Classical Density Functional Theory Calculations Research Articles

Computational design of quinone electrolytes for redox flow batteries using high-throughput machine learning and theoretical calculations

Molecular design of redox-active materials with higher solubility and greater redox potential windows is instrumental in enhancing the performance of redox flow batteries Here we propose a computational procedure for a systematic evaluation of organic redox-active species by combining machine learning, quantum-mechanical, and classical density functional theory calculations. 1,517 small quinone molecules were generated from the building blocks of benzoquinone, naphthoquinone, and anthraquinone with different substituent groups. The physics-based methods were used to predict HOMO-LUMO gaps and solvation free energies that account for the redox potential differences and aqueous solubility, respectively. The high-throughput calculations were augmented with the quantitative structure-property relationship analyses and machine learning/graph network modeling to evaluate the materials’ overall behavior. The computational procedure was able to reproduce high-performance cathode electrolyte materials consistent with experimental observations and identify new electrolytes for RFBs by screening 100,000 di-substituted quinone molecules, the largest library of redox-active quinone molecules ever investigated. The efficient computational platform may facilitate a better understanding of the structure-function relationship of quinone molecules and advance the design and application of all-organic active materials for RFBs.

CDFTPY: A python package for performing classical density functional theory calculations for molecular liquids

Classical density functional theory (CDFT) provides a rigorous theoretical framework for the statistical mechanics based analysis of many-body systems. This approach has proven to be successful in simulations of mono-atomic, i.e. simple liquids, and there is an ongoing theoretical effort in extending it to more complex polyatomic, molecular liquid systems. Sharing these developments in the form of open-source and easily accessible codes could greatly benefit these efforts. In this work, we present python-based CDFT code that contains both conventional Reference Interaction Site Model (RISM) and recently developed renormalized site density theory (RSDFT) approach. The current implementation is focused on ion solvation - the problem of both fundamental and practical importance. It allows the calculation of individual ions as well as comparative analysis across a range of interaction parameters. Program summaryProgram Title: cdftpyCPC Library link to program files:https://doi.org/10.17632/p8dsgz5n4g.1Developer's repository link:https://github.com/opencdftLicensing provisions: GPLv3Programming language: python 3.9+Nature of problem: Computational modeling of molecular liquids at the atomistic level of resolution is an important capability across many scientific areas. Classical density functional theory (CDFT) approaches this problem by building statistical mechanics model of the system in terms of its average atomic (site) density. Such an approach can provide orders of magnitudes improvements in efficiency compared to conventional molecular dynamics simulations, but requires special treatment of multi-scale interactions in a molecular liquid. A practical utility of our open-source python based implementation of CDFT is the study the problem solvation of ions or Lennard-Jones particles.Solution method: Python package developed in this work provides two CDFT implementations for molecular liquids - renormalized site density functional theory and reference interaction site model. It enables calculations of thermodynamic and structural properties related to solvation of spherical solutes. The nonlinear integral equations associated with the two methods are solved iteratively, utilizing Fast Fourier Transform (FFT) for the calculation of the numerically intensive convolution integrals. The resulting code provides near instantaneous evaluation of the solvated properties of individual solutes and high-throughput screening across the range of different solute parameters.

Investigation about validity of the Derjaguin approximation for electrostatic interactions for a sphere-sphere system

Validity of the Derjaguin approximation for sphere-sphere electrostatic interactions is investigated by explicitly determining the interactions between two spherical colloids using classical density functional theory (CDFT) solved in bispherical coordinates. The validity rules are summarized as follows. (i) For 1:1 type electrolyte, the Derjaguin approximation is effective for colloid sphere having a diameter down to three times the ion diameter only if the bulk concentration is higher than 0.1 M. (ii) With presence of higher-valence counter-ion, the threshold value bulk concentration rises, and increasing the colloid sphere diameter can lower greatly the threshold value bulk concentration. Encouragingly, over the valid parameter region of the Derjaguin approximation a like-charge attraction can be reproduced accurately. (iii) Both too low and too high surface charge strengths contribute to lower the quality of the Derjaguin approximation; increasing the medium permittivity or system temperature improves the accuracy of the Derjaguin approximation. (iv) Based on the mechanism analysis on the above observations, it is concluded that what matters in determining the validity of the Derjaguin approximation is the potential range of the pure inter-surface electrostatic interactions and the local Debye length rather than the bulk Debye length. Besides, the different expressivity of the influencing factors causing the effective inter-surface electrostatic interactions at different conditions determines the behavior the Derjaguin approximation deviates from the full CDFT calculations.

