure 5d.
3.2. Effects of solvent dynamics
We have already noted instances where solvation dynamics affect the energetics of the reaction. Here, we present a more detailed analysis on select elementary steps where these effects are
more pronounced.
In Figure 6 we have analysed the pmf for the first water removal
into energy and entropy contributions, DF ¼ DU T DS; and the
QM þ DU vdW þ DU q .
thermodynamic energy further as DU ¼ DE
QM is the unbiased conditional expectation of the energy (PM3)
DE
of the system in the QM region—the part of the energy that is calculated quantum mechanically and, in analogy, the energy one
would obtain if there was no solvent in the system and the reaction
was ‘run’ in vacuo. DU vdW is the van der Waals component of the
total energy of the system and includes interactions between the
MM solvent molecules and interactions between the solvent
molecules and the molecules in the QM region. Similarly, DU q denotes the electrostatic interactions.
QM alone, we
Looking at the first dehydration by considering DE
see that it has a high barrier to reaction and is surely endoergic.
The significantly low barrier in DF is primarily due to solvent reorganization. What drives this re-organization is the need of the
system to optimize unfavourably strong Coulomb interactions that
are generated by the charge re-distribution that occurs in fructose
as the C2–O2 is breaking and a water molecule departs. The solvent
re-organization does not appear to be entropically favoured, as we
see the term T DS to rise. It also leads to some solvent ‘packing’
around the fructose molecule, which one infers from the concomitant increase in DU vdW . Thus, the barrier in DF could be characterized as an entropic one. As fragmentation in the gas phase is
entropically favourable, the observed entropic barrier must be
attributed to the presence of the solvent.
The elementary reactions that involve intramolecular hydride
transfer are among the slowest in the mechanism. An analysis of
the free-energy profile for H- transfer from C1 to C2 (3?4 in
Fig. 2) is shown in Figure 7. Here, the reaction proceeds from large
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S. Caratzoulas, D. G. Vlachos / Carbohydrate Research 346 (2011) 664–672
ΔF
ΔU
-T ΔS
ΔEQM
Mulliken partial charges
50
C1
0.4
Energy (kBT units)
ΔUvdW
ΔUq
0
C2
0.2
hydride
0
ring-O
-0.2
O1
-50
-0.4
1
2
1.5
Hydride -- Accepting carbon separation (Å)
1
2
3
4
5
C2--O2 separation (Å)
Figure 6. First dehydration energy profiles. The potential of mean force, DF, is
analysed into thermodynamic energy, DU, and entropy, T DS, contributions. The
QM , and
energy DU is further analysed into the quantum mechanical contribution, DE
the van der Waals, DU vdW , and electrostatic, DU q , interaction energies.
values of the reaction coordinate (H–C2 separation) to small ones
and we clearly see that the free-energy barrier is mostly due to
DU—specifically, the electrostatic component DU q . In fact, the situation appears typical of charge transfer reactions between two redox states with asymmetrical charge distributions (see Fig. 8). In a
hydride transfer, the H atom is carrying an extra electron, which
must transfer from one carbon to another or from one redox state
to another. For that to occur we must first have symmetrization of
the wave function at the transition state or, in other words, the two
localized states (orbitals) situated on the two carbon atoms must
become degenerate, neither preferred energetically. Only then will
the quantum mechanical probability for electron transfer be large.
From the perspective of the solvent, the polar environment
organizes around the asymmetrical charge distribution in such a
way as to give favourable solvation energy. The loss of asymmetry
in the charge distribution will, therefore, be associated with a loss
of that favourable energy. This means that passing from a state in
which electronic charge is localized on one centre to a state where
the charge is distributed over two centres (symmetrization) will be
associated with an increase in energy. The latter, resonating state,
Figure 8. Charge asymmetry between the two stable states in the hydride transfer
described by the step 3?4 of the mechanism.
is the transition state for hydride transfer, and the increase in energy to reach it is the activation energy for the hydride transfer.
Once attained through some random thermal fluctuation of the
environment, the system—reacting fructose plus environment—
can move downhill in energy or free energy either by falling back
to where it started, or by falling towards the other charge localized
state. In the latter case, hydride transfer occurs. So, the hydride
transfer occurs due to environmental fluctuations. The energy required for the transfer must come from the bath—the surrounding
solvent—and it entails a fluctuation of the molecular environment.
