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.

Extended similarity methods for efficient data mining in imaging mass spectrometry

Imaging mass spectrometry is a label-free imaging modality that allows for the spatial mapping of many compounds directly in tissues. In an imaging mass spectrometry experiment, a raster of the tissue surface produces a mass spectrum at each sampled x, y position, resulting in thousands of individual mass spectra, each comprising a pixel in the resulting ion images. However, efficient analysis of imaging mass spectrometry datasets can be challenging due to the hyperspectral characteristics of the data. Each spectrum contains several thousand unique compounds at discrete m/z values that result in unique ion images, which demands robust and efficient algorithms for searching, statistical analysis, and visualization. Some traditional post-processing techniques are fundamentally ill-equipped to dissect these types of data. For example, while principal component analysis (PCA) has long served as a useful tool for mining imaging mass spectrometry datasets to identify correlated analytes and biological regions of interest, the interpretation of the PCA scores and loadings can be non-trivial. The loadings often contain negative peaks in the PCA-derived pseudo-spectra, which are difficult to ascribe to underlying tissue biology. Herein, we have utilized extended similarity indices to streamline the interpretation of imaging mass spectrometry data. This novel workflow uses PCA as a pixel-selection method to parse out the most and least correlated pixels, which are then compared using the extended similarity indices. The extended similarity indices complement PCA by removing all non-physical artifacts and streamlining the interpretation of large volumes of imaging mass spectrometry spectra simultaneously. The linear complexity, O(N), of these indices suggests that large imaging mass spectrometry datasets can be analyzed in a 1 : 1 scale of time and space with respect to the size of the input data. The extended similarity indices algorithmic workflow is exemplified here by identifying discrete biological regions of mouse brain tissue.

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.

k-Means NANI: an improved clustering algorithm for Molecular Dynamics simulations

One of the key challenges of k-means clustering is the seed selection or the initial centroid estimation since the clustering result depends heavily on this choice. Alternatives such as k-means++ have mitigated this limitation by estimating the centroids using an empirical probability distribution. However, with high-dimensional and complex datasets such as those obtained from molecular simulation, k-means++ fails to partition the data in an optimal manner. Furthermore, stochastic elements in all flavors of k-means++ will lead to a lack of reproducibility. K-means N-Ary Natural Initiation (NANI) is presented as an alternative to tackle this challenge by using efficient n-ary comparisons to both identify high-density regions in the data and select a diverse set of initial conformations. Centroids generated from NANI are not only representative of the data and different from one another, helping k-means to partition the data accurately, but also deterministic, providing consistent cluster populations across replicates. From peptide and protein folding molecular simulations, NANI was able to create compact and well-separated clusters as well as accurately find the metastable states that agree with the literature. NANI can cluster diverse datasets and be used as a standalone tool or as part of our MDANCE clustering package.

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.

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.

Extended Similarity Methods for Efficient Data Mining in Imaging Mass Spectrometry

Imaging mass spectrometry is a label-free imaging modality that allows for the spatial mapping of many compounds directly in tissues. In an imaging mass spectrometry experiment, a raster of the tissue surface produces a mass spectrum at each sampled x , y position, resulting in thousands of individual mass spectra, each comprising a pixel in the resulting ion images. However, efficient analysis of imaging mass spectrometry datasets can be challenging due to the hyperspectral characteristics of the data. Each spectrum contains several thousand unique compounds at discrete m/z values that result in unique ion images, which demands robust and efficient algorithms for searching, statistical analysis, and visualization. Some traditional post-processing techniques are fundamentally ill-equipped to dissect these types of data. For example, while principal component analysis (PCA) has long served as a useful tool for mining imaging mass spectrometry datasets to identify correlated analytes and biological regions of interest, the interpretation of the PCA scores and loadings can be non-trivial. The loadings often containing negative peaks in the PCA-derived pseudo-spectra, which are difficult to ascribe to underlying tissue biology. Herein, we have utilized extended similarity indices to streamline the interpretation of imaging mass spectrometry data. This novel workflow uses PCA as a pixel-selection method to parse out the most and least correlated pixels, which are then compared using the extended similarity indices. The extended similarity indices complement PCA by removing all non-physical artifacts and streamlining the interpretation of large volumes of IMS spectra simultaneously. The linear complexity, O ( N ) , of these indices suggests that large imaging mass spectrometry datasets can be analyzed in a 1:1 scale of time and space with respect to the size of the input data. The extended similarity indices algorithmic workflow is exemplified here by identifying discrete biological regions of mouse brain tissue.

