hydrogen bond interactions between acetone and supercritical water
TRANSCRIPT
Hydrogen bond interactions between acetone and supercritical water
Tertius L. Fonseca,*aKaline Coutinho
band Sylvio Canuto
b
Received 22nd December 2009, Accepted 2nd March 2010
First published as an Advance Article on the web 21st April 2010
DOI: 10.1039/b926527a
Hydrogen bond interactions between acetone and supercritical water are investigated using a
combined and sequential Monte Carlo/quantum mechanics (S-MC/QM) approach. Simulation
results show a dominant presence of configurations with one hydrogen bond for different
supercritical states, indicating that this specific interaction plays an important role on the
solvation properties of acetone in supercritical water. Using QM MP2/aug-cc-pVDZ the
calculated average interaction energy reveals that the hydrogen-bonded acetone–water complex
is energetically more stable under supercritical conditions than ambient conditions and its stability
is little affected by variations of temperature and/or pressure. All average results reported here are
statistically converged.
1. Introduction
The hydrogen bond (HB) is a specific intermolecular inter-
action that plays an important role in many physical
properties of a large variety of molecular systems.1,2 Such
intermolecular forces of attraction are dramatically affected at
high temperature and pressure and results in unusual solvation
properties of water under supercritical (SC) conditions, where
temperature and pressure conditions are higher than 374 1C
and 22 MPa, respectively. For example, changes in the
dielectric constant of water from ambient to SC conditions
make it an excellent solvent for many organic compounds.3–5
Several experimental6–11 and computer simulation (using different
molecular models for water)12–20 studies on the structural
properties of supercritical water have shown that the hydrogen
bonds are still present even at elevated temperatures. With
increasing temperature or decreasing density the tetrahedral
ordering of the water molecules present under ambient conditions
is broken and a substantial amount of hydrogen bonds between
water molecules are disrupted.12 As a result the number of HBs is
smaller than those under ambient conditions. For a better under-
standing of these unusual solvent effects it is very important to
characterize the physical properties of solute–solvent interactions
under supercritical conditions.
In a previous study21 the hydrogen bond strength of an
acetone–water complex in the gas-phase has been calculated using
different correlated ab initio methods and basis sets. The results
showed that the incorporation of high-order electron correlation
effects have little importance for the binding energy of this
complex. The binding energy of the geometry-optimized complex
at CCSD(T)/6-311++G(d) level was estimated to be
5.6 kcal mol�1. Minimum-energy structures lead to a more
attractive binding energy than that obtained for the corresponding
structure in liquid.22 More recently, Takebayashi et al.23 have
analyzed the structural properties of acetone in supercritical water
with respect to the water density. Their results suggest that the
orientation of an acetone–water HB formation is affected by the
tetrahedral HB network between solvent molecules.
In computer simulation studies the identification of the
hydrogen bonds have been based on a geometric12–14,24 or
energetic criterion.15,25,26 Both geometric and energetic criteria
are unambiguously defined at ambient conditions. Kalinichev
and Bass16,17 have employed the above definitions for selecting
hydrogen bonded molecular pairs in supercritical water. Their
results showed that the simultaneous application of both
energetic and geometric criteria represent a very efficient
scheme to select hydrogen-bonded structures.
In this work we study the hydrogen bond strength of an
acetone–water complex in aqueous solution under ambient and
supercritical conditions using sequential Monte Carlo/quantum
mechanics methodology.27–29 We have chosen this complex
because acetone has an important carbonyl group and is stable
in supercritical conditions. MC simulations are performed to
generate the structure of the liquid composed by the solute and
the solvent molecules in thermodynamic equilibrium. Because of
the intrinsic statistical nature of the liquid an appropriate descrip-
tion of solvent effects requires the determination of a representa-
tive number of molecular configurations. After the simulation, the
autocorrelation function of the energy is used to obtain a
sampling of statistically uncorrelated configurations28,29 under
different thermodynamic conditions. We have used geometric
and energetic criteria to select the hydrogen bonded structures
from uncorrelated MC configurations. The interaction energy of
several hydrogen-bonded acetone–water complexes is calculated
using the second-order perturbation theory (MP2) with the
correlation-consistent aug-cc-pVDZ basis set. Important
characteristics of hydrogen bonds such as hydrogen bond length
and strength are addressed in this study.
