Conformer Selection Upon Dilution with Water: The Fascinating Case of Liquid Ethylene Glycol Studied via Molecular Dynamics Simulations

Abstract

The aqueous solution of ethylene glycol (EG) is a binary liquid mixture that displays rich conformational and structural behaviour, which has not yet been adequately explored through atomistic molecular dynamics simulations. Herein, employing an accurate force field for EG, several physical properties of this solution are calculated to be in quantitative agreement with experimental data. While 79 % of molecules in neat liquid EG exist with their central OCCO dihedral in the gauche state, this fraction increases to 89 % in the dilute aqueous solution, largely in response to the increase in the static dielectric constant of the solution from that of neat liquid EG. The increase in gauche conformers increases the mean dipole moment of EG molecules in the solution which is additionally contributed by specific conformational states of the two terminal HOCC dihedral angles.

How does the polarity of an aqueous solution affect the molecular conformation of a solute? Molecular dynamics simulations show that the dipole moment magnitude of a small, yet conformationally rich molecule, ethylene glycol, increases upon its dilution in water, enabled by changes in its conformer populations. The fraction of ethylene glycol molecules with their central OCCO dihedral in gauche conformation increases from 79 % in the neat liquid diol to 89 % at near infinite dilution.

Introduction

Water has been used as a coolant in automobile industries since the early 20th century; however, it is not used in its pure form. Rather, anti‐freezing agents such as ethylene glycol (EG) and propylene glycol along with corrosion inhibitors are mixed with water.[ ¹ , ² , ³ , ⁴ ] Mixing EG with water increases its boiling point and reduces the freezing point, hence providing a wider liquidus range than neat water. ^[5] Needless to say, physical properties are inherently related to intermolecular interactions; therefore, the water‐EG mixture has been studied extensively using various experimental techniques such as Raman, ^[6] ATR‐FTIR, ^[7] near‐infrared (NIR), ^[8] and sum‐frequency generation (SFG) ^[9] spectroscopy.

Water and EG[ ⁶ , ¹⁰ ] are completely miscible at all concentrations. Wang et al. ^[6] observed considerable changes in the Raman scattering features corresponding to O−H symmetric and O−H asymmetric stretching modes of water at EG volume fraction (V _EG ) of 0.5. They concluded that EG‐water hydrogen bonded structures dominate over water‐water clusters at high EG concentration. ^[6] The EG molecule has one central OCCO and two terminal HOCC dihedral angles (see Figure 1). The HOCC dihedral is less hindered to rotate as opposed to the OCCO dihedral. ^[11]

Figure 1.

Molecular structure of ethylene glycol molecule (a) gTg’ conformation and (b) tGg’ conformation. Atom types for ethylene glycol used in modelling are, HO: hydroxyl hydrogen, OG: hydroxyl oxygen, CG: methylene carbon, HG: methylene hydrogen. (c) Atom types of water are, Hw: hydrogen, Ow: oxygen.

Molecular structures of ethylene glycol (EG) and of water along with the atom types used in modelling them are shown in Figure 1. The nomenclature to refer an EG molecule is based on its dihedral angle values. If a dihedral angle is between ±150° and ±180° it is termed as trans (t/T) and if the range is between ±30 to ±90°, it is termed as gauche (g/G). Upper case T and G are used for the OCCO dihedral angle while lower case t and g are used for HOCC dihedral angles rotated clockwise and t’ and g’ for HOCC dihedral angles rotated anticlockwise. In this paper, our main focus is on the central OCCO dihedral angle, hence in the paper trans (T) and gauche (G) EG conformers are referred based on the OCCO dihedral angle.

In its gas phase, EG adopts a conformation with its central OCCO dihedral in the gauche state.[ ¹² , ¹³ ] The same is true for crystalline EG as well. ^[14] However, in its neat liquid state, around 21 % of EG molecules have their OCCO dihedral in the trans conformation.[ ¹¹ , ¹⁵ , ¹⁶ ] Recent Raman spectroscopic studies ^[6] of aqueous EG solution also showed that the population of trans conformers reduces upon dilution of EG. Guo et al. ^[7] studied the ATR‐FTIR spectra of aqueous EG solution over a wide range of mole fraction of EG (x_EG ), from 0.99 to 0.0007. Combining frequencies obtained from density functional theory (DFT) calculations and ATR‐FTIR results and particularly focusing on the skeletal stretching vibration (ν _{O−C−C−O} ) and CH₂ rocking vibration, they concluded that between 0.71 > x_EG > 0.05, water molecules interrupt the hydrogen bonds between EG molecules and instead form a EG‐water network. Further, much of the EG molecules present in the trans EG conformation were reported to change to the gauche conformation.

