# Influence of Ethanol Parametrization on Diffusion Coefficients Using OPLS-AA Force Field

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}[17].

_{2}, and CH

_{3}groups are treated as single unified interaction centers with masses corresponding to the sum of the masses of C and H atoms in the CH

_{x}group; and (iii) all-atom, such as the General AMBER Force Field (GAFF) [27] and the All-Atom Optimized Potential for Liquid Simulations (OPLS-AA) [28], where all atoms are represented individually. The force fields are under continuous improvement, and new versions are published on a regular basis. For example, OPLS-AA has been the cornerstone of other force fields, e.g., L-OPLS-AA [29,30], OPLS-AA/M [31], and OPLS4 [32], which were introduced to overcome some limitations of the original set of parameters. The L-OPLS-AA enabled a more accurate reproduction of liquid properties of long alkanes, alcohols, esters, and glyceryl monooleate that was not possible using the OPLS-AA [29,30]; the OPLS-AA/M improved on previous iterations of the OPLS-AA force fields regarding its ability to reproduce both gas-phase conformer energies for longer peptides and aqueous phase experimental properties [31]; in OPLS4, the new parameters allowed for more accurately predicting protein–ligand binding affinities by addressing limitations in the representation of molecular ions, sulfides, and aryl sulfur and a general improvement in model hydration [32]. Consequently, the accuracy and the precision of the simulations tend to improve with time, which combined with the reducing costs of increasing computational power and efficient algorithms, make classical MD simulation an enticing approach for a ${D}_{12}$ estimation that, in some cases, may even compete with experimental studies.

_{2}. However, have regard for the computation of ${D}_{12}$ of protic solutes in ethanol and ${D}_{11}$ of ethanol [34], as these properties tend to be overestimated when using OPLS-AA, as will be presented further in this work. At this point, it is important to stress that the determination of accurate ${D}_{12}$ of protic solutes in liquid ethanol is of utmost importance to design and optimize industrial equipment and kinetic processes. Despite some correlations available in the literature [14,15,16], including some originating in our group [3], the fact is that there is no general theory to accurately estimate ${D}_{12}$ of polar systems without having experimental (or accurate computational) data. Therefore, new approaches for determining such values are expected to have an impact on the field.

## 2. Results and Discussion

#### 2.1. D_{12} of Quercetin and Gallic Acid in Liquid Ethanol: Optimization of the Oxygen’s Radius

#### 2.2. D_{12} of Organic Solutes in Liquid Ethanol: Oxygen’s Radius Validation and Cases of Applicability

^{−9}± 0.08 × 10

^{−9}m

^{2}s

^{−1}when considering ${\sigma}_{\mathrm{OH}}$ = 0.312 nm and ${D}_{12}^{\mathrm{MD}}$ = 1.85 × 10

^{−9}± 0.02 × 10

^{−9}m

^{2}s

^{−1}when considering ${\sigma}_{\mathrm{OH}}$ = 0.306 nm, which correspond to RD of 0.00% and −18.86%, respectively. As for propane, the simulations at 323.15 K and 103 bar achieved similar results with ${D}_{12}^{\mathrm{MD}}$ = 3.10 × 10

^{−9}± 0.05 × 10

^{−9}m

^{2}s

^{−1}with ${\sigma}_{\mathrm{OH}}$ = 0.312 nm and ${D}_{12}^{\mathrm{MD}}$ = 2.55 × 10

^{−9}± 0.08 × 10

^{−9}m

^{2}s

^{−1}when ${\sigma}_{\mathrm{OH}}$ = 0.306 nm, corresponding to RD values of 3.68% and −14.72%, respectively.

#### 2.3. ${D}_{11}^{}$ of Liquid Ethanol

#### 2.4. Influence of the Oxygen’s Energy Parameter

#### 2.5. Equilibrium Properties of Ethanol

^{−1}) compares well with the experimental result (42.3 ± 0.4 kJ mol

^{−1}[45]), with RD = −0.71%. When the reparametrized value (${\sigma}_{\mathrm{OH}}$ = 0.306 nm) is used, the computed value of $\mathsf{\Delta}{H}_{\mathrm{vap}}$ increases to 44.8 kJ mol

^{−1}, which is 5.91% higher than the one computed with ${\sigma}_{\mathrm{OH}}$ = 0.312 nm. This difference is mainly due to the computed potential energy of the liquid phase (${U}_{\mathrm{liquid}}$) being around 13% higher when using ${\sigma}_{\mathrm{OH}}$ = 0.312 nm.