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.

Quantitative Solvation Energies from Gas-Phase Calculations: First-Principles Charge Transfer and Perturbation Approaches

We present a first-principles approach for the calculation of solvation energies and enthalpies with respect to different ion pair combinations in various solvents. The method relies on the conceptual density functional theory (DFT) of solvation, from which detailed expressions for the solvation energies can be derived. In addition to fast and straightforward gas phase calculations, we also study the influence of modified chemical reactivity descriptors in terms of electronic perturbations. The corresponding phenomenological changes in molecular energy levels can be interpreted as the influence of continuum solvents. Our approach shows that the introduction of these modified expressions is essential for a quantitative agreement between the calculated and the experimental results.

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.

Chemoinformatics and artificial intelligence colloquium: progress and challenges in developing bioactive compounds

We report the main conclusions of the first Chemoinformatics and Artificial Intelligence Colloquium, Mexico City, June 15-17, 2022. Fifteen lectures were presented during a virtual public event with speakers from industry, academia, and non-for-profit organizations. Twelve hundred and ninety students and academics from more than 60 countries. During the meeting, applications, challenges, and opportunities in drug discovery, de novo drug design, ADME-Tox (absorption, distribution, metabolism, excretion and toxicity) property predictions, organic chemistry, peptides, and antibiotic resistance were discussed. The program along with the recordings of all sessions are freely available at https://www.difacquim.com/english/events/2022-colloquium/ .

Application of Fundamental Chemical Principles for Solvation Effects: A Unified Perspective for Interaction Patterns in Solution

We demonstrate the utility of basic chemical principles like the "|Δμ| big is good" (DMB) rule for the study of solvation interactions between distinct solutes such as ions and solvents. The corresponding approach allows us to define relevant criteria for maximum solvation energies of ion pairs in different solvents in terms of electronegativities and chemical hardnesses. Our findings reveal that the DMB principle culminates into the strong and weak acids and bases concept as recently derived for specific ion effects in various solvents. The further application of the DMB approach highlights a similar condition for the chemical hardnesses with a reminiscence to the hard/soft acids and bases principle. Comparable conclusions can also be drawn with regard to the change of the solvent. We show that favorable solvent interactions are mainly driven by low chemical hardnesses as well as high electronegativity differences between the ions and the solvent. Our findings highlight that solvation interactions are governed by basic chemical principles, which demonstrates the close similarity between solvation mechanisms and chemical reactions.

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.

Molecular interactions from the density functional theory for chemical reactivity: Interaction chemical potential, hardness, and reactivity principles

In the first paper of this series, the authors derived an expression for the interaction energy between two reagents in terms of the chemical reactivity indicators that can be derived from density functional perturbation theory. While negative interaction energies can explain reactivity, reactivity is often more simply explained using the “|dμ| big is good” rule or the maximum hardness principle. Expressions for the change in chemical potential (μ) and hardness when two reagents interact are derived. A partial justification for the maximum hardness principle is that the terms that appear in the interaction energy expression often reappear in the expression for the interaction hardness, but with opposite sign.

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.

Molecular Interactions From the Density Functional Theory for Chemical Reactivity: The Interaction Energy Between Two-Reagents

Reactivity descriptors indicate where a reagent is most reactive and how it is most likely to react. However, a reaction will only occur when the reagent encounters a suitable reaction partner. Determining whether a pair of reagents is well-matched requires developing reactivity rules that depend on both reagents. This can be achieved using the expression for the minimum-interaction-energy obtained from the density functional reactivity theory. Different terms in this expression will be dominant in different circumstances; depending on which terms control the reactivity, different reactivity indicators will be preferred.

