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ModelHamiltonian is a free, open source, and cross-platform Python library designed to express model Hamiltonians, including spin-based Hamiltonians (Heisenberg and Ising models) and occupation-based Hamiltonians (Pariser-Parr-Pople, Hubbard, and Hückel models) in terms of 1- and 2-electron integrals, so that these systems can be easily treated by traditional quantum chemistry software programs. ModelHamiltonian was originally intended to facilitate the testing of new electronic structure methods using HORTON but emerged as a stand-alone research tool that we recognize has wide utility, even in an educational context. ModelHamiltonian is written in Python and adheres to modern principles of software development, including comprehensive documentation, extensive testing, continuous integration/delivery protocols, and package management. While we anticipate that most users will use ModelHamiltonian as a Python library, we include a graphical user interface so that models can be built without programming, based on connectivity/parameters inferred from, for example, a SMILES string. We also include an interface to ChatGPT so that users can specify a Hamiltonian in plain language (without learning ModelHamiltonian's vocabulary and syntax). This article marks the official release of the ModelHamiltonian library, showcasing its functionality and scope., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

PyCI is a free and open-source Python library for setting up and running arbitrary determinant-driven configuration interaction (CI) computations, as well as their generalizations to cases where the coefficients of the determinant are nonlinear functions of optimizable parameters. PyCI also includes functionality for computing the residual correlation energy, along with the ability to compute spin-polarized one- and two-electron (transition) reduced density matrices. PyCI was originally intended to replace the ab initio quantum chemistry functionality in the HORTON library but emerged as a standalone research tool, primarily intended to aid in method development, while maintaining high performance so that it is suitable for practical calculations. To this end, PyCI is written in Python, adopting principles of modern software development, including comprehensive documentation, extensive testing, continuous integration/delivery protocols, and package management. Computationally intensive steps, notably operations related to generating Slater determinants and computing their expectation values, are delegated to low-level C++ code. This article marks the official release of the PyCI library, showcasing its functionality and scope., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Context: We rationalize the excellent performance of information-theoretic descriptors for predicting atomic and molecular polarizabilities. It seems that descriptors which capture information about the change in valence-shell structure, especially the relative Fisher information measures, are particularly useful. Using this, we can rationalize why the G3 form of the relative Fisher information, which measures the deviation of effective nuclear charge between an atom-in-a-molecule and the reference pro-atom, is especially effective as a predictor of molecular polarizability., Methods: There are no methods used in this paper, which relies on mathematical derivation and analysis., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Context: The reaction force constant ( κ ), introduced by Professor Alejandro Toro-Labbé, plays a pivotal role in characterizing the reaction pathway by assessing the curvature of the potential energy profile along the intrinsic reaction coordinate. This study establishes a novel link between κ and the reactivity descriptors of conceptual density functional theory (c-DFT). Specifically, we derive expressions that relate the reaction force constant to nuclear softness and variations in chemical potential. Our findings indicate that regions of the reaction pathway where κ is negative match with significant electronic structure rearrangements, while positive κ regions match mostly with geometric rearrangements. This correlation between κ and c-DFT reactivity descriptors enhances our understanding of the underlying forces driving chemical reactions and offers new perspectives for analyzing reaction mechanisms., Methods: The internal reaction path for the proton transfer in SNOH, chemical potential, and nuclear softness were computed using DFT with B3LYP exchange-correlation functional and 6-311++G(d,2p) basis set., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

GBasis is a free and open-source Python library for molecular property computations based on Gaussian basis functions in quantum chemistry. Specifically, GBasis allows one to evaluate functions expanded in Gaussian basis functions (including molecular orbitals, electron density, and reduced density matrices) and to compute functionals of Gaussian basis functions (overlap integrals, one-electron integrals, and two-electron integrals). Unique features of GBasis include supporting evaluation and analytical integration of arbitrary-order derivatives of the density (matrices), computation of a broad range of (screened) Coulomb interactions, and evaluation of overlap integrals of arbitrary numbers of Gaussians in arbitrarily high dimensions. For circumstances where the flexibility of GBasis is less important than high performance, a seamless Python interface to the Libcint C package is provided. GBasis is designed to be easy to use, maintain, and extend following many standards of sustainable software development, including code-quality assurance through continuous integration protocols, extensive testing, comprehensive documentation, up-to-date package management, and continuous delivery. This article marks the official release of the GBasis library, outlining its features, examples, and development., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

The Hohenberg-Kohn theorem of density functional theory (DFT) stipulates that energy is a universal functional of electron density in the ground state, so energy can be thought of having encoded essential information for the density. Based on this, we recently proposed to quantify energetic information within the framework of information-theoretic approach (ITA) of DFT ( J. Chem. Phys . 2022 , 157, 101103). In this study, we systematically apply energetic information to a variety of chemical phenomena to validate the use of energetic information as quantitative measures of physicochemical properties. To that end, we employed six ITA quantities such as Shannon entropy and Fisher information for five energetic densities, yielding twenty-six viable energetic information quantities. Then, they are applied to correlate with physicochemical properties of molecular systems, including chemical bonding, conformational stability, intermolecular interactions, acidity, aromaticity, cooperativity, electrophilicity, nucleophilicity, and reactivity. Our results show that different quantities of energetic information often behave differently for different properties but a few of them, such as Shannon entropy of the total kinetic energy density and information gain of the Pauli energy density, stand out and strongly correlate with several properties across different categories of molecular systems. These results suggest that they can be employed as quantitative measures of physicochemical properties. This work not only enriches the body of our knowledge about the relationship between energy and information, but also provides scores of newly introduced explicit density functionals to quantify physicochemical properties, which can serve as robust features for building machine learning models in future studies.

