Additive energy functions have predictable landscape topologies.

Recent work [Mirth et al., J. Chem. Phys. 154, 114114 (2021)] has demonstrated that sublevelset persistent homology provides a compact representation of the complex features of an energy landscape in 3 N-dimensions. This includes information about all transition paths between local minima (connected by critical points of index ≥1) and allows for differentiation of energy landscapes that may appear similar when considering only the lowest energy pathways (as tracked by other representations, such as disconnectivity graphs, using index 1 critical points). Using the additive nature of the conformational potential energy landscape of n-alkanes, it became apparent that some topological features-such as the number of sublevelset persistence bars-could be proven. This work expands the notion of predictable energy landscape topology to any additive intramolecular energy function on a product space, including the number of sublevelset persistent bars as well as the birth and death times of these topological features. This amounts to a rigorous methodology to predict the relative energies of all topological features of the conformational energy landscape in 3N dimensions (without the need for dimensionality reduction). This approach is demonstrated for branched alkanes of varying complexity and connectivity patterns. More generally, this result explains how the sublevelset persistent homology of an additive energy landscape can be computed from the individual terms comprising that landscape.

pH dependent reactivity of boehmite surfaces from first principles molecular dynamics.

pH dependent interfacial chemistry depends upon the distribution and respective pKa values of different surface active sites. This is highly relevant to the chemistry of nanoparticle morphologies that expose faces with varying surface termination. Recent synthetic advances for nanoparticles of various minerals, including AlO(OH) (boehmite), present an excellent opportunity to compare and contrast predicted surface pKa on low Miller index planes so as to reinterpret reported interfacial properties (i.e., point of zero charge - PZC) and reactivity. This work employs ab initio molecular dynamics and empirical models to predict site-specific pKa values of accurate (benchmarked) surface models of boehmite. Using the different surface site populations, the PZC is determined and the influence this has upon reported interfacial chemistry is described.

Concentration dependent interfacial chemistry of the NaOH(aq): gibbsite interface.

Caustic conditions are often employed for dissolution of a wide variety of minerals, where ion sorption, surface diffusion, and interfacial organization impact surface reactivity. In the case of gibbsite, γ-Al(OH)3, the chemistry at the NaOH(aq) interface is deeply intertwined with industrial processing of aluminum, including metal production and the disposition of Al-containing wastes. To date, little is known about the structure, speciation, and dynamic behavior of gibbsite interfaces (and that of many other minerals) with NaOH(aq)-particularly as a function of ionic strength. Yet concentration-dependent interfacial organization and dynamics are a critical starting point to develop a fundamental understanding of the factors that influence dissolution. This work reports equilibrium molecular dynamics simulations of the γ-Al(OH)3:NaOH(aq) interface, revealing the sorption behavior and speciation of ions from 0.5-10 M [NaOH]. As inner-sphere complexes, Na+ primarily coordinates to the side of the gibbsite hexagonal cavities, while OH- accepts hydrogen-bonding from the surface-OH groups. The mobility of inner-sphere Na+ and OH- ions is significantly reduced due to a strong surface affinity in comparison to previous reports of NaCl, CaCl2, or BaCl2 electrolytes. At high [NaOH], contact ion pairing that is observed in the bulk solution is partially disrupted upon sorption to the gibbsite surface by the individual ion-surface interactions. The molecular-scale changes to surface speciation and competition between ion-surface vs. ion-ion interactions influence surface characterization of gibbsite and potential dissolution processes, providing a valuable baseline for starting conditions needed within future reactive molecular simulations.

Shear stress dependence of force networks in 3D dense suspensions.

