Improving One-Electron Exact-Two-Component Relativistic Methods with the Dirac-Coulomb-Breit-Parameterized Effective Spin-Orbit Coupling

In photochemical processes, spin-orbit coupling plays a crucial role in determining the outcome of the reaction. However, the exact treatment of the Dirac-Coulomb-Breit two-electron operator required for rigorous inclusion of spin-orbit coupling is computationally prohibitive. To address this challenge, we present a Dirac-Coulomb-Breit-parameterized screened-nuclear spin-orbit factor to approximate two-electron spin-orbit couplings in the effective one-electron spin-orbit Hamiltonian. We propose two schemes, the universal and row-dependent parameterizations, to further improve the accuracy of the method. Benchmark calculations on both atomic and molecular systems are performed and compared to results from the computationally expensive four-component Dirac-Coulomb-Breit method. The Dirac-Coulomb-Breit-parameterized approach offers a more computationally feasible method for accurate spin-orbit coupling calculations.

Behavior of Linear and Nonlinear Dimensionality Reduction for Collective Variable Identification of Small Molecule Solution-Phase Reactions

Identifying collective variables (CVs) for chemical reactions is essential to reduce the 3N-dimensional energy landscape into lower dimensional basins and barriers of interest. However, in condensed phase processes, the nonmeaningful motions of bulk solvent often overpower the ability of dimensionality reduction methods to identify correlated motions that underpin collective variables. Yet solvent can play important indirect or direct roles in reactivity, and much can be lost through treatments that remove or dampen solvent motion. This has been amply demonstrated within principal component analysis (PCA), although less is known about the behavior of nonlinear dimensionality reduction methods, e.g., uniform manifold approximation and projection (UMAP), that have become recently utilized. The latter presents an interesting alternative to linear methods though often at the expense of interpretability. This work presents distance-attenuated projection methods of atomic coordinates that facilitate the application of both PCA and UMAP to identify collective variables in the presence of explicit solvent and further the specific identity of solvent molecules that participate in chemical reactions. The performance of both methods is examined in detail for two reactions where the explicit solvent plays very different roles within the collective variables. When applied to raw molecular dynamics data in solution, both PCA and UMAP representations are dominated by bulk solvent motions. On the other hand, when applied to data preprocessed by our attenuated projection methods, both PCA and UMAP identify the appropriate collective variables (though varying sensitivity is observed due to the presence of explicit solvent that results from the projection method). Importantly, this approach allows identification of specific solvent molecules that are relevant to the CVs and their importance.

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)₆^2- is favored with respect to the dihydroxo-bridged Al₂(OH)₈^2-, 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)₈^2- 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.

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.

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.

Anticorrelated Contributions to Pre-edge Features of Aluminate Near-Edge X-ray Absorption Spectroscopy in Concentrated Electrolytes

Ion pairing within complex solutions and electrolytes is a difficult phenomenon to measure and investigate, yet it has significant impact upon macroscopic processes, such as crystal formation. Traditional methods of detecting and characterizing ion pairing are sensitive to contact ion pairs, may require minimum concentrations that limit applicability, and can have difficulty in characterizing solutions with many components. Because of its element specificity and sensitivity to local environment, X-ray absorption near edge structure (XANES) is a promising tool for investigating ion pairing in complex solutions. In concentrated sodium aluminate solutions, a shift in the pre-edge shoulder correlated to sodium concentration is observed, and the physical origins of that shift are investigated using energy specific time-dependent density functional theory of subensembles obtained from ab initio molecular dynamics. Two transitions are found to contribute to the pre-edge feature, yet they are anticorrelated with respect to the sodium···aluminate distance. Unexpectedly, this causes Al XANES to be an effective probe for longer-range ion interactions than the traditional counterparts of NMR or vibrational spectroscopies. Given the nature of the transitions involved, this observation may be extended to other systems where ion-ion interactions dominate; however, a complete understanding of the contributing transitions is necessary for accurate analysis of XANES pre-edge features in concentrated electrolytes.