We present a new, nonarbitrary, internally consistent, and unambiguous framework for spin-polarized conceptual density-functional theory (SP-DFT). We explicitly characterize the convex hull of energy, as a function of the number of electrons and their spin, as the only accessible ground states in spin-polarized density functional theory. Then, we construct continuous linear and quadratic models for the energy. The nondifferentiable linear model exactly captures the simplicial geometry of the complex hull about the point of interest and gives exact representations for the conceptual DFT reactivity indicators. The continuous quadratic energy model is the paraboloid of maximum curvature, which most tightly encloses the point of interest and neighboring vertices. The quadratic model is invariant to the choice of coordinate system (i.e., { N , S } vs { N α , N β }) and reduces to a sensible formulation of spin-free conceptual DFT in the appropriate limit. Using the quadratic model, we generalize the Parr functions { P + ( r ), P - ( r )} (and their derivatives with respect to number of electrons) to this new spin-polarized framework, integrating the Parr function concept into the context of (spin-polarized) conceptual DFT, and extending it to include higher-order effects.

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., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

We propose a new perturbation theory framework that can be used to help with the projective solution of the Schrödinger equation for arbitrary wave functions. This Flexible Ansatz for N -body Perturbation Theory (FANPT) is based on our previously proposed Flexible Ansatz for the N -body Configuration Interaction (FANCI). We derive recursive FANPT expressions, including arbitrary orders in the perturbation hierarchy. We show that the FANPT equations are well-behaved across a wide range of conditions, including static correlation-dominated configurations and highly nonlinear wave functions.

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., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Electron pairs have an illustrious history in chemistry, from powerful concepts to understanding structural stability and reactive changes to the promise of serving as building blocks of quantitative descriptions of the electronic structure of complex molecules and materials. However, traditionally, two-electron wavefunctions (geminals) have not enjoyed the popularity and widespread use of the more standard single-particle methods. This has changed recently, with a renewed interest in the development of geminal wavefunctions as an alternative to describing strongly correlated phenomena. Hence, there is a need to find geminal methods that are accurate, computationally tractable, and do not demand significant input from the user (particularly via cumbersome and often ill-behaved orbital optimization steps). Here, we propose new families of geminal wavefunctions inspired by the pair coupled cluster doubles ansatz. We present a new hierarchy of two-electron wavefunctions that extends the one-reference orbital idea to other geminals. Moreover, we show how to incorporate single-like excitations in this framework without leaving the quasiparticle picture. We explore the role of imposing seniority restrictions on these wavefunctions and benchmark these new methods on model strongly correlated systems., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

In this work, we have observed that some chiral boron clusters (B16-, B20-, B24-, and B28-) can simultaneously have helical molecular orbitals and helical spin densities; these seem to be the first compounds discovered to have this intriguing property. We show that chiral Jahn-Teller distortion of quasi-planar boron clusters drives the formation of the helical molecular spin densities in these clusters and show that elongation/enhancement in helical molecular orbitals can be achieved by simply adding more building blocks via a linker. Aromaticity of these boron clusters is discussed. Chiral boron clusters may find potential applications in spintronics, such as molecular magnets.

Simultaneous prediction of the molecular response properties, such as polarizability and the NMR shielding constant, at a low computational cost is an unresolved issue. We propose to combine a linear-scaling generalized energy-based fragmentation (GEBF) method and deep learning (DL) with both molecular and atomic information-theoretic approach (ITA) quantities as effective descriptors. In GEBF, the total molecular polarizability can be assembled as a linear combination of the corresponding quantities calculated from a set of small embedded subsystems in GEBF. In the new GEBF-DL(ITA) protocol, one can predict subsystem polarizabilities based on the corresponding molecular wave function (thus electron density and ITA quantities) and DL model rather than calculate them from the computationally intensive coupled-perturbed Hartree-Fock or Kohn-Sham equations and finally obtain the total molecular polarizability via a linear combination equation. As a proof-of-concept application, we predict the molecular polarizabilities of large proteins and protein aggregates. GEBF-DL(ITA) is shown to be as accurate enough as GEBF, with mean absolute percentage error <1%. For the largest protein aggregate (>4000 atoms), GEBF-DL(ITA) gains a speedup ratio of 3 compared with GEBF. It is anticipated that when more advanced electronic structure methods are used, this advantage will be more appealing. Moreover, one can also predict the NMR chemical shieldings of proteins with reasonably good accuracy. Overall, the cost-efficient GEBF-DL(ITA) protocol should be a robust theoretical tool for simultaneously predicting polarizabilities and NMR shieldings of large systems.

