Free Energy Difference Research Articles

Dissolution of amyloid aggregates by direct addition of alkali halides

The development of standard dissolution agents for various amyloid aggregates in vitro is essential to acquire basic information on pharmaceutical treatment strategies and improve the recovery rate for target expressed proteins. Nevertheless, no standard dissolution agents are currently applied to many amyloid aggregates. Thus, to proceed one step further, the dissolution ability of α-synuclein amyloid aggregates (α-synuclein amyloid) formed under mild conditions (pD 7.5 and 310 K) was investigated using the direct addition of alkali halides. Fourier-transform infrared spectroscopy and Congo red assay were used to evaluate the efficacy of the dissolution agents of alkali halides for amyloid aggregates. The effects of alkali halides on α- synuclein amyloid were classified into three types: (i) dissolution effect, (ii) no effect, and (iii) promotion effect. These effects correlate with the disruption ability of cations (the direct effect) and the solvation free energy difference (ΔΔGSolv) between the cations and anions (the indirect effect). Remarkably, lithium iodide (LiI) has the strongest dissolution ability for α-synuclein amyloid among the examined alkali halides. Furthermore, dialysis can recover the monomer state from α-synuclein amyloid dissolved in LiI. In addition, LiI also exhibits a strong dissolution ability for bovine insulin amyloid aggregates formed under extreme conditions (pD 1.6 and 363 K). These findings show that LiI has the potential as a standard dissolution agent applied to amyloid aggregates among the alkali halides.

Understanding the transformations of nanoplastic onto phospholipid bilayers: Mechanism, microscopic interaction and cytotoxicity assessment

The ubiquitous nanoplastics are now considered emergent pollutants in environments. Bioaccumulation of nanoplastics is an important indicator of their hazard. In this work, molecular dynamics were used to study the uptake of five nanoplastics (polyvinyl chloride (PVC), polystyrene (PS), polylactic acid (PLA), polypropylene (PP), and polyethylene terephthalate (PET)) onto DPPC (dipalmitoylphosphatidylcholine) bilayers. Results suggest that nanoplastics became compact after they were deposited in the human body. For PET, PLA, and PS nanoplastics, a free energy barrier of 4–22 kcal mol−1 needed to be overcome to transfer these polymers from the interface region to the center of the DPPC bilayer. Besides, the free energy difference of PVC and PP from the bulk H2O to the surface of DPPC was −18.67 kcal mol−1 and −25.94 kcal mol−1, respectively. After uptake, the interaction between nanoplastics and lipid bilayer was dominated by the van der Waals rather than electrostatic interaction. Furthermore, the cytotoxicity of nanoplastics was also evaluated and it is reflected in their ability to decrease the thickness of the lipid bilayer. Overall, this work provides implications for understanding the bioaccumulation and toxicity of nanoplastic at the molecular level.

Interface engineering of hybrid ZnCo2O4@Ni2.5Mo6S6.7 structures for flexible energy storage and alkaline water splitting

Designing electrodes with hybrid structures is significant for improving energy storage and conversion efficiency. Overall, single-component metal oxides suffer from poor working stability and slow ionic electron mobility. In order to solve these problems, based on the easy-to-modify properties of spinel-structured ZnCo2O4, hybrid-structured ZnCo2O4@Ni2.5Mo6S6.7 was successfully grown on nickel foam through hydrothermal synthesis. The hybrid-structured ZnCo2O4@Ni2.5Mo6S6.7 exhibits high specific capacitance of 848 C g−1 at 1 A g−1, and excellent stability. The assembled supercapacitor device reaches a high energy density of 177.9 W kg−1 at 2700 Wh kg−1, excellent cycle performance, and mechanical flexibility. In alkaline water splitting, this hybrid structure presents low overpotentials, low water splitting cell voltage, and excellent stability. Density functional theory calculations confirm that the construction of Ni2.5Mo6S6.7 sulfide shell can reduce hydrogen adsorption energy, increase charge carrier density on the catalyst surface, and achieve a small Gibbs free energy difference in the fundamental rate-determining step, suggesting the improved electrocatalytic performance.