In Situ Liquid Cell TEM Reveals Bridge-Induced Contact and Fusion of Au Nanocrystals in Aqueous Solution.

Duringnanoparticle coalescence in aqueous solution, dehydration and initial contact of particles are critically important but poorly understood processes. In this work, we used in situ liquid-cell transmission electron microscopy to directly visualize the coalescence process of Au nanocrystals. It is found that the Au atomic nanobridge forms between adjacent nanocrystals that are separated by a ∼0.5 nm hydration layer. The nanobridge structure first induces initial contact of Au nanocrystals over their hydration layers and then surface diffusion and grain boundary migration to rearrange into a single nanocrystal. Classical density functional theory calculations and ab initio molecular dynamics simulations suggest that the formation of the nanobridge can be attributed to the accumulation of auric ions and a higher local supersaturation in the gap, which can promote dehydration, contact, and fusion of Au nanocrystals. The discovery of this multistep process advances our understanding of the nanoparticle coalescence mechanism in aqueous solutions.

Direct Measure of the Dense Methane Phase in Gas Shale Organic Porosity by Neutron Scattering

We report the first direct measurements of methane density in shale gas using small-angle neutron scattering. At a constant pressure, the density of methane in the inorganic pores is similar to the gas bulk density of the system conditions. In contrast, the methane density is 2.1 ± 0.2 times greater in the organic mesopores. Classical density functional theory calculations show that this excess density in the organic pores persists to elevated temperatures, typical of shale gas reservoir conditions, providing new insight into the hydrocarbon storage mechanisms within these reservoirs.

Hard spheres at a planar hard wall: Simulations and density functional theory

Hard spheres are a central and important model reference system for both homogeneous and inhomogeneous fluid systems. In this paper we present new high-precision molecular-dynamics computer simulations for a hard sphere fluid at a planar hard wall. For this system we present benchmark data for the density profile $\rho(z)$ at various bulk densities, the wall surface free energy $\gamma$, the excess adsorption $\Gamma$, and the excess volume $v_{ex}$, which is closely related to $\Gamma$. We compare all benchmark quantities with predictions from state-of-the-art classical density functional theory calculations within the framework of fundamental measure theory. While we find overall good agreement between computer simulations and theory, significant deviations appear at sufficiently high bulk densities.

The Role of Correlation and Solvation in Ion Interactions with B-DNA

The ionic atmospheres around nucleic acids play important roles in biological function. Large-scale explicit solvent simulations coupled to experimental assays such as anomalous small-angle x-ray scattering can provide important insights into the structure and energetics of such atmospheres but are time- and resource intensive. In this article, we use classical density functional theory to explore the balance among ion-DNA, ion-water, and ion-ion interactions in ionic atmospheres of RbCl, SrCl2, and CoHexCl3 (cobalt hexamine chloride) around a B-form DNA molecule. The accuracy of the classical density functional theory calculations was assessed by comparison between simulated and experimental anomalous small-angle x-ray scattering curves, demonstrating that an accurate model should take into account ion-ion correlation and ion hydration forces, DNA topology, and the discrete distribution of charges on the DNA backbone. As expected, these calculations revealed significant differences among monovalent, divalent, and trivalent cation distributions around DNA. Approximately half of the DNA-bound Rb+ ions penetrate into the minor groove of the DNA and half adsorb on the DNA backbone. The fraction of cations in the minor groove decreases for the larger Sr2+ ions and becomes zero for CoHex3+ ions, which all adsorb on the DNA backbone. The distribution of CoHex3+ ions is mainly determined by Coulomb and steric interactions, while ion-correlation forces play a central role in the monovalent Rb+ distribution and a combination of ion-correlation and hydration forces affect the Sr2+ distribution around DNA. This does not imply that correlations in CoHex solutions are weaker or stronger than for other ions. Steric inaccessibility of the grooves to large CoHex ions leads to their binding at the DNA surface. In this binding mode, first-order electrostatic interactions (Coulomb) dominate the overall binding energy as evidenced by low sensitivity of ionic distribution to the presence or absence of second-order electrostatic correlation interactions.