Establishing a chemical reactivity theory in density functional theory (DFT) language has been our intense research interest in the past two decades, exemplified by the determination of steric effect and stereoselectivity, evaluation of electrophilicity and nucleophilicity, identification of strong and weak interactions, and formulation of cooperativity, frustration, and principle of chirality hierarchy. In this Featured Article, we first overview the four density-based frameworks in DFT to appreciate chemical understanding, including conceptual DFT, use of density associated quantities, information-theoretic approach, and orbital-free DFT, and then present a few recent advances of these frameworks as well as new applications from our studies. To that end, we will introduce the relationship among these frameworks, determining the entire spectrum of interactions with Pauli energy derivatives, performing topological analyses with information-theoretic quantities, and extending the density-based frameworks to excited states. Applications to examine physiochemical properties in external electric fields and to evaluate polarizability for proteins and crystals are discussed. A few possible directions for future development are followed, with the special emphasis on its merger with machine learning.

The energy of a many-particle system is not convex with respect to particle number for r-k interparticle repulsion potentials if k > log34 ≈ 1.262. With such potentials, some finite electronic systems have ionization potentials that are less than the electron affinity: they have negative band gap (chemical hardness). Although the energy may be a convex function of the number of electrons (for which k = 1), it suggests that finding an analytic proof of convexity will be very difficult. The bound on k is postulated to be tight. An apparent signature of non-convex behavior is that the Dyson orbital corresponding to the lowest-energy mode of electron attachment has a vanishingly small amplitude., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

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., (© 2023 The Authors. Journal of Computational Chemistry published by Wiley Periodicals LLC.)

To accurately and efficiently predict the molecular response properties (such as polarizability) at post-Hartree-Fock levels for condensed-phase systems under periodic boundary conditions (PBC) is still an unaccomplished and ongoing task. We demonstrate that static isotropic polarizabilities can be cost-effectively predicted at post-Hartree-Fock levels by combining the linear-scaling generalized energy-based fragmentation (GEBF) and information-theoretic approach (ITA) quantities. In PBC-GEBF, the total molecular polarizability of an extended system is obtained as a linear combination of the corresponding quantities of a series of small embedded subsystems of several monomers. Here, we show that in the PBC-GEBF-ITA framework, one can obtain the molecular polarizabilities and establish linear relations to ITA quantities. Once these relations are established for smaller subsystems, one can predict the polarizabilities of larger subsystems directly from the molecular wavefunction (or electron density) via ITA quantities. Alternatively, one can determine the total molecular polarizability via a linear combination equation in PBC-GEBF. We have corroborated that this newly proposed PBC-GEBF-ITA protocol is much more efficient than the original PBC-GEBF approach but is not much less accurate and that this conclusion holds for both many-body perturbation theory and the coupled cluster calculations. Good efficiency and transferability of the PBC-GEBF-ITA protocol are demonstrated for periodic systems with several hundred atoms in a unit cell.

We have witnessed considerable research interest in the recent literature about the development and applications of quantities from the information-theoretic approach (ITA) in density functional theory. These ITA quantities are explicit density functionals, whose local distributions in real space are continuous and well-behaved. In this work, we further develop ITA by systematically analyzing the topological behavior of its four representative quantities, Shannon entropy, two forms of Fisher information, and relative Shannon entropy (also called information gain or Kullback-Leibler divergence). Our results from their topological analyses for 103 molecular systems provide new insights into bonding interactions and physiochemical properties, such as electrophilicity, nucleophilicity, acidity, and aromaticity. We also compare our results with those from the electron density, electron localization function, localized orbital locator, and Laplacian functions. Our results offer a new methodological approach and practical tool for applications that are especially promising for elucidating chemical bonding and reactivity propensity., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

The linear response kernel also referred to as linear response function (LRF) in the framework of conceptual density functional theory has gained tremendous success in time-dependent density functional theory. Comparatively less attention has been devoted to the LRF from a chemical reactivity perspective in its time- or frequency-independent context, although it has recently been used to qualitatively describe electron delocalization, (anti-)aromaticity, inductive and mesomeric effects, etc. Despite these successes, which were obtained by approximating the LRF using the independent particle approximation deriving from a coupled-perturbed Kohn-Sham computation, the robustness of this LRF approach needs to be assessed. In this work, we compute the LRF at four levels of approximation (independent particle approximation, random phase approximation, Hartree-Fock approximation, and the (exact) DFT (density functional theory) expression) using functionals from the first four rungs of Jacob's ladder of exchange-correlation energy functionals. To scrutinize the impact of these approximations, new visualization strategies are discussed and systematized. The overall conclusion is that the independent particle approximation yields qualitatively correct results (ergo previous conceptual applications of the LRF are trustworthy), but for quantitative results, LRF expressions including coulomb and exchange(-correlation) terms should be included. With respect to functionals, density-gradient contributions to the exchange-correlation kernel are less than 10% and may be omitted safely where that is preferable computationally.