2. Calculation details
The MC simulations have been performed using the Metropolis
sampling technique30 in the isothermal–isobaric (NPT)
a Instituto de Fısica, Universidade Federal de Goias, CP 131,74001-970, Goiania GO, Brazil. E-mail: [email protected];Fax: +55.62.3512-1014
b Instituto de Fısica, Universidade de Sao Paulo, CP 66318,05315-970, Sao Paulo SP, Brazil
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ensemble. The system consisted of 1 acetone molecule plus
703 water molecules in a cubic box with periodic boundary
conditions. The temperature and pressure of the thermo-
dynamic states of the simulations were chosen in the SC region
of water. The simulated SC states above the critical point of
the water were: P = 340.2 atm and T = 773 K, and
P = 3400.2 atm and T = 673 K. The molecules interact by
the Lennard-Jones plus Coulomb pair-wise potential. The
OPLS parameters were used for acetone31 and the atomic
charges were obtained by electrostatic potential fit (CHELPG)
at the HF/6-3111++G(d,p) level of calculation as implemented
in the GAUSSIAN 03 program.32 The atomic charges and the
Lennard-Jones parameters as well as the MP2/6-311++G(d)
optimized geometric parameters of the acetone are described
and given in ref. 33. For water, we have used the extended
simple point charges (SPC/E) model since it predicts the
critical point with good agreement to the real critical point
of water.34 The cutoff distance in which each molecule interacts
with all other molecules is truncated at half the box length.
Long range electrostatic corrections for the Lennard-Jones
and Coulomb potentials, for separations larger than the cutoff
distance, were calculated using the pair radial distribution
function and the reaction field method with dipole inter-
actions, respectively. In all MC simulations the thermalization
stage of the MC simulation is of 4.2 � 107 MC steps. After
thermalization, 14.1 � 107 MC steps were performed as the
averaging stage of the MC simulation. The average density
calculated during the averaging stage is 0.17 � 0.01 g cm�3
[0.87 � 0.01 g cm�3] at 340.2 atm and 773 K [3400.2 atm and
673 K] conditions. The uncertainties are standard deviations
of the average value. The MC simulation was performed with
the DICE program.35
We have sampled statistically uncorrelated configurations
calculating the interval of statistical correlation using the auto-
correlation function of the energy.28,29 An efficient sampling of
configurations is crucial to assure a fast and systematic
convergence pattern of the average of the QM calculations.
Here we have used intervals in which the selected configurations
have less than 12% correlation. Based on previous
studies22,32,36 100 uncorrelated configurations composed of
acetone–water structures were selected to be used in quantum
mechanical calculations. QM calculations of the hydrogen
bonding interaction in acetone–water complexes were
performed using the MP2/aug-cc-pVDZ method implemented
in the GAUSSIAN 03 program.32 All results presented here
are corrected for basis set superposition error (BSSE) using the
counterpoise method of Boys and Bernardi.37 Our result for
the interaction energy of the optimized acetone–water complex
using the MP2/aug-cc-pVDZ level is 5.99 kcal mol�1, after
correcting for BSSE. This is in very good agreement with the
corresponding result of 5.67 kcal mol�1 obtained with the
CCSD(T)/6-311++G(d) level.21
3. Results and discussion
It is expected that the average number of water molecules
interacting with the acetone under ambient conditions should
be modified in SC conditions. From a microscopic point of
view this is supported, for example, by structural changes on
the radial distribution function (RDF) with increasing
temperature and pressure. In Fig. 1 and 2 the RDF between
oxygen–oxygen, GOO(r), of solute–solvent and solvent-solvent
molecules, are displayed respectively. We have included, for
the sake of comparison, the results for acetone–water GOO(r)
obtained in the SC state of 340.2 atm and 673 K and at the
ambient state of 1 atm and 298 K reported in a previous
work.38 The number of nearest neighbour solvent molecules
around the solute can be obtained from a spherical integration
of the first peak in GOO(r). The first peak in acetone–water
GOO(r) [water–water GOO(r)] is, respectively, centered at
