Grid: A Python library for molecular integration, interpolation, differentiation, and more.

Grid is a free and open-source Python library for constructing numerical grids to integrate, interpolate, and differentiate functions (e.g., molecular properties), with a strong emphasis on facilitating these operations in computational chemistry and conceptual density functional theory. Although designed, maintained, and released as a stand-alone Python library, Grid was originally developed for molecular integration, interpolation, and solving the Poisson equation in the HORTON and ChemTools packages. Grid is designed to be easy to use, extend, and maintain; this is why we use Python and adopt many principles of modern software development, including comprehensive documentation, extensive testing, continuous integration/delivery protocols, and package management. We leverage popular scientific packages, such as NumPy and SciPy, to ensure high efficiency and optimized performance in grid development. This article is the official release note of the Grid library showcasing its unique functionality and scope.

The tale of HORTON: Lessons learned in a decade of scientific software development.

HORTON is a free and open-source electronic-structure package written primarily in Python 3 with some underlying C++ components. While HORTON's development has been mainly directed by the research interests of its leading contributing groups, it is designed to be easily modified, extended, and used by other developers of quantum chemistry methods or post-processing techniques. Most importantly, HORTON adheres to modern principles of software development, including modularity, readability, flexibility, comprehensive documentation, automatic testing, version control, and quality-assurance protocols. This article explains how the principles and structure of HORTON have evolved since we started developing it more than a decade ago. We review the features and functionality of the latest HORTON release (version 2.3) and discuss how HORTON is evolving to support electronic structure theory research for the next decade.

Managing Expectations and Imbalanced Training Data in Reactive Force Field Development: An Application to Water Adsorption on Alumina.

ReaxFF is a computationally efficient model for reactive molecular dynamics simulations that has been applied to a wide variety of chemical systems. When ReaxFF parameters are not yet available for a chemistry of interest, they must be (re)optimized, for which one defines a set of training data that the new ReaxFF parameters should reproduce. ReaxFF training sets typically contain diverse properties with different units, some of which are more abundant (by orders of magnitude) than others. To find the best parameters, one conventionally minimizes a weighted sum of squared errors over all of the data in the training set. One of the challenges in such numerical optimizations is to assign weights so that the optimized parameters represent a good compromise among all the requirements defined in the training set. This work introduces a new loss function, called Balanced Loss, and a workflow that replaces weight assignment with a more manageable procedure. The training data are divided into categories with corresponding "tolerances", i.e., acceptable root-mean-square errors for the categories, which define the expectations for the optimized ReaxFF parameters. Through the Log-Sum-Exp form of Balanced Loss, the parameter optimization is also a validation of one's expectations, providing meaningful feedback that can be used to reconfigure the tolerances if needed. The new methodology is demonstrated with a nontrivial parametrization of ReaxFF for water adsorption on alumina. This results in a new force field that reproduces both the rare and frequent properties of a validation set not used for training. We also demonstrate the robustness of the new force field with a molecular dynamics simulation of water desorption from a γ-Al2O3 slab model.

The significance of fluctuating charges for molecular polarizability and dispersion coefficients.

The influence of fluctuating charges or charge flow on the dynamic linear response properties of isolated molecules from the TS42 database is evaluated, with particular emphasis on dipole polarizability and C6 dispersion coefficients. Two new descriptors are defined to quantify the charge-flow contribution to response properties, making use of the recoupled dipole polarizability to separate isotropic and anisotropic components. Molecular polarizabilities are calculated using the "frequency-dependent atom-condensed Kohn-Sham density functional theory approximated to second order," i.e., the ACKS2ω model. With ACKS2ω, the charge-flow contribution can be constructed in two conceptually distinct ways that appear to yield compatible results. The charge-flow contribution is significantly affected by molecular geometry and the presence of polarizable bonds, in line with previous studies. We show that the charge-flow contribution qualitatively reproduces the polarizability anisotropy. The contribution to the anisotropic C6 coefficients is less pronounced but cannot be neglected. The effect of fluctuating charges is only negligible for small molecules with at most one non-hydrogen atom. They become important and sometimes dominant for larger molecules or when highly polarizable bonds are present, such as conjugated, double, or triple bonds. Charge flow contributions cannot be explained in terms of individual atomic properties because they are affected by non-local features such as chemical bonding and geometry. Therefore, polarizable force fields and dispersion models can benefit from the explicit modeling of charge flow.