After studying the near‐infrared spectra of EG‐water solutions at various temperatures, Chen et al. too arrived at similar conclusions as Wang et al. ^[6] and Guo et al., ^[7] that EG‐water association is preferred over that of water‐water at less than 50 weight‐% water content. ^[8] They inferred that in EG‐water mixtures, water molecules cluster around EG, and that the size of the cluster is proportional to the amount of water.

Apart from spectroscopy, theoretical methods such as classical molecular dynamics and quantum chemical calculations have also been employed to obtain a molecular level understanding of aqueous EG solutions.[ ¹⁷ , ¹⁸ , ¹⁹ , ²⁰ , ²¹ , ²² , ²³ , ²⁴ , ²⁵ ] Cramer and Truhlar carried out quantum chemical calculations of all conformers of EG both in gas and in implicit water phases. ^[25] The fraction of trans conformer of EG in the aqueous medium was estimated to be around 12 %, increased from a value of 2 % in gas phase. Chaudhari and Lee studied EG‐water _n (n=1–3) clusters using DFT calculations. ^[24] They reported that for all the individual clusters, the most stable configuration pertains to structures wherein water molecule(s) bridges the two hydroxyl groups of an EG molecule. ^[24] Kumar et al. ^[22] too carried out DFT calculations on EG _m ‐water _n (m=1–3, n=0–4) clusters and reported that the most stable EG dimer configuration consists of three hydrogen bonds; the addition of two water molecules to it (resulting in the most stable EG₂‐water₂ cluster) breaks one of the EG‐EG hydrogen bond in EG₂. ^[22] Using localized molecular orbital energy decomposition analysis, they concluded that EG‐water interactions dominate over EG‐EG and water‐water interactions.

Classical molecular dynamics (MD) simulations have been performed using various force fields to study the dynamics and physical properties of the liquid EG‐water binary mixture. Gubskaya and Kusalik ^[21] employed the OPLS‐UA ^[26] force field to study structural aspects of this solution using radial and spatial distribution functions (RDFs and SDFs). They reported a sudden increase in the population of trans conformers at x_EG =0.03 from 0 % to 56 %, which is not in accordance with available spectroscopic and quantum chemical results discussed earlier. de Oliveira and Freitas ^[20] studied the structural and thermodynamic properties using three OPLS‐AA based force fields. Kaiser et al. ^[18] examined dynamical properties to understand EG‐water dielectric spectra using the OPLS‐AA‐SEI‐M ^[20] force field. However, at ambient conditions, the reported translational diffusion coefficient and dielectric constant calculated using the same force field for pure EG is 86 % and 89 % away respectively, from the experimental values. ^[18] Geerke and Gunsteren ^[23] developed two non‐polarizable (G04 and G05) and three polarizable (COS/E10, COS/E08, and COS/E06) united atom FFs to reproduce the solvation free enthalpy of argon in EG‐water solution and the physical properties of neat liquid EG. While their non‐polarizable FFs predicted the dielectric constant more accurately, the polarizable FF COS/E10 predicted the viscosity more accurately. A recently developed GAFF ^[27] based force field parametrized by us (FF‐v1) ^[16] provides the best agreement with various experimentally measured physical properties of neat EG. The translational self‐diffusion coefficient of EG was calculated to be just 5 % higher while the dielectric constant was 35 % lesser than the experimental values. ^[16] To the best of our knowledge, except for FF‐v1, none of the force fields reproduces the experimentally reported dynamical properties of EG well. In particular, FF‐v1 is the only force field which reproduces the conformer populations in the neat liquid EG correctly in accordance with both experiment and ab initio MD simulation results. Hence, we felt it important to investigate EG‐water solutions using this newly developed force field, ^[16] FF‐v1.