The geometric organization and force networks of 3D dense suspensions that exhibit both shear thinning and thickening have been examined as a function of varying strength of interparticle attractive interactions using lubrication flow discrete element simulations. Significant rearrangement of the geometric topology does not occur at either the local or global scale as these systems transition across the shear thinning and shear thickening regimes. In contrast, massive rearrangements in the balance of attractive, lubrication, and contact forces are observed with interesting behavior of network growth and competition. In agreement with prior work, in shear thinning regions the attractive force is dominant, however as the shear thickening region is approached there is growth of lubrication forces. Lubrication forces oppose the attraction forces, but as viscosity continues to increase under increasing shear stress, the lubrication forces are dominated by contact forces that also resist attraction. Contact forces are the dominant interactions during shear thickening and are an order of magnitude higher than their values in the shear-thinning regime. At high attractive interaction strength, contact networks can form even under shear thinning conditions, however high shear stress is still required before contact networks become the driving mechanism of shear thickening. Analysis of the contact force network during shear thickening generally indicates a uniformly spreading network that rapidly forms across empty domains; however the growth patterns exhibit structure that is significantly dependent upon the strength of interparticle interactions, indicating subtle variations in the mechanism of shear thickening.

Theory-Guided Inelastic Neutron Scattering of Crystalline Alkaline Aluminate Salts Bearing Principal Motifs of Solution-State Species.

Aluminate salts precipitated from caustic alkaline solutions exhibit a correlation between the anionic speciation and the identity of the alkali cation in the precipitate, with the aluminate ions occurring either in monomeric (Al(OH)4-) or dimeric (Al2O(OH)62-) forms. The origin of this correlation is poorly understood as are the roles that oligomeric aluminate species play in determining the solution structure, prenucleation clusters, and precipitation pathways. Characterization of aluminate solution speciation with vibrational spectroscopy results in spectra that are difficult to interpret because the ions access a diverse and dynamic configurational space. To investigate the Al(OH)4- and Al2O(OH)62- anions within a well-defined crystal lattice, inelastic neutron scattering (INS) and Raman spectroscopic data were collected and simulated by density functional theory for K2[Al2O(OH)6], Rb2[Al2O(OH)6], and Cs[Al(OH) 4]·2H2O. These structures capture archetypal solution aluminate species: the first two salts contain dimeric Al2O(OH)62- anions, while the third contains the monomeric Al(OH)4- anion. Comparisons were made to the INS and Raman spectra of sodium aluminate solutions frozen in a glassy state. In contrast to solution systems, the crystal lattice of the salts results in well-defined vibrations and associated resolved bands in the INS spectra. The use of a theory-guided analysis of the INS of this solid alkaline aluminate series revealed that differences were related to the nature of the hydrogen-bonding network and showed that INS is a sensitive probe of the degree of completeness and strength of the bond network in hydrogen-bonded materials. Results suggest that the ionic size may explain cation-specific differences in crystallization pathways in alkaline aluminate salts.

Cluster Identification Using Modularity Optimization to Uncover Chemical Heterogeneity in Complex Solutions.

Structural heterogeneity is commonly manifested in solutions and liquids that feature competition of different interparticle forces. Identifying and characterizing heterogeneity across different length scales requires multimodal experimental measurement and/or the application of new techniques for the interrogation of atomistic simulation data. Within the latter, the parsing of networks of interparticle interactions (chemical networks) has been demonstrated to be a valuable tool for identifying subensembles of chemical environments. However, chemical networks can adopt a wide variety of topologies that challenge generalizable methods for identifying heterogeneous behavior, and few network analysis algorithms have been proposed for multiscale resolution. In this study, we apply a method of partitioning using the graph theoretic concept of clusters and communities. Using a modularity optimization algorithm, the cluster partition creates subgraphs based on their relative internal and external connectivities. The methodology is tested on two soft matter systems that have significantly different network topologies so as to probe its ability to identify multiple scale features and its generalizability. A binary Lennard-Jones fluid is first examined, where one component causes subgraphs that have high internal network connectivity yet are still connected to the rest of the interparticle network of interactions. The impact of connectivity and edge weighting on the cluster partition is investigated. In the second system, hierarchically organized molecular structures comprised of hydrogen bonded water molecules are identified at a liquid/liquid interface. These structures have a much more sparse network with significantly varied internal connectivity that is a challenge to differentiate from the background hydrogen bonding network of water molecules at the instantaneous interface. The organized macrostructures are effectively isolated from the background network using the cluster partition, and a time-dependent implementation allows us to reveal their reactivity. These studies indicate that cluster partitioning based upon intermolecular network connectivity patterns is broadly generalizable, depending only on user-defined intermolecular connectivity, is operable across different length scales, and is extensible to the study of dynamic phenomena.

