Metal–ligand interactions provide a means for modulating the mechanical properties of metallopolymers as well as an avenue toward understanding the connection between cross-link interaction strength and macroscale mechanical properties. In this work, we used nickel carboxylate as the tunable cross-linking interaction in a metallopolymer. Different numbers and types of neutral ligands that coordinate to the metal center are introduced as an easy approach to adjust the strength of the ionic interactions in the nickel carboxylate cross-links, thus allowing macroscale mechanical properties to be tuned. Density functional theory (DFT) calculations, with the external forces explicitly included (EFEI) approach, were used to quantify how the number and type of ligands affect the stiffness, strength, and thermodynamic stability of the nickel carboxylate cross-linking interactions. Interpreting the bulk material properties in the context of these DFT results suggests that the stiffness and strength of the cross-linking interactions primarily control the initial stiffness and yield strength of the metallopolymer, while the mechanical behavior at higher strain is controlled by dynamical bond re-formation and interactions with the polymer environment. The physicochemical insight gained from this work can be used in the rational design of metallopolymers with a wide scope of targeted mechanical properties.

In this work, we present NENCI-2021, a benchmark database of ∼8000 Non-Equilibirum Non-Covalent Interaction energies for a large and diverse selection of intermolecular complexes of biological and chemical relevance. To meet the growing demand for large and high-quality quantum mechanical data in the chemical sciences, NENCI-2021 starts with the 101 molecular dimers in the widely used S66 and S101 databases and extends the scope of these works by (i) including 40 cation–π and anion–π complexes, a fundamentally important class of non-covalent interactions that are found throughout nature and pose a substantial challenge to theory, and (ii) systematically sampling all 141 intermolecular potential energy surfaces (PESs) by simultaneously varying the intermolecular distance and intermolecular angle in each dimer. Designed with an emphasis on close contacts, the complexes in NENCI-2021 were generated by sampling seven intermolecular distances along each PES (ranging from 0.7× to 1.1× the equilibrium separation) and nine intermolecular angles per distance (five for each ion–π complex), yielding an extensive database of 7763 benchmark intermolecular interaction energies (Eint) obtained at the coupled-cluster with singles, doubles, and perturbative triples/complete basis set [CCSD(T)/CBS] level of theory. The Eint values in NENCI-2021 span a total of 225.3 kcal/mol, ranging from −38.5 to +186.8 kcal/mol, with a mean (median) Eint value of −1.06 kcal/mol (−2.39 kcal/mol). In addition, a wide range of intermolecular atom-pair distances are also present in NENCI-2021, where close intermolecular contacts involving atoms that are located within the so-called van der Waals envelope are prevalent—these interactions, in particular, pose an enormous challenge for molecular modeling and are observed in many important chemical and biological systems. A detailed symmetry-adapted perturbation theory (SAPT)-based energy decomposition analysis also confirms the diverse and comprehensive nature of the intermolecular binding motifs present in NENCI-2021, which now includes a significant number of primarily induction-bound dimers (e.g., cation–π complexes). NENCI-2021 thus spans all regions of the SAPT ternary diagram, thereby warranting a new four-category classification scheme that includes complexes primarily bound by electrostatics (3499), induction (700), dispersion (1372), or mixtures thereof (2192). A critical error analysis performed on a representative set of intermolecular complexes in NENCI-2021 demonstrates that the Eint values provided herein have an average error of ±0.1 kcal/mol, even for complexes with strongly repulsive Eint values, and maximum errors of ±0.2–0.3 kcal/mol (i.e., ∼±1.0 kJ/mol) for the most challenging cases. For these reasons, we expect that NENCI-2021 will play an important role in the testing, training, and development of next-generation classical and polarizable force fields, density functional theory approximations, wavefunction theory methods, and machine learning based intra- and inter-molecular potentials.

