We establish necessary and sufficient conditions for the N-representability of the universal one-electron reduced density matrix functional. Functionals satisfying these conditions are guaranteed to yield variational upper bounds on the true energy in one-electron reduced density matrix functional theory, regardless of the strength of the interparticle repulsion. Conversely, any functional violating these conditions will necessarily underestimate the true energy for certain systems. These exact constraints impose a stringent restriction on density matrix functional approximations, as many existing functionals-including the Hartree-Fock functional-appear to violate them. This mathematical formalism, therefore, can guide the development of new approximate functionals and numerical algorithms.

Accurate modeling of bond breaking remains a central challenge for reduced density matrix functional theory (RDMFT). Although some modern functionals can yield reasonably accurate dissociation energies, they often fail to reproduce key properties of the dissociated fragments, such as a vanishing fragment population covariance (also known as the delocalization index) and the correct total spin angular momentum of each fragment (local spin). In this study, we revisit the construction of natural orbital functionals by correcting the cumulant contribution produced by the PNOF5 functional. Our method enforces known contributions of the cumulant to local spin fragments and the delocalization index at the dissociation limit. We obtain the closest cumulant consistent with these physically motivated constraints and subsequently purify the corresponding one- and two-electron reduced density matrices by imposing the standard P, Q, and GN-representability conditions. The resulting functional yields improved behavior in strongly correlated regimes. Benchmarking on the dissociation of the singlet states of N2, NO+, O2, S2, and CO shows that, in the dissociation regime, the energies computed from the updated cumulant exactly reproduce the complete active space self-consistent field energies. We further analyze the limitations of the approach and identify scenarios in which the current approach performs poorly. This study provides a pathway for systematically improving natural orbital functionals to achieve reliable bond-breaking calculations within RDMFT.

We propose a method to solve the Schr & ouml;dinger equation for systems with static/strong electron correlation using Hamiltonian transformations. Building on our previous work on seniority-zero canonical transformation theory, which seeks a unitary transformation that maps the Hamiltonian into the seniority-zero space, this method presents an alternative way of evaluating the Baker-Campbell-Hausdorff (BCH) expansion based on quadratic canonical transformation theory. The extension aims to relax the small-generator constraint by allowing approximate four-body contributions in the expansion, thus expanding the class of excitations previously allowed in SZ-LCT, where only approximate three-body operators were retained. Numerical tests reveal that the seniority-zero quadratic canonical transformation method (SZ-QCT) delivers good accuracy, with most errors within chemical accuracy. In particular, SZ-QCT shows sub-milli Hartree errors in cases where larger generators are needed to recover the residual dynamic correlation. The computational scaling of SZ-QCT is the same as that of SZ-LCT, , where is the number of cores available for the computation.

Fanpy is a Python library for developing new wavefunction methods. It enables users to quickly convert mathematical expressions into working code through a modular design based on the Flexible Ansatz for N-electron Configuration Interaction (FANCI) theory. This architecture facilitates a straightforward extension of the codebase. Here we present version 2.0 of the Fanpy package. This release includes several new wavefunction implementations, including coupled- cluster-inspired geminal approaches. A new analysis module enables a more detailed inspection of computational results and lays the groundwork for future features. In addition, the PySCF interface has been redesigned, and an interface to the PyCI package has been introduced to offload computationally expensive components. Finally, we introduce an improved software development environment, including automated testing and issue tracking.

A unified theoretical framework for interpolating the energy and other molecular properties as a function of the number of electrons is presented. For any smooth interpolatory model of charge transfer, including the ubiquitous quadratic model, the electron density is always negative for some regions of space and some numbers of electrons. This has practical implications; e.g., we observe that parabolic interpolation predicts HF+0.5 has an unphysical negative population on hydrogen for sufficiently compressed bonds. This suggests that the only sensible model for charge transfer, in most cases, is linear (zero-temperature grand canonical) interpolation.

Because the gradient expansion for the kinetic energy functionals around the uniform electron gas limit diverges for molecular systems, hyperasymptotic resummation techniques seem appealing. We discuss some renormalization approaches including rational Pad & eacute; and Meijer-G resummation methods that are well-adapted to strongly divergent expansions and evaluate their performance. In general, the problem of kinetic energy functionals appears extremely challenging. Imposing constraints on the kinetic energy functional may be beneficial and potentially provide guidance for future investigations.

