Structure and Dynamics of the Hematite/Liquid Water Interface

The hematite/liquid water interface is of interest for a wide range of applications. This work investigates structural and dynamic properties of the interface for several experimentally relevant combinations of crystal cuts, termination and protonation schemes. To this end, molecular dynamics simulations at hybrid functional DFT level have been performed for both neutral and charged systems. For bulk hematite, this work shows that the commonly used GGA+U level of theory gives good results for geometric properties, but cannot capture electronic structure equally well. However, a modified hybrid functional based on HSE06 is able to describe both geometric and electronic properties with sufficient accuracy. The two most common crystal surfaces and their most common terminations have been investigated and compared to experiment where possible. The resulting structural information is in good agreement with experiment, but highlights the importance of dynamic equilibria for the solvation structure. This work also shows that classical force fields cannot readily describe the surface protonation structure and dynamics. Besides an atomistic view of the surface structure, protonation dynamics, surface restructuring mechanisms and interconversion of surface aquo groups to bulk solvent are discussed. Two new methods are suggested in this work: (i) a screening method for Hartree-Fock exchange forces that significantly accelerates hybrid functional-based molecular dynamics calculation and (ii) a guided thermodynamic integration scheme for free energy estimation from short trajectories. The implementation thereof is tested and benchmarked and applied to the hematite/liquid water interface. To accelerate the calculation of HFX forces in a molecular dynamics force screening scheme is proposed. For actual systems of interest, this can speed up the whole molecular dynamics run by a factor of three. The method is assessed on a wide range of materials and for various properties including energy conservation. Finally, the pKa value of a surface protonation is calculated. By means of thermodynamic integration, the free energy difference between a proton at the surface of hematite and a solvated proton in bulk water is quantified. Various integration schemes are evaluated and a new analysis method is proposed to reduce human bias in the analysis and to automatically detect convergence of the vertical energy gap time series

Rapid and accurate molecular deprotonation energies from quantum alchemy

We assess the applicability of alchemical perturbation density functional theory (APDFT) for quickly and accurately estimating deprotonation energies. We have considered all possible single and double deprotonations in one hundred small organic molecules drawn at random from QM9 [Ramakrishnan et al., JCTC, 2015]. Numerical evidence is presented for 5160 deprotonated species at both HF/def2-TZVP and CCSD/6-31G* levels of theory. We show that the perturbation expansion formalism of APDFT quickly converges to reliable results: using CCSD electron densities and derivatives, regular Hartree-Fock calculations are outperformed at the second or third order for ranking all possible doubly or singly deprotonated molecules, respectively. CCSD single deprotonation energies are reproduced within 1.4 kcal mol-1 on average within third order APDFT. We introduce a hybrid approach where the computational cost of APDFT is reduced even further by mixing first order terms at a higher level of theory (CCSD) with higher order terms at a lower level of theory only (HF). We find that this approach reaches 2 kcal mol-1 accuracy in absolute deprotonation energies compared to CCSD at 2% of the computational cost of third order APDFT

Simplifying inverse material design problems for fixed lattices with alchemical chirality

Massive brute-force compute campaigns relying on demanding ab initio calculations routinely search for novel materials in chemical compound space, the vast virtual set of all conceivable stable combinations of elements and structural configurations which form matter. Here we demonstrate that 4-dimensional chirality, arising from anti-symmetry of alchemical perturbations, dissects that space and defines approximate ranks which effectively reduce its formal dimensionality, and enable us to break down its combinatorial scaling. The resulting distinct `alchemical' enantiomers must share the exact same electronic energy up to third order -- independent of respective covalent bond topology, and imposing relevant constraints on chemical bonding. Alchemical chirality deepens our understanding of chemical compound space and enables the `on-the-fly' establishment of new trends without empiricism for any materials with fixed lattices. We demonstrate its efficacy for three such cases: i) new formulas for estimating electronic energy contributions to chemical bonding; ii) analysis of the perturbed electron density of BN doped benzene; and iii) ranking stability estimates for BN doping in over 2,000 naphthalene and over 400 million picene derivatives

Simplifying inverse materials design problems for fixed lattices with alchemical chirality

Brute-force compute campaigns relying on demanding ab initio calculations routinely search for previously un- known materials in chemical compound space (CCS), the vast set of all conceivable stable combinations of elements and structural configurations. Here, we demonstrate that four-dimensional chirality arising from antisymmetry of alchemical perturbations dissects CCS and defines approximate ranks, which reduce its formal dimensionality and break down its combinatorial scaling. The resulting "alchemical" enantiomers have the same electronic energy up to the third order, independent of respective covalent bond topology, imposing relevant constraints on chemical bonding. Alchemical chirality deepens our understanding of CCS and enables the establishment of trends without empiricism for any materials with fixed lattices. We demonstrate the efficacy for three cases: (i) new rules for elec- tronic energy contributions to chemical bonding; (ii) analysis of the electron density of BN-doped benzene; and (iii) ranking over 2000 and 4 million BN-doped naphthalene and picene derivatives, respectively

Understanding Representations by Exploring Galaxies in Chemical Space

We present a Monte Carlo approach for studying chemical feature distributions of molecules without training a machine learning model or performing exhaustive enumeration. The algorithm generates molecules with predefined similarity to a given one for any representation. It serves as a diagnostic tool to understand which molecules are grouped in feature space and to identify shortcomings of representations and embeddings from unsupervised learning. In this work, we first study clusters surrounding chosen molecules and demonstrate that common representations do not yield a constant density of molecules in feature space, with possible implications for learning behavior. Next, we observe a connection between representations and properties: a linear correlation between the property value of a central molecule and the average radial slope of that property in chemical space. Molecules with extremal property values have the largest property derivative values in chemical space, which provides a route to improve the data efficiency of a representation by tailoring it towards a given property. Finally, we demonstrate applications for sampling molecules with specified metric-dependent distributions to generate molecules biased toward graph spaces of interest

Toward the design of chemical reactions: Machine learning barriers of competing mechanisms in reactant space

The interplay of kinetics and thermodynamics governs reactive processes, and their control is key in synthesis efforts. While sophisticated numerical methods for studying equilibrium states have well advanced, quantitative predictions of kinetic behavior remain challenging. We introduce a reactant-to-barrier (R2B) machine learning model that rapidly and accurately infers activation energies and transition state geometries throughout the chemical compound space. R2B exhibits improving accuracy as training set sizes grow and requires as input solely the molecular graph of the reactant and the information of the reaction type. We provide numerical evidence for the applicability of R2B for two competing text-book reactions relevant to organic synthesis, E2 and S N 2, trained and tested on chemically diverse quantum data from the literature. After training on 1-1.8k examples, R2B predicts activation energies on average within less than 2.5 kcal/mol with respect to the coupled-cluster singles doubles reference within milliseconds. Principal component analysis of kernel matrices reveals the hierarchy of the multiple scales underpinning reactivity in chemical space: Nucleophiles and leaving groups, substituents, and pairwise substituent combinations correspond to systematic lowering of eigenvalues. Analysis of R2B based predictions of ∼11.5k E2 and S N 2 barriers in the gas-phase for previously undocumented reactants indicates that on average, E2 is favored in 75% of all cases and that S N 2 becomes likely for chlorine as nucleophile/leaving group and for substituents consisting of hydrogen or electron-withdrawing groups. Experimental reaction design from first principles is enabled due to R2B, which is demonstrated by the construction of decision trees. Numerical R2B based results for interatomic distances and angles of reactant and transition state geometries suggest that Hammond's postulate is applicable to S N 2, but not to E2