Statistical Mechanics-Based Theoretical Investigation of Solvation

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Statistical Mechanics-Based Theoretical Investigation of Solvation Effects on Glucose Anomer Preferences Arifin *, Daisuke Yokogawa, Udo Schnupf, and Stephan Irle J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b10270 • Publication Date (Web): 07 Dec 2017 Downloaded from http://pubs.acs.org on December 8, 2017

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The Journal of Physical Chemistry

Statistical Mechanics-Based Theoretical Investigation of Solvation Effects on Glucose Anomer Preferences Arifin†‡, Daisuke Yokogawa*†‡, Udo Schnupf,§ Stephan Irle*†‡ †

Department of Chemistry, Graduate School of Science, Nagoya University, Chikusa, Nagoya 464-8601, Japan

‡

Institute of Transformative Bio-Molecules (WPI-ITbM), Nagoya University, Chikusa, Nagoya 464-8602, Japan

§

Mund-Lagowski Department of Chemistry & Biochemistry, Bradley University, Peoria, IL 61625, USA

AUTHOR INFORMATION Corresponding Authors *Phone: +81-52-747-6397. E-mail addresses: [email protected] (D. Yokogawa); [email protected] (S. Irle)

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ABSTRACT The importance of solvation effects on the stability of the glucose anomers have been studied by the combination of quantum mechanics (QM) and statistical mechanics, namely the reference interaction site model self-consistent field spatial electron density distribution (RISM-SCF-SEDD). The preferences of α- and β-glucose in H2O are well reproduced with the obtained ratio was 35:65 for α- and β-glucose, respectively. Indirect interactions and bulk effects, described by Onsager model, are relatively small compared to the direct solutesolvent interactions, especially in [DMIM]Cl and DMSO. From the decomposition of solvation free energy and solvation structures, it is can be seen that the interactions with the solvent molecules greatly contribute to the anomer preferences.


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INTRODUCTION Solvation effects are fundamental and may exert important contributions to the chemical reactivity, such as interchange in frontier molecular orbitals.1 Related to the contribution of direct and indirect solute-solvent interactions to the solvation effects, the currently held idea is that direct, specific interactions can be effectively described by supermolecule calculations involving a solute surrounded by a number of explicitly treated solvent molecules, whereas continuum methods generally describe indirect electrostatic interactions.2 Recently, solvation effects have been studied in many areas of physical chemistry, e.g. nuclear shielding,3 solvatochromic properties,4 charge-transfer process,5 chemical reaction and equilibria.6 It is well-known that the thermodynamics properties and stabilities in gas phase of the molecules, e.g. glucose7,8 and glycine9, are greatly effected by introducing solvation effects. Thus, advances in experimental technologies and theoretical models on solvation effects are in great demand to gain a more comprehensive understanding of their effects. Glucose, as one of the most abundant monosaccharides, is gaining more interest in recent times due to its potential use as feedstock for sustainable chemical processes. 5hydroxymethylfurfural (HMF), as one of the dehydration product of glucose, is considered to be one of the key intermediates to produce the many value added chemicals and alternative fuels. The dehydration of glucose has been reported to occur in acidic aqueous solution10–12 or organic solvents.13,14 Recently, several types of ionic liquids (ILs), such as imidazolium salts, show great potential to process glucose effectively.15–17 It is expected that the study of the effects of solvents will greatly accelerate the optimization of this chemical process in the future. However, there are only few studies that focused on the solvation of glucose in ILs and other solvents at the molecular or atomistic level.18–20 The anomeric center is critical to determine the reactivity of carbohydrates, e.g. specific enzymatic phosphoglucose isomerase which preferentially reacts on the α-pyranose isomer.21