Mechanisms of Al3+ Dimerization in Alkaline Solutions.

The molecular speciation of aluminum (Al3+) in alkaline solutions is fundamental to its precipitation chemistry within a number of industrial applications that include ore refinement and industrial processing of Al wastes. Under these conditions, Al3+ is predominantly Al(OH)4-, while at high [Al3+] dimeric species are also known to form. To date, the mechanism of dimer formation remains unclear and is likely influenced by complex ion···ion interactions. In the present work, we investigate a suite of potential dimerization pathways and the role of ion pairing on energetics using static DFT calculations and DFT and density functional tight binding molecular dynamics. Specific cation effects imparted by the background electrolyte cations Na+, Li+, and K+ have been examined. Our simulations predict that, when the Al species are ion-paired with either cation, the formation of the oxo-bridged Al2O(OH)62- is favored with respect to the dihydroxo-bridged Al2(OH)82-, in agreement with previous spectroscopic work. The formation of both dimers first proceeds by bridging of two monomeric units via one hydroxo ligand, leading to a labile Al2(OH)82- isomer. The effect of contact ion pairing of Li+ and K+ on the dimerization energetics is distinctly more favorable than that of Na+, which may have an effect on further oligomerization.

Solid-State Recrystallization Pathways of Sodium Aluminate Hydroxy Hydrates.

Crystallization of Al3+-bearing solid phases from highly alkaline Na2O:Al2O3:H2O solutions commonly necessitates an Al3+ coordination change from tetrahedral to octahedral, but intermediate coordination states are often difficult to isolate. Here, a similar Al3+ coordination change process is examined during the solid-state recrystallization of monosodium aluminate hydrate (MSA) to nonasodium bis(hexahydroxyaluminate) trihydroxide hexahydrate (NSA) at ambient temperature. While the MSA structure contains solely oxolated tetrahedral Al3+, the NSA structure is a molecular aluminate salt solely based upon monomeric octahedral Al3+. Spontaneous recrystallization of MSA and excess sodium hydroxide hydrate into NSA over 3 days of reaction time was clearly evident in X-ray diffractograms and in Raman spectra. In situ single-pulse 27Al magic angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy and 27Al multiple quantum (MQ) MAS NMR spectroscopy showed no evidence of intermediate aluminates, suggesting that transitional states, such as pentacoordinate Al3+, are short-lived and require spectroscopy with greater time resolution to detect. Such research is advancing upon a detailed mechanistic understanding of Al3+ coordination change mechanisms in these highly alkaline systems, with relevance to aluminum refining, corrosion sciences, and nuclear waste processing.

Hierarchical phenomena in multicomponent liquids: simulation methods, analysis, chemistry.

Complex, multicomponent, solutions have often been studied solely through the lens of specific applications of interest. Yet advances to both simulation methodologies (enhanced sampling, etc.) and analysis techniques (network analysis algorithms and others), are creating a trove of data that reveal transcending characteristics across vast compositional phase space. This perspective discusses technical considerations of the reliable and accurate simulations of complex solutions, followed by the advances to analysis algorithms that elucidate coupling of different length and timescale behavior (hierarchical phenomena). The different manifestations of hierarchical phenomena are presented across an array of solution environments, emphasizing fundamental and ongoing science questions. With a more advanced molecular understanding in hand, a quintessential application (solvent extraction) is discussed, where significant opportunities exist to re-imagine the technical scope of an established technology.

Al27 NMR chemical shift of Al(OH)4 - calculated from first principles: Assessment of error cancellation in chemically distinct reference and target systems.