Three-body potential amongst similarly or differently charged cylinder colloids immersed in a simple electrolyte solution

.2D classical density functional theory (CDFT) calculations are performed for three similarly or differently charged cylinder colloids immersed in a 1 : 1 electrolyte solution. Three-body potential is extracted from the calculated grand potential information and main conclusions reached for the three-body potential are summarized as follows: (i) It is indicated that even in the electrostatic systems only involved with the 1 : 1 electrolyte solution and characterized with coupling parameters less than 1.0, wherein the Poisson–Boltzmann equation (PBE) is generally believed to be reliable, the PBE predicts the three-body potential to be in partial conflict with those calculated by the CDFT, whereas the CDFT calculations are in qualitative agreement with computer simulations in similar situations; (ii) The CDFT three-body potential is characterized with a repulsion at short distances plus an attraction even in the 1 : 1 electrolyte solution or a repulsion at large distances (depending on solution conditions) and a continuous decay to zero at longer distances, and the attraction tends to become weaker with the counter-ion diameter; (iii) Given a constant total surface charge magnitude on the three cylinder rods, the three-body potential tends to become less repulsive when the three rods are similarly charged, and conversely, tends to be less attractive when the three rods are differently charged; and (iv) When the three-rod system is differently charged, the three-body potential is relatively insensitive to the counter-ion diameter. Based on analysis of the 3D density profiles of the salt ions calculated by the CDFT, the above findings are explained by a ‘hydrogen-bond’ type mechanism augmented by an aggregation repulsion effect.

Surface Reaction, Solvent Inhomogeneity, and Ion Transport in Electric Double Layers: Predictions from a Classical Density Functional Theory

Electric double layers (EDLs) are formed at the interface of a charged fluid in contact with an electrified surface or an electrode leading to drastic changes in the fluid structure and local thermodynamic properties. Whereas conventional theories of EDLs are often concerned with the local inhomogeneity in terms of ionic distributions near a planar surface, the simplistic model is insufficient to capture many important properties relevant to emerging electrochemical processes for energy storage and conversion. In this talk, we present a few recent applications of the classical density functional theory (CDFT) that account for not only ionic excluded volume effects and electrostatic correlations ignored in conventional theories of EDLs but also electrode geometry and pore size distributions, the local solvent and dielectric inhomogeneity, surface reactions, and hydrodynamic effects. The CDFT calculations will be illustrated with practical examples for unusual ion transport in nanopores, optimization of capacitive energy extraction processes, design of nanostructured electrodes for flow supercapacitors and pseudo-capacitors. The theoretical predictions are validated with experiment results and provide insights for novel electrochemical behavior that are not captured in conventional EDL theories. Acknowledgements: This research is sponsored by the Fluid Interface Reactions, Structures, and Transport (FIRST) Center and the U.S. Department of Energy (DE-FG02-06ER46296). The numerical calculations were performed at the National Energy Research Scientific Computing Center (NERSC).

Unusual effects of solvent polarity on capacitance for organic electrolytes in a nanoporous electrode.