Accurately and efficiently predicting redox potentials and Hammett constants using simple density-based functions derived from information-theoretic approach (ITA) quantities remains an unresolved challenge. In this work, we employ two recently proposed protocols, DL(ITA) (deep learning) and QML(ITA) (quantum machine learning), to a broad range of quinone derivatives with available experimental data. The molecular electrostatic potential (MEP) at the nucleus of the acidic atom and the sum of valence natural atomic orbital (NAO) energies are used within a linear regression (LR) framework to assess the first redox potentials and Hammett parameters of these quinone derivatives. The DL(ITA) protocol enables the construction of a transferable model trained on quinone derivatives that can be applied to both quinone and non-quinone systems. Interestingly, the QML(ITA) model exhibits superior performance compared to the DL(ITA) approach. Moreover, the structure of the QML(ITA) method suggests that it may be readily implemented on real quantum hardware in the near future.

We present a second-derivative-corrected extension of the Flexible Ansatz for N-body Perturbation Theory (FANPT) for solving nonlinear Flexible Ansatz for N-body Configuration Interaction (FANCI) wavefunction equations. The original quasilinear FANPT approximation neglects second- and higher-order derivatives of the determinant overlap with respect to wavefunction parameters. In this work, we retain the overlap Hessian and neglect only third- and higher-order parameter derivatives, thereby including the leading nonlinear response of the wavefunction ansatz while preserving the same response-matrix structure used in the original FANPT formulation. The resulting additional terms enter only through the constant vector of the response equations and are implemented for coupled-cluster wavefunctions in the FanPy/FANCI framework. The new approximation is tested on the Lithium Hydride molecule and the insertion of Beryllium into H_2 using seniority-restricted coupled-cluster wavefunctions in the STO-6G basis. The main advantage of the second-derivative correction is that it provides a better initial guess for solving the projected FANCI equations at the next point along the adiabatic connection. This improvement is diagnosed by comparing the FANPT-propagated parameters with the independently optimized FANCI parameters at the same value of λ. For nonlinear coupled-cluster ansatzes, especially when larger λ-steps are used, the corrected approximation reduces the same-λ parameter deviations and suppresses large parameter-space excursions. These results show that the leading nonlinear overlap correction improves the reliability of FANPT as a continuation strategy for nonlinear wavefunction equations.

We introduce a novel class of coupled cluster (CC) methods that leverage the seniority concept to enhance efficiency and accuracy in electronic structure calculations. While existing approaches, such as the pair coupled cluster doubles (pCCD) method, are limited to seniority-zero (Ω = 0) wave functions, we propose a more flexible framework: seniority-restricted coupled cluster (sr-CC). This new methodology selectively constrains the seniority sectors accessible through excitation operators in the cluster expansion, enabling a more systematic exploration of electron correlation effects. By balancing computational cost and accuracy, sr-CC provides a promising pathway for advancing electronic structure theory, particularly in strongly correlated systems. We benchmark sr-CCSD(0), sr-CCSDTQ(0), and sr-CCSDT(2)Q(0) on BeH2 insertion, linear and cubic H8, and F2 dissociation. The sr-CC hierarchy remains robust in strongly correlated regimes where conventional single-reference CC methods deteriorate. For H8 and F2 dissociation, sr-CCSDT(2)Q(0) and sr-CCSDTQ(0) reproduce FCI energies to near machine precision across the full dissociation range, while bypassing the need for orbital optimization, although intermediate geometries remain more demanding. Overall, excitation-rank-dependent seniority restrictions provide a systematically improvable strategy for extending coupled cluster theory into strongly correlated regimes within a unified exponential framework.

This paper introduces a novel alignment-free method for characterizing molecular surfaces and their properties with broad applications in cheminformatics. We present a spectral approach that quantifies the shape of a surface and its associated property, such as ethe electrostatic potential, by converting them into characteristic spectra This method is grounded in shape analysis and the Laplace-Beltrami operator that continuously changing as the surface/property changes, capturing both topological changes due to post-bond rupture into radicals and functional group identification of small organic molecules. We demonstrate its effectiveness in organic compound classification and in assessing protein-surface similarity between thermophilic and mesophilic proteins. Our approach is concise, interpretable, and capable of distinguishing molecular shapes and functional groups. This method offers significant potential for advancing data-driven models in material sciences and drug discovery.

