A Molecular Dynamics Approach to Calculate the Thermodiffusion (Soret and Seebeck) Coefficients of Salts in Aqueous Solutions

<div><div><div><p>An approach to investigate the physical parameters related to the ions thermodiffusion in aqueous solution is proposed herein by calculating the equilibrium hydration free energy and the self-diffusion coefficient as a function of temperature, ranging from 293 to 353 K, using molecular dynamics simulations of infinitely diluted ions in aqueous solutions. Several ion force field parameters are used in the simulations and new parameters are proposed for some ions to better describe their hydration free energy. Such a theoretical framework enables the calculation of some single-ion properties, such as heat of transport, Soret coefficient and mass current density, as well as properties of salts, such as effective mass and thermal diffusion, Soret and Seebeck coefficients. These calculated properties are compared with experimental data available from optical measurements and showed good agreement revealing an excellent theoretical predictability of salt thermodiffusion properties. Differences in single-ion Soret and self-diffusion coefficients of anions and cations give rise to a thermoelectric field, which affects the system response that is quantified by the Seebeck coefficient. The fast and slow Seebeck coefficients are calculated and discussed, resulting in values with mV/K order-of-magnitude, as observed in experiments involving several salts, such as K+Cl−, Na+Cl−, H+Cl−, Na+OH−, TMA+OH− and TBA+OH−. The present approach can be adopted for any ion or charged particle dispersed in water with the aim of predicting the thermoelectric field induced through the fluid. It has potential applications in designing electrolytes for ionic thermoelectric devices in order to harvest energy and thermoelectricity in biological nanofluids.</p></div></div></div>

A Molecular Dynamics Approach to Calculate the Thermodiffusion (Soret and Seebeck) Coefficients of Salts in Aqueous Solutions

<div><div><div><p>An approach to investigate the physical parameters related to the ions thermodiffusion in aqueous solution is proposed herein by calculating the equilibrium hydration free energy and the self-diffusion coefficient as a function of temperature, ranging from 293 to 353 K, using molecular dynamics simulations of infinitely diluted ions in aqueous solutions. Several ion force field parameters are used in the simulations and new parameters are proposed for some ions to better describe their hydration free energy. Such a theoretical framework enables the calculation of some single-ion properties, such as heat of transport, Soret coefficient and mass current density, as well as properties of salts, such as effective mass and thermal diffusion, Soret and Seebeck coefficients. These calculated properties are compared with experimental data available from optical measurements and showed good agreement revealing an excellent theoretical predictability of salt thermodiffusion properties. Differences in single-ion Soret and self-diffusion coefficients of anions and cations give rise to a thermoelectric field, which affects the system response that is quantified by the Seebeck coefficient. The fast and slow Seebeck coefficients are calculated and discussed, resulting in values with mV/K order-of-magnitude, as observed in experiments involving several salts, such as K+Cl−, Na+Cl−, H+Cl−, Na+OH−, TMA+OH− and TBA+OH−. The present approach can be adopted for any ion or charged particle dispersed in water with the aim of predicting the thermoelectric field induced through the fluid. It has potential applications in designing electrolytes for ionic thermoelectric devices in order to harvest energy and thermoelectricity in biological nanofluids.</p></div></div></div>

Absolute ion hydration free energy scale and the surface potential of water via quantum simulation

With a goal of determining an absolute free energy scale for ion hydration, quasi-chemical theory and ab initio quantum mechanical simulations are employed to obtain an accurate value for the bulk hydration free energy of the Na+ion. The free energy is partitioned into three parts: 1) the inner-shell or chemical contribution that includes direct interactions of the ion with nearby waters, 2) the packing free energy that is the work to produce a cavity of size λ in water, and 3) the long-range contribution that involves all interactions outside the inner shell. The interfacial potential contribution to the free energy resides in the long-range term. By averaging cation and anion data for that contribution, cumulant terms of all odd orders in the electrostatic potential are removed. The computed total is then the bulk hydration free energy. Comparison with the experimentally derived real hydration free energy produces an effective surface potential of water in the range −0.4 to −0.5 V. The result is consistent with a variety of experiments concerning acid–base chemistry, ion distributions near hydrophobic interfaces, and electric fields near the surface of water droplets.