Physical properties of the aqueous solution such as density, translational self‐diffusion coefficient, and static dielectric constant calculated here for a range of mole fraction of aqueous EG solution are in excellent agreement with experimental data. We also report an interesting behaviour in the population of trans conformers of EG, with increasing concentration of water. The variation of static dielectric constant of the solution with EG concentration is consistent with the change in the distribution of molecular dipole moment of EG, which is impacted more by gauche conformers than the trans ones.

Computational Details

Equilibrium Molecular Dynamics Simulations

Classical MD simulations at several compositions of EG‐water binary mixtures (mole fraction, x_EG =0.0, 0.05, 0.30, 0.50, 0.80 and 0.95) in the liquid phase (see Table S1) were carried out using GROMACS‐2020.4[ ²⁸ , ²⁹ , ³⁰ ] software. For each composition, a cubic box of side length approximately 51 Å was packed with EG and water molecules, using PACKMOL, ^[31] at the density reported experimentally. All the EG molecules were present in the gauche conformation in all these initial configurations. A GAFF ^[27] based FF (FF‐v1) proposed recently by our group was used for EG ^[16] and the SPC/E ^[32] model was used to represent water. Lorentz–Berthelot combination rules were used to compute cross Lennard–Jones (LJ) interactions.

Following standard practice, LJ and Coulomb interactions in a molecule were excluded for pairs that are connected by two covalent bonds or lesser. LJ and Coulomb interactions for pairs that are connected by three covalent bonds were scaled by 0.5 and 0.8333, respectively. A cutoff radius of 10 Å was used for short‐range interactions with an additional 2 Å buffer to update the pair list every ten steps using the Verlet cutoff ^[33] scheme. Energy and pressure corrections were applied. Long‐range Coulomb interactions were calculated using the particle mesh Ewald ^[34] method with interpolation order of 4 and 0.12 nm grid spacing and a relative tolerance of 10⁻⁵. The equations of motion were integrated using the leap‐frog integrator with a time step of 1 fs. All the covalent bonds involving hydrogen atoms were constrained using LINCS ^[35] algorithm. Temperature and pressure were controlled using Nosé–Hoover[ ³⁶ , ³⁷ ] thermostat and Parrinello–Rahman ^[38] barostat, respectively. The temperature and pressure coupling time constants were 1 ps and 10 ps, respectively.

At each composition, the system was subjected to energy minimization using steepest descent algorithm followed by a 3 ns NVT run, of which 2 ns was used to increase the temperature slowly to 298.15 K. Using the last frame of the 3 ns NVT run, an NPT simulation for 25 ns was carried out at 298.15 K and 1 bar. The last 5 ns trajectory of the NPT run was used to compute the average density. Thereafter, a 2 ns equilibration NVT simulation was performed at the average density at 298.15 K, followed by a 50 ns NVT simulation. From this 50 ns NVT simulation, five simulation box frames were extracted only for x_EG =0.0, 0.3, 0.5, and 0.8 in the interval of 10 ns to calculate self‐diffusion coefficients and static dielectric constant. These five frames were used to perform another five independent NVT simulations using different seeds for initial velocity generation at 298.15 K, each simulation being 50 ns long.

In the following, we provide details of procedures followed for the calculation of various quantities.

Self‐diffusion Coefficient

The six 50 ns NVT simulations were used to compute the translational self‐diffusion coefficient (D _self ) for EG and water, after discarding the initial 5 ns from each simulation for equilibration. D _self was computed using the Einstein Equation[ ³⁹ , ⁴⁰ ] (Equation 1). The mean square displacement (MSD) of individual species was averaged over six independent runs. Equation 1 is valid only when the system is in diffusive regime, therefore D _self was calculated after careful identification of the diffusive regime (see Section S2). Cross correlations between the diffusing species have not been considered for the calculation of D _self . Finite box size correction ^[41] too is not accounted for, while computing D _self .

(1)

where,

$${\displaystyle MSD\left(t\right)=\frac{1}{N}\sum _{i=1}^N⟨{\left(r_i\left(t\right)-r_i\left(0\right)\right)}^2⟩}$$ (2)

where t is time, N is the total number of molecules, r_i is the center of mass position of molecule i, and angular brackets represent averaging over multiple time origins.