Specific Ion Effects in Different Media: Current Status and Future Challenges

We discuss the current state of research as well as the future challenges for a deeper understanding of specific ion effects in protic and aprotic solvents as well as various additional media. Despite recent interest in solute or interfacial effects, we focus exclusively on the specific properties of ions in bulk electrolyte solutions. Corresponding results show that many mechanisms remain unknown for these simple media, although theoretical, computational, and experimental studies have provided some insights into explaining individual observations. In particular, the importance of local interactions and electronic properties is emphasized, which enabled a more consistent interpretation of specific ion effects over the past years. Despite current insufficient knowledge, we also discuss future challenges in relation to dynamic properties as well as the influence of different concentrations, different solvents, and solute contributions to gain a deeper understanding of specific ion effects for technological applications.

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.

Chemoinformatic Characterization of Synthetic Screening Libraries Focused on Epigenetic Targets

The importance of epigenetic drug and probe discovery is on the rise. This is not only paramount to identify and develop therapeutic treatments associated with epigenetic processes but also to understand the underlying epigenetic mechanisms involved in biological processes. To this end, chemical vendors have been developing synthetic compound libraries focused on epigenetic targets to increase the probabilities of identifying promising starting points for drug or probe candidates. However, the chemical contents of these data sets, the distribution of their physicochemical properties, and diversity remain unknown. To fill this gap and make this information available to the scientific community, we report a comprehensive analysis of eleven libraries focused on epigenetic targets containing more than 50,000 compounds. We used well-validated chemoinformatics approaches to characterize these sets, including novel methods such as automated detection of analog series and visual representations of the chemical space based on Constellation Plots and Chemical Library Networks. This work will guide the efforts of experimental groups working on high-throughput and medium-throughput screening of epigenetic-focused libraries. The outcome of this work can also be used as a reference to design and describe novel focused epigenetic libraries.

Electronic Properties of Protein Destabilizers and Stabilizers: Implications for Preferential Binding and Exclusion Mechanisms

We study the electronic properties of low-weight organic co-solutes by means of conceptual density functional theory calculations. Our results highlight the important role of certain chemical reactivity descriptors such as chemical hardness, electronegativity, nucleofugality, and the electrofugality as important criteria to classify protein stabilizers and destabilizers. Our results imply Lewis basic properties with lower chemical hardness for stabilizers, while destabilizers show higher Lewis acidity with higher chemical hardness. Further consideration of analytical calculations in terms of transfer energies reveals the crucial role of co-solute-protein interactions which significantly change the interaction pattern of the stabilizing or destabilizing species. The corresponding outcomes connect statistical thermodynamics with the electronic properties of co-solutes and also allow us to define general principles for strong stabilizers and destabilizers.

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.

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.

Extended many-item similarity indices for sets of nucleotide and protein sequences

Quantification of similarities between protein sequences or DNA/RNA strands is a (sub-)task that is ubiquitously present in bioinformatics workflows, and is usually accomplished by pairwise comparisons of sequences, utilizing simple (e.g. percent identity) or more intricate concepts (e.g. substitution scoring matrices). Complex tasks (such as clustering) rely on a large number of pairwise comparisons under the hood, instead of a direct quantification of set similarities. Based on our recently introduced framework that enables multiple comparisons of binary molecular fingerprints (i.e., direct calculation of the similarity of fingerprint sets), here we introduce novel symmetric similarity indices for analogous calculations on sets of character sequences with more than two (t) possible items (e.g. DNA/RNA sequences with t = 4, or protein sequences with t = 20). The features of these new indices are studied in detail with analysis of variance (ANOVA), and demonstrated with three case studies of protein/DNA sequences with varying degrees of similarity (or evolutionary proximity). The Python code for the extended many-item similarity indices is publicly available at: https://github.com/ramirandaq/tn_Comparisons.