DFT-Quality Adsorption Simulations in Metal-Organic Frameworks Enabled by Machine Learning Potentials.

Nanoporous materials such as metal-organic frameworks (MOFs) have been extensively studied for their potential for adsorption and separation applications. In this respect, grand canonical Monte Carlo (GCMC) simulations have become a well-established tool for computational screenings of the adsorption properties of large sets of MOFs. However, their reliance on empirical force field potentials has limited the accuracy with which this tool can be applied to MOFs with challenging chemical environments such as open-metal sites. On the other hand, density-functional theory (DFT) is too computationally demanding to be routinely employed in GCMC simulations due to the excessive number of required function evaluations. Therefore, we propose in this paper a protocol for training machine learning potentials (MLPs) on a limited set of DFT intermolecular interaction energies (and forces) of CO2 in ZIF-8 and the open-metal site containing Mg-MOF-74, and use the MLPs to derive adsorption isotherms from first principles. We make use of the equivariant NequIP model which has demonstrated excellent data efficiency, and as such an error on the interaction energies below 0.2 kJ mol-1 per adsorbate in ZIF-8 was attained. Its use in GCMC simulations results in highly accurate adsorption isotherms and heats of adsorption. For Mg-MOF-74, a large dependence of the obtained results on the used dispersion correction was observed, where PBE-MBD performs the best. Lastly, to test the transferability of the MLP trained on ZIF-8, it was applied to ZIF-3, ZIF-4, and ZIF-6, which resulted in large deviations in the predicted adsorption isotherms and heats of adsorption. Only when explicitly training on data for all ZIFs, accurate adsorption properties were obtained. As the proposed methodology is widely applicable to guest adsorption in nanoporous materials, it opens up the possibility for training general-purpose MLPs to perform highly accurate investigations of guest adsorption.

An information-theoretic approach to basis-set fitting of electron densities and other non-negative functions.

The numerical ill-conditioning associated with approximating an electron density with a convex sum of Gaussian or Slater-type functions is overcome by using the (extended) Kullback-Leibler divergence to measure the deviation between the target and approximate density. The optimized densities are non-negative and normalized, and they are accurate enough to be used in applications related to molecular similarity, the topology of the electron density, and numerical molecular integration. This robust, efficient, and general approach can be used to fit any non-negative normalized functions (e.g., the kinetic energy density and molecular electron density) to a convex sum of non-negative basis functions. We present a fixed-point iteration method for optimizing the Kullback-Leibler divergence and compare it to conventional gradient-based optimization methods. These algorithms are released through the free and open-source BFit package, which also includes a L2-norm squared optimization routine applicable to any square-integrable scalar function.

A Reactive Molecular Dynamics Study of Chlorinated Organic Compounds. Part II: A ChemTraYzer Study of Chlorinated Dibenzofuran Formation and Decomposition Processes.

The front cover artwork is provided by Prof. K. Leonhard's group at RWTH Aachen University. The image shows ChemTraYzer, a virtual robot, while analyzing the reaction network related to the formation and oxidation of Chloro-Dibenzofuranes. Read the full text of the Research Article at 10.1002/cphc.202200783.

Sensitivity Analysis for ReaxFF Reparametrization Using the Hilbert-Schmidt Independence Criterion.

