Quantum chemical topology (QCT) descriptors as substitutes for appropriate Hammett constants

Implementation of machine learning protocols to predict the hydrolysis reaction properties of organophosphorus substrates using descriptors of electron density topology

Prediction of catalytic reaction efficiency is one of the most intriguing and challenging applications of machine learning (ML) algorithms in chemistry. In this study, we demonstrated a strategy for utilizing ML protocols applied to Quantum Theory of Atoms In Molecules (QTAIM) parameters to predict the ability of the A17 L47K catalytic antibody to covalently capture organophosphate pesticides. We found that the novel "composite" DFT functional B97-3c could be effectively employed for fast and accurate initial geometry optimization, aligning well with the input dataset creation. QTAIM descriptors proved to be well-established in describing the examined dataset using density-based and hierarchical clustering algorithms. The obtained clusters exhibited correlations with the chemical classes of the input compounds. The precise physical interpretation of the QTAIM properties simplifies the explanation of feature impact for both supervised and unsupervised ML protocols. It also enables acceleration in the search for entries with desired properties within large databases. Furthermore, our findings indicated that Ridge Regression with Laplacian kernel and CatBoost Regressor algorithms demonstrated suitable performance in handling small datasets with non-trivial dependencies. They were able to predict the actual reaction barrier values with a high level of accuracy. Additionally, the CatBoost Classifier proved reliable in discriminating between "active" and "inactive" compounds.

Experimental Quantum Chemistry: A Hammett-inspired Fingerprinting of Substituent Effects

The quantum mechanically calculable Q descriptor is shown to be a potent quantifier of chemical reactivity in complex molecules - it shows a strong correlation to experimentally derived field effects in non-aromatic substrates and Hammett σm and σp parameters. Models for predicting substituent effects from Q are presented and applied, including on the elusive pentazolyl substituent. The presented approach enables fast computational estimation of substituent effects, and, in extension, medium-throughput screening of molecules and compound design. An experimental dataset is suggested as a candidate benchmark for aiding the general development and comparison of electronic structure analyses. It is here used to evaluate the experimental quantum chemistry (EQC) framework for chemical bonding analysis in larger molecules.

Quantum theory of atoms in molecules, electron localization function, and localized-orbital locator investigations on trans-(NHC)PtI2(para-NC5H4X) complexes

In this study, the MPW1PW91 method is applied to analyze the quantum theory of atoms in molecules, the electron localization function, and the localized-orbital locator in trans-(NHC)PtI2( para-NC5H4X) (X = H, F, COOH, CN, NO2, Me, OH, NH2) complexes. The substituent effect is assessed in the presence of electron-withdrawing groups and electron-donating groups and their influence on the Pt–C and Pt–N bonds of the molecules is analyzed using quantum theory of atoms in molecules, electron localization function, and localized-orbital locator methods. In addition, the eta index (η) is used to evaluate the Pt–C and Pt–N bonds in the studied complexes. The correlations between electron localization function, localized-orbital locator, and the η index values of Pt–C and Pt–N bonds with Hammett constants (σp) and dual parameters (σI and σR) are given.

π-Hydrogen Bonding Probes the Reactivity of Aromatic Compounds: Nitration of Substituted Benzenes

The shifts of phenol O-H stretching vibration frequencies [Δν(OH)_exp] upon π-hydrogen bonding with aromatic compounds is proposed as a spectroscopic probe of the reactivity of aromatic substrates toward electrophiles. A single infrared spectrum reflecting the Δν(OH)_exp shift for an aromatic species in a reference solvent (CCl₄ in this study) provides a good estimate of reactivity. The methodology is applied in rationalizing reactivity trends for the BF₃ catalyzed nitration by methylnitrate in nitromethane of 20 aromatic reactants, including benzene, 11 methylbenzenes, several monoalkyl benzenes, the four halobenzenes, and anisole. Literature kinetic data are employed in the analysis. Very good correlations between relative rates of nitration and Δν(OH)_exp are obtained. The approach is best applied to reactions, where the initial interactions between the reactants controls the rates. A new theoretical quantity, the shifts (with respect to benzene) of the molecular electrostatic potential at 1.5 Å over the centroid of the aromatic ring [Δ V(1.5)] is defined and shown to provide a good description of substituent effects on properties of the aromatic species. B3LYP density functional and MP2 ab initio methods combined with the 6-311++G(3df,2pd) basis set are employed in evaluating the Δ V(1.5) values.