We generate an electronegativity scale based on the ability of atoms and functional groups in molecules to take electrons from the other atoms and functional groups therein. To do this, we construct the minimum weighted feedback arc set, which provides a ranking of moieties' electronegativity based on the number of electrons they accept, or donate, from other moieties. A rating scale for electronegativity is then constructed by projecting data about the pairwise electronegativity difference onto a one-dimensional manifold. Our results are broadly in line with more traditional scales of the electronegativity and electronic chemical potential, especially Pauling's definition.

Chemical hardness is one of the fundamental concepts in chemical reactivity theory, rigorously defined within the framework of Conceptual Density Functional Theory (CDFT). The associated maximum hardness principle (MHP), which postulates that a favorable direction of reaction is toward the state of maximum hardness, has been widely applied as a guiding rule to govern the direction of chemical reactions. However, several studies have questioned its validity. In this work, we investigated the quantitative applicability of the MHP using two reaction datasets, viz, a dipolar cycloaddition dataset of 5269 reaction profiles and the more comprehensive BH9 dataset of 449 reactions. We adopted different approximations to compute the hardness, including Kohn-Sham orbital based frontier molecular orbital (FMO) and the finite difference approximation (FDA). The effect of using different definitions to compute the average hardness of bimolecular reactions is analyzed on the validity of MHP. Our analysis revealed dependence of hardness values on the level of theory, definitions and approximations used which should be kept in mind before criticizing the MHP. Among 5269 cycloaddition reactions, approximately 80% of the reactions are found to obey the MHP. For BH9 dataset, MHP is found to better supported for unimolecular reactions, while remaining strongly dependent on the definition used to compute the average hardness for bimolecular reactions. Reactions in which the individual hardness of the reactants differs significantly are more likely to disobey MHP. Nonetheless, since these electronic structure principles are qualitative in nature, their validity cannot be expected to be universal.

We show how to add the effects of residual electron correlation to a reference seniority-zero wave function by transforming the true electronic Hamiltonian into seniority-zero form. The transformation is treated via the Baker-Campbell-Hausdorff (BCH) expansion, and the seniority-zero structure of the reference is exploited to evaluate the first three commutators exactly; the remaining contributions are handled with a recursive commutator approximation, as is typical in canonical transformation methods. By choosing a seniority-zero reference and using parallel computation, this method is practical for small- to medium-sized systems. Numerical tests show high accuracy, with errors ∼10-4 Hartree.

We present examples where successive ionization potentials of an isolated electronic system are nonincreasing; ergo, the energy is a nonconvex function of particle number. The basic strategy, which is based on minimizing the energy of the N ± 1-electron systems by leveraging solutions to the Thomson problem, seems quite general, giving large families of systems with nonconvex behavior; we show examples for N = 5 and N = 7 charged particles. As with previous counterexamples in the literature, the key ingredient is a qualitative change in configuration upon ionization. We propose two families of molecular structures, F4Br65- and F6Br87-, that are expected to show nonconvex behavior with respect to the number of electrons.

We propose a method to solve the electronic Schrödinger equation for strongly correlated systems by applying a unitary transformation to reduce the complexity of the physical Hamiltonian. In particular, we seek a transformation that maps the Hamiltonian into the seniority-zero space: seniority-zero wavefunctions are computationally simpler, but still capture strong correlation within electron pairs. The unitary rotation is evaluated using the Baker-Campbell-Hausdorff expansion, truncated to two-body operators through the operator decomposition strategy of canonical transformation (CT) theory, which rewrites higher-rank terms approximately in terms of one- and two-body operators. Unlike conventional approaches to CT theory, the generator is chosen to minimize the size of non-seniority-zero elements of the transformed Hamiltonian. Numerical tests reveal that this Seniority-zero Linear Canonical Transformation (SZ-LCT) method delivers highly accurate results, usually with sub-milliHartree error. The effective computational scaling of SZ-LCT is O(N8/nc), where nc is the number of cores available for the computation.