Static Dielectric Constant

During all the six 50 ns NVT simulations, the dipole moment of the simulation box ($\overrightarrow{M}$ ) was written every 1 fs using PLUMED‐2.6.2 ^[42] for the computation of static dielectric constant, ε. ε was computed using fluctuations in $\overrightarrow{M}$ , ^[43] using Equation 3. Cumulative running averages of static dielectric constant calculated from the six independent NVT simulations are shown in Figures S2 and S3.

$${\displaystyle ϵ=1+\frac{4\pi }{3{ϵ}_0{k}_{B}TV}(⟨\overrightarrow{M^2}⟩-{⟨\overrightarrow{M}⟩}^2)}$$ (3)

where ε ₀ is the permittivity of vacuum, V is the volume of the system, k_B is the Boltzmann‐constant, and T is the temperature.

Isothermal Compressibility and Thermal Expansion

For neat liquid EG, isothermal compressibility (β_T ) and thermal expansion (α_P ) were also calculated from the last 10 ns of a 25 ns NPT run at 298.15 K and 1 bar using box volume fluctuations. ^[44] The 10 ns trajectory was divided in five equal parts to calculate the standard error.

Radial Distribution Functions

Several radial distribution functions (RDF) and corresponding coordination numbers were calculated using the last 10 ns of one 50 ns NVT simulation at various x_EG compositions (x_EG =0.0, 0.05, 0.30, 0.50, 0.80 and 0.95). Equation 4 was used to compute RDFs between atom types a and b, g _ab (r). ^[40]

(4)

where,

(5)

In Equation 4, N _a and N _b are the number of atoms of type a and b, respectively. $\overrightarrow{r_i}$ denotes coordinate of atom i, Δr is bin width, ρ_b is number density of atom type b, V is volume of the simulation box. Δr was chosen to be 0.02 Å.

Dihedral and Dipole Moment Distribution

Distributions of dihedral angles and molecular dipole moment were calculated using the last 40 ns of the single 50 ns NVT simulation at various x_EG . The probability density for each distribution was calculated by binning the property of interest and then normalizing it by the total number of EG molecules times bin width. Bin width of one degree and 0.27 Debye were used for the dihedral angle and dipole moment distributions, respectively.

For neat liquid EG, all the above analyses were carried out using the simulation trajectories reported earlier. ^[16]

Well‐tempered Metadynamics Simulation

Gromacs‐2020.4 ^[30] patched with PLUMED‐2.6.2 ^[42] was used to perform the well‐tempered metadynamics ^[45] simulation (WTMetaD). The simulation was performed for 1 EG in a bath of 4496 water molecules, which corresponds to x_EG =0.00022. System details are presented in Table S2. Before starting the WTMetaD simulation, a 25 ns long NPT simulation at 298.15 K and 1 bar followed by a 50 ns NVT run were performed at the average density to equilibrate the system. The WTMetaD simulation was performed to obtain the free energy profile of the OCCO dihedral angle of one EG molecule soaked in a water bath. Hence, the OCCO dihedral angle was chosen as the collective variable (CV). WTMetaD simulation parameters and convergence check are presented in Section S4 of the Supporting Information (see Table S3 and Figure S4). The last 40 ns of the 50 ns unbiased NVT simulation was used to calculate the dipole moment distribution at x_EG =0.00022.

Results and Discussion

Physical Properties

The static dielectric constant of the solution, and the molecular translational self‐diffusion coefficients were calculated at four different EG mole fractions (x_EG ). These physical properties as a function of x_EG are displayed in Figure 2. Density was calculated at various mole fractions of EG (x_EG ) and compared against experimental ^[46] data (Figure 2a). The maximum deviation in the density of the solution from experimental value ^[46] is −1.4 %, which is acceptable. D _self for both EG and water are in remarkable agreement with experimental ^[47] data (Figure 2b). The largest deviation of 14.6 % is seen in the D _self for pure water. D _self for both EG and water increase with decrease in x_EG , due to the thinning of the solution. ^[49] Water has a higher diffusion coefficient at all the compositions than EG because of smaller size; however, its diffusion coefficient reduces drastically in the range x_EG =0 to x_EG =0.3. This observation suggests that the motion of water molecules is hindered just by mixing a small amount of EG; Loskutov and Kosova ^[50] too reported a drastic increase in viscosity from a value of 1.2 cP at x_EG =0.01 to 5.46 cP at x_EG =0.31. Mixing EG with water also affects dielectric polarization. The calculated static dielectric constant is compared against experimental data ^[48] in Figure 2c. It monotonously increases with decrease in the amount of EG. ^[48] The largest deviation of −35.5 % in dielectric constant is seen for pure EG. Nevertheless, the behaviour of the calculated dielectric constant as a function of x_EG matches that seen in experiments. The increase in static dielectric constant of the solution influences the conformer populations of EG molecules (vide infra).