Quantitative Structure-Activity/Property/Toxicity Relationships through Conceptual Density Functional Theory-Based Reactivity Descriptors

Developing effective structure-activity/property/toxicity relationships (QSAR/QSPR/QSTR) is very helpful in predicting biological activity, property, and toxicity of a given set of molecules. Regular change in these properties with the structural alteration is the main reason to obtain QSAR/QSPR/QSTR models. The advancement in making different QSAR/QSPR/QSTR models to describe activity, property, and toxicity of various groups of molecules is reviewed in this chapter. The successful implementation of Conceptual Density Functional Theory (CDFT)-based global as well as local reactivity descriptors in modeling effective QSAR/QSPR/QSTR is highlighted.

Revealing the role of catechol moieties in the interactions between peptides and inorganic surfaces

Catechol (1,2-dihydroxy benzene) moieties are being widely used today in new adhesive technologies. Understanding their mechanism of action is therefore of high importance for developing their applications in materials science. This paper describes a single-molecule study of the interactions between catechol-related amino acid residues and a well-defined titanium dioxide (TiO2) surface. It is the first quantified measurement of the adhesion of these residues with a well-defined TiO2 surface. Single-molecule force spectroscopy measurements with AFM determined the role of different substitutions of the catechol moiety on the aromatic ring in the adhesion to the surface. These results shed light on the nature of interactions between these residues and inorganic metal oxide surfaces. This information is important for the design and fabrication of catechol-based materials such as hydrogels, coatings, and composites. Specifically, the interaction with TiO2 is important for the development of solar cells.

Fuzzy electron density fragments in macromolecular quantum chemistry, combinatorial quantum chemistry, functional group analysis, and shape-activity relations

Conspectus Just as complete molecules have no boundaries and have "fuzzy" electron density clouds approaching zero density exponentially at large distances from the nearest nucleus, a physically justified choice for electron density fragments exhibits similar behavior. Whereas fuzzy electron densities, just as any fuzzy object, such as a thicker cloud on a foggy day, do not lend themselves to easy visualization, one may partially overcome this by using isocontours. Whereas a faithful representation of the complete fuzzy density would need infinitely many such isocontours, nevertheless, by choosing a selected few, one can still obtain a limited pictorial representation. Clearly, such images are of limited value, and one better relies on more complete mathematical representations, using, for example, density matrices of fuzzy fragment densities. A fuzzy density fragmentation can be obtained in an exactly additive way, using the output from any of the common quantum chemical computational techniques, such as Hartree-Fock, MP2, and various density functional approaches. Such "fuzzy" electron density fragments properly represented have proven to be useful in a rather wide range of applications, for example, (a) using them as additive building blocks leading to efficient linear scaling macromolecular quantum chemistry computational techniques, (b) the study of quantum chemical functional groups, (c) using approximate fuzzy fragment information as allowed by the holographic electron density theorem, (d) the study of correlations between local shape and activity, including through-bond and through-space components of interactions between parts of molecules and relations between local molecular shape and substituent effects, (e) using them as tools of density matrix extrapolation in conformational changes, (f) physically valid averaging and statistical distribution of several local electron densities of common stoichiometry, useful in electron density databank mining, for example, in medicinal drug design, and (g) tools for combinatorial quantum chemistry approaches using fuzzy fragment databanks and rapid construction of a large number of approximate electron densities for large sets of related molecules, relevant in theoretical molecular and nanostructure design.

Modeling biophysical and biological properties from the characteristics of the molecular electron density, electron localization and delocalization matrices, and the electrostatic potential

The electron density and the electrostatic potential are fundamentally related to the molecular hamiltonian, and hence are the ultimate source of all properties in the ground- and excited-states. The advantages of using molecular descriptors derived from these fundamental scalar fields, both accessible from theory and from experiment, in the formulation of quantitative structure-to-activity and structure-to-property relationships, collectively abbreviated as QSAR, are discussed. A few such descriptors encode for a wide variety of properties including, for example, electronic transition energies, pK(a)'s, rates of ester hydrolysis, NMR chemical shifts, DNA dimers binding energies, π-stacking energies, toxicological indices, cytotoxicities, hepatotoxicities, carcinogenicities, partial molar volumes, partition coefficients (log P), hydrogen bond donor capacities, enzyme-substrate complementarities, bioisosterism, and regularities in the genetic code. Electronic fingerprinting from the topological analysis of the electron density is shown to be comparable and possibly superior to Hammett constants and can be used in conjunction with traditional bulk and liposolubility descriptors to accurately predict biological activities. A new class of descriptors obtained from the quantum theory of atoms in molecules' (QTAIM) localization and delocalization indices and bond properties, cast in matrix format, is shown to quantify transferability and molecular similarity meaningfully. Properties such as "interacting quantum atoms (IQA)" energies which are expressible into an interaction matrix of two body terms (and diagonal one body "self" terms, as IQA energies) can be used in the same manner. The proposed QSAR-type studies based on similarity distances derived from such matrix representatives of molecular structure necessitate extensive investigation before their utility is unequivocally established.