Extended similarity indices: the benefits of comparing more than two objects simultaneously. Part 2: speed, consistency, diversity selection

Despite being a central concept in cheminformatics, molecular similarity has so far been limited to the simultaneous comparison of only two molecules at a time and using one index, generally the Tanimoto coefficent. In a recent contribution we have not only introduced a complete mathematical framework for extended similarity calculations, (i.e. comparisons of more than two molecules at a time) but defined a series of novel idices. Part 1 is a detailed analysis of the effects of various parameters on the similarity values calculated by the extended formulas. Their features were revealed by sum of ranking differences and ANOVA. Here, in addition to characterizing several important aspects of the newly introduced similarity metrics, we will highlight their applicability and utility in real-life scenarios using datasets with popular molecular fingerprints. Remarkably, for large datasets, the use of extended similarity measures provides an unprecedented speed-up over “traditional” pairwise similarity matrix calculations. We also provide illustrative examples of a more direct algorithm based on the extended Tanimoto similarity to select diverse compound sets, resulting in much higher levels of diversity than traditional approaches. We discuss the inner and outer consistency of our indices, which are key in practical applications, showing whether the n-ary and binary indices rank the data in the same way. We demonstrate the use of the new n-ary similarity metrics on t-distributed stochastic neighbor embedding (t-SNE) plots of datasets of varying diversity, or corresponding to ligands of different pharmaceutical targets, which show that our indices provide a better measure of set compactness than standard binary measures. We also present a conceptual example of the applicability of our indices in agglomerative hierarchical algorithms. The Python code for calculating the extended similarity metrics is freely available at: https://github.com/ramirandaq/MultipleComparisons

Extended similarity indices: the benefits of comparing more than two objects simultaneously. Part 1: Theory and characteristics†

Quantification of the similarity of objects is a key concept in many areas of computational science. This includes cheminformatics, where molecular similarity is usually quantified based on binary fingerprints. While there is a wide selection of available molecular representations and similarity metrics, there were no previous efforts to extend the computational framework of similarity calculations to the simultaneous comparison of more than two objects (molecules) at the same time. The present study bridges this gap, by introducing a straightforward computational framework for comparing multiple objects at the same time and providing extended formulas for as many similarity metrics as possible. In the binary case (i.e. when comparing two molecules pairwise) these are naturally reduced to their well-known formulas. We provide a detailed analysis on the effects of various parameters on the similarity values calculated by the extended formulas. The extended similarity indices are entirely general and do not depend on the fingerprints used. Two types of variance analysis (ANOVA) help to understand the main features of the indices: (i) ANOVA of mean similarity indices; (ii) ANOVA of sum of ranking differences (SRD). Practical aspects and applications of the extended similarity indices are detailed in the accompanying paper: Miranda-Quintana et al. J Cheminform. 2021. https://doi.org/10.1186/s13321-021-00504-4 . Python code for calculating the extended similarity metrics is freely available at: https://github.com/ramirandaq/MultipleComparisons .

Differential Consistency Analysis: Which Similarity Measures can be Applied in Drug Discovery?

Similarity measures are widely used in various areas from taxonomy to cheminformatics. To this end, a large number of similarity and distance measures (or, collectively, comparative measures) have been introduced, with only a few studies directed to revealing their inner relationships. We present a thorough analytical study of the conditions leading to two comparative measures providing equivalent results over a given set of molecules. A key part of this work is the introduction of a novel way to study the consistency between comparative measures: the differential consistency analysis (DCA). This tool reveals how the consistency can be established in an analytical way with minimal (or no) assumptions. We found that the consensus between Tanimoto and the Cosine coefficients improved by choosing a reference whose similarity to the rest of the molecules varies less, or by representing the molecules in a way that does not depend strongly on their size (i. e. bit frequency in the chosen fingerprint representation). The presented derivations are just some generic examples; DCA can be applied widely and for all binary similarity coefficients introduced so far, independently from the molecular representations.