High-throughput electronic structure calculations (often performed using density functional theory (DFT)) play a central role in screening existing and novel materials, sampling potential energy surfaces, and generating data for machine learning applications. By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal DFT and furnish a more accurate description of the underlying electronic structure, albeit at a computational cost that often prohibits such high-throughput applications. To address this challenge, we have constructed a robust, accurate, and computationally efficient framework for high-throughput condensed-phase hybrid DFT and implemented this approach in the module of (). The resulting approach ( = SCDM + + ACE) combines and seamlessly integrates: (i) the selected columns of the density matrix method (SCDM, a robust noniterative orbital localization scheme that sidesteps system-dependent optimization protocols), (ii) a recently extended version of (a black-box linear-scaling EXX algorithm that exploits sparsity between localized orbitals in real space when evaluating the action of the standard/full-rank operator), and (iii) adaptively compressed exchange (ACE, a low-rank approximation). In doing so, harnesses three levels of computational savings: pair selection and domain truncation from SCDM + (which only considers spatially overlapping orbitals on orbital-pair-specific and system-size-independent domains) and low-rank approximation from ACE (which reduces the number of calls to SCDM + during the self-consistent field (SCF) procedure). Across a diverse set of 200 nonequilibrium (H2O)64 configurations (with densities spanning 0.4–1.7 g/cm3), provides a 1−2 order-of-magnitude speedup in the overall time-to-solution, i.e., ≈8−26× compared to the convolution-based implementation in and ≈78−247× compared to the conventional approach, and yields energies, ionic forces, and other properties with high fidelity. As a proof-of-principle high-throughput application, we trained a deep neural network (DNN) potential for ambient liquid water at the hybrid DFT level using via an actively learned data set with ≈8,700 (H2O)64 configurations. Using an out-of-sample set of (H2O)512 configurations (at nonambient conditions), we confirmed the accuracy of this -trained potential and showcased the capabilities of by computing the ground-truth ionic forces in this challenging system containing >1,500 atoms.

In this work, we present a general framework that unites the two primary strategies for constructing density functional approximations (DFAs): nonempirical (NE) constraint satisfaction and empirical (E) data-driven optimization. The proposed method employs B-splines, bell-shaped spline functions with compact support, to construct each inhomogeneity correction factor (ICF). This choice offers several distinct advantages over traditional polynomial expansions by enabling explicit enforcement of linear and nonlinear constraints as well as ICF smoothness using Tikhonov and penalized B-splines (P-splines) regularization. As proof-of-concept, we use the so-called CASE (constrained and smoothed empirical) framework to construct a constraint-satisfying and data-driven global hybrid that exhibits enhanced performance across a diverse set of chemical properties. We argue that the CASE approach can be used to generate DFAs that maintain the physical rigor and transferability of NE-DFAs while leveraging high-quality quantum-mechanical data to remove the arbitrariness of ansatz selection and improve performance.

A new methodology to analyze two-component molecular tagging velocimetry image pairs is presented. Velocity measurements with high spatial resolution are achieved by determining grid displacements at the intersections as well as along the grid lines using a multivariate adaptive regression splines parameterization along the segments connecting adjacent grid intersections. The methodology can detect the orientation of the grid, contains redundant steps for increased reliability, and handles cases where parts of the grid are missing, indicating potential for automation. Initial demonstration of the algorithm’s performance was illustrated using synthetic data sets derived from Computational Fluid Dynamics simulations and compared to Hough-transform and cross-correlation methodologies. Besides providing comparable results in terms of precision and accuracy to previously reported methodologies, the analysis of images by the proposed methodology results in significantly increased spatial resolution of the flow displacement determinations along the grid lines with comparable precision and accuracy. This methodology’s ability to handle different grid orientations without modifications was assessed using synthetic datasets with grids formed by sets of parallel lines at 90, 45, and 30 degrees from the vertical axis. Comparable results in terms of precision and accuracy were obtained across grid orientations, with all uncertainties below 0.1 pixel for images with signal-to-noise levels exceeding 5, and within 0.5 pixel for the noisiest image sets.