2.75 A [2.75 A], starts at 2.45 A [2.45 A] and ends at 3.20 A
[3.35 A]. In all cases the position of the first peak is not affected
when either temperature or pressure are increased, but the
position of the first minimum in GOO(r)s is slightly shifted
toward larger distances. Thus, the number of nearest water
molecules for acetone and for water presented at the Table 1
was obtained using the integration intervals obtained under
ambient conditions, regardless of the thermodynamic
conditions. Table 1 shows that for both acetone and water
appreciable changes on the average number of nearest neighbours
can be mainly attributed to the increase in temperature rather
than pressure. For example, in comparison with the result at
340.2 atm and 673 K (0.46 � 0.03 g cm�1), the number of
solvent molecules around acetone [water] decreases by 48%
[53%] as the temperature is increased from T = 673 K to
773 K (0.17 � 0.01 g cm�1). In contrast, similar results are
obtained for the corresponding coordination number at
ambient (1.02 � 0.01 g cm�1) and at 3400.2 atm and 673 K
(0.87� 0.01 g cm�3) indicating that the temperature has only a
minor influence at elevated pressures. The distinct second peak
in the water–water RDF GOO(r) is attributed to the tetrahedral
arrangement of hydrogen bonded water molecules at ambient
conditions.12 This peak vanishes with increasing temperature
characterizing the disruption of hydrogen bonds in solvent
molecules, in agreement with previous computer simulation
studies.12,14,18
To take into account the orientation and energetic aspects
of HBs, we have used a geometric–energetic criterion22,29 for
selecting hydrogen bonds between acetone and water molecules
from simulation results. In a systematic study of the hydrogen
bonds in SC water, Kalinichev and Bass16,17 showed that
for most SC states the minimum of the pair-wise energy
Fig. 1 Radial distribution functions between the oxygen atom of
acetone and the oxygen atom of water for different SC states.
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distribution vanishes with increasing temperature and hence
some uncertainties arise with respect to the definition of an
energetic criterion. As small variations in the energetic threshold
value do not quantitatively affect the HB picture, the same
value defined at ambient conditions has been used as an
energetic threshold irrespective of the thermodynamic
state.16,20 Also, for all SC states considered here an energetic
threshold is not well defined and we have adopted 2.7 kcal mol�1,
following previous works.16,20 This energetic threshold value,
obtained from a histogram of pair-wise energy distribution at
ambient conditions, has the same value reported in a previous
MC simulation study.33 Thus, the hydrogen bonds are defined
when the separation ROO r 3.2 A (first minimum of the
acetone–water GOO(r) at ambient conditions), the angle
+O� � �O–H r 301 and the interaction energy is larger than
2.7 kcal mol�1.
Our results for the HB between acetone and water molecules
are also listed in Table 1. The average number of HB was
obtained from 600 uncorrelated configurations. For the sake
of comparison, the results obtained under ambient conditions
and at 340.2 atm and 673 K38 are also included in this table.
The comparison of the results reveals that there are significant
redistributions of the hydrogen bonds with increasing
temperature and pressure. One can see, from inspection of
Table 1, the predominance of structures with one HB.
Furthermore, at 340.2 atm and 773 K the hydrogen bond
pattern is essentially characterized by this type of structure,
emphasizing the importance of this specific interaction on the
solvation of acetone in low density SC conditions. These
results also show, in comparison with the results at ambient
conditions, a remarkable reduction in the structures with two
HBs for all SC states. This suggests that the stability of
configurations with more than one water is further affected
by breaking the hydrogen bond network of solvent molecules.
At 340.2 atm, for instance, the number of configurations with
two [no] HBs decreases [increases] from 8.5% [42%] to 1.6%
[70.8%] with increasing temperature from 673 K to 773 K.
For this highest temperature state, the average hydrogen bond
number is 0.31, 54% smaller than that obtained at 673 K.
