Sandra Luber

External electric fields play a crucial role in chemistry, materials, and biology. However, accurately capturing external field effects remains a challenge for machine learning interatomic potentials (MLIPs). By revealing the limitations of conventional architectures in predicting field-dependent response properties, we introduce a physics-informed field-aware equivariant neural network framework that predicts response properties to external electric fields. External electric fields are incorporated through an equivariant embedding layer that concatenates field representations with atomic features, preserving rotational equivariance. The model leverages an energy-derivative approach to predict response properties in a single unified architecture. Furthermore, we embed a charge-equilibration electrostatic layer into the model to capture long-range electrostatic interactions. The close agreement between charged-based and energy derivative-based electric dipoles indicates that the model learns the correct underlying physics. The unified framework performs robustly for the prediction of response properties and simulation of IR and Raman spectra across molecular and periodic systems under different external field strengths. By incorporating physical principles into the model, we establish a general and transferable framework for modeling molecular and condensed-phase response under external electric fields, providing a robust routine for response properties prediction in external electric fields.

Here we present a density matrix penalization method for finite basis Kohn-Sham (KS) matrix reconstruction in Gaussian basis representations. The method constructs a matrix-represented auxiliary KS Hamiltonian whose self-consistent density matrix and corresponding Gaussian-basis-representable real-space electron density reproduce a prescribed target, without assuming the recovery of a unique continuum local KS or exchange-correlation potential. This finite basis formulation is motivated by the numerical difficulties encountered by conventional inverse KS-DFT approaches, such as the Zhao-Morrison-Parr (ZMP) method, when a real-space penalty potential is projected onto a limited set of Gaussian basis matrix elements. Such a projection can strongly coarse-grain the constraining potential and lead to poorly constrained and inefficient self-consistent-field (SCF) optimizations. In the present method, the density matrix mismatch is defined in a Löwdin-orthogonalized basis, yielding a penalty functional that is invariant under basis rotations in that representation. The corresponding penalty Hamiltonian matrix contribution is derived analytically in the original nonorthogonal Gaussian basis. Across a wide range of penalty strengths, SCF optimization remains robust and efficient for various open-shell molecular and condensed-phase systems, while progressively tightening the penalty drives the density matrix and the associated real-space density into near machine precision agreement with the target for most systems. Benchmarks show that the method achieves substantially smaller attainable density deviations than conventional ZMP calculations in Gaussian bases. The method provides a stable, fast, and accurate route to finite basis KS matrix reconstruction and establishes a practical framework for density-matrix-based inverse reconstruction in Gaussian basis electronic structure calculations.

Harnessing functional groups in the outer coordination sphere to direct catalytic pathways is characteristic for enzymes, yet rather underexplored for man‐made catalysts. Here, following our earlier work on Ru(bda) water oxidation catalysts (bda = 2,2′‐bipyridine‐6,6′‐dicarboxylate), we demonstrate how a carboxyl‐functionalized Ru(bda)‐based macrocycle enables an oxide relay mechanism in light‐driven water oxidation via an O─O bond formation between carboxylate and Ru ^V = O units positioned on opposing sides. Through a combination of photocatalytic water oxidation studies, NMR and single crystal analysis, and ¹⁸ O‐labeling experiments, we provide evidence for the mechanistically distinct oxide relay pathway under photocatalytic conditions. Our findings underscore the role of second coordination sphere engineering in modulating reaction pathways and advancing molecular catalyst design.

Harnessing functional groups in the outer coordination sphere to direct catalytic pathways is characteristic for enzymes, yet rather underexplored for man‐made catalysts. Here, following our earlier work on Ru(bda) water oxidation catalysts (bda = 2,2′‐bipyridine‐6,6′‐dicarboxylate), we demonstrate how a carboxyl‐functionalized Ru(bda)‐based macrocycle enables an oxide relay mechanism in light‐driven water oxidation via an O─O bond formation between carboxylate and Ru ^V = O units positioned on opposing sides. Through a combination of photocatalytic water oxidation studies, NMR and single crystal analysis, and ¹⁸ O‐labeling experiments, we provide evidence for the mechanistically distinct oxide relay pathway under photocatalytic conditions. Our findings underscore the role of second coordination sphere engineering in modulating reaction pathways and advancing molecular catalyst design.