## 3. Materials and Methods

#### 3.1. Database

#### 3.2. Molecular Dynamics Simulation Procedure

#### 3.3. Self-Diffusion and Binary Diffusion Coefficients

^{−23}m

^{2}kg s

^{−2}K

^{−1}), $\xi $ is a dimensional constant of value 2.837297, and ${\mu}_{1}$ the viscosity. This second approach was adopted in this work since it is computationally cheaper, and the ${D}_{11}^{\mathrm{MD},\infty}$ results are equivalent to those obtained by the linear regression method, as depicted in Figure S1 (see Supplementary Materials). A total of 1500 ethanol molecules were used per simulation at each condition.

#### 3.4. Calculation of Equilibrium Properties

#### 3.4.1. Enthalpy of Vaporization

^{−1}mol

^{−1}). To calculate ${U}_{\mathrm{liquid}}$, we used the last 15 ns of the simulation used to compute ${D}_{11}^{}$. The Barrera and Jorge [23] procedure was used to calculate ${U}_{\mathrm{gas}}$, with one molecule being placed inside a cubic box (15 nm × 15 nm × 15 nm), with no boundary conditions and all cutoff radii set to 0. The simulation was carried out in NVT using the leap-frog stochastic dynamics integrator, which adds a friction and a noise term to Newton’s equation of motion [74]. The run was carried out for 50 ns, and the first 10 ns of the simulation were discarded.

#### 3.4.2. Density

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Relative deviations (RD) of ${D}_{12}$ of (

**a**) quercetin (triangles) and of (

**b**) gallic acid (circles) in liquid ethanol versus ethanol’s oxygen diameter (${\sigma}_{\mathrm{OH}}$). Empty symbols are individual RD values at different $T$ and $P$ conditions, while filled symbols are average relative deviations computed from the RD values obtained at each condition.

**Figure 2.**Experimental (${D}_{12}^{\mathrm{exp}}$, ■) and computed (${D}_{12}^{\mathrm{MD}}$, *) diffusion coefficients in liquid ethanol versus Stokes–Einstein abscissae ($T/{\mu}_{1}$): (

**a**) quercetin, and (

**b**) gallic acid. The viscosity values were estimated by the Mamedov equation, as proposed by Cano-Gómez et al. [44].

**Figure 3.**Experimental (${D}_{12}^{\mathrm{exp}}$, ■) and computed (${D}_{12}^{\mathrm{MD}}$, *) diffusion coefficients in liquid ethanol versus Stokes–Einstein abscissae ($T/{\mu}_{1}$) for (

**a**) ibuprofen and (

**b**) butan-1-ol. The viscosity values were estimated by the Mamedov equation, as proposed by Cano-Gómez et al. [44].

**Figure 4.**Experimental (${D}_{11}^{\mathrm{exp}}$, ■) and computed (${D}_{11}^{\mathrm{MD}}$, *) self-diffusion coefficients of ethanol versus Stokes–Einstein abscissae. The viscosity values were estimated by the Mamedov equation, as proposed by Cano-Gómez et al. [44].

**Table 1.**Experimental (${D}_{12}^{\mathrm{exp}}$) and computed (${D}_{12}^{\mathrm{MD}}$) diffusion coefficients of quercetin and gallic acid in liquid ethanol at various temperatures and pressures. The computer simulations used ${\sigma}_{\mathrm{OH}}$ = 0.306 nm for ethanol, and the calculated diffusivities were evaluated in comparison with experimental data in terms of the relative deviation (RD), average relative deviation (ARD), and average absolute relative deviation (AARD).