Predicting accurate nuclear magnetic resonance chemical shieldings relies upon cancellation of different types of errors between the theoretically calculated shielding constant of the analyte of interest and the reference. Often, the intrinsic error in computed shieldings due to basis sets, approximations in the Hamiltonian, description of the wave function, and dynamic effects is nearly identical between the analyte and reference, yet if the electronic structure or sensitivity to local environment differs dramatically, this cannot be taken for granted. Detailed prior work has examined the octahedral trivalent cation Al(H2O)6 3+, accounting for ab initio intrinsic errors. However, the use of this species as a reference for the chemically distinct tetrahedral anion Al(OH)4 - requires an understanding of how these errors cancel in order to define the limits of accurately predicting Al27 chemical shielding in Al(OH)4 -. In this work, we estimate the absolute shielding of the Al27 nucleus in Al(OH)4 - at the coupled cluster level (515.1 ± 5.3 ppm). Shielding sensitivity to the choice of method approximation and atomic basis sets used has been evaluated. Solvent and thermal effects are assessed through ensemble averaging techniques using ab initio molecular dynamics. The contribution of each type of intrinsic error is assessed for the Al(H2O)6 3+ and Al(OH)4 - ions, revealing significant differences that fundamentally hamper the ability to accurately calculate the Al27 chemical shift of Al(OH)4 - from first principles.

Surfactant-enhanced heterogeneity of the aqueous interface drives water extraction into organic solvents.

Liquid/liquid extraction (LLE) is one of the most industrially relevant separation methods, successfully leveraging the variable solubility of solutes (or their complexes) between two immiscible solvents. Independent of the relative solubilities of those solutes and complexes (which determine their distribution between phases), the dynamics of phase transfer processes are impacted by the molecular interactions and structure of those species at the interface. A simple example includes the formation and extraction of water-extractant adducts observed in the ternary water/organic/tri-n-butyl phosphate (TBP) system. Despite its implications for LLE, a detailed description of the structural and dynamic mechanisms by which such adducts are formed at the interface is not established. Describing that process requires connecting the evolving interfacial molecular organization in the presence of surfactants to dynamic surface fluctuations and interfacial heterogeneity. Herein, molecular dynamics simulation is combined with state-of-the-art network theory analysis to reveal features of interfacial structures and their relationship to the extraction of water in the water/n-hexane/TBP system. Surfactant adsorption enhances interfacial roughness which in turn causes directly interfacial water to become less connected through hydrogen bonding to subjacent layers, particularly upon formation of the water-bridged TBP dimer adduct. Furthermore, heterogeneity within the interface itself is enhanced by surfactant adsorption and serves as the basis for the formation of protrusions of water into the organic phase at the extremes of surface fluctuations. These features disproportionately incorporate the water-bridged TBP dimer and are the primary means by which water is transferred to the organic phase. This work presents for the first time a holistic understanding of how interfacial heterogeneity and spatial fluctuations become amplified in the presence of surfactants, enabling water extraction into the organic phase. It further affords the opportunity to study how solution conditions can control interfacial behavior to create more efficient solvent extraction systems.

Resolving local configurational contributions to X-ray and neutron radial distribution functions within solutions of concentrated electrolytes - a case study of concentrated NaOH.

Extreme conditions of complex materials often lead to a manifold of local environments that challenge characterization and require new advances at the intersection of modern experimental and theoretical techniques. In this contribution, highly caustic and viscous aqueous NaOD solutions were characterized with a combination of X-ray and neutron radial distribution function (RDF) analyses, molecular dynamics simulations and sub-ensemble analysis. While this system has been the topic of some study, the current work expands upon the state of knowledge regarding the extent to which water is perturbed within this chemically extreme solution. Further, we introduce analyses that goes beyond merely identifying the different local environments (ion solvation and coordination environments) that are present, but toward understanding their relative contributions to the ensemble solution RDF. This integrated approach yields unique insight into the experimental sensitivity of RDFs to changes in local geometries, the composition of solvation environments about ions, and the challenge of experimentally differentiating the ensemble of all superimposed local environments-a feature of increasing importance within the extreme condition of high ionic strength.

Effect of Ions on the Optical Absorption Spectra of Aqueously Solvated Chromophores.