We apply a global sensitivity method, the Hilbert-Schmidt independence criterion (HSIC), to the reparametrization of a Zn/S/H ReaxFF force field to identify the most appropriate parameters for reparametrization. Parameter selection remains a challenge in this context, as high-dimensional optimizations are prone to overfitting and take a long time but selecting too few parameters leads to poor-quality force fields. We show that the HSIC correctly and quickly identifies the most sensitive parameters and that optimizations done using a small number of sensitive parameters outperform those done using a higher-dimensional reasonable-user parameter selection. Optimizations using only sensitive parameters (1) converge faster, (2) have loss values comparable to those found with the naive selection, (3) have similar accuracy in validation tests, and (4) do not suffer from problems of overfitting. We demonstrate that an HSIC global sensitivity is a cheap optimization preprocessing step that has both qualitative and quantitative benefits which can substantially simplify and speed up ReaxFF reparametrizations.

Nuclear quantum effects on zeolite proton hopping kinetics explored with machine learning potentials and path integral molecular dynamics.

Proton hopping is a key reactive process within zeolite catalysis. However, the accurate determination of its kinetics poses major challenges both for theoreticians and experimentalists. Nuclear quantum effects (NQEs) are known to influence the structure and dynamics of protons, but their rigorous inclusion through the path integral molecular dynamics (PIMD) formalism was so far beyond reach for zeolite catalyzed processes due to the excessive computational cost of evaluating all forces and energies at the Density Functional Theory (DFT) level. Herein, we overcome this limitation by training first a reactive machine learning potential (MLP) that can reproduce with high fidelity the DFT potential energy surface of proton hopping around the first Al coordination sphere in the H-CHA zeolite. The MLP offers an immense computational speedup, enabling us to derive accurate reaction kinetics beyond standard transition state theory for the proton hopping reaction. Overall, more than 0.6 µs of simulation time was needed, which is far beyond reach of any standard DFT approach. NQEs are found to significantly impact the proton hopping kinetics up to ~473 K. Moreover, PIMD simulations with deuterium can be performed without any additional training to compute kinetic isotope effects over a broad range of temperatures.

A Reactive Molecular Dynamics Study of Chlorinated Organic Compounds. Part II: A ChemTraYzer Study of Chlorinated Dibenzofuran Formation and Decomposition Processes.

In our two-paper series, we first present the development of ReaxFF CHOCl parameters using the recently published ParAMS parametrization tool. In this second part, we update the reactive Molecular Dynamics - Quantum Mechanics coupling scheme ChemTraYzer and combine it with our new ReaxFF parameters from Part I to study formation and decomposition processes of chlorinated dibenzofurans. We introduce a self-learning method for recovering failed transition-state searches that improves the overall ChemTraYzer transition-state search success rate by 10 percentage points to a total of 48 %. With ChemTraYzer, we automatically find and quantify more than 500 reactions using transition state theory and DFT. Among the discovered chlorinated dibenzofuran reactions are numerous reactions that are new to the literature. In three case studies, we discuss the set of reactions that are most relevant to the dibenzofuran literature: (i) bimolecular reactions of the chlorinated-dibenzofuran precursors phenoxy radical and 1,3,5-trichlorobenzene, (ii) dibenzofuran chlorination and pyrolysis, and (iii) oxidation of chlorinated dibenzofurans.

Fanpy: A python library for prototyping multideterminant methods in ab initio quantum chemistry.

Fanpy is a free and open-source Python library for developing and testing multideterminant wavefunctions and related ab initio methods in electronic structure theory. The main use of Fanpy is to quickly prototype new methods by making it easier to convert the mathematical formulation of a new wavefunction ansätze to a working implementation. Fanpy is designed based on our recently introduced Flexible Ansatz for N-electron Configuration Interaction (FANCI) framework, where multideterminant wavefunctions are represented by their overlaps with Slater determinants of orthonormal spin-orbitals. In the simplest case, a new wavefunction ansatz can be implemented by simply writing a function for evaluating its overlap with an arbitrary Slater determinant. Fanpy is modular in both implementation and theory: the wavefunction model, the system's Hamiltonian, and the choice of objective function are all independent modules. This modular structure makes it easy for users to mix and match different methods and for developers to quickly explore new ideas. Fanpy is written purely in Python with standard dependencies, making it accessible for various operating systems. In addition, it adheres to principles of modern software development, including comprehensive documentation, extensive testing, quality assurance, and continuous integration and delivery protocols. This article is considered to be the official release notes for the Fanpy library.