The interplay between ions and solvent molecules inside the nanoporous electrodes of a supercapacitor has not been well understood but could be a fertile ground for new insights into the device's performance. By tuning the dipole moment of the solvent in an organic electrolyte, we find, from classical density functional theory calculations, pronounced oscillation of capacitance with the pore size for a moderately to weakly polar solvent. A quantitative analysis of the electric-double-layer (EDL) structure indicates that the capacitance oscillation shares a similar physical origin to that of an ionic liquid electrolyte: the oscillatory behavior arises from the formation of alternating layers of counterions and coions near strongly charged surfaces. More interestingly, we find that in the large-pore region, the capacitance versus the pore size has a volcano-shaped trend; in other words, there exists a solvent dipole moment that yields a maximal capacitance. These theoretical predictions can be validated with future experiments and highlight the great potential in tuning the organic solvent to achieve optimal performance of EDL capacitors.

Response behavior of diblock copolymer brushes in explicit solvent

The understanding of phase behavior of copolymer brushes is of fundamental importance for the design of smart materials. In this paper, we have performed classical density functional theory calculations to study diblock copolymer brushes (A-B) in an explicit solvent which prefers the A block to B block. With increasing B-block length (N(B)), we find a structural transition of the copolymer brush from mixed to collapsed, partial-exposed, and exposed structure, which is qualitatively consistent with experiments. The phase transitions are attributed to the interplay between entropic cost of folding copolymer brushes and enthalpic effect of contact between unlike components. In addition, we examine the effect of different parameters, such as grafting density (ρ(g)), the bottom block length (N(A)), and the chain length of solvent (N(S)) on the solvent response of copolymer brushes. The transition chain length (N(B)) increases with decreasing ρ(g) and N(A), and a smaller solvent molecule makes the collapsed structure less stable due to its lower penetration cost. Our results provide the insight to phase behavior of copolymer brushes in selective solvents from a molecular view.

Solvent response of mixed polymer brushes

We have performed classical density functional theory calculations to study the behavior of mixed polymer brushes tethered to a planar surface. We assume no lateral segregation of the polymer at the grafting density studied and consider an implicit solvent. For a binary mixture of short and long athermal polymer chains, the short chain is compressed while the long chain is stretched compared with corresponding pure polymer chains at the same grafting density, which is consistent with simulation. This results from configurational entropy effects. Furthermore, we add a mean-field interaction for each polymer brush to simulate their different response towards a solvent. The long chain is forced to dislike the solvent more than the short chain. Through the interplay between the solvent effects and configurational entropy effects, a switch of the polymer brush surface (or outer) layer is found with increasing chain length of the long chain. The transition chain length (long chain) increases with increasing the solvent selectivity, and decreases with increasing the grafting density of the long chain. These results can provide guidance for the design of smart materials based on mixed polymer brushes.

Low-Density/High-Density Liquid Phase Transition for Model Globular Proteins

The effect of molecule size (excluded volume) and the range of interaction on the surface tension, phase diagram, and nucleation properties of a model globular protein is investigated using a combination of Monte Carlo simulations and finite temperature classical density functional theory calculations. We use a parametrized potential that can vary smoothly from the standard Lennard-Jones interaction characteristic of simple fluids to the ten Wolde-Frenkel model for the effective interaction of globular proteins in solution. We find that the large excluded volume characteristic of large macromolecules such as proteins is the dominant effect in determining the liquid-vapor surface tension and nucleation properties. The variation of the range of the potential is important only in the case of small excluded volumes such as for simple fluids. The DFT calculations are then used to study the homogeneous nucleation of the high-density phase from the low-density phase including the nucleation barriers, nucleation pathways, and rate. It is found that the nucleation barriers are typically only a few k(B)T and that the nucleation rates are substantially higher than would be predicted by classical nucleation theory.

Theoretical Evidence for a Dense Fluid Precursor to Crystallization

We present classical density functional theory calculations of the free-energy landscape for fluids below their triple point as a function of density and crystallinity. We find that, both for a model globular protein and for a simple atomic fluid modeled with a Lennard-Jones interaction, it is free-energetically easier to crystallize by passing through a metastable dense fluid in accord with the Ostwald rule of stages but in contrast to the alternative of ordering and densifying at once as assumed in the classical picture of crystallization.