A density functional approach to nucleation in microemulsions

A material with memory typically has a set of many free energy functionals associated with it, all members of which yield the same constitutive relations. An alternative interpretation of this set is explored in the present work. Explicit formulae are derived for the free energy and total dissipation of an arbitrary material in the cases of step function and sinusoidal/exponential histories. Expressions for the fraction of stored and dissipated energy are deduced. Also, various formulae are given for discrete spectrum materials. For materials with relaxation function containing one decaying exponential, the associated Day functional is the physical free energy. For more general materials, we seek a best fit of the relaxation function with one decaying exponential to that chosen for the general case. The free energy, total dissipation and fractions of stored and dissipated energies relating to the Day material are derived for the various histories. Similar data, in the case of the general material, are explored for the minimum and maximum free energies and also for a centrally located free energy given in the literature. Various plots of aspects of this data, including comparisons between the behaviour for general and Day materials, are presented and discussed.

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.

Inhomogeneous solvation theory (IST) and classical density functional theory (DFT) each provide a framework for relating distribution functions of solutions to their thermodynamic properties. As reviewed in this work, both IST and DFT can be formulated in a way that use two "end point" simulations, one of the pure solvent and the other of the solution, to determine the solute chemical potential and other thermodynamic properties of the solution and of subvolumes in regions local to the solute containing hydrating waters. In contrast to IST, where expressions for the excess energy and entropy of solution are the object of analysis, in the DFT end point formulation of the problem, the solute-solvent potential of mean force (PMF) plays a central role. The indirect part of the PMF corresponds to the lowest order (1-body) truncation of the IST expression. Because the PMF is a free energy function, powerful numerical methods can be used to estimate it. We show that the DFT expressions for the solute excess chemical potential can be written in a form which is local, involving integrals only over regions proximate to the solute. The DFT end point route to estimating solvation free energies provides an alternative path to that of IST for analyzing solvation effects on molecular recognition and conformational changes in solution, which can lead to new insights. In order to illustrate the kind of information that is contained in the solute-solvent PMF, we have carried out simulations of β-cyclodextrin in water. This solute is a well studied "host" molecule to which "guest" molecules bind; host-guest systems serve as models for molecular recognition. We illustrate the range of values the direct and indirect parts of the solute-solvent PMF can have as a water molecule is brought to the interface of β-cyclodextrin from the bulk; we discuss the "competition" between these two terms, and the role it plays in molecular recognition.

Energetics of Storage and Diffusion of Water and Cyclo-Octasulfur for a Nonpolar Cavity of RHCC Tetrabrachion by Molecular Dynamics Simulations

The energetic contributions of individual DNA-contacting side chains to specific DNA recognition in the human papillomavirus 16 E2C-DNA complex is small (less than 1.0 kcal mol(-1)), independent of the physical and chemical nature of the interaction, and is strictly additive. The sum of the individual contributions differs 1.0 kcal mol(-1) from the binding energy of the wild-type protein. This difference corresponds to the contribution from the deformability of the DNA, known as "indirect readout." Thus, we can dissect the energetic contribution to DNA binding into 90% direct and 10% indirect readout components. The lack of high energy interactions indicates the absence of "hot spots," such as those found in protein-protein interfaces. These results are compatible with a highly dynamic and "wet" protein-DNA interface, yet highly specific and tight, where individual interactions are constantly being formed and broken.