Quantum Free Energy Profiles for Molecular Proton Transfers.

Although many molecular dynamics simulations treat the atomic nuclei as classical particles, an adequate description of nuclear quantum effects (NQEs) is indispensable when studying proton transfer reactions. Herein, quantum free energy profiles are constructed for three typical proton transfers, which properly take NQEs into account using the path integral formalism. The computational cost of the simulations is kept tractable by deriving machine learning potentials. It is shown that the classical and quasi-classical centroid free energy profiles of the proton transfers deviate substantially from the exact quantum free energy profile.

A Reactive Molecular Dynamics Study of Chlorinated Organic Compounds. Part I: Force Field Development.

This work presents a novel parametrization for the ReaxFF formalism as a means to investigate reaction processes of chlorinated organic compounds. Force field parameters cover the chemical elements C, H, O, Cl and were obtained using a novel optimization approach involving relaxed potential energy surface scans as training targets. The resulting ReaxFF parametrization shows good transferability, as demonstrated on two independent ab initio validation sets. While this first part of our two-paper series focuses on force field parametrization, we apply our parameters to the simulation of chlorinated dibenzofuran formation and decomposition processes in Part II.

A new framework for frequency-dependent polarizable force fields.

A frequency-dependent extension of the polarizable force field "Atom-Condensed Kohn-Sham density functional theory approximated to the second-order" (ACKS2) [Verstraelen et al., J. Chem. Phys. 141, 194114 (2014)] is proposed, referred to as ACKS2ω. The method enables theoretical predictions of dynamical response properties of finite systems after partitioning of the frequency-dependent molecular response function. Parameters in this model are computed simply as expectation values of an electronic wavefunction, and the hardness matrix is entirely reused from ACKS2 as an adiabatic approximation is used. A numerical validation shows that accurate models can already be obtained with atomic monopoles and dipoles. Absorption spectra of 42 organic and inorganic molecular monomers are evaluated using ACKS2ω, and our results agree well with the time-dependent DFT calculations. Also for the calculation of C6 dispersion coefficients, ACKS2ω closely reproduces its TDDFT reference. When parameters for ACKS2ω are derived from a PBE/aug-cc-pVDZ ground state, it reproduces experimental values for 903 organic and inorganic intermolecular pairs with an MAPE of 3.84%. Our results confirm that ACKS2ω offers a solid connection between the quantum-mechanical description of frequency-dependent response and computationally efficient force-field models.

Nonbonded Force Field Parameters from Minimal Basis Iterative Stockholder Partitioning of the Molecular Electron Density Improve CB7 Host-Guest Affinity Predictions.

Binding affinity prediction by means of computer simulation has been increasingly incorporated in drug discovery projects. Its wide application, however, is limited by the prediction accuracy of the free energy calculations. The main error sources are force fields used to describe molecular interactions and incomplete sampling of the configurational space. Organic host-guest systems have been used to address force field quality because they share similar interactions found in ligands and receptors, and their rigidity facilitates configurational sampling. Here, we test the binding free energy prediction accuracy for 14 guests with an aromatic or adamantane core and the CB7 host using molecular electron density derived nonbonded force field parameters. We developed a computational workflow written in Python to derive atomic charges and Lennard-Jones parameters with the Minimal Basis Iterative Stockholder method using the polarized electron density of several configurations of each guest in the bound and unbound states. The resulting nonbonded force field parameters improve binding affinity prediction, especially for guests with an adamantane core in which repulsive exchange and dispersion interactions to the host dominate.

Constrained iterative Hirshfeld charges: A variational approach.