In the condensed phase, ions often create heterogeneous local environments around a solute, which may impart chemical reactivity or perturbations to physicochemical properties. Although the former has been the subject of some study, the latter-particularly as is pertains to optical absorption spectroscopy-is much less understood. In this work, the computed UV-vis absorption spectrum is examined for the aqueously solvated chromophore anion of green fluorescent protein for different local ion configurations. The strong ability of water to screen the ions from the chromophore results in little change in excitation energy compared to a purely aqueous environment. However, upon forming a contact ion pair with a sodium ion at either of the two electronegative oxygen sites of the chromophore, there is a spectral shift to either higher or lower energies. Surprisingly, our analysis suggests that the cause of the spectral shift is dominated not by the electrostatic presence of the ion but instead by ion disruption of the hydrogen bond network at the oxygen contact ion pair site.

PageRank as a collective variable to study complex chemical transformations and their energy landscapes.

A reduced set of reaction coordinates is often employed in chemistry to describe the collective change between reactants and products within the context of rare event theories and the exploration of energy landscapes. Yet selecting the proper collective variable becomes increasingly challenging as the systems under study become more complex. Recent advancement of new descriptions of collective molecular coordinates has included graph-theoretical metrics, including social permutation invariant and PageRank (PR) coordinates, based upon the network of interactions about molecules and atoms within a system. Herein we continue the development of PR by (1) presenting a new formulation that is continuous along a reaction path, (2) illustrating that the fluctuations in PR are demonstrative of the fundamental motions of the atoms/molecules, and (3) providing the analytical derivatives with respect to atomic coordinates. The latter is subsequently combined with a harmonic bias to create the potential of mean force (PMF). As an example, we first consider the transformation of tetrahedral [Al(OH)4](aq) - to octahedral [Al(OH)4(H2O)2](aq) - using the PR PMF. Second, we explore the interchange of contact ion pair and solvent separated ion pairs of aqueous Na⋯OH, where the distance-biased PMF is projected onto PR space. In turn, this reveals where solvent rearrangement has the most impact upon the reaction pathway.

Competitive Interactions Within Cm(III) Solvation in Binary Water/Methanol Solutions.

Competitive forces exist in multicomponent solutions, and within electrolytes they consist of both ion-solvent and solvent-solvent interactions. These can influence a myriad of processes, including ligand complexation. In the case of water/alcohol solutions, recent work revealed an interesting dilemma regarding the overall solution dynamics and organization as compared to solute-solvent interactions. This is particularly true for highly charged ions in solution, whose ion-solvent interactions were demonstrated to be highly sensitive to the composition of the immediate solvation environment. Faster solvent exchange should be observed about the ion, considering that second-order Møller-Plesset perturbation theory predicts an average decrease in ion-solvent dissociation energy when methanol enters the first solvation shell of Cm3+(aq). Yet the addition of methanol to water causes the dynamic features of the hydrogen-bond network of the entire solution to slow. The apparent competition between these contrary forces was examined using a combination of electronic structure calculations with both ab initio and classical molecular dynamics simulations, using binary water/methanol solutions and Cm3+ as a representative solute. This combination of theoretical methods predicts that, among the competitive effects of the solvent-solvent and ion-solvent interactions, the solution-phase dynamics imparted by the addition of methanol to water kinetically restricts the solvation exchange rates about Cm3+ in these binary solutions.

In Situ 27Al NMR Spectroscopy of Aluminate in Sodium Hydroxide Solutions above and below Saturation with Respect to Gibbsite.