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Therefore, the structural properties of glucose in aqueous phase and many other solvents have been studied during the past few decades. It is well known that the ratio between α-glucose and β-glucose is 36:64 and 45:55 in aqueous solutions and dimethylsulfoxide (DMSO), respectively.8,22–26 On other hand, Zhao et al. observed that the α-anomer is dominant when glucose is dissolved in the ionic liquid 1-ethyl-3-methyl imidazolium chloride ([EMIM]Cl).15 Molteni et al. have theoretically investigated the structural aspects of the anomeric equilibrium in aqueous solution and evaluated the hydrogen bonds between glucose and solvent molecules by a molecular dynamics (MD) study.27 Youngs et al. have performed comprehensive MD studies about the β-glucose solvation structures and its conformations in 1,3-dimethyl imidazolium chlorides ([DMIM]Cl).19,20 However, the main reason of anomer preference in different solvents is still not completely understood. One of the standard approaches to analyze the solvent effects is based on the dielectric continuum model. In this model, the solvation effects are estimated by considering the interaction of the dipole moment of the solute with the reaction field, where the solute is placed in a spherical cavity of continuous medium with a dielectric constant ε.28 This approach treats the bulk solvation effect very well, but not adequately treated the specific interactions between solute and solvent molecules. An alternative method to study the solvation effects is the so-called “reference interaction site model” (RISM),29,30 which uses integral equation theory based on the statistical mechanics for molecular liquids. RISM requires the same initial input data and produces data such as radial distribution functions similar as in standard MD simulation methods, however with great reduction in computational cost. Furthermore, RISM considers an infinite number of solvent molecules and requires no ‘simulation box’ for periodic boundary conditions. In a sense, RISM can treat the short-range direct interactions excellently. In addition, this method has already successfully been applied to investigate the preferences of glucose and 4,6-dimethyl-2-


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methoxytetrahydropyran in aqueous solutions.26,31 It was noted in previous works that the thermodynamic stability of saccharides is generally very small, thus, both high accuracy and consideration of a large number of conformational degrees of freedom are required in theoretical studies at the same time.26 A hybrid method between quantum chemical (QM) and RISM was recently developed by Yokogawa et al.,

32–34

combining RISM with a self-

consistent field spatial electron density distribution (RISM-SCF-SEDD). This method improves the accuracy of conventional RISM-SCF33,35 at the quantum level with reasonable computational cost. RISM-SCF-SEDD has already successfully been applied for the study of Diels-Alder36 and SN2-type reactions,37 cellobiose hydrolysis,38 and glucose transformation to HMF in aqueous and ILs solvents.39 In the present study, we applied the dielectric continuum model and RISM-SCF-SEDD solvation theory to investigate the direct and indirect solvation effect on glucose anomer preferences. Our investigation will allow for a more comprehensive understanding of the those solvent effects.

COMPUTATIONAL DETAILS In RISM-SCF(-SEDD), the free energy of a system (∆) is defined as,32–34 ∆ = + + ∆ . (1)

is the energy of the solute from ab initio MO theory,

= Ψ ||Ψ , (2)

where Ψ stands for the wavefunctions in gas phase. As Eq. 1 was used to obtained the free

energy Δ, it has to be noted that the entropy contribution to Δ is obtained via normal mode

analysis ( ), based on the harmonic approximation.40–42 ∆ is free energy change by the solvation. There are two terms in ∆ , which given given by33,38 ACS Paragon Plus Environment

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1 ∆ = −

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1 & 1 (")Θ(−ℎ (")) + ℎ (")$ (")* + + , (3) !" #$ (") − ℎ 2 2

where is the number of density of solvent site - and = /

.

01

. 23 is the Boltzmann

constant and T is the temperature. Θ is the Heaviside step function. ℎ (") and $ (") are

respectively total and direct correlation functions between site 4 (in solute) and - (in

5678 solvent). The first term in Eq. 3 is the solvation free energy (Δ ) computed by RISM

theory coupled with Kovalenko-Hirata (KH) closure.43 + is the addition energy of the solvation effects to the electronic structure of the solute molecules,

+ = 9Ψ ::Ψ ; − , (4)

where Ψ is corresponds to the wavefunctions in the solution phase.

In a previous study of the structure/energy relationship between glucose conformations,

489 optimized structures were investigated by B3LYP in gas phase.8 Using those structures as starting points, we calculated the energy of the solvated structures by the RISM-SCFSEDD solvation model at the B3LYP/6-31+G* level of theory and selected nineteen lowenergy confirmations (relative energy < 5 kcal/mol), of which twelve and seven structures are correspond to α- and β-glucose respectively. These structures were further optimized in each solvent by the RISM-SCF-SEDD-DFT at the same level of theory. As representative weakly and strongly interacting solvents, we selected acetone (Me2CO), acetonitrile (MeCN), dimethylsulfoxide (DMSO), water (H2O), and [DMIM]Cl as a model for ionic liquids.36–38 The single point energies were calculated by employing the gold-standard of in quantum chemistry, known as coupled cluster single, double, and pertubative triple excitation CCSD(T), with Dunning type basis set aug-cc-pVDZ to achieve better accuracy. The initial structures and Lennard-Jones parameters44,45 of solute and solvents for the RISM calculations


