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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Computational modeling of physical processes in metal-organic frameworks (MOFs) is highly challenging due to the presence of spatial heterogeneities and complex operating conditions which affect their behavior. Density functional theory (DFT) may describe interatomic interactions at the quantum mechanical level, but is computationally too expensive for systems beyond the nanometer and picosecond range. Herein, we propose an incremental learning scheme to construct accurate and data-efficient machine learning potentials for MOFs. The scheme builds on the power of equivariant neural network potentials in combination with parallelized enhanced sampling and on-the-fly training to simultaneously explore and learn the phase space in an iterative manner. With only a few hundred single-point DFT evaluations per material, accurate and transferable potentials are obtained, even for flexible frameworks with multiple structurally different phases. The incremental learning scheme is universally applicable and may pave the way to model framework materials in larger spatiotemporal windows with higher accuracy. [ABSTRACT FROM AUTHOR]

We present an improved electronic linear response model to incorporate polarization and charge-transfer effects in polarizable force fields. This model is a generalization of the Atom-Condensed Kohn-Sham Density Functional Theory (DFT), approximated to second order (ACKS2): it can now be defined with any underlying variational theory (next to KS-DFT) and it can include atomic multipoles and off-center basis functions. Parameters in this model are computed efficiently as expectation values of an electronic wavefunction, obviating the need for their calibration, regularization, and manual tuning. In the limit of a complete density and potential basis set in the ACKS2 model, the linear response properties of the underlying theory for a given molecular geometry are reproduced exactly. A numerical validation with a test set of 110 molecules shows that very accurate models can already be obtained with fluctuating charges and dipoles. These features greatly facilitate the development of polarizable force fields. [ABSTRACT FROM AUTHOR]

The mechanisms of human soluble epoxide hydrolase (sEH) and the corresponding epoxide hydrolase enzyme from Mycobacterium tuberculosis (EHB) are studied computationally, using the quantum mechanics/molecular mechanics (QM/MM) method. To do this, we modeled the alkylation and the hydrolysis steps of three substrates: trans-1,3-diphenylpropene oxide, trans-stilbene oxide and cis-stilbene oxide. Studying the regioselectivity for trans-1,3-diphenylpropene oxide, we determined that both enzymes prefer ring opening via attack on the benzylic carbon. In agreement with experimental studies, our computations show that the rate-limiting step is hydrolysis of the ester intermediate, with reaction barriers of approximately 13 to 18 kcal/mol. Using the barrier energies of this rate-limiting step, the three epoxides were ranked in order of reactivity. Though the reactivity order was correctly predicted for sEH, the predicted order for EHB did not correspond to experimental observations. Next, the electrostatic contributions of individual residues on the barrier height of the rate-limiting step were also studied. This revealed several residues important for catalysis. The secondary tritium kinetic isotope effect for the alkylation step was determined using a cluster model for the active site of sEH. The calculated value was 1.27, suggesting a late transition state for the rate-limiting step. Finally, we analyzed the reactivity trends using reactivity indicators from conceptual density functional theory, allowing us to identify ease of electron transfer as the primary driving force for the reaction. [ABSTRACT FROM AUTHOR]

We consider the problem of defining an appropriate local descriptor corresponding to an arbitrary global descriptor. Although it does not seem easy to rigorously and uniquely define local analogues of derived global descriptors (e.g., the electrophilicity) or the fundamental global descriptors associated with the canonical ensemble (e.g., the hardness), the local response of these global descriptors can be defined unambiguously. We look at the local response of the global electrophilicity and compare it to the conventional, ad hoc, definition of the local electrophilicity. The local response of global nucleofugality and electrofugality is also discussed. [ABSTRACT FROM AUTHOR]

Many benchmarks of density-functional theory with respect to experiment suggest the error on predicted equilibrium volumes to scale with the volume. Relative volume errors are therefore often used as a decisive argument to select one exchange–correlation functional over another. We show that the error on the volume (after correcting for systematic deviations) is only approximately relative. A simple analytic model, validated by rigorous Monte Carlo simulations, reveals that a more accurate error estimate can be derived from the inverse of the bulk modulus. This insight is not only instrumental for the selection or design of suitable functionals. It also calls for a new attitude towards computational errors: to report computational errors on electronic-structure calculations, identify systematic deviations and distinguish between relative and absolute effects. [ABSTRACT FROM AUTHOR]

We present explicit formulas for arbitrary-order derivatives of the energy, grand potential, electron density, and higher-order response functions with respect to the number of electrons, and the chemical potential for any smooth and differentiable model of the energy versus the number of electrons. The resulting expressions for global reactivity descriptors (hyperhardnesses and hypersoftnesses), local reactivity descriptors (hyperFukui functions and local hypersoftnesses), and nonlocal response functions are easy to evaluate computationally. Specifically, the explicit formulas for global/local/nonlocal hypersoftnesses of arbitrary order are derived using Bell polynomials. Explicit expressions for global and local hypersoftness indicators up to fifth order are presented. [ABSTRACT FROM AUTHOR]