Figure 2.

(a) Density (b) Translational self‐diffusion coefficient (D _self ), and (c) Static dielectric constant calculated at various mole fractions of EG (x_EG ) at 298.15 K and 1 bar. Experimental data for density, self‐diffusion coefficients, and static dielectric constant are taken from Refs. [46–48], respectively. Range of deviation from experimental values for density, D _self , and dielectric constant are 0.16 to 1.40 %, 0.00 to 14.57 %, 7.32 to 35.53 %, respectively. Numerical values of these quantities and error on the mean are presented in Tables S4, S5, and S6, respectively. Error bars are smaller than the symbol size, hence are not shown.

The β_T and α_P values obtained from the neat liquid EG simulation are 4.72±0.17×10⁻⁵ bar⁻¹ (3.34×10⁻⁵ bar⁻¹) ^[51] and 9.34±0.12×10⁻⁴ K⁻¹ (6.7×10⁻⁵ K⁻¹) ^[52] respectively (experimental values in parentheses). The calculated β_T and α_P values deviate from experimental values by 41 % and 39 %, respectively.

Although the FF‐v1 force field was not refined to reproduce β_T and α_P , the comparison between simulated and experimental results is decent. A precise evaluation of these values from simulations would require much larger system sizes (5000 molecules as employed in Ref. [53]) than employed herein.

Radial Distribution Functions

EG and water are completely miscible and both possess hydrogen bonding donor and acceptor sites. ^[54] As discussed in the Introduction, many spectroscopic studies have reported the presence of hydrogen bonds between EG‐EG, EG‐water, and water‐water in EG‐water binary mixtures. Hence, we calculated radial distribution functions (RDFs) related to intermolecular hydrogen bonding, as shown in Figures 3 and 4. The coordination number calculated from the RDFs are presented in Table 1. The position of the first minimum of the RDFs varies from 2.3 Å to 2.5 Å, and these were used as cut‐off to obtain the coordination numbers. The first peak, corresponding to the most probable hydrogen bond distance, is between 1.7 and 1.8 Å for EG‐EG, EG‐water, and water‐water pairs. A comparison of the peak heights of the Ow‐HO and OG‐HO g(r)s is in order. At x_EG =0.95, wherein the water mole fraction is low, the first peak of Ow‐HO g(r) is much taller than that of OG‐HO g(r) when x_EG =0.05. This implies that water molecules have a higher propensity to hydrogen bond with the hydroxyl hydrogens of EG when the water amount is low, whereas EG, at the same corresponding low amount is unable to do so to the same extent. The same conclusion can be drawn by a comparison of Ow‐Hw and OG‐Hw g(r) first peak heights at x_EG =0.95 (former) and at x_EG =0.05 (latter). Thus, at low water contents, water is likely to cluster around each other, such clusters solvated by EG, as pointed out earlier by Kusalik and coworkers ^[21] and confirmed via oxygen‐oxygen RDFs, center of mass RDFs and visual inspection as well (Figures S5, S6, and S7, respectively).

Figure 3.

Intermolecular radial distribution function between oxygen atoms of water molecules (Ow) and (a) hydrogen atoms of other water molecules (Hw), (b) hydroxyl hydrogen atoms of EG molecules (HO). Legends represent mole fraction of EG.

Figure 4.

Intermolecular radial distribution function between oxygen atoms of EG molecules (OG) and (a) hydroxyl hydrogen atoms of other EG molecules (HO), (b) hydrogen atoms of water molecules (Hw). Legends represent mole fraction of EG.

Table 1.