Accurate and efficient determination of excited-state polarizabilities ( α ) is an open problem both experimentally and computationally. Following our previous work, (Phys. Chem. Chem. Phys. 2023, 25, 2131-2141), in which we employed simple ground-state (S 0 ) density-related functions from the information-theoretic approach (ITA) to accurately and efficiently evaluate the macromolecular polarizabilities, in this work we aimed to predict the lowest excited-state (S 1 ) polarizabilities. The philosophy is to use density-based functions to depict excited-state polarizabilities. As a proof-of-principle application, employing 2-(2'-hydroxyphenyl)benzimidazole (HBI), its substituents, and some other commonly used ESIPT (excited-state intramolecular proton transfer) fluorophores as model systems, we verified that either with S 0 or S 1 densities as an input, ITA quantities can be strongly correlated with the excited-state polarizabilities. When transition densities are considered, both S 0 and S 1 polarizabilities are in good relationships with some ITA quantities. The transferability of the linear regression model is further verified for a series of molecules with little or no similarity to those molecules in the training set. Furthermore, the excitation energies can be predicted based on multivariant linear regression equations of ITA quantities. This study also found that the nature of both the ground-state and excited-state polarizabilities of these species are due to the spatial delocalization of the electron density.

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., (© 2022 Wiley Periodicals LLC.)

Accurately and efficiently predicting macromolecules' polarizabilities is an open problem. In this work, we employ a few simple density-based quantities from the information-theoretic approach (ITA) to predict polarizability of proteins. We first build quantitative structure/property relationships between molecular polarizabilities and ITA quantities. We then verify the broad applicability of ITA quantities for polarizability prediction for inorganic, organic, and biological systems with both localized and delocalized electronic structure. As a proof-of-concept application, we predict the molecular polarizabilities of complex proteins. Based on the linear regression equations for 20 natural amino acid residues, 400 dipeptides, and 8000 tripeptides, one then predicts the molecular polarizability of a larger peptide or even a protein once the molecular wavefunction is obtained. Because it is extremely costly to determine the wavefunction for a macromolecule like a protein, we propose to combine the ITA with the linear-scaling generalized energy-based fragmentation (GEBF) method to predict the macromolecular polarizability. In GEBF, the total molecular polarizability is obtained as a linear combination of the corresponding quantities from a series of small subsystems. We can predict them based on the subsystem wavefunction and linear regression equations rather than compute them from the nearly-intractable coupled-perturbed Hartree-Fock or Kohn-Sham equations for the whole macromolecule. Computational results showcase that the GEBF-ITA protocol should be an inexpensive yet accurate theoretical tool for predicting macromolecular polarizabilities.

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Reaction of [(XA 2 )U(CH 2 SiMe 3 ) 2 ] (1; XA 2 = 4,5-bis(2,6-diisopropylanilido)-2,7-di- tert -butyl-9,9-dimethylxanthene) with 1 equivalent of [Ph 3 C][B(C 6 F 5 ) 4 ] in arene solvents afforded the arene-coordinated uranium alkyl cations, [(XA 2 )U(CH 2 SiMe 3 )(η n -arene)][B(C 6 F 5 ) 4 ] {arene = benzene (2), toluene (3), bromobenzene (4) and fluorobenzene (5)}. Compounds 2, 3, and 5 were crystallographically characterized, and in all cases the arene is π-coordinated. Solution NMR studies of 2-5 suggest that the binding preferences of the [(XA 2 )U(CH 2 SiMe 3 )] + cation follow the order: toluene ≈ benzene > bromobenzene > fluorobenzene. Compounds 2-4 generated in C 6 H 5 R (R = H, Me or Br, respectively) showed no polymerization activity under 1 atm of ethylene. By contrast, 5 and 5-Th (the thorium analogue of 5) in fluorobenzene at 20 and 70 °C achieved ethylene polymerization activities between 16 800 and 139 200 g mol -1 h -1 atm -1 , highlighting the extent to which common arene solvents such as toluene can suppress ethylene polymerization activity in sterically open f-element complexes. However, activation of [(XA 2 )An(CH 2 SiMe 3 ) 2 ] {M = U (1) or Th (1-Th)} with [Ph 3 C][B(C 6 F 5 ) 4 ] in n -alkane solvents did not afford an active polymerization catalyst due to catalyst decomposition, illustrating the critical role of PhX (X = H, Me, Br or F) coordination for alkyl cation stabilization. Gas phase DFT calculations, including fragment interaction calculations with energy decomposition and ETS-NOCV analysis, were carried out on the cationic portion of 2'-Th, 2', 3' and 5' (analogues of 2-Th, 2, 3 and 5 with hydrogen atoms in place of ligand backbone methyl and tert -butyl groups), providing insight into the nature of actinide-arene bonding, which decreases in strength in the order 2'-Th > 2' ≈ 3' > 5'., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

An overview of mathematical properties of the non-local second order derivatives of the canonical, grand canonical, isomorphic, and grand isomorphic ensembles is given. The significance of their positive or negative semidefiniteness and the implications of these properties for atoms and molecules are discussed. Based on this property, many other interesting properties can be derived, such as the expansion in eigenfunctions, bounds on the diagonal and off-diagonal elements, and the eigenvalues of these kernels. We also prove Kato's theorem for the softness kernel and linear response and the dissociation limit of the linear responses as the sum of the linear responses of the individual fragments when dissociating a system into two non-interacting molecular fragments. Finally, strategies for the practical calculation of these kernels, their eigenfunctions, and their eigenvalues are discussed.