Solute | $\mathit{T}$ (K) | $\mathit{P}$ (bar) | ${\mathit{D}}_{12}^{\mathbf{e}\mathbf{x}\mathbf{p}}\pm \mathbf{\Delta}{\mathit{D}}_{12}^{\mathbf{e}\mathbf{x}\mathbf{p}}$ (10 ^{−9} m^{2} s^{−1}) | ${\mathit{D}}_{12}^{\mathbf{M}\mathbf{D}}\pm \mathbf{\Delta}{\mathit{D}}_{12}^{\mathbf{M}\mathbf{D}}$ (10 ^{−9} m^{2} s^{−1}) | RD (%) |
---|---|---|---|---|---|

Quercetin | 303.15 | 1 | 0.459 ± 0.003 | 0.430 ± 0.014 | −6.30 |

303.15 | 150 | 0.414 ± 0.002 | 0.409 ± 0.010 | −1.21 | |

323.15 | 1 | 0.681 ± 0.002 | 0.702 ± 0.003 | 3.13 | |

323.15 | 150 | 0.616 ± 0.003 | 0.642 ± 0.036 | 4.22 | |

ARD = −0.04% | |||||

AARD = 3.71% | |||||

Gallic acid | 303.15 | 1 | 0.508 ± 0.009 | 0.481 ± 0.014 | −5.31 |

323.15 | 1 | 0.758 ± 0.006 | 0.776 ± 0.028 | 2.37 | |

333.15 | 1 | 0.905 ± 0.011 | 0.960 ± 0.028 | 6.08 | |

ARD = 1.05% | |||||

AARD = 4.59% |

**Table 2.**Experimental (${D}_{12}^{\mathrm{exp}}$) and computed (${D}_{12}^{\mathrm{MD}}$) diffusion coefficients of ibuprofen and butan-1-ol in liquid ethanol at various temperatures and pressures. The computer simulations used ${\sigma}_{\mathrm{OH}}$ = 0.306 nm for ethanol, and the calculated diffusivities were evaluated in comparison with experimental data in terms of the relative deviation (RD), average relative deviation (ARD), and average absolute relative deviation (AARD).

Solute | $\mathit{T}$ (K) | $\mathit{P}$ (bar) | ${\mathit{D}}_{12}^{\mathbf{e}\mathbf{x}\mathbf{p}}\pm \mathbf{\Delta}{\mathit{D}}_{12}^{\mathbf{e}\mathbf{x}\mathbf{p}}$ (10 ^{−9} m^{2} s^{−1}) | ${\mathit{D}}_{12}^{\mathbf{M}\mathbf{D}}\pm \mathbf{\Delta}{\mathit{D}}_{12}^{\mathbf{M}\mathbf{D}}$ (10 ^{−9} m^{2} s^{−1}) | RD (%) |
---|---|---|---|---|---|

ibuprofen | 298.15 | 100 | 0.518 ± 0.070 | 0.528 ± 0.011 | 1.93 |

308.15 | 1 | 0.693 ± 0.070 | 0.686 ± 0.023 | −1.01 | |

308.15 | 300 | 0.581 ± 0.070 | 0.567 ± 0.007 | −2.41 | |

323.15 | 1 | 0.928 ± 0.070 | 0.936 ± 0.020 | 0.86 | |

323.15 | 300 | 0.754 ± 0.070 | 0.754 ± 0.018 | 0.00 | |

333.15 | 100 | 1.04 ± 0.07 | 1.04 ± 0.02 | 0.10 | |

333.15 | 200 | 0.986 ± 0.070 | 1.03 ± 0.03 | 4.26 | |

333.15 | 300 | 0.910 ± 0.070 | 0.927 ± 0.011 | 1.87 | |

ARD = 0.70% | |||||

AARD = 1.55% | |||||

butan-1-ol | 298.15 | 1 | 0.927 | 0.920 ± 0.011 | −0.76 |

333.15 | 1 | 1.84 | 2.00 ± 0.06 | 8.86 | |

ARD = 4.05% | |||||

AARD = 4.81% |

**Table 3.**Experimental (${D}_{11}^{\mathrm{exp}}$) and computed (${D}_{11}^{\mathrm{MD}}$) self-diffusion coefficient of ethanol. The computer simulations used ${\sigma}_{\mathrm{OH}}$ = 0.306 nm for ethanol, and the calculated diffusivities were evaluated in comparison with experimental data in terms of the relative deviation (RD), average relative deviation (ARD), and average absolute relative deviation (AARD).