First shell coordination number (C.N.) of intermolecular pairs at several mole fractions of EG, x_EG .

xEG	Ow‐Hw	Ow‐HO	OG‐HO	OG‐Hw
1.00	–	–	0.97	–
0.95	0.06	1.31	0.94	0.05
0.80	0.29	1.13	0.82	0.21
0.50	0.77	0.78	0.58	0.59
0.30	1.17	0.50	0.38	0.89
0.05	1.75	0.09	0.08	1.38
0.00	1.89	–	–	–

The RDF for intermolecular OG‐OG and OG‐Ow pairs were also computed for EG molecules where the reference OG atoms belongs to a molecule either in gauche EG conformation or in trans EG conformation, to analyse whether the two conformer types show any difference in hydrogen bond formation in the liquid state. Note that in these calculations, the reference (or central) atoms belong to a EG molecule of a specific conformation, while its neighbor can be of any conformation. These RDFs and coordination numbers at x_EG =0.05, 0.5, 1.0 are presented in Figure S8 and Table S8, respectively. Although the peak position and peak height of the RDFs do not change significantly between these two conformer types, the coordination number for reference gauche conformers is slightly larger than that for the trans conformer; the difference ranging from 0.02 to 0.15, except for OG‐Ow at x_EG =0.5. This observation suggests that gauche conformers possess a marginally greater tendency to form intermolecular hydrogen bonds than the trans conformers. Our results are in line with those of Jindal and Vasudevan, ^[55] who calculated the free energy of formation of hydrogen bond between gauche‐gauche and gauche‐trans conformers in neat liquid EG, from a Car–Parrinello MD simulation trajectory. They obtained a more negative free energy value (by 0.5 kJ/mol) for the gauche‐gauche pair than for the trans‐gauche pair.

Fortes and Suard reported the crystal structure of a 1 : 1 molar mixture of EG‐water at a temperature of 210 K. ^[56] They reported hydrogen bond distances of 1.7 to 1.8 Å between EG and water. The hydrogen bond distance obtained herein compares very well with corresponding values in the crystal structure. The coordination number of water hydrogen atoms (Hw) around water oxygen atoms (Ow) and around EG oxygen atoms (OG) increases with increase in the mole fraction of water (see Table 1). In contrast, the same for hydroxyl hydrogen atoms (HO) around Ow and OG atoms decreases. RDFs and first shell coordination number between oxygen atoms of EG and water at various mole fractions of EG are presented in SI (Figure S5 and Table S9). The change in the oxygen‐oxygen first shell coordination number as a function of x_EG is also shown in Figure 5. Note that the coordination numbers in the Figure are per oxygen atom. At the equimolar composition, although both EG's OG and water's Ow are prima facie on equal grounds for other molecules to interact with, Ow is able to hydrogen bond with more partners as it has two donor sites (i. e., two Hw atoms), while EG's OG has only one, being a hydroxyl group. This conclusion can be drawn from the values of the coordination numbers presented in Table 1, as well as from Figure 5.

Figure 5.

Various oxygen‐oxygen coordination numbers as a function of mole fraction of EG (x_EG ).

Population of EG Conformers: Compositional Dependence

Several spectroscopic studies[ ⁶ , ⁷ ] and quantum chemical calculations ^[25] have shown that the population of EG molecules with their central OCCO dihedral in the trans conformation reduces upon dilution of liquid EG with water. Using Raman spectroscopy, Wang et al. ^[6] showed that the intensity of the peak at 2728 cm⁻¹, which is attributed to this trans conformation decreases with increasing amounts of water in the solution, indicating a reduction in the population of the trans conformer. Guo et al., ^[7] using FTIR‐ATR spectroscopy, showed that the ratio of the area of bands corresponding to OCCO trans and gauche conformers decreases with increasing water concentration, once again pointing to a reduction in the trans population. However, to the best of our knowledge, this fascinating phenomenon has not been reproduced so far in any empirical force field based MD simulation. The distribution of OCCO dihedral angles at various mole fractions of EG obtained from our simulations are shown in Figure 6a and the population of trans conformers in Figure 6b. In neat liquid EG, the trans conformer fraction is 21 %, which is seen to monotonously reduce upon dilution of EG with water. The trans population at the lowest concentration studied here (x_EG =0.05) is 13.1 %.