We develop a variational procedure for the iterative Hirshfeld (HI) partitioning scheme. The main practical advantage of having a variational framework is that it provides a formal and straightforward approach for imposing constraints (e.g., fixed charges on certain atoms or molecular fragments) when computing HI atoms and their properties. Unlike many other variants of the Hirshfeld partitioning scheme, HI charges do not arise naturally from the information-theoretic framework, but only as a reverse-engineered construction of the objective function. However, the procedure we use is quite general and could be applied to other problems as well. We also prove that there is always at least one solution to the HI equations, but we could not prove that its self-consistent equations would always converge for any given initial pro-atom charges. Our numerical assessment of the constrained iterative Hirshfeld method shows that it satisfies many desirable traits of atoms in molecules and has the potential to surpass existing approaches for adding constraints when computing atomic properties.

Zeo-1, a computational data set of zeolite structures.

Fast, empirical potentials are gaining increased popularity in the computational fields of materials science, physics and chemistry. With it, there is a rising demand for high-quality reference data for the training and validation of such models. In contrast to research that is mainly focused on small organic molecules, this work presents a data set of geometry-optimized bulk phase zeolite structures. Covering a majority of framework types from the Database of Zeolite Structures, this set includes over thirty thousand geometries. Calculated properties include system energies, nuclear gradients and stress tensors at each point, making the data suitable for model development, validation or referencing applications focused on periodic silica systems.

GloMPO (Globally Managed Parallel Optimization): a tool for expensive, black-box optimizations, application to ReaxFF reparameterizations.

In this work we explore the properties which make many real-life global optimization problems extremely difficult to handle, and some of the common techniques used in literature to address them. We then introduce a general optimization management tool called GloMPO (Globally Managed Parallel Optimization) to help address some of the challenges faced by practitioners. GloMPO manages and shares information between traditional optimization algorithms run in parallel. We hope that GloMPO will be a flexible framework which allows for customization and hybridization of various optimization ideas, while also providing a substitute for human interventions and decisions which are a common feature of optimization processes of hard problems. GloMPO is shown to produce lower minima than traditional optimization approaches on global optimization test functions, the Lennard-Jones cluster problem, and ReaxFF reparameterizations. The novel feature of forced optimizer termination was shown to find better minima than normal optimization. GloMPO is also shown to provide qualitative benefits such a identifying degenerate minima, and providing a standardized interface and workflow manager.

Modeling Electronic Response Properties with an Explicit-Electron Machine Learning Potential.

Explicit-electron force fields introduce electrons or electron pairs as semiclassical particles in force fields or empirical potentials, which are suitable for molecular dynamics simulations. Even though semiclassical electrons are a drastic simplification compared to a quantum-mechanical electronic wave function, they still retain a relatively detailed electronic model compared to conventional polarizable and reactive force fields. The ability of explicit-electron models to describe chemical reactions and electronic response properties has already been demonstrated, yet the description of short-range interactions for a broad range of chemical systems remains challenging. In this work, we present the electron machine learning potential (eMLP), a new explicit electron force field in which the short-range interactions are modeled with machine learning. The electron pair particles will be located at well-defined positions, derived from localized molecular orbitals or Wannier centers, naturally imposing the correct dielectric and piezoelectric behavior of the system. The eMLP is benchmarked on two newly constructed data sets: eQM7, an extension of the QM7 data set for small molecules, and a data set for the crystalline ß-glycine. It is shown that the eMLP can predict dipole moments, polarizabilities, and IR-spectra of unseen molecules with high precision. Furthermore, a variety of response properties, for example, stiffness or piezoelectric constants, can be accurately reproduced.

Super-ions of sodium cations with hydrated hydroxide anions: inorganic structure-directing agents in zeolite synthesis.

In inorganic zeolite formation, a direct correspondence between liquid state species in the synthesis and the supramolecular decoration of the pores in the as-made final zeolite has never been reported. In this paper, a direct link between the sodium speciation in the synthesis mixture and the pore structure and content of the final zeolite is demonstrated in the example of hydroxysodalite. Super-ions with 4 sodium cations bound by mono- and bihydrated hydroxide are identified as structure-directing agents for the formation of this zeolite. This documentation of inorganic solution species acting as a templating agent in zeolite formation opens new horizons for zeolite synthesis by design.