Accurate prediction of molecular electric dipole moments is crucial for determining molecular properties and understanding molecular reactivity. Recent developments in equivariant machine learning enable direct prediction of electric dipole moments as vector quantities. This raises the question as to whether it is still necessary to consider physics-informed charge-based principles in the model to achieve satisfactory performance. In this work, we systematically compare direct equivariant electric dipole prediction using MACE with charge-based approaches using adapted MACE which incorporates a variant charge equilibrium equation (QEq) into the MACE framework. Across diverse datasets including QM7b, QM9, as well as subsets of the SPICE and SN2 data sets, we demonstrate that both direct equivariant electric dipole prediction and physics-informed QEq approaches show good performance for short-to-medium range interaction datasets. The charge-based QEq model shows slightly better performance than direct prediction beyond small training data sizes. Notably, the charge-based QEq model outperforms direct electric dipole prediction for the systems with long range interactions. Our results highlight the importance of incorporating physics into the model for improved model interpretability and transferability.

External electric fields play a crucial role in chemistry, materials, and biology. However, accurately capturing external field effects remains a challenge for machine learning interatomic potentials (MLIPs). By revealing the limitations of conventional architectures in predicting field-dependent response properties, we introduce a physics-informed field-aware equivariant neural network framework that predicts response properties to external electric fields. External electric fields are incorporated through an equivariant embedding layer that concatenates field representations with atomic features, preserving rotational equivariance. The model leverages an energy derivative approach to predict response properties in a single unified architecture. Furthermore, we embed a variational charge equilibration scheme into the model to capture long-range electrostatic interactions. The close agreement between charged-based and energy derivative-based electric dipoles indicates that the model learns the correct underlying physics. The unified framework performs robustly for the prediction of response properties and simulation of IR and Raman spectra across molecular and periodic systems under different external field strengths. By incorporating physical principles into the model, we establish a general and transferable framework for modeling molecular response under external electric fields, providing a robust routine for response properties prediction in external electric fields.

We present a deterministic all‐parameter optimization method based on analytic derivatives for vibrational wave functions in a separable product form represented in a distributed Gaussian basis. The optimization of the center and width parameters of the basis allows for compact wave function representations at a small basis size. We illustrate the approach by computing ground and excited vibrational states of anharmonic model systems and the 9‐dimensional formic acid monomer.

Perovskite oxynitride LaTiO₂N holds promise for visible-light-driven photocatalytic water splitting, yet its surface dynamics at the catalyst-water interface remain elusive. This study employs state-of-the-art density functional theory molecular dynamics (DFT-MD) and electrochemical measurements to unravel the intricate interplay of water arrangement and adsorption on the LaTiO₂N(100) surface. By considering explicit solvent effects, we reveal a pronounced hydrophilic character, with spontaneous water dissociation forming hydroxyl groups at undercoordinated Ti sites at the surface, stabilizing the latter and potentially enhancing the OER activity. Our simulations identify the thermodynamically stable termination and demonstrate its role in fostering robust hydrogen-bond networks that facilitate proton-coupled electron transfer. The surface Pourbaix diagram underscores hydroxylated configurations across diverse electrochemical conditions, corroborated by DFT-MD insights. These findings highlight the critical role of treating an explicit solvent environment and its dynamics at a given temperature in the modeling of LaTiO₂N, offering a blueprint for designing high-performance, sustainable water-splitting catalysts.

Singlet excited electronic states can be directly constructed with the ΔSCF method using a single electronic density by applying fractional occupation numbers. While the advantages and disadvantages of such a DFT-based ΔSCF method were demonstrated in several studies, the spurious energy shift of the singlet electronic states when constructed using hybrid DFT functionals remains unexplained. Here, we explain in detail the origin of the effect of losing the idempotence properties of density matrices on the DFT energy terms with hybrid-based DFT functionals, as well as a procedure to eliminate the artificial shift from ΔSCF singlet excited state energies when obtained using the hybrid-based DFT functionals.

Integration of Ru(bda) [bda = (2,2'-bipyridine)-6,6'-dicarboxylate] water oxidation catalysts together with dibenzofuran, dibenzothiophene, or carbazole heterocycles within macrocycles 1-3 affords structures with different conformational preferences. The latter are dictated by noncovalent interactions of the bda oxygens with NH (hydrogen bond) or S (chalcogen bond). The different orientations afford changes in the secondary coordination sphere, thereby influencing the rate and mechanism of photocatalytic water oxidation for the three mononuclear Ru(bda)-based catalysts, with the dibenzothiophene- and carbazole-based ones favoring the unimolecular pathway (first-order kinetics), typically related to water nucleophilic attack (WNA), and the dibenzofuran one operating via a bimolecular pathway (second-order kinetics), typically related to the interaction of two metal-oxo species (I2M). NMR and single crystal X-ray analyses provided insight into the conformational preferences of the precursor macrocycles in the Ru(II) state. Photocatalytic studies including the H/D kinetic isotope effect (KIE) in deuterated water together with theoretical studies on the orientation angle-dependent energy profile for macrocycles in the Ru(V) state afforded a structure-property relationship that explains the outcome of the water oxidation experiments.