hydrogen bond interactions between acetone and supercritical water

6
Hydrogen bond interactions between acetone and supercritical water Tertius L. Fonseca,* a Kaline Coutinho b and 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 experimental 6–11 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 study 21 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 geometric 12–14,24 or energetic criterion. 15,25,26 Both geometric and energetic criteria are unambiguously defined at ambient conditions. Kalinichev and Bass 16,17 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 configurations 28,29 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 technique 30 in the isothermal–isobaric (NPT) a Instituto de Fı´sica, Universidade Federal de Goia ´s, CP 131, 74001-970, Goia ˆnia GO, Brazil. E-mail: [email protected]; Fax: +55.62.3512-1014 b Instituto de Fı´sica, Universidade de Sa ˜o Paulo, CP 66318, 05315-970, Sa ˜o Paulo SP, Brazil 6660 | Phys. Chem. Chem. Phys., 2010, 12, 6660–6665 This journal is c the Owner Societies 2010 PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics Published on 21 April 2010. Downloaded by Central Michigan University on 29/10/2014 13:37:08. 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Page 1: Hydrogen bond interactions between acetone and supercritical water

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

6660 | Phys. Chem. Chem. Phys., 2010, 12, 6660–6665 This journal is �c the Owner Societies 2010

PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics

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Page 2: Hydrogen bond interactions between acetone and supercritical water

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.

This journal is �c the Owner Societies 2010 Phys. Chem. Chem. Phys., 2010, 12, 6660–6665 | 6661

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Page 3: Hydrogen bond interactions between acetone and supercritical water

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.

6662 | Phys. Chem. Chem. Phys., 2010, 12, 6660–6665 This journal is �c the Owner Societies 2010

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Page 4: Hydrogen bond interactions between acetone and supercritical water

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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Page 5: Hydrogen bond interactions between acetone and supercritical water

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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