Effect of hydrophobic groups on adsorption of arginine-based amino acids to solid surfaces in water

We calculate the free energies of adsorption between a solid wall and various arginine derivatives in water using molecular dynamics simulations. We vary the hydrophobic group size of the amino acids in two ways and the hydrophilicity of the solid wall in five ways. The free energy of adsorption decreases by increasing the hydrophilicity of the solid wall, regardless of the size of the hydrophobic group. Amino acids with small hydrophobic groups are adsorbed on the solid wall with the strongest hydrophilicity, but the free energy of the amino acids with large hydrophobic groups is relatively small. The free energy of adsorption in benzene solvent is increased by increasing the hydrophilicity of the solid wall; however, analogous to results in water solvent, it is independent of the size of the hydrophobic group. We attribute these differences in free energy to the effect of solvent molecules localized on the solid wall. Thus, these results may modulate peptide adsorption on a solid surface by the size of the peptide’s hydrophobic groups.

PyMM: An Open-Source Python Program for QM/MM Simulations Based on the Perturbed Matrix Method.

Quantum mechanical/molecular mechanics (QM/MM) methods are important tools in molecular modeling as they are able to couple an extended phase space sampling with an accurate description of the electronic properties of the system. Here, we describe a Python software package, called PyMM, which has been developed to apply a QM/MM approach, the perturbed matrix method, in a simple and efficient way. PyMM requires a classical atomic trajectory of the whole system and a set of unperturbed electronic properties of the ground and electronic excited states. The software output includes a set of the most common perturbed properties, such as the electronic excitation energies and the transitions dipole moments, as well as the eigenvectors describing the perturbed electronic states, which can be then used to estimate whatever electronic property. The software is composed of a simple and complete command-line interface, a set of internal input validation, and three main analyses focusing on (i) the perturbed eigenvector behavior, (ii) the calculation of the electronic absorption spectrum, and (iii) the estimation of the free energy differences along a reaction coordinate.

Anharmonic lattice dynamics and structural phase transition of SnTe monolayer from first principles

In this work we investigate the role of quartic anharmonicity on the lattice- and thermo-dynamic properties of rectangular () and square (β) phases of two-dimensional (2D) SnTe monolayer (ML) by using self-consistent phonon (SCP) theory, based on the first-principles calculations. For both phases, as compared to the usual harmonic approximation (HA), the renormalized phonon frequency at the optical modes (4–10) is found to be increased upon the inclusion of quartic anharmonicity via the SCP method, where the effects of cubic anharmonicity are neglected. At the experimentally observed transition temperature (T c = 270 K), the difference in the vibrational free-energy between the square and rectangular phases of SnTe ML, calculated by using the anharmonic SCP correction is found to be much closer to the structural energy gain as compared to that obtained by using only the quasi-harmonic contribution. This validates the significance of SCP approach over the HA to explain the lattice dynamics properties and predict the T c for SnTe ML and similar 2D compounds. The calculated lattice thermal conductivity of square SnTe ML (e.g. 10.67 W m−1K−1 at 300 K) is higher than that of the rectangular SnTe ML (e.g. 6.72 W m−1K−1 at 300 K) due to the relatively higher corresponding thermodynamic parameters: specific heat capacity, group velocity, and phonon lifetime obtained for the square SnTe ML. Particularly, the low energy phonon modes are found to transport most of the heat in the system and, hence, played major role to the total lattice thermal conductivity.

Hydration Free Energies of Polypeptides from Popular Implicit Solvent Models versus All-Atom Simulation Results Based on Molecular Quasichemical Theory.