Calcium-dependent lectin I from Pseudomonas aeruginosa (PA-IL) binds specifically to oligosaccharides presenting an alpha-galactose residue at their nonreducing end, such as the disaccharides alphaGal1-2betaGalOMe, alphaGal1-3betaGalOMe, and alphaGal1-4betaGalOMe. This provides a unique model for studying the effect of the glycosidic linkage of the ligands on structure and thermodynamics of the complexes by means of experimental and theoretical tools. The structural features of PA-IL in complex with the three disaccharides were established by docking and molecular dynamics simulations and compared with those observed in available crystal structures, including PA-IL.alphaGal1-2betaGalOMe complex, which was solved at 2.4 A resolution and reported herein. The role of a structural bridge water molecule in the binding site of PA-IL was also elucidated through molecular dynamics simulations and free energy calculations. This water molecule establishes three very stable hydrogen bonds with O6 of nonreducing galactose, oxygen from Pro-51 main chain, and nitrogen from Gln-53 main chain of the lectin binding site. Binding free energies for PA-IL in complex with the three disaccharides were investigated, and the results were compared with the experimental data determined by titration microcalorimetry. When the bridge water molecule was included in the free energy calculations, the simulations predicted the correct binding affinity trends with the 1-2-linked disaccharide presenting three times stronger affinity ligand than the other two. These results highlight the role of the water molecule in the binding site of PA-IL and indicate that it should be taken into account when designing glycoderivatives active against P. aeruginosa adhesion.

To understand water-protein interactions in solution, the electrostatic field is calculated by solving the Poisson-Boltzmann equation, and the free energy surface of water is mapped by translating and rotating an explicit water molecule around the protein. The calculation is applied to T4 lysozyme with data available on the conservation of solvent binding sites in 18 crystallographically independent molecules. The free energy maps around the ordered water sites provide information on the relationship between water positions in crystal structure and in solution. Results show that almost all conserved sites and the majority of nonconserved sites are within 1.3 A of local free energy minima. This finding is in sharp contrast to the behavior of randomly placed water molecules in the boundary layer, which, on the average, must travel more than 3 A to the nearest free energy minimum. Thus, the solvation sites are at least partially determined by protein-water interactions rather than by crystal packing alone. The characteristic water residence times, obtained from the free energies at the local minima, are in good agreement with nuclear magnetic resonance experiments. Only about half of the potential sites show up as ordered water in the 1.7 A resolution X-ray structure. Crystal packing interactions can stabilize weak or mobile potential sites (in fact, some ordered water positions are not close to free energy minima) or can prevent water from occupying certain sites. Apart from a few buried water molecules that are strong binders, the free energies are not very different for conserved and nonconserved sites. We show that conservation of a water site between two crystals occurs if the positions of protein atoms, primarily contributing to the free energy at the local minimum, do not substantially change from one structure to the other. This requirement can be correlated with the nature of the side chain contacting the water molecule in the site.

Fulvic (FA) and humic acids (HA) from the solubilization of organic matter are significant agents of the complex of metallic ions in soil and water. Cadmium ions are important natural water pollutants which are discharged along with electroplating and zinc metallurgy liquid wastes, zinc and cadmium being always associated with isomorphic substitution. In this paper we study the complexes formed by Zn2+ and Cd2+ with fulvic acids, using computational chemistry. We carried out relative free energy calculations using a thermodynamic cycle and Free Energy Pertubation (FEP) and Density Functional Theory (DFT-B3LYP/6-31G**) methods. We also computed the interaction energies between orbitals from Natural Bond Order (NBO) calculations. Cd-FA complexes, octahedral with four water molecules in the coordination sphere are more stable than Zn-FA complexes, tetrahedral with two water molecules. This means that FA should be a better ligand for Cd2+ bioavailability and toxicity in natural aquatic environments.

We studied the low-pressure (0–10 GPa) phase diagram of crystalline benzene using quantum Monte Carlo and density functional theory (DFT) methods. We performed diffusion quantum Monte Carlo (DMC) calculations to obtain accurate static phase diagrams as benchmarks for modern van der Waals density functionals. Using density functional perturbation theory, we computed the phonon contributions to the free energies. Our DFT enthalpy-pressure phase diagrams indicate that the Pbca and P21/c structures are the most stable phases within the studied pressure range. The DMC Gibbs free-energy calculations predict that the room temperature Pbca to P21/c phase transition occurs at 2.1(1) GPa. This prediction is consistent with available experimental results at room temperature. Our DMC calculations give 50.6 ± 0.5 kJ/mol for crystalline benzene lattice energy.