Figure 6.

(a) Distribution of OCCO dihedral angle of ethylene glycol (EG) at various mole fractions of EG (x_EG ) in aqueous EG solution. The probability density was calculated by dividing probability by bin width. (b) Fraction of conformers in the Trans state of the OCCO dihedral of EG as a function of x_EG . Line connecting the data points in panel (b) is a guide to the eye.

Cramer and Truhlar ^[25] calculated the trans percentage using implicit solvent quantum chemical calculations and reported a value of 12 % in water. We performed WTMetaD simulation of 1 EG molecule in a bath of 4496 water molecules (x_EG =0.00022) to mimic the dilute aqueous conditions. The collective variable was the OCCO dihedral angle. The free energy profile for 1 EG in the bath of water is shown in Figure 7. The corresponding profile in neat liquid EG, obtained by us earlier, ^[16] is also shown in Figure 7 for the sake of comparison. The free energy difference between the gauche and trans states of one EG molecule soaked in liquid water is 3.5 kJ/mol, which is around twice the same as in neat liquid EG. This free energy difference corresponds to a trans population of 10.9 %. Our empirical force field based MD simulation results are thus in accordance with spectroscopic observations and quantum chemical calculations. In the subsequent section, we shall examine the reasons underlying the variation in the trans population with the mole fraction of EG in the aqueous EG solution.

Figure 7.

Free energy (F) profile as a function of the OCCO dihedral angle of EG in a dilute aqueous EG solution (1 EG molecule in a bath of 4496 water molecules) and in neat liquid EG obtained using well‐tempered MD simulations. The latter data is from our earlier work.^[16] A representative EG molecule corresponding to each minimum and the transition state are displayed. EG molecule color code: H: white, O: red, C: black. The free energy difference between trans and gauche conformers (F(T)–F(G)) in dilute aq. EG solution is 3.5 kJ/mol and that in neat EG is 1.7 kJ/mol.

Distribution of Molecular Dipole Moment Magnitudes of EG

In general, the trans conformer of EG tends to have a lower dipole moment than the gauche conformer. ^[25] Thus, the reduction in OCCO trans fraction with increase in water content has been attributed to the higher dielectric constant of water than that of liquid EG. ^[6] However, as noted by Jindal and Vasudevan, ^[57] not all OCCO trans conformers have zero dipole moment; the molecule's dipole moment is also dependent on the conformational state of the two HOCC terminal dihedral angles. We calculated the dipole moment distribution of EG molecules with their central OCCO dihedral present in either the trans or the gauche state as a function of EG concentration in the aqueous solution, and the same is displayed in Figure 8. The distributions for trans EG and gauche EG molecules are bimodal and trimodal, respectively. A representative EG conformer corresponding to each maximum are shown in Figure 8 and their atomic coordinates are provided in Section S7 of the Supporting Information. Most trans conformers have a high dipole moment (around 3.5 Debye). Furthermore, there is no significant change in the trans EG dipole moment distribution with change in x_EG . However, the dipole moment distribution for gauche EG molecules shows a non‐negligible shift to the right increase in dipole moment while going from x_EG =1.0 to x_EG =0.05, particularly in the higher dipole moment range. The mean dipole moment for trans EG, gauche EG, and for all the EG molecules (irrespective of the conformational state of the OCCO dihedral) at all the compositions are presented in Table S10.

Figure 8.

Distribution of magnitude of molecular dipole moment for EG molecules which are in (a) trans conformation and (b) gauche conformation at various mole fractions of EG (x_EG ). For every maximum in panels (a) and (b), a representative EG molecule conformer that contributes to the maximum is shown. EG molecule color code: H: white, O: red, C: black. Coordinates of the five EG molecules are provided in Section S7 of Supporting Information. Symbols are shown at every alternate data point for clarity and lines are drawn as a guide to the eye.

The shift in the dipole moment distribution of gauche EG towards larger dipole moment values is in response to an increase in the static dielectric constant of the medium, from a value of 41 in neat liquid EG to a value of 78 in neat liquid water. This increase not only increases the fraction of gauche conformers (in the central dihedral), but also enhances the access of conformational states in the terminal dihedral angles with large dipole moment values (vide infra).