Calculating the hydration free energy of a macromolecule in all-atom simulations has long remained a challenge, necessitating the use of models wherein the effect of the solvent is captured without explicit account of solvent degrees of freedom. This situation has changed with developments in the molecular quasi-chemical theory (QCT)─an approach that enables calculation of the hydration free energy of macromolecules within all-atom simulations at the same resolution as is possible for small molecular solutes. The theory also provides a rigorous and physically transparent framework to conceptualize and model interactions in molecular solutions and thus provides a convenient framework to investigate the assumptions in implicit solvent models. In this study, we compare the results using molecular QCT versus predictions from EEF1, ABSINTH, and GB/SA implicit solvent models for polyglycine and polyalanine solutes covering a range of chain lengths and conformations. The hydration free energies or the differences in hydration free energies between conformers obtained from the implicit solvent models do not agree with explicit solvent results, with the deviations being largest for the group additive EEF1 and ABSINTH models. GB/SA does better in capturing the qualitative trends seen in explicit solvent results. Analysis founded on QCT reveals the critical importance of the cooperativity of hydration that is inherent in the hydrophilic and hydrophobic contributions to hydration─physics that is not well captured in additive models but somewhat better accounted for by means of a dielectric in the GB/SA approach.

The effects of methanol clustering on methanol-water nucleation.

The formation of subcritical methanol clusters in the vapor phase is known to complicate the analysis of nucleation measurements. Here, we investigate how this process affects the onset of binary nucleation as dilute water-methanol mixtures in nitrogen carrier gas expand in a supersonic nozzle. These are the first reported data for water-methanol nucleation in an expansion device. We start by extending an older monomer-dimer-tetramer equilibrium model to include larger clusters, relying on Helmholtz free energy differences derived from Monte Carlo simulations. The model is validated against the pressure/temperature measurements of Laksmono et al. [Phys. Chem. Chem. Phys. 13, 5855 (2011)] for dilute methanol-nitrogen mixtures expanding in a supersonic flow prior to the appearance of liquid droplets. These data are well fit when the maximum cluster size imax is 6-12. The extended equilibrium model is then used to analyze the current data. On the addition of small amounts of water, heat release prior to particle formation is essentially unchanged from that for pure methanol, but liquid formation proceeds at much higher temperatures. Once water comprises more than ∼24 mol% of the condensable vapor, droplet formation begins at temperatures too high for heat release from subcritical cluster formation to perturb the flow. Comparing the experimental results to binary nucleation theory is challenged by the need to extrapolate data to the subcooled region and by the inapplicability of explicit cluster models that require a minimum of 12 molecules in the critical cluster.

Thermal and Quantum Fluctuation Effects on Non-Spherical Nuclei: The Case of Spin-1 System

In this work, we investigate the collective role of thermal and quantum fluctuations on non-equilibrium thermodynamics of a quantum system, specifically, the quantum-thermodynamic description of spin-1 nuclei based on the concepts of quantum and statistical mechanics. We explore the dynamical response of the system when driven out of equilibrium by a work parameter and compute analytically the full distribution of the work generated by the process. Considering work performed on the system as a random variable, we collect data for a large number of repeated cyclic processes of finite time. These data of finite time non-equilibrium processes will permit us to derive equilibrium values in quantities such as the free energy difference between the final and initial states of the system. Various properties of the system’s work distribution are explored.

Evidence supporting reversible martensitic transformation under cyclic loading on Fe–Mn–Si–Al alloys using in situ neutron diffraction

