Graphical Approach to Interpreting and Efficiently Evaluating Geminal Wavefunctions.

We consider wavefunctions built from antisymmetrized products of two-electron wavefunctions (geminals), which is arguably the simplest extension of the antisymmetrized product of one-electron wavefunctions (orbitals) (i.e., a Slater determinant).

Impact of confining hydrogen molecule inside fullerenes: A glance through DFT study.

Context: In this work, we have studied different properties of a series of fullerenes, from C to C by confining hydrogen molecule inside their cavity. The compression of the hydrogen molecule upon encapsulation is evidenced by its altered bond length, while a slight expansion of the fullerene cages due to H confinement is also noted. The chemical reactivity parameters of both the empty and H confined fullerenes are computed, alongside an examination of the energy components through energy decomposition analysis.

Meijer-G and other resummation strategies for the Møller-Plesset perturbation series.

We compare various resummation techniques on truncated Møller-Plesset perturbation series. Our main results are for Padé, Borel-Padé, and Meijer G resummation techniques. All these resummation techniques improve the energies from truncated Møller-Plesset perturbation theory when the perturbation series is not-too-ill-behaved, but the Meijer-G resummation is arguably the best resummation, at least for low orders.

Temperature and external fields in conceptual density functional theory.

Until quite recently, Conceptual DFT (CDFT) was mainly based on the energy functional, [,], where the number of electrons and the external potential are state variables. One of the strengths of CDFT, however, is the ease with which additional and/or different state variables can be incorporated. Here, the incorporation of new variables-namely temperature and external fields-is discussed, outlining the motivation for these extensions, sketching their theoretical/computational context, and presenting some elucidative examples.

The Analysis of Electron Densities: From Basics to Emergent Applications.

The electron density determines all properties of a system of nuclei and electrons. It is both computable and observable. Its topology allows gaining insight into the mechanisms of bonding and other phenomena in a way that is complementary to and beyond that available from the molecular orbital picture and the formal oxidation state (FOS) formalism.

Variational Hirshfeld Partitioning: General Framework and the Additive Variational Hirshfeld Partitioning Method.

We introduce the general mathematical framework of variational Hirshfeld partitioning, wherein the best possible approximation to a molecule's electron density is obtained by minimizing the -divergence between the molecular density and a non-negative linear combination of (normalized) basis functions. This framework subsumes several existing methods that variationally optimize their pro-atoms, like (Gaussian) iterative stockholder analysis (ISA and GISA) and minimal basis iterative stockholder partitioning (MBIS), and provides a solid foundation for developing mathematically rigorous partitioning schemes. In this paper, we delve into the mathematical underpinnings of Hirshfeld-inspired partitioning schemes and show that among all the valid -divergence measures only the extended Kullback-Leibler is a suitable choice.

Inferring the existence of hydrogen bonds directly from statistical analysis of molecular dynamics trajectories.

As a demonstration of how fundamental chemical concepts can be gleaned from data using machine learning methods, we demonstrate the automated detection of hydrogen bonds by statistical analysis of molecular dynamics trajectories. In particular, we infer the existence and nature of electrostatically driven noncovalent interactions by examining the relative probability of supramolecular configurations with and without electrostatic interactions. Then, using Laplacian eigenmaps clustering, we identify hydrogen bonding motifs in hydrogen fluoride, water, and methanol.

Slope of the Delocalization Function Is Proportional to Analytical Hardness.

Conceptual Density Functional Theory (CDFT) has been extended beyond its traditional role in elucidating chemical reactivity to the development of density functional theory methods, e.g., the investigation of the delocalization error.

PyCI: A Python-scriptable library for arbitrary determinant CI.

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.

Why are information-theoretic descriptors powerful predictors of atomic and molecular polarizabilities.

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.

On the link between the reaction force constant and conceptual DFT.

Context: The reaction force constant ( ), 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 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.

GBasis: A Python library for evaluating functions, functionals, and integrals expressed with Gaussian basis functions.

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.

Energetic Information from Information-Theoretic Approach in Density Functional Theory as Quantitative Measures of Physicochemical Properties.

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 (. , 157, 101103).

Spin-Polarized Conceptual Density Functional Theory from the Convex Hull.

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.

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.

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.

Flexible Ansatz for -Body Perturbation Theory.

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 -body Perturbation Theory (FANPT) is based on our previously proposed Flexible Ansatz for the -body Configuration Interaction (FANCI). We derive recursive FANPT expressions, including arbitrary orders in the perturbation hierarchy.

Chiral Jahn-Teller Distortion in Quasi-Planar Boron Clusters.

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.

Coupled cluster-inspired geminal wavefunctions.

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.

Fragment-Based Deep Learning for Simultaneous Prediction of Polarizabilities and NMR Shieldings of Macromolecules and Their Aggregates.

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.

Some Recent Advances in Density-Based Reactivity Theory.

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.

Energy is not a convex function of particle number for r-k interparticle potentials with k > log34.

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).

Accurate and Efficient Prediction of Post-Hartree-Fock Polarizabilities of Condensed-Phase Systems.

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.

Topological analysis of information-theoretic quantities in density functional theory.

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).