Conversely, the large increase in pressure from 340.2 atm to
3400.2 atm at 673 K leads to an increase [decrease] from 8.5%
[42%] to 17.3% [26.1%] in the number of configurations with
two [no] HB. For the highest pressure the average number of
hydrogen bonds is 0.94, representing an increase of 40.3%
when compared with the result obtained at 340.2 atm. Note
that the number of configurations with three HBs, even under
ambient conditions, is very small, being statistically negligible.
Our results are obtained from classical simulation and of
course neglect possible quantum effects. Within these confines
the average number of HBs increases with increasing water
density in agreement with Takebayashi et al.23 at similar
thermodynamic conditions.
As already observed for the hydrogen bond solvation shells,
there are also significant modifications in the different
solvation shells of acetone when the temperature is increased.
The solvation shells for acetone are more appropriately
defined from the radial distribution function between the
center-of-mass, GCM–CM(r), of acetone and water. Fig. 3 shows
the GCM–CM(r) at 340.2 atm and 773 K and at 3400.2 atm and
673 K. For the SC state at 773 K the structures of the solvation
shells are not well defined, indicating that the interactions
between acetone and its shells of neighbouring solvent
molecules are nearly isotropic. Conversely, the increase in
density for the SC state at 3400.2 atm leads to formation of
a first solvation shell, as a direct consequence of interaction of
acetone with the solvent environment. This shell starts at 3.0 A
and ends at 6.1 A. These are the same numbers obtained in a
previous study.38 Thus, the integration of GCM–CM(r) with the
above values at 340.2 atm and 773 K [3400.2 atm and 673 K]
gives 5 [24] water molecules around the acetone as the total
number of solvent water molecules up to the first solvation
shell. For comparison, the corresponding results at 340.2 atm
and 673 K [1 atm and 298 K] using the same geometric limits,
is 14.30 It is interesting to note that the reduced numbers of
solvent molecules in every SC condition, compared to the
Table 1 Coordination number of acetone and water and statistics of hydrogen bonds formed between acetone and water molecules under ambientand different SC conditions. The results for the hydrogen bonds were obtained as an average over 600 uncorrelated configurations
Coordination number 1.0 atm (298 K)a 340.2 atm (673 K)a 340.2 atm (773 K) 3400.2 atm (673 K)
Acetone 2.08 1.03 0.54 1.71Water 4.82 2.47 1.17 4.22Number HB0 1.4% 42% 70.8% 26.1%1 40.3% 49.2% 27.6% 55.1%2 55.2% 8.5% 1.6% 17.3%3 3.1% 0.3% 0% 1.5%hHBi 1.60 0.67 0.31 0.94
a Results obtained from ref. 38.
Fig. 2 Radial distribution functions between the oxygen atoms of
water for different SC states.
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normal case, reflect the ratio between the densities of water in
the different conditions.
We now present the results of the temperature and pressure
effects on the solute–solvent interaction energies obtained
from the classical MC simulations. In Table 2 the MC results
are listed for the solute–solvent interaction energies obtained
at 340.2 atm and 773 K, and 3400.2 atm and 673 K. The
solute–solvent interaction energies are separated into short
and long-range terms. For completeness, the corresponding
results obtained at 340.2 atm and 673 K and 1 atm and 298 K
are also included.38 The table also gives the results for the
short-range solvent–solvent interaction energies. Thus, for the
highest temperature and pressure SC states the average HB
strengths are very similar, with a value of ca. 5.4 kcal mol�1
per hydrogen bond. However, as acetone makes on average
0.31 [0.94] HB at 340.2 atm and 773 k [3400.2 atm and 673 K],
this leads to a total solute–solvent HB interaction of
�1.68 � 1.11 kcal mol�1 [�5.07 � 1.20 kcal mol�1].
In comparison with results under normal conditions, the
stability of the complex in this SC condition is reduced by
ca. 7.28 kcal mol�1 [3.89 kcal mol�1] at 340.2 atm and 773 K
[3400.2 atm and 673 K] with a sizable contribution from the
hydrogen-bond solvation shells. Similarly the long-range
contributions increase this difference, making solute–solvent
interactions more attractive in normal conditions than in
supercritical water. At 340.2 atm and 773 K [3400.2 atm and
673 K], the first solvation shell at R = 6.1 A gives a difference
in interaction energy of ca. 15.26 kcal mol�1 [6.8 kcal mol�1]
while a further extension in the bulk leads to the final
differential interaction energy of 18.17 kcal mol�1
[7.11 kcal mol�1]. It is worth mentioning that there is a clear
correspondence between solute–solvent interaction and water
density. In addition, we have also analyzed the influence of
acetone on the solvent–solvent HB interaction within the
limits of the first solvation shell, computing the difference
between the interaction energies with and without the acetone.