Sampling the shallow free energy surface of hydrated atmospheric molecular clusters is a significant challenge. Using computational methods, we present an efficient approach to obtain minimum free energy structures for large hydrated clusters of atmospheric relevance. We study clusters consisting of two to four sulfuric acid (sa) molecules and hydrate them with up to five water (w) molecules. The structures of the "dry" clusters are obtained using the ABCluster program to yield a large pool of low-lying conformer minima with respect to free energy. The conformers (up to ten) lowest in free energy are then hydrated using our recently developed systematic hydrate sampling technique. Using this approach, we identify a total of 1145 unique (sa)2-4(w)1-5 cluster structures. The cluster geometries and thermochemical parameters are calculated at the ωB97X-D/6-31++G(d,p) level of theory, at 298.15 K and 1 atm. The single-point energy of the most stable clusters is calculated using a high-level DLPNO-CCSD(T0)/aug-cc-pVTZ method. Using the thermochemical data, we calculate the equilibrium hydrate distribution of the clusters under atmospheric conditions and find that the larger (sa)3 and (sa)4 clusters are significantly more hydrated than the smaller (sa)2 cluster or the sulfuric acid (sa)1 molecule. These findings indicate that more than five water molecules might be required to fully saturate the sulfuric acid clusters with water under atmospheric conditions. The presented methodology gives modelers a tool to take the effect of water explicitly into account in atmospheric particle formation models based on quantum chemistry.

The mechanism of forming an oxime from nucleophilic addition of a hydroxylamine to a ketone is taught early on in most courses of organic chemistry. Here I subject the first step of this reaction to form a tetrahedral intermediate to quantum mechanical scrutiny. The first decision is to decide which atom of the hydroxylamine acts as the nucleophile. Reaction 1 shows the oxygen and reaction 2 the nitrogen. The text books will tell you that nitrogen nucleophiles are better than oxygen ones. This is because nitrogen is less electronegative than oxygen (it has a smaller nuclear charge) and so binds its single lone pair less tightly than oxygen does its two lone pairs. Sometimes the Klopman-Salem equation is invoked, which tells you that the reactivity is directly proportional to the overlap between the donor MO and the (empty) acceptor MO, and inversely proportional to the energy gap between these two orbitals. Nitrogen wins out because its lone pair is “larger” and hence overlaps better, and because its donor MO energy is higher than oxygen and hence the energy gap between it and the π* C=O acceptor is lower. Reality check: We need to construct a suitable transition state for both possibilities, and then compare their free energies. There is a choice of choosing a stepwise pathway (the one shown in all the text books) in which the bond from N or O to C is formed in an initial step, and then followed by a step often just labelled PT to transfer the proton using solvent molecules. These two steps can also be conflated into a single concerted mechanism involving a 6-membered ring transition state. Quantum mechanically, this latter option has the advantage of avoiding any great build up of charge separation at any stage in the mechanism, but has the disadvantage that the entropic loss at the transition state is greater (although “borrowing” a water molecule from a bulk solvent for this purpose is easier than doing so from an infinite distance away). Shown below is a ωB97XD/6-311G(d,p)/SCRF=water calculation of the transition