Insights into Hildebrand Solubility Parameters - Contributions from Cohesive Energies or Electrophilicity Densities?

We introduce certain concepts and expressions from conceptual density functional theory (DFT) to study the properties of the Hildebrand solubility parameter. The original form of the Hildebrand solubility parameter is used to qualitatively estimate solubilities for various apolar and aprotic substances and solvents and is based on the square root of the cohesive energy density. Our results show that a revised expression allows the replacement of cohesive energy densities by electrophilicity densities, which are numerically accessible by simple DFT calculations. As an extension, the reformulated expression provides a deeper interpretation of the main contributions and, in particular, emphasizes the importance of charge transfer mechanisms. All calculated values of the Hildebrand parameters for a large number of common solvents are compared with experimental values and show good agreement for non- or moderately polar aprotic solvents in agreement with the original formulation of the Hildebrand solubility parameters. The observed deviations for more polar and protic solvents define robust limits from the original formulation which remain valid. Likewise, we show that the use of machine learning methods leads to only slightly better predictability.

Flexible Ansatz for N-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 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.

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. 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.

Fanpy: A python library for prototyping multideterminant methods in ab initio quantum chemistry.

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.

Can we predict ambident regioselectivity using the chemical hardness?

The hard/soft acid/base (HSAB) principle is a cornerstone in our understanding of chemical reactivity preferences. Motivated by the success of the original ("global") version of this rule, a "local" counterpart was readily proposed to account for regioselectivity preferences, in particular, in ambident reactions. However, ample experimental evidence indicates that the local HSAB principle often fails to provide meaningful predictions. Here we examine the assumptions behind the standard proof of the local HSAB rule, showing that it is based on a flawed premise. By solving this issue, we show that it is critical to consider not only the charge transferred between the different reacting centers but also the charge reorganization within the non-reacting parts of the molecule. We propose different reorganization models and derive the corresponding regioselectivity rules for each.

Sampling and Mapping Chemical Space with Extended Similarity Indices.

Visualization of the chemical space is useful in many aspects of chemistry, including compound library design, diversity analysis, and exploring structure-property relationships, to name a few. Examples of notable research areas where the visualization of chemical space has strong applications are drug discovery and natural product research. However, the sheer volume of even comparatively small sub-sections of chemical space implies that we need to use approximations at the time of navigating through chemical space. ChemMaps is a visualization methodology that approximates the distribution of compounds in large datasets based on the selection of satellite compounds that yield a similar mapping of the whole dataset when principal component analysis on a similarity matrix is performed. Here, we show how the recently proposed extended similarity indices can help find regions that are relevant to sample satellites and reduce the amount of high-dimensional data needed to describe a library's chemical space.

Molecular Dynamics Simulations and Diversity Selection by Extended Continuous Similarity Indices.

Molecular dynamics (MD) is a core methodology of molecular modeling and computational design for the study of the dynamics and temporal evolution of molecular systems. MD simulations have particularly benefited from the rapid increase of computational power that has characterized the past decades of computational chemical research, being the first method to be successfully migrated to the GPU infrastructure. While new-generation MD software is capable of delivering simulations on an ever-increasing scale, relatively less effort is invested in developing postprocessing methods that can keep up with the quickly expanding volumes of data that are being generated. Here, we introduce a new idea for sampling frames from large MD trajectories, based on the recently introduced framework of extended similarity indices. Our approach presents a new, linearly scaling alternative to the traditional approach of applying a clustering algorithm that usually scales as a quadratic function of the number of frames. When showcasing its usage on case studies with different system sizes and simulation lengths, we have registered speedups of up to 2 orders of magnitude, as compared to traditional clustering algorithms. The conformational diversity of the selected frames is also noticeably higher, which is a further advantage for certain applications, such as the selection of structural ensembles for ligand docking. The method is available open-source at https://github.com/ramirandaq/MultipleComparisons.

Diversity and Chemical Library Networks of Large Data Sets.