Fe–Mn–Si-based alloys, such as Fe–30Mn–4Si–2Al and Fe–15Mn–10Cr–8Ni–4Si (in mass%), show superior resistance to plastic fatigue compared to the conventional steels, which is ascribed to the reversible back-and-forth movement of {111}〈112¯〉γ Shockley partial dislocations associated with a reversible martensitic transformation between the face-centered cubic γ-austenite and hexagonal close-packed ε-martensite. The purpose of this study was to gather evidence of the reversible martensitic transformation using in situ neutron diffraction under cyclic loading. Three Fe–30Mn–Si–Al alloys with different Gibbs free energy differences at 298 K: Fe–30Mn–6Si (ΔGγ→ε = −250 J/mol), Fe–30Mn–5Si–1Al (ΔGγ→ε = −128 J/mol), and Fe–30Mn–4Si–2Al (ΔGγ→ε = −8.5 J/mol), were studied to unravel the effect of phase stability on the degree of reversibility. The reversible martensitic transformation between γ-austenite and ε-martensite during tension–compression loading is demonstrated as bulk-averaged insights in the Fe–30Mn–4Si–2Al alloy. The forward γ → ε transformation was induced by tensile loading, and the formed ε plates were reversed to γ during unloading and subsequent compressive loading. Furthermore, successive compressive loading induced a different variant of the ε plates from the variant formed under tensile loading, which also reverted to γ by subsequent tensile loading. Such repetition of the γ ↔ ε transformation in the Fe–30Mn-4Si–2Al alloy is thought to increase the plastic fatigue life compared to the Fe–30Mn–6Si and Fe–30Mn–Si–1Al alloys, in which the γ ↔ ε transformation is rarely reversible. Herein, we discuss the mechanism of the deformation-induced reverse transformation and propose an optimum thermodynamic condition: a negative close-to-zero ΔGγ→ε.

Salt Effect on Donnan Equilibrium in Montmorillonite Demonstrated with Molecular Dynamics Simulations.

Donnan equilibrium governs the distribution of ions in many systems such as ion exchange membranes and biological cells in contact with an external electrolyte. Herein, Donnan equilibrium between bulk salt solution and bihydrated montmorillonite was investigated because such a system is of great importance for many nuclear waste disposal concepts. Specifically, we used molecular dynamics simulations to determine the partition coefficient of chloride, which was achieved by calculating the free-energy difference of chloride in the interlayer and the bulk using enhanced sampling methodology. Montmorillonite in equilibrium with either NaCl or CaCl2 was examined to elucidate the general difference between 1:1 and 2:1 salts. The concentration dependence of the partition coefficient for each salt was determined using three and four concentrations for NaCl and CaCl2, respectively. In the case of NaCl, we found that the partition coefficient increased linearly with the concentration, while for CaCl2, the increase was proportional to the square root of the concentration. A derivation of the partition coefficient using general Donnan theory that includes excess free energy contributions beyond the electrostatic Donnan potential is also presented. For both salts, the agreement between the partition coefficient from the simulations and Donnan theory was excellent. Although Donnan theory is a continuum theory derived without any reference to atomistic details, the present results justify its application to systems with nanoscale pores.

Interfacial engineering of CoMn2O4/NC induced electronic delocalization boosts electrocatalytic nitrogen oxyanions reduction to ammonia

Electrocatalytic nitrate (NO3−) reduction reaction (NO3−RR) is a promising avenue for wastewater treatment and value-added ammonia (NH3) generation. Herein, cobalt manganese spinel nanoparticles embedded in multichannel carbon fibers (CoMn2O4/NC) to obtain optimal NH3 Faradaic efficiency is 92.4% with a yield rate of 144.5 mmol h−1 g−1 at − 0.7 V versus reversible hydrogen electrode (vs. RHE). The interfacial between CoMn2O4 and NC induces the 3d orbital electrons of Co and Mn in less localized states, which promotes *NH3 desorption. Electrochemical in situ Raman spectra and online differential electrochemical mass spectrometry (DEMS) identified the intermediates and products. The theoretical calculation demonstrates that the existence of NC could reduce the free energy difference of the rate-determining step (RDS, 0.42 eV) of NO3−RR, suppressing hydrogen evolution reaction (HER) by enhancing the interaction of *H. Coupled benzyl alcohol oxidation reaction (BOR) with NO2−RR to obtain lower reduction voltage and high value-added anode products.