state for N-attack. It has a dipole moment of 6.2D, which is really quite small, and far from that expected for the zwitterionic intermediate shown in the stepwise mechanism (that would be between 15-30D). Cyclic transition state for N-attack. Click for animation of transition mode. The intrinsic reaction coordinate shows a concerted reaction with quite a small barrier. It is small because the nitrogen is in fact a super-nucleophile, its nucleophilicity has been augmented over that of a simple amine by a so-called α-effect from the adjacent two pairs of lone pairs on the oxygen activating the nitrogen lone pair by lone-pair repulsions. The gradient norm along the coordinate also shows an almost synchronous reaction. The only blip occurs at around IRC +1.3, and this corresponds to the transfer of a proton from NH to a water molecule. An earlier proton transfer from water to the carbonyl oxygen was essentially synchronous with formation of the N-C bond. This synchronicity is what helps avoid any large build up of charge separation. For this reason, I cannot help but feel that the text books could absorb this lesson and show a cyclic concerted reaction mechanism as a probable alternative to two stepwise processes. Next, O-attack. The IRC for this isomeric mode shows a significantly higher barrier compared to N (the computed relative free energies show the O to be higher by 8.3 kcal/mol than the N) and smaller exothermicity. It reveals even greater synchrony of the two proton transfers with the O-C bond formation. So we have a reality check of the text-books on this point in the form of an energy difference, which is always useful. O-attack. Click for animation of reaction mode. Now that our proton transfers are involved in the mechanism, it is time to take a closer look at the geometry of these transfers. On this point, the text books tell us that the most favourable geometry for a proton transfer is having the proton co-linear with the two oxygens. Whilst this is largely true for the geometries shown above, the resulting 6-membered ring as a result adopts a triangular shape, which is not ideal for the bond angles. This could be solved by incorporating a second water molecule, to give us model 3 shown above. A second water molecule can be placed in two alternative positions. The first simply solvates the 6-ring transition state. The second actively participates via an enlarged 8-membered ring transition state. It turns out that the latter is lower by 4.5 kcal/mol in free energy, largely due to the far better bond angles and the almost exactly linear proton transfers now possible. O-Transition state with two water molecules, one merely hydrogen bonding to the 6-ring (magenta arrow). O-Transition state with two water molecules, both part of a cyclic transition state. So the following is our best model. It is 10.4 kcal/mol lower in free energy than the isomeric O-attack transition state. The timing of the bonds shows that N-C formation coincides with the first proton transfer to the carbonyl oxygen, followed by an O to O proton transfer and finally N to O. The dipole moment at the transition state is 5.9D, revealing little explicit charge separation. N-attack via an 8-ring transition state. Click to view animation of reaction mode. It is worth concluding this exploration by reiterating that the models above are not complete. A bulk solvent would allow (statistical) participation of more than just two solvent molecules, and the dynamics of such a (very complex) process has yet to be explored. But I hope what you see here is a bit closer to “reality” than many a text-book author has when they illustrate their books. doi:10042/a3uxl