In the first paper of this series, the authors derived an expression for the interaction energy between two reagents in terms of the chemical reactivity indicators that can be derived from density functional perturbation theory. While negative interaction energies can explain reactivity, reactivity is often more simply explained using the "|dμ| big is good" rule or the maximum hardness principle. Expressions for the change in chemical potential ( μ ) and hardness when two reagents interact are derived. A partial justification for the maximum hardness principle is that the terms that appear in the interaction energy expression often reappear in the expression for the interaction hardness, but with opposite sign., Competing Interests: The reviewer (WT) declared a past co-authorship with the author (CC) to the handling editor., (Copyright © 2022 Miranda-Quintana, Heidar-Zadeh, Fias, Chapman, Liu, Morell, Gómez, Cárdenas and Ayers.)

Reactivity descriptors indicate where a reagent is most reactive and how it is most likely to react. However, a reaction will only occur when the reagent encounters a suitable reaction partner. Determining whether a pair of reagents is well-matched requires developing reactivity rules that depend on both reagents. This can be achieved using the expression for the minimum-interaction-energy obtained from the density functional reactivity theory. Different terms in this expression will be dominant in different circumstances; depending on which terms control the reactivity, different reactivity indicators will be preferred., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Miranda-Quintana, Heidar-Zadeh, Fias, Chapman, Liu, Morell, Gómez, Cárdenas and Ayers.)

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.

The highly-selective blood-brain barrier (BBB) prevents neurotoxic substances in blood from crossing into the extracellular fluid of the central nervous system (CNS). As such, the BBB has a close relationship with CNS disease development and treatment, so predicting whether a substance crosses the BBB is a key task in lead discovery for CNS drugs. Machine learning (ML) is a promising strategy for predicting the BBB permeability, but existing studies have been limited by small datasets with limited chemical diversity. To mitigate this issue, we present a large benchmark dataset, B3DB, complied from 50 published resources and categorized based on experimental uncertainty. A subset of the molecules in B3DB has numerical log BB values (1058 compounds), while the whole dataset has categorical (BBB+ or BBB-) BBB permeability labels (7807). The dataset is freely available at https://github.com/theochem/B3DB and https://doi.org/10.6084/m9.figshare.15634230.v3 (version 3). We also provide some physicochemical properties of the molecules. By analyzing these properties, we can demonstrate some physiochemical similarities and differences between BBB+ and BBB- compounds., (© 2021. The Author(s).)

The drive to develop maximal atom-efficient catalysts coupled to the continuous striving for more sustainable reactions has led to an ever-increasing interest in single-atom catalysis. Based on a periodic conceptual density functional theory (cDFT) approach, fundamental insights into the reactivity and adsorption of single late transition metal atoms supported on a fully hydroxylated amorphous silica surface have been acquired. In particular, this investigation revealed that the influence of van der Waals dispersion forces is especially significant for a silver (98 %) or gold (78 %) atom, whereas the oxophilicity of the Group 8-10 transition metals plays a major role in the interaction strength of these atoms on the irreducible SiO 2 support. The adsorption energies for the less-electronegative row 4 elements (Fe, Co, Ni) ranged from -1.40 to -1.92 eV, whereas for the heavier row 5 and 6 metals, with the exception of Pd, these values are between -2.20 and -2.92 eV. The deviating behavior of Pd can be attributed to a fully filled d-shell and, hence, the absence of the hybridization effects. Through a systematic analysis of cDFT descriptors determined by using three different theoretical schemes, the Fermi weighted density of states approach was identified as the most suitable for describing the reactivity of the studied systems. The main advantage of this scheme is the fact that it is not influenced by fictitious Coulomb interactions between successive, charged reciprocal cells. Moreover, the contribution of the energy levels to the reactivity is simultaneously scaled based on their position relative to the Fermi level. Finally, the obtained Fermi weighted density of states reactivity trends show a good agreement with the chemical characteristics of the investigated metal atoms as well as the experimental data., (© 2020 Wiley-VCH GmbH.)

IOData is a free and open-source Python library for parsing, storing, and converting various file formats commonly used by quantum chemistry, molecular dynamics, and plane-wave density-functional-theory software programs. In addition, IOData supports a flexible framework for generating input files for various software packages. While designed and released for stand-alone use, its original purpose was to facilitate the interoperability of various modules in the HORTON and ChemTools software packages with external (third-party) molecular quantum chemistry and solid-state density-functional-theory packages. IOData is designed to be easy to use, maintain, and extend; this is why we wrote IOData in Python and adopted many principles of modern software development, including comprehensive documentation, extensive testing, continuous integration/delivery protocols, and package management. This article is the official release note of the IOData library., (© 2020 Wiley Periodicals LLC.)