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.

Evaluation of the molecular inclusion process of β-hexachlorocyclohexane in cyclodextrins

The present work aimed to study the guest–host complexes of β-hexachlorocyclohexane (β-HCH), a pesticide with high environmental stability that can cause severe health problems, with the most common cyclodextrins (α-, β-, and γ-CDs). The formation reactions of these molecular inclusion complexes were addressed in this research. The multiple minima hypersurface methodology, quantum calculations based on density functional theory and a topological exploration of the electron density based on the quantum theory of atoms in molecules approach were used to characterize the interaction spaces of the pollutant with the three CDs. Additionally, charge distribution, charge transfer and dual descriptor analyses were employed to elucidate the driving forces involved in the formation of these molecular inclusion complexes. Three types of fundamental interactions were observed: total occlusion, partial occlusion and external interaction (non-occlusion). Finally, experiments were performed to confirm the formation of the studied complexes. The most stable complexes were obtained when γ-CD was the host molecule. The interactions between the pesticide and CDs have fundamentally dispersive natures, as was confirmed experimentally by spectroscopic results. All the obtained results suggest the possibility of using CDs for the purification and treatment of water polluted with β-HCH.

The present work aimed to study the guest–host complexes of β-hexachlorocyclohexane (β-HCH), a pesticide with high environmental stability that can cause severe health problems, with the most common cyclodextrins (α-, β-, and γ-CDs).

How Biochemical Environments Fine-Tune a Redox Process: From Theoretical Models to Practical Applications

In this study, we give a new physical insight into how enzymatic environments influence a redox process. This is particularly important in a biochemical context, in which oxidoreductase enzymes and low-molecular-weight cofactors create a microenvironment, fine-tuning their specific redox potential. We present a new theoretical model, quantitatively backed up by quantum chemically calculated data obtained for key biological sulfur-based model reactions involved in preserving the cellular redox homeostasis during oxidative stress. We show that environmental effects can be quantitatively predicted from the thermodynamic cycle linking ΔΔ G(OX/RED)_ref-ligand values to the differential interaction energy ΔΔ G_int of the reduced and oxidized species with the environment. Our obtained data can be linked to hydrogen-bond patterns found in protein active sites. The thermodynamic model is further understood in the framework of molecular orbital theory. The key insight of this work is that the intrinsic properties of neither a redox couple nor the interacting environment (e.g., ligand) are enough by themselves to uniquely predict reduction potentials. Instead, system-environment interactions need to be considered. This study is of general interest as redox processes are pivotal to empower, protect, or damage organisms. Our presented thermodynamic model allows a pragmatically evaluation on the expected influence of a particular environment on a redox process, necessary to fully understand how redox processes take place in living organisms.

Elementary Derivation of the "|Δμ| Big Is Good" Rule

Thirty years ago, Parr and Yang postulated that favorable chemical processes are associated with large changes in the electronic chemical potential or, equivalently, the electronegativity. They called this the "|Δμ| big is good" rule and noted that if the rule could be justified, then it "would constitute a validation of frontier theory from first principles." We provide a simple and insightful justification for the "|Δμ| big is good" rule, with special emphasis on electron-transfer reactions. Furthermore, we show that it implies Pearson's hard/soft acid/base principle mathematically and confirm this result with numerical examples. This supports Parr's intuition that many other reactivity precepts arise as corollaries to the more fundamental "|Δμ| big is good" rule. In all of this, it is essential to consider the intensive nature of the chemical potential.

Electronegativity and redox reactions

Using the maximum hardness principle, we show that the oxidation potential of a molecule increases as its electronegativity increases and also increases as its electronegativity in its oxidized state increases.

Fractional electron number, temperature, and perturbations in chemical reactions

The mathematical framework of conceptual density functional theory is extended to use the eigenstates and eigenvalues of perturbed subsystems. This unites, justifies, and extends, several previously proposed models.