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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The article discusses the celebration of Professor Pratim Kumar Chattaraj's 65th birthday and his academic achievements. An international conference was organized in his honor, which brought together experts from various scientific disciplines to understand complex systems and processes. Professor Chattaraj's research work spans a wide range of topics, including ab initio calculations, density functional theory, chemical reactivity theory, and machine learning. To commemorate his birthday, a collection of papers from the conference is being published in the Theoretical Chemistry Accounts journal. The papers cover diverse topics such as chemical reactivity descriptors, aromaticity, energy components, electron density, and various applications in different research domains. The article expresses gratitude to Professor Chattaraj for his contributions to science and his support for young scientists. [Extracted from the article]

We provide a general (yet elementary) proof of Pearson's hard/soft acid/base principle. Contrary to previous attempts to justify this rule, we go beyond the venerable parabolic model of Parr and Pearson. This new treatment encompasses more realistic E versus N dependencies, while emphasizing the importance of the correct normalization of these models. [ABSTRACT FROM AUTHOR]

We provide a (strong) inductive proof of Borchardt's theorem for calculating the permanent of a Cauchy matrix via the determinants of auxiliary matrices. This result has implications for antisymmetric products of interacting geminals (APIG), and suggests that the restriction of the APIG coefficients to Cauchy form (typically called APr2G) is special in its tractability. [ABSTRACT FROM AUTHOR]

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]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 (S0) 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 (S1) 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 S0 or S1 densities as an input, ITA quantities can be strongly correlated with the excited-state polarizabilities. When transition densities are considered, both S0 and S1 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this work, we have observed that some chiral boron clusters ( B 16 − , B 20 − , B 24 − , and B 28 − ) 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Molecular solubility is among the key properties that determine the clinical performance of a drug candidate because poor molecular solubility often indicates inadequate bioavailability. Using the CombiSolv-Exp database, we test several models (Gaussian process regression, decision trees, k-nearest neighbors) for hydration free energies by integrating Δ -learning and a universal quantum-chemistry continuum solvation model, SMD. The optimal model is Gaussian process regression with MAE of 0.63 kcal/mol. The reported models improve the accuracy of SMD, but have negligible additional computational cost. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Using the energy components associated with density-functional theory (DFT) calculations and various descriptors from the density-functional reactivity theory (conceptual DFT), we explore which chemical effects are most important for determining the ordering the conformers of the twenty natural amino acids in terms of their relative energetic stability. Electrostatic and steric (alternatively, electrostatic and exchange–correlation) interactions are found to be most descriptive of conformer stability. We also introduce an approach for determining how well one or more descriptors order the conformers, without requiring a linear (or any other) correlation between the descriptors. This ordering/ranking paradigm is likely to be useful in many other contexts also. [ABSTRACT FROM AUTHOR]