Extraction of ergotropy: free energy bound and application to open cycle engines

The second law of thermodynamics uses change in free energy of macroscopic systems to set a bound on performed work. Ergotropy plays a similar role in microscopic scenarios, and is defined as the maximum amount of energy that can be extracted from a system by a unitary operation. In this analysis, we quantify how much ergotropy can be induced on a system as a result of system's interaction with a thermal bath, with a perspective of using it as a source of work performed by microscopic machines. We provide the fundamental bound on the amount of ergotropy which can be extracted from environment in this way. The bound is expressed in terms of the non-equilibrium free energy difference and can be saturated in the limit of infinite dimension of the system's Hamiltonian. The ergotropy extraction process leading to this saturation is numerically analyzed for finite dimensional systems. Furthermore, we apply the idea of extraction of ergotropy from environment in a design of a new class of stroke heat engines, which we label open-cycle engines. Efficiency and work production of these machines can be completely optimized for systems of dimensions 2 and 3, and numerical analysis is provided for higher dimensions.

One-pot synthesis of 2,5-bis(hydroxymethyl)furan from biomass derived 5-(chloromethyl)furfural in high yield

5-(Chloromethyl)furfural (CMF), as a new platform molecular, has become a hot topic in the field of biorefinery. Herein, the one-pot conversion of CMF to 2,5-bis(hydroxymethyl)furan (BHMF) in the water phase was demonstrated for the first time. A 91% BHMF yield was obtained over Ru/CuOx catalyst, and BHMF was mainly produced by the consecutive hydrolysis and hydrogenation of CMF with 5-hydroxymethylfurfural (HMF) as an intermediate. Kinetic studies revealed that the conversion of HMF to BHMF was the rate-determining step. Remarkably, the characterizations and density functional theory (DFT) calculations further revealed the lower electron density of Ru NPs in Ru/CuOx catalyst, resulting in a larger adsorption energy and a smaller free energy difference for the formation of alcohols. The present findings offered a new pathway for biomass-derived diol production through CMF as a potential source.

Enantioseparation of planar chiral ferrocenes on cellulose-based chiral stationary phases: Benzoate versus carbamate pendant groups.

In this study, the enantioseparation of 14 planar chiral ferrocenes containing halogen atoms, and methyl, iodoethynyl, phenyl, and 2-naphthyl groups, as substituents, was explored with a cellulose tris(4-methylbenzoate) (CMB)-based chiral column under multimodal elution conditions. n-Hexane/2-propanol (2-PrOH) 95:5 v/v, pure methanol (MeOH), and MeOH/water 90:10 v/v were used as mobile phases (MPs). With CMB, baseline enantioseparations were achieved for nine analytes with separation factors (α) ranging from 1.24 to 1.77, whereas only three analytes could be enantioseparated with 1.14 ≤ α ≤ 1.51 on a cellulose tris(3,5-dimethylphenylcarbamate) (CDMPC)-based column, used as a reference for comparison, under the same elution conditions. Pendant group-dependent reversal of the enantiomer elution order was observed in several cases by changing CMB to CDMPC. The impact of analyte and chiral stationary phase (CSP) structure, and MP polarity on the enantioseparation, was evaluated. The two cellulose-based CSPs featured by different pendant groups were also compared in terms of thermodynamics. For this purpose, enthalpy (ΔΔH°), entropy (ΔΔS°) and free energy (ΔΔG°) differences, isoenantioselective temperatures (Tiso ), and enthalpy/entropy ratios (Q), associated with the enantioseparations, were derived from van 't Hoff plots by using n-hexane/2-PrOH 95:5 v/v and methanol/water 90:10 v/v as MPs. With the aim to disclose the functions of the different substituents in mechanisms and noncovalent interactions underlying analyte-selector complex formation at molecular level, electrostatic potential (V) analysis and molecular dynamics simulations were used as computational techniques. On this basis, enantioseparations and related mechanisms were investigated by integrating theoretical and experimental data.