Aluminum hydroxide (Al(OH)3, gibbsite) dissolution and precipitation processes in alkaline environments play a commanding role in aluminum refining and nuclear waste processing, yet mechanistic aspects underlying sluggish kinetics during crystallization have remained obscured due to a lack of in situ probes capable of isolating incipient ion pairs. At a molecular level Al is cycling between tetrahedral ( T d) coordination in solution to octahedral ( O h) in the solid. We explored dissolution of Al(OH)3 that was used to produce variably saturated aluminate (Al(OH)4-)-containing solutions under alkaline conditions (pH >13) with in situ 27Al magic angle spinning (MAS)-nuclear magnetic resonance (NMR) spectroscopy, and interrogated the results with ab initio molecular dynamics (AIMD) simulations complemented with chemical shift calculations. The collective results highlight the overall stability of the solvation structure for T d Al in the Al(OH)4- oxyanion as a function of both temperature and Al concentration. The observed chemical shift did not change significantly even when the Al concentration in solution became supersaturated upon cooling and limited precipitation of the octahedral Al(OH)3 phase occurred. However, subtle changes in Al(OH)4- speciation correlated with the dissolution/precipitation reaction were found. AIMD-informed chemical shift calculations indicate that measurable perturbations should begin when the Al(OH)4-···Na+ distance is less than 6 Å, increasing dramatically at shorter distances, coinciding with appreciable changes to the electrostatic interaction and reorganization of the Al(OH)4- solvation shell. The integrated findings thus suggest that, under conditions incipient to and concurrent with gibbsite crystallization, nominally expected contact ion pairs are insignificant and instead medium-range (4-6 Å) solvent-separated Al(OH)4-···Na+ pairs predominate. Moreover, the fact that these medium-range interactions bear directly on resulting gibbsite characteristics was demonstrated by detailed microscopic and X-ray diffraction analysis and by progressive changes in the fwhm of the O h resonance, as measured by in situ NMR. Sluggish gibbsite crystallization may arise from the activation energy associated with disrupting this robust medium-range ion pair interaction.

Acceleration of metal-ligand complexation kinetics by electrospray ionization.

Electrospray ionization mass spectrometry (ESI-MS) is a valuable and frequently used analytical technique across nearly all branches of chemistry, and has recently seen increasing use in the study of metal-ligand solution equilibria. Despite its prevalence, the method by which ESI produces gas-phase ions from solutions containing metal-ligand complexes is not fully understood, with recent reports showing significant changes to solution equilibria during ESI analysis. This study examines perturbations to the formation kinetics of metal-ligand complexes during the ESI process, showing how quickly new equilibria - reflective of the ionization process and not solution - can be established. Electrospray ionization mass spectrometry (ESI-MS) and ion mobility spectrometry (IMS) are used to examine the well studied Lu-DOTA (1,4,7,10-tetraazacyclododecane-N,N',N'',N'''-tetraacetic acid) complexation reaction, with collision cross section modeling based on density functional theory (DFT) optimized structures used to aid in the interpretation of the ion mobility results. The electrospray process was found to significantly accelerate the formation kinetics, increasing the formation rate constant by more than an order of magnitude over its previously determined solution-phase value.

A Combined Density Functional Theory and Spectrophotometry Study of the Bonding Interactions of [NpO2·M]4+ Cation-Cation Complexes.

The equilibrium constants for [NpO2·M]4+ (M = Al3+, In3+, Sc3+, Fe3+) in µ = 10 M nitric acid and [NpO2·Ga]4+ in µ = 10 M hydrochloric acid media have been determined. The trend in the interaction strength follows: Fe3+ > Sc3+ ≥ In3+ > Ga3+ ≫ Al3+. These equilibrium constants are compared to those of previously reported values for NpO2+ complexes with Cr3+ and Rh3+ within the literature. Thermodynamic parameters and bonding modes are discussed, with density functional theory and natural bond orbital analysis indicating that the NpO2+ dioxocation acts as a π-donor with transition-metal cations and a σ-donor with group 13 cations. The small changes in electron-donating ability is modulated by the overlap with the coordinating metal ion's valence atomic orbitals.

Structural and Thermodynamic Properties of the Cm(III) Ion Solvated by Water and Methanol.

The geometric and electronic structures of the 9-coordinate Cm(3+) ion solvated with both water and methanol are systematically investigated in the gas phase at each possible solvent-shell composition and configuration using density functional theory and second-order Møller-Plesset perturbation theory. Ab initio molecular dynamics simulations are employed to assess the effects of second and third solvent shells on the gas-phase structure. The ion-solvent dissociation energy for methanol is greater than that of water, potentially because of increased charge donation to the ion made possible by the electron-rich methyl group. Further, the ion-solvent dissociation energy and the ion-solvent distance are shown to be dependent on the solvent-shell composition. This has implications for solvent exchange, which is generally the rate-limiting step in complexation reactions utilized in the separation of curium from complex metal mixtures that derive from the advanced nuclear fuel cycle.