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are given in the Supporting Information. All calculations were performed with a modified GAMESS-US program package.46

RESULTS AND DISCUSSIONS Most stable conformations The most stable structures obtained by RISM-SCF-SEDD are illustrated in Figure 1. The structures of α- and β-glucose in the gas phase and Me2CO are similar; all possess ‘r’-gg (gauch+) conformation and optimized from A12 and B1 for α- and β-glucose, respectively. In MeCN, α-glucose with ‘r’-gt (gauch-) (A7) structure becomes slightly more stable than A12 by 0.2 kcal/mol (see Table 1). Interestingly, when solvated in Me2CO and MeCN, the hydroxyl groups still keep the intramolecular interactions and the structures still able to be designated as ‘c’ or ‘r’ conformations. In contrary, the orientations of hydroxyl groups are oriented outside to face the solvent molecules in DMSO, H2O, and [DMIM]Cl. This is one indication that the solvation effects are getting stronger for those solvents. Furthermore, the most stable structures in [DMIM]Cl and DMSO are very much alike, suggesting a the similarity in the solvent effects.

Relative free energy Table 1 summarizes the relative free energy of glucose conformations relatively to the most stable conformation in each solvent =ΔΔ>,? B . The free energy differences for some @,A

conformations of glucose are relatively small (less than 2 kcal/mol). To better represent the

properties of all low energy structures we computed the effective physical properties (C+DD ) with the following equation,


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Figure 1. The most stable structures of glucose in different solvent. The label names are based on initial geometries before optimization (see Supporting Information). C+DD = C> @,A

where R is the gas constant. C>

@,A

>O.

@,A

E

e

G

K,L

HHIJ M1

∑>O. e

G

K,L

HHIJ M1

P , (5)

and ΔΔ> are the calculated physical values, e.g. dipole @,A

moment ( R ), and the relative free energy of each conformer i for α- and β-glucose,

respectively. This also allows the relative free energy between α- and β-glucose to be defined @→A

in the effective manner (ΔΔ+DD ).

The experimental dielectric constants (T) and ΔΔ+DD

@→A

values with the percentage of α-

glucose in gas phase and other solvents obtained from our calculations are given in Table 2. It shows that α-glucose is more favorable in gas phase, Me2CO, MeCN, DMSO and [DMIM]Cl, and that the β-anomer is more stabilized in H2O. The calculated ratio of α- and β-glucose in H2O (35:65) is reasonably agreed well with previous works (38:62),8,22–26 with the difference is 3%. In the case of DMSO, stability of α-glucose is overestimated by RISM-SCF-SEDD. The experimental observed % α-glucose in DMSO are between 38-46%, which corresponds to -0.1 kcal/mol,23,25 where the calculated ΔΔ+DD

@→A

value is 1.4 kcal/mol. However, it was


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Table 1. Relative free energy at RISM-SCF-SEDD-CCSD(T)/aug-cc-pVDZ//B3LYP/631+G* level of theory for each conformations relatively to the most stable conformation in each solvent. Structures that have imaginary frequencies or large conformational similarity are excluded in calculations of effective properties. All energy values are given in kcal/mol. Gas

Me2CO

MeCN

H2 O

[DMIM]Cl

A1

0.6

1.0

1.9

0.2

5.5**

4.0**

A2

1.6

1.6

1.2

1.3*

0.0

0.0

A3

1.9

1.9

1.2

1.2

0.1**

0.1**

A4

4.6

4.3

3.0

0.5

5.7

4.6

A5

2.2

2.4

2.6

0.6

7.7

6.1

A6

2.4

2.1

1.1

1.7

3.0

5.8**

A7

0.5

0.9

0.0

1.6

2.8

2.3

A8

1.8

1.8

1.2

1.5

3.1**

5.8

A9

3.4

3.5

3.0

N/A

8.0

4.9

A10

1.7

2.3

3.1

0.8

7.5

5.8

A11

0.9

1.1

1.6

2.2

2.2

1.8

A12

0.0

0.0

0.2

1.1

5.2

3.5

B1

1.0

1.1

0.7

0.0

3.8

2.3

B2

3.1

3.3

2.2

0.1

9.5

3.2

B3

4.0

3.9

1.6

1.0

1.8

1.3**

B4

1.4

1.8

1.2

1.5

2.8

2.3

B5

2.5

2.9

2.5

2.8*

4.7

4.0

B6

3.4

3.4

1.8

0.6

2.3**

1.2

B7

1.7

2.1

1.3

0.5

3.0

1.6

Initial

DMSO

* Structure possesses one imaginary frequency in semi-numerical normal mode analysis. ** The structure is similar with other conformations in the same solvent.