The quantification of chemical diversity has many applications in drug discovery, organic chemistry, food, and natural product chemistry, to name a few. As the size of the chemical space is expanding rapidly, it is imperative to develop efficient methods to quantify the diversity of large and ultralarge chemical libraries and visualize their mutual relationships in chemical space. Herein, we show an application of our recently introduced extended similarity indices to measure the fingerprint-based diversity of 19 chemical libraries typically used in drug discovery and natural products research with over 18 million compounds. Based on this concept, we introduce the Chemical Library Networks (CLNs) as a general and efficient framework to represent visually the chemical space of large chemical libraries providing a global perspective of the relation between the libraries. For the 19 compound libraries explored in this work, it was found that the (extended) Tanimoto index offers the best description of extended similarity in combination with RDKit fingerprints. CLNs are general and can be explored with any structure representation and similarity coefficient for large chemical libraries.

Extended continuous similarity indices: theory and application for QSAR descriptor selection.

Extended (or n-ary) similarity indices have been recently proposed to extend the comparative analysis of binary strings. Going beyond the traditional notion of pairwise comparisons, these novel indices allow comparing any number of objects at the same time. This results in a remarkable efficiency gain with respect to other approaches, since now we can compare N molecules in O(N) instead of the common quadratic O(N2) timescale. This favorable scaling has motivated the application of these indices to diversity selection, clustering, phylogenetic analysis, chemical space visualization, and post-processing of molecular dynamics simulations. However, the current formulation of the n-ary indices is limited to vectors with binary or categorical inputs. Here, we present the further generalization of this formalism so it can be applied to numerical data, i.e. to vectors with continuous components. We discuss several ways to achieve this extension and present their analytical properties. As a practical example, we apply this formalism to the problem of feature selection in QSAR and prove that the extended continuous similarity indices provide a convenient way to discern between several sets of descriptors.

Electronic properties of amino acids and nucleobases: similarity classes and pairing principles from chemical reactivity indices.

We present a new classification scheme for amino acids and nucleobases based on the electronic properties of the individual molecules. Using chemical reactivity indices such as electronegativity, electrophilicity, and chemical hardness, we can identify similarities and differences between each class of amino acids and nucleobases. Notable differences emerge in particular with regard to high, neutral or low electronegativity as well as different combinations of chemical hardness. Our approach allows us to relate these insights to the properties of the side groups in terms of a unique reference scheme. We further show that hydrophobic differences between amino acids are rather negligible in the context of electronic properties. Our classification scheme also rationalizes the occurrence of distinct stable nucleobase pairs and clearly emphasizes certain differences between individual molecules. The stability and abundant occurrence of Watson-Crick nucleobase pairs is further discussed in the context of the minimum electrophilicity principle.

Combination of explainable machine learning and conceptual density functional theory: applications for the study of key solvation mechanisms.

We present explainable machine learning approaches for the accurate prediction and understanding of solvation free energies, enthalpies, and entropies for different salts in various protic and aprotic solvents. As key input features, we use fundamental contributions from the conceptual density functional theory (DFT) of solutions. The most accurate models with the highest prediction accuracy for the experimental validation data set are decision tree-based approaches such as extreme gradient boosting and extra trees, which highlight the non-linear influence of feature values on target predictions. The detailed assessment of the importance of features in terms of Gini importance criteria as well as Shapley Additive Explanations (SHAP) and permutation and reduction approaches underlines the prominent role of anion and cation solvation effects in combination with fundamental electronic properties of the solvents. These results are reasonably consistent with previous assumptions and provide a solid rationale for more recent theoretical approaches.

Charge transfer at finite temperature: The "|Δµ| big is good" principle.

We show that the "|Δµ| big is good" principle holds at temperatures above absolute zero (the so-called "finite-T regime"). We also provide the first conditions hinting at the validity of this reactivity rule in cases where the chemical reactions involved have different signs in their chemical potential variations.

Improving the analysis of biological ensembles through extended similarity measures.

We present new algorithms to classify structural ensembles of macromolecules based on the recently proposed extended similarity measures. Molecular dynamics provides a wealth of structural information on systems of biological interest. As computer power increases, we capture larger ensembles and larger conformational transitions between states. Typically, structural clustering provides the statistical mechanics treatment of the system to identify relevant biological states. The key advantage of our approach is that the newly introduced extended similarity indices reduce the computational complexity of assessing the similarity of a set of structures from O(N2) to O(N). Here we take advantage of this favorable cost to develop several highly efficient techniques, including a linear-scaling algorithm to determine the medoid of a set (which we effectively use to select the most representative structure of a cluster). Moreover, we use our extended similarity indices as a linkage criterion in a novel hierarchical agglomerative clustering algorithm. We apply these new metrics to analyze the ensembles of several systems of biological interest such as folding and binding of macromolecules (peptide, protein, DNA-protein). In particular, we design a new workflow that is capable of identifying the most important conformations contributing to the protein folding process. We show excellent performance in the resulting clusters (surpassing traditional linkage criteria), along with faster performance and an efficient cost-function to identify when to merge clusters.