OBJECTIVES: Predicting the carcinogenicity of polycyclic aromatic hydrocarbons (PAHs) is challenging due to their structural complexity and diverse biological activity. Carcinogenic potential is strongly influenced by molecular structure mainly ring arrangement and substitution patterns that affect metabolic activation and DNA reactivity. To improve predictive modeling, we compiled a dataset of 302 polycyclic aromatic hydrocarbons featuring novel topological indices-Bay, Fjord, Harbor, and Canyon (BFHC)-along with experimental carcinogenicity classifications, log P, and log Iball values. PAHs were further classified according to their fused-benzene ring topology as linear, angular (cata-condensed), or peri-condensed (clustered) structures. The BFHC indices were developed as part of a PhD dissertation ( https://rcin.org.pl/publication/63491 ). DATA DESCRIPTION: The dataset provides structural and experimental information for 302 PAHs, including both unsubstituted and hydrocarbon-substituted molecules (such as alkyl, benzyl, and small ring substituents). Each compound is characterized by XYZ Gaussian input files, IUPAC name, molecular structure, carbon and hydrogen counts, and counts of four topological indices - Bay, Fjord, Harbor, and Canyon -collectively referred to as BFHC indices. The dataset also includes experimental carcinogenicity classified into seven qualitative categories, physicochemical properties such as log P (131 compounds) and log Iball (117 compounds), and fused benzene ring-based topology classification (linear, angular, peri-condensed). The dataset is publicly available and suitable for Quantitative Structure-Activity Relationships (QSAR) and machine learning applications in toxicology and carcinogenic potency of PAHs.

The N-electron wavefunction can be approximated by a rectangular determinant. The resulting wavefunction ansatz is exact for two electrons and provides a parsimonious but approximate parameterization of nonorthogonal configuration interaction wavefunctions for N>2.

We use the elongated hydrogen chain as an illustration to affirmatively answer the question, “Can the FCI energies/properties be predicted with Hartree–Fock (HF) or density function theory (DFT) densities?” as proposed by the late Bob Parr. We employ some simple physics-inspired density-based quantities from the information-theoretic approach (ITA) to linearly correlate with the full configuration interaction (FCI) energies with the approximate DMRG (density matrix renormalization group) method as a solver. We have showcased that the deviations between the calculated and predicted ground-state energies are only about a few milliHartree. Moreover, with the “gold standard” CCSD(T) (coupled cluster with singles and doubles, and perturbative triples) polarizabilities as a reference, we have found a way to systematically reduce the severe overestimation of the molecular polarizabilities as calculated by the approximate DFT functionals. Accordingly, we have applied this strategy to simultaneously predict the energies and molecular properties of strongly correlated systems only with the ground-state electron densities as an input, which should be a good starting point for more complex systems.

We extend the traditional conceptual density functional theory (CDFT) to conceptual density matrix functional theory (CDMFT) by replacing the external potential v( r ) by the one-electron integral h rs in the energy functional. This approach provides a new path for investigating intrinsic bond properties such as bond reactivity. The derivation of the Fukui matrix, i.e., derivative of the density matrix P with respect to the number of electrons N, is elucidated, and the result is illustrated in a case study on H2O. The matrix is shown to play a crucial role in quantifying changes of bond strength for electron removal or addition processes via the bond order derivative ( partial derivative B partial derivative N ) - . Using the Mayer bond order and different atoms-in-molecules partitioning methods, we show that as a first-order response quantity, the bond order derivative agrees well with the finite difference bond order changes. The bond order derivative (bond Fukui function) is a bond reactivity descriptor. We demonstrate this by predicting the regioselectivity of a classical electrophilic addition reaction (the bromination of alkenes) and predicting the initial electron-driven bond cleavage in mass spectrometry. Specifically, the bond order derivative captures all of the major signals from the experimental mass spectra for a series of small molecules with a variety of functional groups.

Employing some simple physics-inspired density-based information-theoretic approach (ITA) quantities to predict the electron correlation energies remains an open challenge. In this work, we expand the scope of the LR(ITA) (LR means linear regression) protocol to more complex systems, including (i) 24 octane isomers; (ii) polymeric structures, polyyne, polyene, all-trans-polymethineimine, and acene; (iii) molecular clusters, such as metallic Ben and Mgn, covalent Sn, hydrogen-bonded protonated water clusters H+(H2O)n, and dispersion-bound carbon dioxide (CO2)n, and benzene (C6H6)n clusters. With LR(ITA), one can simply predict the post-Hartree-Fock (such as MP2 and coupled cluster) electron correlation energies at the cost of Hartree-Fock calculations, even with chemical accuracy. For large molecular clusters, we employ the linear-scaling generalized energy-based fragmentation (GEBF) method to gauge the accuracy of LR(ITA). Employing benzene clusters as an illustration, the LR(ITA) method shows similar accuracy to that of GEBF. Overall, we have verified that ITA quantities can be used to predict the post-Hartree-Fock electron correlation energies of various complex systems.