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Table 2. Experimental dielectric constants (T), relative free energy between α- and β-glucose @→A

(ΔΔ+DD ) and the percentage of α-glucose in gas phase and other solvents obtained from our calculations. All energy values are given in kcal/mol.

U

VVWXYY

%α

0.8

80

15.0a

2.0

95

Me2CO

20.5

0.9

83

MeCN

35.7

0.7

76

DMSO

46.8

1.4

92

H2 O

78.4

-0.4

35

Solvent Gas phase [DMIM]Cl

a

Z→[

1

Reference 47

noted that the mutarotation reaction of glucose in DMSO is slow; hence the equilibration is difficult to be achieved.23,25 The stabilizations of α-glucose is greatly enhanced in ILs, which result the % α-anomer to 95%. Unfortunately, the published quantitative experimental mutarotation data of glucose in other than H2O and DMSO are not available. It is interesting to note that in the case of acetone, acetonitrile, and H2O, % α-glucose and static dielectric constant of the solvents are inversely proportional, which indicates that solvent effects are an important factor to determine the preferences of glucose anomeric ratios.


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Direct and indirect solvation effects To probe the importance of the solvation, we decomposed ΔΔ+DD

@→A

obtained from our

calculations into direct and indirect parts by employing the classical Onsager reaction field model; the simplest and widespread used approach to estimate the free energy of solvation. In this model, it is possible to estimate the effects of solute-solvent electrostatic interactions to the stabilization of an anomer. The Onsager solvation free energy change ΔΔ\] is given @→A

by48

ΔΔ\] = − @→A

1 ( T ` − 1) & (R − R@& ). (6) ^_ (2T` + 1) A

RA and R@ are the scalar values of dipole moment of α-and β-glucose, respectively. ^

corresponds to the radius of the spherical cavity of glucose obtained by Gaussian 09 program

package.49 The value of ^ was 8.3 a.u. The decomposition of ΔΔ+DD

@→A

into the solute energy Δ

@→A

, thermal corrections

Δ , and solvation free energy ΔΔ are given in Table 3. Without solvation, Δ @→A

@→A

@→A

between glucose anomer is 1.4 kcal/mol. The solvation effects in Me2CO are very small and the contributions from the solute and thermal corrections are similar to the gas phase energies. In MeCN, the difference of Δ

@→A

between glucose anomers is the largest. The differences in

decomposed energies between α- and β-glucose in H2O are small and the thermal corrections

contributes the most with -0.8 kcal/mol. Interestingly, ΔΔ in DMSO and [DMIM]Cl are @→A

large compare to the other solvents with 3.1 kcal/mol. ΔΔ\] values (listed in Table 3) are @→A

the lowest for Me2CO, MeCN and H2O, ranging between -0.1 to -0.3 kcal/mol. This suggests that the bulk electrostatic polarization effects are similar between α-glucose and β-glucose in

those solvents. The ΔΔ\] energies having the negative values in all solvents which @→A


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Table 3. The decomposition ΔΔ+DD

@→A

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into the solute energy Δ

@→A

, thermal corrections

Δ , solvation free energy ΔΔ . ΔΔ\] and the subtraction of this energy from @→A

@→A

@→A

ΔΔ were also listed. All energy values are given in kcal/mol. @→A

Solvent Gas phase

Vbc

Z→[

1.4

VWdee" Z→[

-0.5

VVWfeg

VVWhif

Z→[

Z→[

0

0

VVWfeg − VVWhif Z→[

Z→[

0

[DMIM]Cl

0.2

-1.2

3.1

-1.0

4.1

Me2CO

1.3

-0.3

-0.1

-0.1

0.0

MeCN

1.9

0.0

-1.1

-0.3

-0.8

DMSO

-0.5

-1.1

3.1

-0.7

3.8

0.2

-0.8

0.2

-0.3

0.5

H2 O

correspond to the stabilization of β-glucose. As ΔΔ\] corresponds to the indirect solvation @→A

effects, the difference between ΔΔ and ΔΔ\] is an estimate for the solvent effects @→A

@→A

through the direct site-specific interactions between solute and solvents. For [DMIM]Cl and DMSO, the values are 4.1 and 3.8 kcal/mol, which represent a remarkably large stabilization of α-glucose. It shows there should exists an important interactions between solute and solvent molecules, especially in DMSO and [DMIM]Cl, that strongly influence the stability of the α-glucose.