Our findings indicate that the HB interaction among water
molecules is more affected by acetone for the SC state with
3400.2 atm and 673 K. Exception is made for NC in which the
water molecules form a tetrahedral HB network, this latter result
is consistent with the formation of a first solvation shell around
acetone observed for the highest pressure state (see Fig. 2).
Now we focus on the quantitative estimate of the short-
range solute–solvent interaction energy using QM treatment,
with inclusion of electron correlation effects. MP2/aug-cc-
pVDZ results of the interaction energy between acetone and
one water molecule at ambient and SC conditions as function
of average density are presented in Fig. 4. All results are
corrected for BSSE and the uncertainties are statistical errors
of the average value. The MP2 results show that either at
ambient or SC conditions the energy of the complex is always
negative, indicating that hydrogen bond formation is exothermic,
as seen also in the classical analysis above. The complex at
340.2 atm and 673 K is found to be the most stable with an
Table 2 MC simulation energy results for hydrogen bond, solute–solvent interaction (ESX) and solvent–solvent interaction (ESS). All results are inkcal mol�1.
Interaction energy P = 1.0 atm (T = 298 K)a P = 340.2 atm (T = 673 K)a P = 340.2 atm (T = 773 K) P = 3400.2 atm (T = 673 K)
EHBSX per HB �5.60 � 1.23 �5.64 � 1.12 �5.42 � 1.11 �5.39 � 1.20
EHBSS per HBb �5.07 � 1.02 �4.76 � 1.00 �4.66 � 0.91 �4.85 � 0.97
EHBSS per HBc �4.50 � 1.58 �4.08 � 1.68 �3.90 � 1.72 �3.85 � 1.89
EHBSX �8.96 � 1.23 �3.78 � 1.12 �1.68 � 1.11 �5.07 � 1.20
E1st ShellSX
d �19.93 � 1.51 �9.73 � 1.54 �4.67 � 1.68 �13.13 � 1.47
EBulkSX
e �24.13 � 3.39 �11.39 � 4.14 �5.96 � 3.72 �17.02 � 4.51
a Results for solute–solvent interaction energies were obtained from ref. 38. b Results obtained from MC simulations using 704 water molecules.
The hydrogen bonds were selected using ROO r 3.2 A, the angle+O� � �O–Hr 301 and the interaction energy is at least 2.7 kcal mol�1. c Effect of
acetone on the HB energy computed with respect to the first solvation shell. d The first solvation shell has 5 [24] water molecules at 340.2 atm and
773 K [3400.2 atm and 673 K] (within a spherical radius of 6.1 A [6.1 A]). e The total solvation shell has 326 [360] water molecules at 340.2 atm and
773 K [3400.2 atm and 673 K] (within a spherical radius of 23.77 A [14.51 A]).
Fig. 4 Average interaction energy of acetone–water complexes for
different SC states as a function of the water density. Uncertainty is the
statistical error.
Fig. 3 Radial distribution functions between the centers-of-mass of
acetone and water for different SC states.