$\mathit{T}$ (K) | $\mathit{P}$ (bar) | ${\mathit{D}}_{11}^{\mathbf{e}\mathbf{x}\mathbf{p}}$ (10 ^{−9} m^{2} s^{−1}) | ${\mathit{D}}_{11}^{\mathbf{M}\mathbf{D}}$ (10 ^{−9} m^{2} s^{−1}) | RD (%) |
---|---|---|---|---|

298.15 | 1 | 1.05 | 1.01 | −3.81 |

308.15 | 1 | 1.30 | 1.29 | −0.77 |

318.15 | 1 | 1.68 | 1.61 | −4.17 |

328.15 | 1 | 2.06 | 2.00 | −2.91 |

333.15 | 1 | 2.37 | 2.23 | −5.91 |

ARD = −3.51% | ||||

AARD = 3.51% |

**Table 4.**Ethanol’s experimental $\left({\rho}_{}^{\mathrm{exp}}\right)$ and computed (${\rho}^{\mathrm{MD}}$) density and respective relative deviation (RD). The computer simulations used ${\sigma}_{\mathrm{OH}}$ = 0.306 nm for ethanol.

$\mathit{T}$ (K) | $\mathit{P}$ (bar) | ${\mathit{\rho}}_{}^{\mathbf{e}\mathbf{x}\mathbf{p}}$ (kg m ^{−3}) | ${\mathit{\rho}}^{\mathbf{M}\mathbf{D}}$ (kg m ^{−3}) | RD (%) |
---|---|---|---|---|

298.15 | 1 | 786 | 806 | 2.54 |

308.15 | 1 | 776 | 796 | 2.58 |

308.15 | 300 | 795 | 817 | 2.77 |

318.15 | 1 | 767 | 785 | 2.08 |

328.15 | 1 | 759 | 773 | 1.84 |

333.15 | 1 | 754 | 768 | 1.59 |

333.15 | 300 | 782 | 793 | 1.41 |

ARD = 2.12% | ||||

AARD = 2.12% |

**Table 5.**Experimental properties studied for binary (ethanol/solute) or unary (ethanol) systems, number of data points (NDP), temperature ($T$) range, pressure ($P$) range, and data sources.

System | Property | NDP | $\mathit{T}$ (K) | $\mathit{P}$ (bar) | Source |
---|---|---|---|---|---|

EtOH/quercetin | ${D}_{12}$ | 4 | 303.15–323.15 | 1–150 | [46] |

EtOH/gallic acid | ${D}_{12}$ | 3 | 303.15–333.15 | 1 | [5] |

EtOH/ibuprofen | ${D}_{12}$ | 8 | 298.15–333.15 | 1–300 | [4] |

EtOH/butan-1-ol | ${D}_{12}$ | 2 | 298.15–333.15 | 1 | [47] |

EtOH/propanone | ${D}_{12}$ | 2 | 298.15–333.15 | 1 | [48] |

EtOH/butanal | ${D}_{12}$ | 2 | 298.15–333.15 | 1 | [48] |

EtOH/benzene | ${D}_{12}$ | 1 | 313.15 | 1 | [47,49] |

EtOH/propane | ${D}_{12}$ | 1 | 323.15 | 103 | [50] |

EtOH | ${D}_{11}$ | 5 | 298.15–333.15 | 1 | [51,52,53,54,55,56,57,58] |

EtOH | $\rho $ | 8 | 298.15–333.15 | 1–300 | [59,60,61,62] |

EtOH | $\mathsf{\Delta}{H}_{\mathrm{vap}}$ | 1 | 298.15 | 1 | [45] |

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## Share and Cite

**MDPI and ACS Style**

Zêzere, B.; Fonseca, T.V.B.; Portugal, I.; Simões, M.M.Q.; Silva, C.M.; Gomes, J.R.B.
Influence of Ethanol Parametrization on Diffusion Coefficients Using OPLS-AA Force Field. *Int. J. Mol. Sci.* **2023**, *24*, 7316.
https://doi.org/10.3390/ijms24087316

**AMA Style**

Zêzere B, Fonseca TVB, Portugal I, Simões MMQ, Silva CM, Gomes JRB.
Influence of Ethanol Parametrization on Diffusion Coefficients Using OPLS-AA Force Field. *International Journal of Molecular Sciences*. 2023; 24(8):7316.
https://doi.org/10.3390/ijms24087316

**Chicago/Turabian Style**

Zêzere, Bruno, Tiago V. B. Fonseca, Inês Portugal, Mário M. Q. Simões, Carlos M. Silva, and José R. B. Gomes.
2023. "Influence of Ethanol Parametrization on Diffusion Coefficients Using OPLS-AA Force Field" *International Journal of Molecular Sciences* 24, no. 8: 7316.
https://doi.org/10.3390/ijms24087316