Solvation free energy and reorganization energy The decomposition of solvation effects ΔΔ

@→A

5678 to solvation free energy ΔΔ and

reorganization energy Δ + (Eq. 4) is given in Table 4. From this decomposition, we can ACS Paragon Plus Environment

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5678 and reorganization Table 4. The decomposition of ΔΔ to solvation free energy ΔΔ @→A

energy Δ + . All energy value are in kcal/mol. Solvent [DMIM]Cl

5678 ΔΔ

5.7

Δ +

-2.6

Me2CO

-0.1

0.0

MeCN

-1.3

0.2

DMSO

5.6

-2.5

-0.8

1.0

H2 O

5678 clearly see that the contributions from ΔΔ are larger than Δ + in most solvents. In

5678 [DMIM]Cl and DMSO, ΔΔ are greatly stabilize the α-glucose, that resulting to the

preferences of α-glucose in those solvents. Thus, we focused on DMSO and [DMIM]Cl in the

latter discussion. In addition, it is interesting to note that there is an inverse correlation

5678 between ΔΔ and Δ + . It suggests that stronger solute-solvent interactions lead to a

larger reorganization of the gas phase electronic structures.

Additional insight can be gained by decomposing the solvation free energy into the contribution of each solute site u, which is formally given by 5678 Δ

j

= Δ , (7) O.

where n is the total number of atomic sites or groups. Figure 2 shows the definition of each atomic group in glucose, labeled A-E. Table 5 summarizes the difference of the solvation @→A

free energy between α- and β-glucose on each group (ΔΔ

).


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Figure 2. Definition of atomic group labels (A-E) in glucose, with the label of hydrogen (Hu) and oxygen (Ou) atoms in hydroxyl group in D group. 5678 Table 5. Decomposition of effective solvation free energy ΔΔ . The label of atomic

groups are shown in Figure 2. All energy values are given in kcal/mol.

VVWc

Z→[

Atomic group

[DMIM]Cl

DMSO

A

-2.5

-1.6

B

2.6

0.8

C

-3.0

0.1

D

6.1

4.7

E

2.5

1.6

From the decomposition analysis, ΔΔ

@→A

values from A group are negatively large in

both solvents. This suggests that the solvent-solute interactions at A site are crucial to stabilize β-glucose. Furthermore, ΔΔ

@→A

energies from D are notably large. As the

stabilizations of D group are important to enhance the stabilization of α-glucose, we will focus on the solvation structure at D sites. We demonstrated the investigation of the solvation structures around D group label only in [DMIM]Cl because the solvation effects in


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[DMIM]Cl and DMSO are similar. The relative free energies between the metastable molecules are large in [DMIM]Cl, so the properties dominantly originated from the most stable conformations. We further investigated the Ou and Hu site in Figure 2 because it has largest contributions in D group site to the stabilization of α-glucose in [DMIM]Cl (see Supporting Information). The radial distribution functions (RDFs) for Ou and Hu sites with the chloride anion site (Clv) and the positively charged carbon site (CRv) in [DMIM]Cl are plotted in Figure 3(a). The peaks in those RDFs are correlated to the site-specific interactions between solute site and solvent site; the peak intensities indicate the interactions between sites. The differences between RDFs of α- and β-glucose are defined as

Δl(") = lβ (") − lα ("). (8)