Effect of phosphorylation on the structural dynamics, thermal stability of human dopamine transporter: A simulation study using normal modes, molecular dynamics and Markov State Model

The Human Dopamine Transporter (hDAT) plays an essential role in modulating the Influx/Efflux of dopamine, and it is involved in the mechanism of certain neurodegenerative diseases such as Parkinson's disease. Several studies have reported important states for Dopamine transport: outward-facing open state (OFo), the outward-facing closed state (OFc), the holo-occluded state closed (holo), and the inward-facing open state (IFo). Furthermore, experimental assays have shown that different phosphorylation conditions in hDAT can affect the rate of dopamine absorption. We present a protocol using hybrid simulation methods to study the conformational dynamics and stability of states of hDAT under different phosphorylation sites. With this protocol, we explored the conformational space of hDAT, identified the states, and evaluated the free energy differences and the transition probabilities between them in each of the phosphorylation cases. We also presented the conformational changes and correlated them with those described in the literature. There is a thesis/hypothesis that the phosphorylation condition corresponding to NP-333 system (where all sites Ser/Thr from residue 2 to 62 and 254 to 613 are phosphorylated, except residue 333) would decrease the rate of dopamine transport from the extracellular medium to the intracellular medium by hDAT as previously described in the literature by Lin et al., 2003. Our results corroborated this thesis/hypothesis and the data reported. It is probably due to the affectation/changes/alteration of the conformational dynamics of this system that makes the intermediate states more likely and makes it difficult to initial states associated with the uptake of dopamine in the extracellular medium, corroborating the experimental results. Furthermore, our results showed that just single phosphorylation/dephosphorylation could alter intrinsic protein motions affecting the sampling of one or more states necessary for dopamine transport. In this sense, the modification of phosphorylation influences protein movements and conformational preferences, affecting the stability of states and the transition between them and, therefore, the transport.

Ion-Pairing Effects on the Absolute Oxidation Potential of the Fc/Fc+ Redox Couple in Complex Non-Aqueous Environments

Ferrocene (Fc) is commonly used as an internal redox couple in electrochemical measurements. Therefore, understanding how the absolute oxidation potential of Fc is modulated by different solvents and ion concentrations is important for facilitating the comparison between different experimental measurements. Standard implicit solvation models are unable to examine these systems since they lack atomistic detail of the solvent structure and ion coordination. Using polarizable forcefields fit to ab initio quantum chemistry calculations, we have computed the absolute oxidation potential of the Fc/Fc+ redox couple in water, acetonitrile, 1,2-dichloroethane, and trichloromethane. Since experimental measurements are often taken in mixtures of nonaqueous solvents and ionic liquids, we have computed the oxidation potential of Fc in mixtures of acetonitrile and 1,2-dichloroethane with an ionic liquid, [BMIM+][BF4-]. In order to elucidate the effect ion-pairing has on the thermodynamics of this electron transfer process, we relate the differential solvation free energy of Fc/Fc+ to anion coordination sampled in molecular simulations. Quantification of these solvation/environmental effects has important implications in how the thermodynamics of electron transfer processes are modulated by ion concentration fluctuations in the electrical double layer at electrode interfaces.

Probing Solvation Thermodynamics of Lithium Battery Electrolytes through Potentiometric Methods