Electron density shape analysis of a family of through-space and through-bond interactions

A family of styrene derivatives has been used to study the effects of through-space and through-bond interactions on the local and global shapes of electron densities of complete molecules and a set of substituents on their central rings. Shape analysis methods which have been used extensively in the past for the study of molecular property-molecular shape correlations have shown that in these molecules a complementary role is played by the through-space and through-bond interactions. For each specific example, the dominance of either one of the two interactions can be identified and interpreted in terms of local shapes and the typical reactivities of the various substituents. Three levels of quantum chemical computational methods have been applied for these structures, including the B3LYP/cc-pVTZ level of density functional methodology, and the essential conclusions are the same for all three levels. The general approach is suggested as a tool for the identification of specific interaction types which are able to modify molecular electron densities. By separately influencing the through-space and through-bond components using polar groups and groups capable of conjugation, some fine-tuning of the overall effects becomes possible. The method described may contribute to an improved understanding and control of molecular properties involving complex interactions with a possible role in the emerging field of molecular design.

The sEDA(=) and pEDA(=) descriptors of the double bonded substituent effect

New descriptors of the double bonded substituent effect, sEDA(=) and pEDA(=), were constructed based on quantum chemical calculations and NBO methodology. They show to what extent the σ and π electrons are donated to or withdrawn from the substituted system by a double bonded substituent. The new descriptors differ from descriptors of the classical substituent effect for which the pz orbital of the ipso carbon atom is engaged in the π-electron system of the two neighboring atoms in the ring. For double bonded substituents, the pz orbital participates in double bond formation with only one external atom. Moreover, the external double bond forces localization of the double bond system of the ring, significantly changing the core molecule. We demonstrated good agreement between our descriptors and the Weinhold and Landis' "natural σ and π-electronegativities": so far only descriptors allowing for evaluation of the substitution effect by a double bonded atom. The equivalency between descriptors constructed for 5- and 6-membered model structures as well as linear dependence/independence of the constructed parameters was discussed. Some interrelations between sEDA(=) and pEDA(=) and the other descriptors of (hetero)cyclic systems such as aromaticity and electron density in the ring and bond critical points were also examined.

Prediction of interaction energies of substituted hydrogen-bonded Watson-Crick cytosine:guanine(8X) base pairs

We investigated the variation in the interaction energy between the Watson-Crick hydrogen-bonded DNA base pairs guanine and cytosine (G(8X):C), where guanine is substituted in the C8 position by 37 different functional groups. Base pairs were optimized at the B3LYP/6-311+G(2d,p) level. A base pair complex containing a more strongly electron-withdrawing group remarkably forms a more stable base pair with C. Multivariate linear regression provided a quantitative relationship between the interaction energies and descriptors generated by the quantum chemical topology (QCT) approach. The descriptors were sampled from the monomers only, not the supermolecular base pair complexes. A model with r2 = 0.96 and a root-mean-square (rms) value of 0.6 kJ/mol was obtained for a training set of 28 base pair complexes. The model was tested by an external test set of 9 complexes, yielding r2 = 0.99 and an rms value of 0.2 kJ/mol. The results indicated that the bonds C6=O6 and N2-H2 at the hydrogen-bonded frontier of the guanine derivatives play an important role in transmitting the substituent effects. A linear correlation between substitution energies and Hammett constants (sigma(m)) was also obtained for all 37 substituents, yielding r2 = 0.82 and an rms value of 1.2 kJ/mol. The model based on QCT descriptors can therefore be used for the prediction of the interaction energy of the base pair G(8x):C, strictly based on data for the G(8x) monomers only.