It is exactly this temporal re-organization that creates a situation
where the two redox states are degenerate. At such a stage, the
H will resonate between both carbon sites and it will localize
again only after the environment moves towards one of the two
solvated configurations.
The situation is exactly the same in the case of the hydride
transfer in the step 7?8 of the mechanism, which is rate-limiting.
4. Conclusion
We have studied the energetics of the closed-ring mechanism
for the acid-catalysed dehydration of D-fructose to HMF in an aqueous medium by calculating free-energy profiles for all the elementary steps of the reaction. A schematic of the overall energy profile
is given in Figure 9. We have found that the protonation of each of
80
50.0
ΔF
ΔU
-T ΔS
ΔEQM
30.0
ΔF (kcal/mol)
Energy (kBT units)
60
ΔUvdW
40
24.8
40.0
ΔUq
20
(6)
21.2
(8’)
31.8
17.2
(8)
20.0
10.0
0.0
(5)
25.3
-50
-70
(4)
12.8
FRU
6
(2)
(7)
(3, 3’)
-10.0
10.8
-20.0
(9)
0
-20
1
1.2
1.4
1.6
1.8
2
2.2
-30.0
HMF
rxn coordinate
Hydride -- accepting carbon separation (Å)
Figure 7. Energy profiles for hydride transfer (3?4) from C1 to C2, after the first
and before the second dehydration.
Figure 9. Overall free-energy profile for the dehydration of D-fructose to HMF, in
units of kcal/mol. Energy differences are marked in red. Species labelling as in
Figure 2.
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S. Caratzoulas, D. G. Vlachos / Carbohydrate Research 346 (2011) 664–672
the three OH groups of the ring, which initiates the reaction, is
equally likely. However, subsequent removal of the protonated
OH of the C2 carbon is much faster and thermodynamically more
favourable than the removal of the other two during the first dehydration of fructose. If the dehydration is initiated at the OH group
on the C4 carbon, subsequent steps lead either to ring opening or
fragmentation products. For the pathway initiated at the OH on
C2, the second dehydration may be followed either by a hydride
transfer to stabilize the resulting intermediate or a charge transfer,
which leads to fragmentation and release of a formyl group (HCO).
There is a considerable energetic cost to the removal of the first
two water molecules, and the rate of re-hydration is significant, as
can been seen in Figure 9. However, the reaction becomes less
reversible after the second dehydration is complete.
We have found that the proton transfer in 4?5 is substantially
accelerated if it is water-mediated. However, we have also found
that too much water in the vicinity of the transferring proton has
an adverse effect. On the other hand, the proton transfer in 8?80
is not affected by the presence of water. From a micro-kinetic point
of view, the slower steps of the reaction are those that involve
intramolecular hydride transfer. We have shown that the high barriers involved in hydride transfer are due to re-organization of the
polar solvent environment and the solvation of asymmetrical electronic charge distributions. The observed solvent effects are in
agreement with Kuster’s reporting that water displacement (by
polyethylene glycol or other co-solvents) can accelerate the formation of HMF from D-fructose.6
The rate-limiting step is the hydride transfer from the C5 to the
C4 carbon prior to the third dehydration, requiring 31.8 kcal/mol of
activation free energy. This amounts to a CLTST thermal rate
k ¼ ðkB T=hÞ expðDF z =kB TÞ 5:8 107 s1 . Kinetics studies by
Moreau et al. report apparent activation energies of 33.7 kcal/mol
in zeolites.25 Using their value for the Arrhenius pre-exponential
factor, the respective conversion rate constant may be estimated
at 1.5 107 s1, at 363 K. The order of magnitude agreement
is very encouraging.
Finally, according to our calculations, for the overall reaction
DF ¼ 20:5 kcal=mol, at 363 K. We are not aware of any experimental values of the free energy of conversion of fructose to
HMF. Thermochemistry studies by Assary et al. at the G4 theory
level and implicit solvation report DG ¼ 32:4 kcal=mol at 298 K.26
Acknowledgements
We wish to thank Professor Doug Doren for useful discussions.
This work was supported as part of the Catalysis Center for Energy
Innovation, an Energy Frontier Research Center funded by the U.S.
Department of Energy, Office of Basic Energy Sciences under Award
Number DE-SC0001004.
Supplementary data
Supplementary data associated with this article can be found, in
the online version, at doi:10.1016/j.carres.2011.01.029.
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