The electrolyte is a principal component of a lithium battery that impacts almost every facet of the battery’s performance. Solvation of lithium ions in electrolyte solution is key to understanding the electrolyte, but our understanding of solvation lags behind its significance. Particularly, estimating solvation free energy has been largely limited to computational simulations. Despite their versatility, simulations can be computationally expensive, and experimental methods to complement simulations are desired.We have recently introduced a potentiometric technique to probe the relative solvation free energy of lithium ions in battery electrolytes. We devised an electrochemical cell composed of two half-cells, with symmetric electrodes but asymmetric electrolytes. Whereas the open circuit potential of a conventional lithium-ion battery measures the free energy differences of lithium ions in the two electrodes, our experimental setup measures the energy differences of the lithium ions in two different electrolytes. By measuring the cell potential with a reference electrolyte, we can quantitatively characterize lithium ion solvation energy of an electrolyte of interest. The effects of concentration, anion and solvent on solvation energy are explored and verified with simulations. Particularly, we establish a correlation between cell potential (Ecell) and cyclability of high-performance electrolytes for lithium metal anodes. We find that solvents with more negative cell potentials and positive solvation energies—those weakly binding to Li+—lead to improved cycling stability. Weaker solvents are conjectured to have more anion-rich solvation structures that lead to anion-derived solid-electrolyte interphases, a hypothesis supported by cryogenic electron microscopy. It reveals that weaker solvation is correlated to an inorganic anion-derived solid-electrolyte interphase that stabilizes cycling.

Quantum algorithms from fluctuation theorems: Thermal-state preparation

Fluctuation theorems provide a correspondence between properties of quantum systems in thermal equilibrium and a work distribution arising in a non-equilibrium process that connects two quantum systems with HamiltoniansH0andH1=H0+V. Building upon these theorems, we present a quantum algorithm to prepare a purification of the thermal state ofH1at inverse temperatureβ≥0starting from a purification of the thermal state ofH0. The complexity of the quantum algorithm, given by the number of uses of certain unitaries, isO~(eβ(ΔA−wl)/2), whereΔAis the free-energy difference betweenH1andH0,andwlis a work cutoff that depends on the properties of the work distribution and the approximation errorϵ>0. If the non-equilibrium process is trivial, this complexity is exponential inβ‖V‖, where‖V‖is the spectral norm ofV. This represents a significant improvement of prior quantum algorithms that have complexity exponential inβ‖H1‖in the regime where‖V‖≪‖H1‖. The dependence of the complexity inϵvaries according to the structure of the quantum systems. It can be exponential in1/ϵin general, but we show it to be sublinear in1/ϵifH0andH1commute, or polynomial in1/ϵifH0andH1are local spin systems. The possibility of applying a unitary that drives the system out of equilibrium allows one to increase the value ofwland improve the complexity even further. To this end, we analyze the complexity for preparing the thermal state of the transverse field Ising model using different non-equilibrium unitary processes and see significant complexity improvements.

Hydrogen Bond Thermodynamics in Aqueous Acid Solutions: A Combined DFT and Classical Force-Field Approach.

The thermodynamics of hydrogen bonds in aqueous and acidic solutions significantly impacts the kinetics and thermodynamics of acid reaction chemistry. We utilize in this work a multiscale approach, combining density functional theory (DFT) with classical molecular dynamics (MD) to model hydrogen bond thermodynamics in an acidic solution. Using thermodynamic cycles, we split the solution phase free energy into its gas phase counterpart plus solvation free energies. We validate this DFT/MD approach by calculating the aqueous phase hydrogen bond free energy between two water molecules (H2O-···-H2O), the free energy to transform an H3O+ cation into an H5O2+ cation, and the hydrogen bond free energy of protonated water clusters (H3O+-···-H2O and H5O2+-···-H2O). The computed equilibrium hydrogen bond free energy of H2O-···-H2O is remarkably accurate, especially considering the large individual contributions to the thermodynamic cycle. Turning to cations, we find the ion to be more stable than H3O+ by roughly 1-2 kBT. This small free energy difference allows for thermal fluctuation between the two idealized motifs, consistent with spectroscopic and simulation studies. Lastly, hydrogen bonding free energies between either H+ cation and H2O in solution were found to be stronger than between two H2O, though much less so than in vacuum because of dielectric screening in solution. Altogether, our results suggest the DFT/MD approach is promising for application in modeling hydrogen bonding and proton transfer thermodynamics in condensed phases.