The bonding and antibonding character of individual molecular orbitals has been previously shown to be related to their orbital energy derivatives with respect to nuclear coordinates, known as dynamical orbital forces. Albeit usually derived from Koopmans' theorem, in this work we show a more general derivation from conceptual DFT, which justifies application in a broader context. The consistency of the approach is validated numerically for valence orbitals in Kohn-Sham DFT. Then, we illustrate its usefulness by showcasing applications in aromatic and antiaromatic systems and in excited state chemistry. Overall, dynamical orbital forces can be used to interpret the results of routine ab initio calculations, be it wavefunction or density based, in terms of forces and occupations., (© 2020 Wiley Periodicals LLC.)

Hydrogen cyanide (HCN) and formaldehyde (H 2 CO) are key precursors to biomolecules such as nucleobases and amino acids in planetary atmospheres. However, many reactions which produce and destroy these species in atmospheres containing CO 2 and H 2 O are still missing from the literature. We use a quantum chemistry approach to find these missing reactions and calculate their rate coefficients using canonical variational transition state theory and Rice-Ramsperger-Kassel-Marcus/master equation theory at the BHandHLYP/aug-cc-pVDZ level of theory. We calculate the rate coefficients for 126 total reactions and validate our calculations by comparing with experimental data in the 39% of available cases. Our calculated rate coefficients are most frequently within a factor of 2 of experimental values and generally always within an order of magnitude of these values. We discover 45 previously unknown reactions and identify 6 from this list that are most likely to dominate H 2 CO and HCN production and destruction in planetary atmospheres. We highlight 1 O + CH 3 → H 2 CO + H as a new key source and H 2 CO + 1 O → HCO + OH as a new key sink, for H 2 CO in upper planetary atmospheres. In this effort, we develop an oxygen extension to our consistent reduced atmospheric hybrid chemical network (CRAHCN-O), building off our previously developed network for HCN production in N 2 -, CH 4 -, and H 2 -dominated atmospheres (CRAHCN). This extension can be used to simulate both HCN and H 2 CO production in atmospheres dominated by any of CO 2 , N 2 , H 2 O, CH 4 , and H 2 .

Ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian are employed as a wavefunction Ansatz to model strong electron correlation in quantum chemistry. This wavefunction is a product of weakly interacting pairs of electrons. While other geminal wavefunctions may only be employed in a projected Schrödinger equation, the present approach may be solved variationally with polynomial cost. The resulting wavefunctions are used to compute expectation values of Coulomb Hamiltonians, and we present results for atoms and dissociation curves that are in agreement with doubly occupied configuration interaction data. The present approach will serve as the starting point for a many-body theory of pairs, much as Hartree-Fock is the starting point for weakly correlated electrons.

A charge transfer model is developed within the framework of the grand canonical ensemble through the analysis of the behavior of the fractional charge as a function of the chemical potential of the bath when the temperature and the external chemical potential are kept fixed. Departing from the fact that, before the interaction between two species, each one has a zero fractional charge, one can identify two situations after the interaction occurs where the fractional charge of at least one of the species is different from zero, indicating that there has been charge transference. One of them corresponds to the case when one of the species is immersed in a bath conformed by the other one, while the other is related to the case in which both species are present in equal amounts (stoichiometric proportion). Correlations between the fractional charges and average energies, thus obtained with experimental equilibrium constants, kinetic rate constants, hydration constants, and bond enthalpies, indicate that, although at the experimental temperatures, they are very small quantities, they have chemically meaningful information. Additionally, in the stoichiometric case, one also finds a rather good correlation between the equalized chemical potential and the one obtained from experimental information for a test set of diatomic and triatomic molecules.

In this publication, we propose a new set of reactivity/selectivity descriptors, derived within a Rayleigh-Schrödinger perturbation theory framework, for chemical systems undergoing an electrostatic (point-charge) perturbation. From the electron density polarization at first order, qualitative insight on reactivity is retrieved, while more quantitative information (noteworthy selectivity) can be obtained from either the second-order energy response or the number of shifted electrons under perturbation. Noteworthily, only a small number of excitations contribute significantly to the overall responses to perturbation, suggesting chemical reactivity could be foreseen by a careful scrutiny of the electron density reorganization upon excitation.

The paper collects the answers of the authors to the following questions: Is the lack of precision in the definition of many chemical concepts one of the reasons for the coexistence of many partition schemes? Does the adoption of a given partition scheme imply a set of more precise definitions of the underlying chemical concepts? How can one use the results of a partition scheme to improve the clarity of definitions of concepts? Are partition schemes subject to scientific Darwinism? If so, what is the influence of a community's sociological pressure in the "natural selection" process? To what extent does/can/should investigated systems influence the choice of a particular partition scheme? Do we need more focused chemical validation of Energy Decomposition Analysis (EDA) methodology and descriptors/terms in general? Is there any interest in developing common benchmarks and test sets for cross-validation of methods? Is it possible to contemplate a unified partition scheme (let us call it the "standard model" of partitioning), that is proper for all applications in chemistry, in the foreseeable future or even in principle? In the end, science is about experiments and the real world. Can one, therefore, use any experiment or experimental data be used to favor one partition scheme over another? © 2019 Wiley Periodicals, Inc., (© 2019 Wiley Periodicals, Inc.)