The peak of Hu-Clv of α-glucose is slightly higher around 1.9 Å (see Figure 3(b)), then dominated by higher peak of β-glucose at 2.2-5.5 Å. The interaction Ou atom label with Clv site in [DMIM]Cl at around 3.1 Å to 4.9 Å are more intense in the case of β-glucose. The OuClv interactions in α-glucose are lower due to the fluctuations of solvent molecules around D sites, which correspond to the broader peak in RDFs. Thus, it is understandable that the large destabilization of β-glucose on the D group comes from the higher repulsion between Ou label atomic sites with the chloride anions. In addition, specific interactions between oxygen Ou and positively charge CRv site at short-range are stronger for α-glucose, which further stabilize D group label in glucose. It shows that the interactions with both anions and cations in [DMIM]Cl are strongly influence the glucose anomer preferences. The interactions between glucose and the solvent molecules are illustrated in Figure 3(c). In strongly interacted solvents, for example [DMIM]Cl, direct mutual interactions between two hydroxyl groups and one solvent molecules are more favorable. These interactions not only increase the attractive interactions, e.g. hydrogen and anions, but also intensify the repulsive


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interactions, e.g. anions and the neighboring oxygen in hydroxyl groups. Thus, the balances between attractive-repulsive interactions are critical to determine the stabilization of glucose.

Figure 3. (a) Radial distribution functions (RDFs) of α- and β-glucose on Hu and Ou atomic sites with the Clv and CRv site in [DMIM]Cl. The solid and dashed lines correspond to the RDFs of α- and β-glucose respectively. (b) The difference of RDFs of α- and β-glucose. (c) Illustrations of interactions between glucose and solvents molecules in [DMIM]Cl.


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CONCLUSION The present work demonstrates the importance of solvation effects to the determination of the preferences of α- and β-glucose in different solvents. Interaction between hydroxyl groups and solvent molecules are critical to determine the stable conformations in each solvent. Very stable structures have been found in Me2CO and MeCN, which keep intramolecular interactions between hydroxyl groups compared to the gas phase. On the contrary, the orientations of hydroxyl groups are oriented outside to face the solvent molecules in DMSO, H2O, and [DMIM]Cl which implies that the solvation effects are stronger than Me2CO and MeCN. Looking at the of energies, the calculations at CCSD(T)/aug-cc-pVDZ level of theory greatly reproduce the stability of glucose anomers in H2O with the ratio is 35:65 for α- and βglucose respectively and difference with the experimental value is only 3%. Energy decomposition analysis shows the importance of indirect and direct solvent effects. The indirect bulk electrostatic polarizations effects are described by classical Onsager model. Although this effect is relatively small, it showed that ΔΔ\] corresponds to the @→A

stabilization of β-glucose. On the hand, site-specific direct interactions show strong influence to the stabilization of α-glucose, especially in [DMIM]Cl and DMSO by 4.1 and 3.8 kcal/mol, respectively. Analysis of the site-site interaction contributions and solvation structures show the important insight that the interactions with the solvent molecules greatly contribute to the anomer preferences. In summary, the results show that the study at the molecular level is fundamentally important to achieve deeper understanding of anomeric preferences in many solvents. In the future, we plan to investigate the anomer preference of other glucose epimers, which will significantly assist in the industrial applications of biomass.


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ASSOCIATED CONTENT Detailed information on the initial structures, Lennard-Jones parameters of solute and solvents, and decomposition of solvation energy. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Authors *Phone: +81-52-747-6397. E-mail addresses: [email protected] (D.Y.); [email protected] (S.I.). Present address: Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 U.S.A. (S.I.).

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT The authors thank the G30 Program Nagoya at University supported by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) and the Nagoya University Program for Leading Graduate Schools-Integrative Graduate Education and Research (IGER) Program in Green Natural Science for the financial supports. D.Y. thanks the Grant-in-Aid for Young Scientists B (No. 24750015) and Scientific Research (c) (No. 15K05385).


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TOC GRAPHICS


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The most stable structures of glucose in different solvent. The label names are based on initial geometries before optimization 221x89mm (300 x 300 DPI)


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Definition of atomic group labels (A-E) in glucose, with the label of hydrogen (Hu) and oxygen (Ou) atoms in hydroxyl group in D group. 94x88mm (300 x 300 DPI)



(a) Radial distribution functions (RDFs) of α- and β-glucose on Hu and Ou atomic sites with the Clv and CRv site in [DMIM]Cl. The solid and dashed lines correspond to the RDFs of α- and β-glucose respectively. (b) The difference of RDFs of α- and β-glucose. (c) Illustrations of interactions between glucose and solvents molecules in [DMIM]Cl. 88x178mm (300 x 300 DPI)


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Statistical Mechanics-Based Theoretical Investigation of Solvation

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