Water Dipole and Quadrupole Moment Contributions to the Ion Hydration Free Energy by the Deep Neural Network Trained with Ab Initio Molecular Dynamics Data

<div>We report a calculation scheme on water molecular dipole and quadrupole moments in the liquid phase through a Deep Neural Network (DNN) model. Employing the the Maximally Localized Wannier Functions (MLWF) for the valence electrons, we obtain the water moments through a post-process on trajectories from \textit{ab-initio} molecular dynamics (AIMD) simulations at the density functional theory (DFT) level. In the framework of the deep potential molecular dynamics (DPMD), we develop a scheme to train a DNN with the AIMD moments data. Applying the model, we calculate the contributions from water dipole and quadrupole moments to the electrostatic potential at the center of a cavity of radius 4.1 \AA\ as -3.87 V, referenced to the average potential in the bulk-like liquid region.</div><div>To unravel the ion-independent water effective local potential contribution to the ion hydration free energy, we estimate the 3rd cumulant term as -0.22 V from simulations totally over 6 ns, a time-scale inaccessible for AIMD calculations. </div>

Water Dipole and Quadrupole Moment Contributions to the Ion Hydration Free Energy by the Deep Neural Network Trained with Ab Initio Molecular Dynamics Data

<div>We report a calculation scheme on water molecular dipole and quadrupole moments in the liquid phase through a Deep Neural Network (DNN) model. Employing the the Maximally Localized Wannier Functions (MLWF) for the valence electrons, we obtain the water moments through a post-process on trajectories from \textit{ab-initio} molecular dynamics (AIMD) simulations at the density functional theory (DFT) level. In the framework of the deep potential molecular dynamics (DPMD), we develop a scheme to train a DNN with the AIMD moments data. Applying the model, we calculate the contributions from water dipole and quadrupole moments to the electrostatic potential at the center of a cavity of radius 4.1 \AA\ as -3.87 V, referenced to the average potential in the bulk-like liquid region.</div><div>To unravel the ion-independent water effective local potential contribution to the ion hydration free energy, we estimate the 3rd cumulant term as -0.22 V from simulations totally over 6 ns, a time-scale inaccessible for AIMD calculations. </div>

A Simple Method for Including Polarization Effects in Solvation Free Energy Calculations When Using Fixed-Charge Force Fields: Alchemically Polarized Charges.

<div><div>The incorporation of polarizability in classical force-field molecular simulations is an ongoing area of research. We focus here on its application to hydration free energy simulations of organic molecules. In contrast to computationally complex approaches involving the development of explicitly polarizable force fields, we present herein a simple methodology for incorporating polarization into such simulations using standard fixed-charge force-fields, which we call the Alchemically Polarized Charges (APolQ) method. APolQ employs a standard classical alchemical free energy change simulation to calculate the free energy difference between a fully polarized solute particle in a condensed phase and its unpolarized state in a vacuum. One electronic structure (ES) calculation to of the electron densities is required for each state: for the former, we use a Polarizable Continuum Model (PCM), and for the latter we use vacuum-phase electronic structure calculations.</div><div><br></div><div>We applied APolQ to hydration free energy data for a test set of 45 neutral solute molecules in the FreeSolv database, and compared results obtained using three different water models (SPC/E, TIP3P, OPC3) and using MBIS and RESP partial charge methodologies. ES calculations were carried out at the MP2 level of theory and with cc-pVTZ and aug-cc-pVTZ basis sets. In comparison with AM1-BCC, we found that APolQ outperforms it for the test set. Despite our method using default GAFF parameters, the MBIS partial charges yield Absolute Average Deviations (AAD) 1.5 to 1.9 kJ·mol⁻¹ lower than AM1-BCC.</div><div><br></div><div>We conjecture that this method can be further improved by fitting the Lennard-Jones and torsional parameters to partial charges derived using MBIS or RESP methodologies. </div></div>

A Simple Method for Including Polarization Effects in Solvation Free Energy Calculations When Using Fixed-Charge Force Fields: Alchemically Polarized Charges.

<div><div>The incorporation of polarizability in classical force-field molecular simulations is an ongoing area of research. We focus here on its application to hydration free energy simulations of organic molecules. In contrast to computationally complex approaches involving the development of explicitly polarizable force fields, we present herein a simple methodology for incorporating polarization into such simulations using standard fixed-charge force-fields, which we call the Alchemically Polarized Charges (APolQ) method. APolQ employs a standard classical alchemical free energy change simulation to calculate the free energy difference between a fully polarized solute particle in a condensed phase and its unpolarized state in a vacuum. One electronic structure (ES) calculation to of the electron densities is required for each state: for the former, we use a Polarizable Continuum Model (PCM), and for the latter we use vacuum-phase electronic structure calculations.</div><div><br></div><div>We applied APolQ to hydration free energy data for a test set of 45 neutral solute molecules in the FreeSolv database, and compared results obtained using three different water models (SPC/E, TIP3P, OPC3) and using MBIS and RESP partial charge methodologies. ES calculations were carried out at the MP2 level of theory and with cc-pVTZ and aug-cc-pVTZ basis sets. In comparison with AM1-BCC, we found that APolQ outperforms it for the test set. Despite our method using default GAFF parameters, the MBIS partial charges yield Absolute Average Deviations (AAD) 1.5 to 1.9 kJ·mol⁻¹ lower than AM1-BCC.</div><div><br></div><div>We conjecture that this method can be further improved by fitting the Lennard-Jones and torsional parameters to partial charges derived using MBIS or RESP methodologies. </div></div>