HCN is a key ingredient for synthesizing biomolecules such as nucleobases and amino acids. We calculate 42 reaction rate coefficients directly involved with or in competition with the production of HCN in the early Earth or Titan atmospheres. These reactions are driven by methane and nitrogen radicals produced via UV photodissociation or lightning. For every reaction in this network, we calculate rate coefficients at 298 K using canonical variational transition state theory (CVT) paired with computational quantum chemistry simulations at the BHandHLYP/aug-cc-pVDZ level of theory. We also calculate the temperature dependence of the rate coefficients for the reactions that have barriers from 50 to 400 K. We present 15 new reaction rate coefficients with no previously known value; 93% of our calculated coefficients are within an order of magnitude of the nearest experimental or recommended values. Above 320 K, the rate coefficient for the new reaction H 2 CN → HCN + H dominates. Contrary to experiments, we find the HCN reaction pathway, N + CH 3 → HCN + H 2 , to be inefficient and suggest that the experimental rate coefficient actually corresponds to an indirect pathway, through the H 2 CN intermediate. We present CVT using energies computed with density functional theory as a feasible and accurate method for calculating a large network of rate coefficients of small-molecule reactions.

The topology of the molecular electron density of benzene dithiol gold cluster complex Au 4 -S-C 6 H 4 -S'-Au' 4 changed when relativistic corrections were made and the structure was close to a minimum of the Born-Oppenheimer energy surface. Specifically, new bond paths between hydrogen atoms on the benzene ring and gold atoms appeared, indicating that there is a favorable interaction between these atoms at the relativistic level. This is consistent with the observation that gold becomes a better electron acceptor when relativistic corrections are applied. In addition to relativistic effects, here, we establish the sensitivity of molecular topology to basis sets and convergence thresholds for geometry optimization., (© 2019 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.)

In this brief report, we show that the three different chemical hardness definitions developed in the framework of the temperature-dependent density functional theory-namely, the electronic, the thermodynamic, and the Helmholtz hardnesses-imply both the hard and soft acids and bases (HSAB) principle and the maximum hardness (MH) principle. These hardnesses are identified as the second derivative of a thermodynamic state function and avoid the somewhat arbitrary approach, based on the parabolic interpolation of the energy versus electron number, that is normally used to justify these principles. This not only leads to a more mathematically sound justification of the HSAB and MH principles in the low-temperature limit but also establishes that the HSAB and the MH principles hold at any temperature of chemical relevance.

A new strategy, recently reported by us to develop local and linear (nonlocal) counterparts of global response functions, is applied to study the local behavior of the global softness and hardness reactivity descriptors. Within this approach a local counterpart is designed to identify the most important molecular fragments for a given chemical response. The local counterpart of the global softness obtained through our methodology corresponds to the well-known definition of local softness and, in agreement with what standard conceptual chemical reactivity in density functional theory dictates, it simply reveals the softest sites in a molecule. For the case of the local hardness, we obtain two expressions that lead to different information regarding the values of the hardness at the different sites within a chemical species. The performance of these two proposal were tested by comparing their corresponding atom-condensed values to experimentally observed reactivity trends for electrophilic attack on benzene and ethene derivatives.

The way the bonding and reactivity of armchair carbon nanotubes depends on the curvature of the nanotube has been investigated using density functional theory. To understand the nature of the interaction between atoms in the nanotube, the Wiberg bond index, natural bond order analysis, and topological electron density analysis have been performed. All these tools confirm that the bonds in the hydrogen-capped carbon nanotubes considered here are primarily covalent. As the diameter of the nanotube decreases and its curvature increases, the covalency (bond order) decreases, a conclusion that is supported by the increase of the bond lengths and also the decrease of the electron density and the energy density along the bond paths as the curvature increases. To shed light on the orbital contribution in bond formation and the most effective interaction between donor bonding orbital and acceptor antibonding orbital, analysis of natural bond orbitals is carried out. We have observed that the higher the nanotube diameter is, the higher the energy gap.

Thirty years ago, Parr and Yang postulated that favorable chemical processes are associated with large changes in the electronic chemical potential or, equivalently, the electronegativity. They called this the "|Δμ| big is good" rule and noted that if the rule could be justified, then it "would constitute a validation of frontier theory from first principles." We provide a simple and insightful justification for the "|Δμ| big is good" rule, with special emphasis on electron-transfer reactions. Furthermore, we show that it implies Pearson's hard/soft acid/base principle mathematically and confirm this result with numerical examples. This supports Parr's intuition that many other reactivity precepts arise as corollaries to the more fundamental "|Δμ| big is good" rule. In all of this, it is essential to consider the intensive nature of the chemical potential.