The change in the gauche EG dipole moment distribution is also reflected in the HOCC (terminal) and OCCO (central) dihedral distribution of gauche EG molecules (Figures 9b and S9b). In contrast, the same for trans EG molecules remains unchanged throughout the range of EG‐water mixture composition, as shown in Figures 9a and S9a.

Figure 9.

Terminal HOCC dihedral distribution of EG molecules in trans and gauche conformations. Legends represent mole fraction of EG. The probability density was calculated by dividing probability by bin width. The error on the mean of the distribution is nearly the same as the line width.

The HOCC dihedral distribution of gauche EG molecules exhibits a decrease in probability from ±50° to ±90° and an increase in probability from ±120° to ±180° with increase in water concentration (Figure 9b). To understand these changes, we calculated the dipole moment of an isolated EG molecule whose OCCO dihedral angle is either 64° (i. e., gauche) or 180° (i. e., trans), as a function of both its HOCC (terminal) dihedral angles, using site charges of our force field. The same is shown in Figure 10. Some of the gauche EG conformers have much higher dipole moment than the trans EG conformers. For the gauche EG conformer, regions of highest dipole moment, shown in yellow, occur either when both the HOCC dihedral angles are in the range 120° to 180° or when one HOCC dihedral angle is from 25° to 100° while the other is from −150° to −180°. An increase in the probability of the HOCC dihedral angle in the range ±120° to ±180° (Figure 9b) increases the mean dipole moment of EG molecules at high water concentrations.

Figure 10.

Magnitude of dipole moment of an isolated EG molecule, calculated using our force field (FF‐v1), whose OCCO (central) dihedral angle is 64° (gauche) (left panel) and 180° (trans) (right panel), as a function of HOCC (terminal) dihedral angles, θ and θ*. Color bars represent magnitude of dipole moment in Debye.

Conclusions

Both water and ethylene glycol are small molecules and ones whose liquid phases are homogeneous in both structural and dynamical domains. Yet, their binary mixture solution which spans the entire composition range shows many surprising observations – the clustering of water molecules at low water concentrations, the larger coordination number around water at the equimolar composition, and the fascinating display of conformational selectivity by the organic molecule upon its dilution with water. The current study, employing a bespoke, non‐polarizable force field for EG, is able to adroitly capture all these key phenomena associated with aqueous EG solution.

The population of EG molecules with their central OCCO dihedral in the trans state reduces from a value of 21 % in neat liquid EG to a value of around 11 % under extremely dilute conditions in water, consistent with several spectroscopic studies and the early quantum chemical work of Cramer and Truhlar. ^[25] To the best of our knowledge, the current work is the first one to demonstrate the same in an empirical force field based MD simulation. The reduction in the trans population with increasing water content is a direct consequence of the increase in the static dielectric constant of the medium, from a value of 41 in neat liquid EG to a value of 78 in neat liquid water. Gauche EG molecules also form marginally more hydrogen bonds with other EG molecules than trans ones do; this propensity too can contribute to the decrease in the fraction of trans EG conformers upon dilution of liquid EG with water. The trans fraction observed in dilute EG solution also correlates well with the free energy difference obtained through well tempered metadynamics simulations.

The simulations also offered microscopic insights on the interplay between molecular dipole moments and their conformations. In the solution, the dipole moment distribution of molecules present in their trans conformation does not change with solute (EG) concentration, while gauche conformers exhibit an additional peak in their dipole moment distribution, at higher moment values, at low EG concentrations. A careful analysis on the origin of this peak leads us to conclude that it arises when the terminal HOCC dihedral angles are around 120° to 170°. Such a conformation makes the EG molecule most extended, leading it to acquire larger dipole moment values, as a response to the enhanced static dielectric constant of the solution, upon dilution with water.

The current work is a demonstration of how the mixture of two fully miscible, hydrogen bonded liquids leads to the emergence of rich phenomena that can be explored through careful molecular simulations. We hope to explore more aspects of such solutions containing ethylene glycol in our future endeavours.

Conflict of interest

The authors declare no conflict of interest.

Supporting information

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Supporting Information

Gaur A., Balasubramanian S., ChemistryOpen 2023, 12, e202200132.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.