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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]

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]

Graphical abstract Highlights • If the wavefunction is sufficiently differentiable, it can be approximated with polynomial cost in the high-accuracy limit. • A strategy for picking configurations is proposed and used to define a selected configuration interaction method called GKCI. • Griebel-Knapek configuration interaction (GKCI) is appropriate for wavefunctions with dominating mixed smoothness. • Errors due to truncating the Slater determinant expansion and the one-electron basis set should be balanced. • GKCI gives promising results when tested for small systems. Abstract Most approaches for solving the electronic Schrödinger equation do not fully exploit the functional-analytic simplicity of the electronic wavefunction. Because of this, the cost of these methods explodes exponentially with increasing electron number, an effect that is often called the curse of dimension. Recent work in mathematics and computer science shows how, by exploiting the smoothness of molecular wavefunctions, one can design methods that achieve the same accuracy as full configuration interaction, but with polynomial cost. The mathematical background of this approach is presented, along with a detailed prescription for identifying the relevant Slater determinants and a demonstration of the method's effectiveness for atomic systems. In the basis-set limit, this truncated configuration interaction method is size-consistent. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • An axiomatic approach for defining and assessing chemical concepts is proposed. • Concepts should be mathematically formulated and assessed against specified axioms. • Ideally, concepts should be defined using physical observables. • The best concept for a given objective is the one whose axioms are most appropriate. Abstract Many concepts that are central to chemical language and thought emerge from the wealth of chemists' historical experience and cannot be precisely defined mathematically from the underlying physics. In such cases, it is useful to take an axiomatic approach: list the chemical, mathematical and computational properties that one desires for a concept to possess, and then find the rigorous (and, if possible, elegant) mathematical formulation of the concept that satisfies those desiderata. This mathematical formulation is most useful if it relies on fundamental quantities—quantum-mechanical observables, reduced density matrices, or the N -electron wavefunction—rather than method-dependent quantities (e.g., orbitals) that are not defined for some computational approaches to the molecular electronic structure problem. This ensures that the pursuit of chemical intuition does not lead one too far from the underlying physics. It also ensures that one can interpret the results of any computational method, even methods (e.g., quantum Monte Carlo) that make no reference to any molecular-orbital or valence-bond model. [ABSTRACT FROM AUTHOR]