Machine learning models for classification tasks related to drug safety.

In this review, we outline the current trends in the field of machine learning-driven classification studies related to ADME (absorption, distribution, metabolism and excretion) and toxicity endpoints from the past six years (2015-2021). The study focuses only on classification models with large datasets (i.e. more than a thousand compounds). A comprehensive literature search and meta-analysis was carried out for nine different targets: hERG-mediated cardiotoxicity, blood-brain barrier penetration, permeability glycoprotein (P-gp) substrate/inhibitor, cytochrome P450 enzyme family, acute oral toxicity, mutagenicity, carcinogenicity, respiratory toxicity and irritation/corrosion. The comparison of the best classification models was targeted to reveal the differences between machine learning algorithms and modeling types, endpoint-specific performances, dataset sizes and the different validation protocols. Based on the evaluation of the data, we can say that tree-based algorithms are (still) dominating the field, with consensus modeling being an increasing trend in drug safety predictions. Although one can already find classification models with great performances to hERG-mediated cardiotoxicity and the isoenzymes of the cytochrome P450 enzyme family, these targets are still central to ADMET-related research efforts.

Theoretical Insights into Specific Ion Effects and Strong-Weak Acid-Base Rules for Ions in Solution: Deriving the Law of Matching Solvent Affinities from First Principles.

We present a detailed study of specific ion effects, volcano plots and the law of matching solvent affinities by means of a conceptual density functional theory (DFT) approach. Our results highlight that specific ion effects and the corresponding implications on the solvation energy are mainly due to differences in the electric chemical potentials and chemical hardnesses of the ions and the solvent. Our approach can be further used to identify reliable criteria for the validity of the law of matching solvent affinities. Basic expressions are derived, which allow us to study the limiting conditions for this empirical observation with regard to matching chemical reactivity indices. Moreover, we show that chaotropic and kosmotropic concepts and their implications for the stability of ion pairs are directly related to a generalized strong and weak acids and bases (SWAB) principle for ions in solution, which is also applicable to rationalize the shape of volcano plots for different solvents. In contrast to previous assumptions, all empirical findings can be explained by the properties of local solvent-ion complexes which dominate the specific global behavior of ion pairs in solution.

Artificial neural networks for the prediction of solvation energies based on experimental and computational data.

The knowledge of thermodynamic properties for novel electrolyte formulations is of fundamental interest for industrial applications as well as academic research. Herewith, we present an artificial neural networks (ANN) approach for the prediction of solvation energies and entropies for distinct ion pairs in various protic and aprotic solvents. The considered feed-forward ANN is trained either by experimental data or computational results from conceptual density functional theory calculations. The proposed concept of mapping computed values to experimental data lowers the amount of time-consuming and costly experiments and helps to overcome certain limitations. Our findings reveal high correlation coefficients between predicted and experimental values which demonstrate the validity of our approach.

Note: Maximum hardness and minimum electrophilicity principles.

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.

Chemical hardness: Temperature dependent definitions and reactivity principles.

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.

Thermodynamic electrophilicity.

We revisit the electrophilicity index proposed by Parr et al., with special emphasis on the working equations used to calculate this descriptor. We show that the standard way to obtain this reactivity index (using the conceptual density functional theory formalism) leads to several issues. In this contribution, we propose to overcome these difficulties by making use of the finite temperature grand-canonical formalism. In this way, we not only bypass the characteristic inconsistencies of the zero temperature formulation but we are able to obtain a simple exact working equation for the electrophilicity in terms of electronic structure magnitudes.

Finite temperature grand canonical ensemble study of the minimum electrophilicity principle.

We analyze the minimum electrophilicity principle of conceptual density functional theory using the framework of the finite temperature grand canonical ensemble. We provide support for this principle, both for the cases of systems evolving from a non-equilibrium to an equilibrium state and for the change from one equilibrium state to another. In doing so, we clearly delineate the cases where this principle can, or cannot, be used.