Very recently [J. Phys. Chem. A 2018, 122 (11), 3087-3095], we proposed to employ the Pauli energy to identify and determine strong covalent interactions (SCI), whose bond order are equal to or larger than two. This is done through the signature isosurface shape between the two bonding atoms. We discovered that the signature shape for a double, triple, and quadruple covalent bond is like a dumbbell, donut (torus), and four-beats, respectively. Systems with even higher bond orders were examined and confirmed. This work is a follow-up study of our previous work. The dependence of the signature isosurface shape on the choice of methodologies and basis sets is systematically investigated. Its effectiveness and robustness in determining bond orders are highlighted again with more examples. In addition, using the molybdenum dimer in different environments, e.g., in vacuum, sandwiched between molecules, and encapsulated in the C 80 cage, as illustrative examples, we show that, generally speaking, bond strength and bond order are two different chemical concepts. For systems containing transition metals, it is not always true that a short metal-metal bond length corresponds to a larger bond order. Put together, these results should provide additional pieces of convincing evidence showing that the SCI index is a robust and reliable density-based descriptor to accurately determine multiple covalent bond orders.

We argue that when one divides a molecular property into atom-in-a-molecule contributions, one should perform the division based on the property density of the quantity being partitioned. This is opposition to the normal approach, where the electron density is given a privileged role in defining the properties of atoms-in-a-molecule. Because partitioning each molecular property based on its own property density is inconvenient, we design a reference-free approach that does not (directly) refer atomic property densities. Specifically, we propose a stockholder partitioning method based on relative influence of a molecule's atomic nuclei on the electrons at a given point in space. The resulting method does not depend on an "arbitrary" choice of reference atoms and it has some favorable properties, including the fact that all of the electron density at an atomic nucleus is assigned to that nucleus and the fact all the atoms in a molecule decay at a uniform asymptotic rate. Unfortunately, the resulting model is not easily applied to spatially degenerate ground states. Furthermore, the practical realizations of this strategy that we tried here gave disappointing numerical results. © 2017 Wiley Periodicals, Inc., (© 2017 Wiley Periodicals, Inc.)

Generalizing our recent work on relativistic generalizations of the quantum theory of atoms in molecules, we present the general setting under which the principle of stationary action for a region leads to open quantum subsystems. The approach presented here is general and works for any Hamiltonian, and when a reasonable Lagrangian is selected, it often leads to the integral of the Laplacian of the electron density on the region vanishing as a necessary condition for the zero-flux surface. Alternatively, with this method, one can design a Lagrangian that leads to a surface of interest (though this Lagrangian may not be, and indeed probably will not be, "reasonable"). For any reasonable Lagrangian for the electronic wave function and any two-component method (related by integration by parts to the Hamiltonian) considered, the Bader definition of an atom is recaptured. © 2018 Wiley Periodicals, Inc., (© 2018 Wiley Periodicals, Inc.)

We provide new arguments supporting the validity of the maximum hardness and the minimum electrophilicity principles, considering the overall change of these descriptors in a charge-transfer reaction. We analyze two cases: (a) how the reactivity is affected when we perturb one reagent, keeping the other constant; (b) how the hardness and electrophilicity change when we treat the interaction between the reagents as a perturbation.

Many population analysis methods are based on the precept that molecules should be built from fragments (typically atoms) that maximally resemble the isolated fragment. The resulting molecular building blocks are intuitive (because they maximally resemble well-understood systems) and transferable (because if two molecular fragments both resemble an isolated fragment, they necessarily resemble each other). Information theory is one way to measure the deviation between molecular fragments and their isolated counterparts, and it is a way that lends itself to interpretation. For example, one can analyze the relative importance of electron transfer and polarization of the fragments. We present key features, advantages, and disadvantages of the information-theoretic approach. We also codify existing information-theoretic partitioning methods in a way that clarifies the enormous freedom one has within the information-theoretic ansatz.

This reply complements the comment of Guégan et al. about our recent work on the revision of the local hardness and the hardness kernel concepts. Guegan et al. analyze our work using a Taylor series expansion of the energy as a functional of the electron density, to show that our procedure opens a new way to define local descriptors. In this contribution we show that the strategy we followed for the local hardness and the hardness kernel is even more general, and that it can be used to derive from a global response function its corresponding local and non-local counterparts by: (1) requiring that the integral over one of the two variables that characterizes the non-local function leads to the local function, and that the integral over the local function leads to the global response index, and (2) assuming that the global and local functions are related through the electronic density, by making use of the chain rule for functional derivatives.

In methods like geminal-based approaches or coupled cluster that are solved using the projected Schrödinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response theory are not N-representable. That is, the response 2-RDM does not correspond to an actual physical N-electron wave function. We present a new algorithm for making these non-N-representable 2-RDMs approximately N-representable, i.e., it has the right symmetry and normalization and it fulfills the P-, Q-, and G-conditions. Next to an algorithm which can be applied to any 2-RDM, we have also developed a 2-RDM optimization procedure specifically for seniority-zero 2-RDMs. We aim to find the 2-RDM with the right properties which is the closest (in the sense of the Frobenius norm) to the non-N-representable 2-RDM by minimizing the square norm of the difference between this initial response 2-RDM and the targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM, Q-matrix, and G-matrix are positive semidefinite, i.e., their eigenvalues are non-negative. Our method is suitable for fixing non-N-representable 2-RDMs which are close to being N-representable. Through the N-representability optimization algorithm we add a small correction to the initial 2-RDM such that it fulfills the most important N-representability conditions.