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interaction energy of �3.02 kcal mol�1 whereas the less stable
complex is found under normal conditions with an interaction
energy of �2.51 kcal mol�1 (see Table 3). The small differences
between these energy values indicate that the stability of the
complex at SC conditions is not much affected by variations of
temperature and/or pressure. We have a slight increase in the
interaction energy with increasing water density as compared
with the corresponding result at 340.2 atm and 673 K. For the
highest density states [0.87 � 0.01 and 1.02 � 0.01 g cm�3] the
small energy difference is estimated to be only 0.07 kcal mol�1
(much smaller than the statistical error). On the contrary, on
going to the highest temperature state the increase in thermal
motion of the molecules leads to a slight increase in the energy
even at lower water density. These findings are in general
agreement with the results at similar SC conditions but they
are in contrast with the positive interaction energy predicted at
ambient conditions.23
As the stabilization of a solute in polar solvent is dominated
by the dipole moment of solute, we have calculated, in
addition, the dipole moment of the hydrogen-bonded
acetone–water complexes. MP2/aug-cc-pVDZ results for the
average dipole moment and the total solute–solvent HB inter-
action are also given in Table 3. The total interaction energies
were obtained using the average number of HBs of
each thermodynamic condition. The MP2 model predicts a
solute–solvent interaction that is more attractive under normal
than SC conditions and that its stability is more affected with
increasing temperature, in overall agreement with the results
obtained using the classical MC analysis. For the highest
temperature SC state, for instance, the stability of the complex
is reduced by ca. 3.15 kcal mol�1, compared to results in
normal conditions. Minimum-energy structures have a larger
binding energy than that obtained for the corresponding
structure in liquid.21 In this case, the MP2 predictions for
HB interaction strength are around of 50% smaller than those
obtained classically (see Table 2). Surprisingly, the classical
results for HB interaction are in very good agreement with the
MP2 binding energy of the geometry-optimized complex
estimated to be 5.99 kcal mol�1. Additionally, the results for
the dipole moment at different thermodynamic conditions are
also consistent with those obtained for solute–solvent inter-
action energy. The largest dipole moment is predicted for the
hydrogen-bonded complex at 1 atm and 298 K, indicating that
it should be more stable in the normal than in the SC
conditions. Statistically converged results for the calculated
interaction energy at ambient and at 340.2 atm and 673 K as a
function of the number of configurations used to obtain the
average, are displayed in Fig. 5. This illustrates the fast
convergence pattern of the average properties considered here.
4. Conclusions
Hydrogen bond strength of acetone–water complexes in super-
critical water have been studied using isothermal-isobaric
Metropolis Monte Carlo simulations and quantum mechanical
calculations based on the MP2/aug-ccpVDZmethod. Statistically
uncorrelated liquid configurations were sampled using the
autocorrelation function of energy. A detailed analysis of the
hydrogen bond data was obtained using an energetic–
geometric criterion. Simulation results showed that significant
modifications in the number of solvent molecules as nearest
neighbours around acetone or around water are related to the
increase in temperature at low-density SC states. Changes in
the temperature have only a minor influence on these
coordination numbers at high-pressure conditions. The
hydrogen bond data showed a clear predominance of structures
with one hydrogen bond for different SC states, emphasizing
the importance of the hydrogen bond interaction involving
acetone and one water molecule on the solvation of acetone in
SC conditions, mainly at high temperature and low density.
MP2 interaction energy results showed that the formation of
an acetone–water complex is exothermic and its stability is
little affected by variations of temperature and/or pressure,
being more favorable at SC conditions rather than at ambient,
by a very small amount – ca. 0.5 kcal mol�1.
Acknowledgements
This work has been partially supported by CNPq, CAPES and
FAPESP (Brazil). T. L. F. thanks FAPESP for providing
financial support that made possible his visit to the Institute of
Physics, USP.
Fig. 5 Statistical convergence of the interaction energy of
acetone–water complexes in normal (1.0 atm and 298 K) and SC
conditions (340.2 atm and 673 K). Uncertainty is the statistical error.
Table 3 MP2 results for average solute–solvent interaction (ESX) (kcal mol�1) and dipole moment (Debye) of acetone–water complexes indifferent SC states. Uncertainty is the statistical error
Interaction energy P = 1.0 atm (T = 298 K)a P = 340.2 atm (T = 673 K)a P = 340.2 atm (T = 773 K) P = 3400.2 atm (T = 673 K)
EHBSX per HB �2.51 � 0.15 �3.02 � 0.15 �2.79 � 0.17 �2.58 � 0.16
EHBSX �4.02 � 0.15 �2.02 � 0.15 �0.87 � 0.17 �2.43 � 0.16
Dipole Momentm 4.76 � 0.07 4.60 � 0.08 4.46 � 0.08 4.63 � 0.08
a Results obtained from ref. 38.
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