In our recent efforts to map protein surfaces using mixed-solvent molecular dynamics (MixMD) (Ghanakota, P.; Carlson, H. A. Moving Beyond Active-Site Detection: MixMD Applied to Allosteric Systems. J. Phys. Chem. B 2016, 120, 8685-8695), we were able to successfully capture active sites and allosteric sites within the top-four most occupied hotspots. In this study, we describe our approach for estimating the thermodynamic profile of the binding sites identified by MixMD. First, we establish a framework for calculating free energies from MixMD simulations, and we compare our approach to alternative methods. Second, we present a means to obtain a relative ranking of the binding sites by their configurational entropy. The theoretical maximum and minimum free energy and entropy values achievable under such a framework along with the limitations of the techniques are discussed. Using this approach, the free energy and relative entropy ranking of the top-four MixMD binding sites were computed and analyzed across our allosteric protein targets: Abl Kinase, Androgen Receptor, Pdk1 Kinase, Farnesyl Pyrophosphate Synthase, Chk1 Kinase, Glucokinase, and Protein Tyrosine Phosphatase 1B.

Silicone/ZnO nanorod composite coating as a marine antifouling surface

Influence of sulfur vacancy on pyrite oxidization by water and oxygen molecules

Despite the interest in renewable energy as a substitute for fossil fuels, renewables make up less than 20%1 of total electrical energy in the United States in part because their intermittency prevents them from being a dominant fraction without storage.2 The redox flow battery (RFB) is a promising energy storage technology because of its high-power density and long lifetime,2 which can be used to address intermittency by decoupling customer demand and renewable electricity generation. Currently, however, RFBs incur substantial energy losses during operation at high current densities and are therefore too costly for market deployment. A promising chemistry for the positive electrode of a RFB which would improve efficiency by increasing the total voltage is the cerium redox couple, which has a potential up to 0.74 V greater than the positive vanadium electrode.3,4 The Ce3+/Ce4+ electron transfer redox potential changes depending on the electrolyte,3 which we hypothesize is due to the anion complexation thermodynamics. It is not currently clear whether only one or both of the Ce ions are complexed by anions in solution. Knowledge of the structures and free energies of cerium ions in acidic electrolytes would enable control over the Ce3+/Ce4+ redox potential for RFB applications. Additionally, understanding whether the Ce3+/Ce4+ redox reaction involves a change in the inner sphere is important for discerning the charge transfer mechanism and kinetics.In addition to a lack of information on the structure of Ce3+ and Ce4+ anions in acids, previous work in zinc-cerium5,6 and hydrogen-cerium7 batteries show that the cerium electrode kinetics are a limiting factor on battery performance. Our preliminary kinetic studies of the redox couple in sulfuric acid indicate that the kinetics are influenced more by the electrolyte than by the electrode material, which is consistent with an outer-sphere electron transfer mechanism. If the Ce3+/Ce4+ electron transfer does proceed via an apparent outer-sphere mechanism, the reorganization energy,8 which is dependent on the electrolyte, will control the rate of reaction. To determine whether the reaction follows an outer-sphere mechanism, we must isolate the behavior of the cerium ions at the electrode interface. In this study, we therefore explore the structure of the electrode-electrolyte interface as well as study the structure of cerium anion complexes.To probe the electrode-electrolyte interface, we use in-situ Extended X-ray Absorption Fine Structure (EXAFS) of the platinum (Pt) L3-edge of a Pt electrode during Ce3+ oxidation in two of the most relevant electrolytes for battery applications, H2SO4 and CH3SO3H. At the high positive potentials applied, the Pt is oxidized, and therefore the relevant electrode is a Pt-oxide. To study the ionic structure in different aqueous acidic electrolytes (i.e., HCl, H2SO4, H3NSO3, CH3SO3H, HNO3, CF3SO3H, and HClO4) and extract free energies of Ce3+ and Ce4+ complexes, we use experimental UV-Vis spectroscopy and EXAFS, and Density Functional Theory (DFT) calculations. Based on the combination of spectroscopy, DFT calculations, and the direction of the redox potential shift from non-complexing media, we hypothesize that Ce4+ is complexed by anions in electrolyte, while Ce3+ is hydrated by water. We find from the UV-Vis spectra that the dominant Ce3+ structure is the same in all acids studied, and that the dominant Ce4+ complex changes with electrolyte. EXAFS of Ce3+ allows us to determine a coordination number of nine water molecules. Our DFT calculations enable us to extract bond lengths of the first coordination shell of the cerium ions. The DFT-predicted free energies of Ce4+ anion complexation agree with free energies we calculated from redox potentials reported in literature, supporting our hypothesis that the shift in redox potential can be attributed to the anion complexation of Ce4+. Additionally, this agreement shows that we can predict standard redox potentials for cerium in simple aqueous electrolytes. Ultimately, these characterization findings clarify the fundamental interactions of cerium ions with their electrolyte environment and a relevant electrode as well as the Ce3+/Ce4+ thermodynamics and will guide kinetics studies of the Ce3+/Ce4+ redox couple for use in redox flow battery applications. U.S. EIA, Electric Power Annual (2019).Weber, A. et al. J. Appl. Electrochem. 41, 1137–1164 (2011).Piro, N. et al. Coord. Chem. Rev. 260, 21–36 (2014).Smith, G. & Getz, C. Ind. Eng. Chem. Res. 10, 191–195 (1938).Walsh, F. et al. Chempluschem 80, 288–311 (2015).Nikiforidis, G. et al. Electrochim. Acta 140, 139–144 (2014).Tucker, M. et al. J. Power Sources 327, 591–598 (2016).Bard, A. & Faulkner, L. (John Wiley & Sons, Inc., 2001).