Predicting the photoinduced electron transfer thermodynamics in polyfluorinated 1,3,5-triarylpyrazolines based on multiple linear free energy relationships

The photophysical properties of 1,3,5-triarylpyrazolines are strongly influenced by the nature and position of substituents attached to the aryl-rings, rendering this fluorophore platform well suited for the design of fluorescent probes utilizing a photoinduced electron transfer (PET) switching mechanism. To explore the tunability of two key parameters that govern the PET thermodynamics, the excited state energy DeltaE(00) and the acceptor potential E(A/A(-)), a library of polyfluoro-substituted 1,3-diaryl-5-phenyl-pyrazolines was synthesized and characterized. The observed trends for the PET parameters were effectively captured through multiple Hammett linear free energy relationships (LFER) using a set of independent substituent constants for each of the two aryl rings. Given the lack of experimental Hammett constants for polyfluoro-substituted aromatics, theoretically derived constants based on the electrostatic potential at the nucleus (EPN) of carbon atoms were employed as quantum chemical descriptors. The performance of the LFER was evaluated with a set of compounds that were not included in the training set, yielding a mean unsigned error of 0.05 eV for the prediction of the combined PET parameters. The outlined LFER approach should be well suited for designing and optimizing the performance of cation-responsive 1,3,5-triarylpyrazolines.

Molecular similarity based on atomic electrostatic potential

We propose a new similarity measure operating in the space spanned by the potential values, evaluated at atoms constituting the benzene ring and the COOH group in para-substituted benzoic acids and at benzene ring atoms in monosubstituted benzenes. The similarity measures are equivalent to the Euclidean distance between points in that space. Only the distances between the potentials at corresponding atoms in different molecules are included. The distances for benzene rings were very similar, regardless of whether they were calculated in para-substituted acids or in monosubstituted benzenes. As reference reactions, dissociation of benzoic acids and nitration of monosubstituted benzenes have been used. The effects of reduction of dimensionality of the potential space on the comparison of similarity measures with the free energies of the reference reactions have been investigated. It became obvious that the potentials at individual atoms in molecules of the acids and monosubstituted benzenes are mutually correlated to a high degree.

Computation of relative bond dissociation enthalpies (DeltaBDE) of phenolic antioxidants from quantum topological molecular similarity (QTMS)

A recently proposed method called quantitative topological molecular similarity (QTMS) generated a model for the computation of the relative substituent effects on the bond dissociation enthalpies (DeltaBDEs) for a set of 39 phenols. The data set includes a diverse set of substituents with monosubstituted and poly-substituted derivatives that exhibit different electronic and steric effects. Many share common structural features with already well-established antioxidants. QTMS reveals the active region of the substituted phenols and identifies the electronic descriptors that best explain the range of DeltaBDEs observed. For substituents in the 4-X position (para) we find that our model requires a correction for radical stabilization enthalpy (RSE). Application of the QTMS methodology yields an unrivalled QSAR with r(2) = 0.98 and q(2) = 0.85 for the bond dissociation enthalpies of this phenolic antioxidant data set.

Validation of critical points in the electron density as descriptors by building quantitative structure-property relationships for the atomic polar tensor

A crucial component of research in the field of quantitative structure-activity/property relationships is the identification of molecular descriptors relevant to the activity or property of interest. Descriptors based on the topology of the electron density as formulated in Bader's theory of atoms in molecules are investigated in detail in this work. In a model study, the authors investigate their ability to predict the atomic polar tensor (the gradient of the molecular dipole moment), which contains information on the vibrational intensities in infrared spectroscopy and constitutes a scheme for partitioning the total charge distribution into atomic charges. The atomic polar tensor may therefore be used to investigate whether the descriptors give adequate information on the local electronic structure in the molecule. Both the trace of the atomic polar tensor and for planar molecules its out-of-plane component may be interpreted as definitions of atomic charges suitable for prediction. Hydrogen and carbon atoms in a set of 60 aromatic compounds with various substituents have been studied. Excellent results for prediction of hydrogen and carbon charges have been achieved with cross-validated squared correlation coefficients between predicted and theoretical values varying from 0.92 and 0.977 for the most complex set of substituents when the value, Laplacian, and ellipticity of the electron density in the bond critical points are used as descriptors. The carbon charges defined from the trace of the atomic polar tensor are correlated with its out-of-plane component whereas such relationship is not observed for the hydrogen charges studied in this work.

Application of quantum topological molecular similarity descriptors in QSPR study of the O-methylation of substituted phenols

The usefulness of a novel type of electronic descriptors called quantum topological molecular similarity (QTMS) indices for describing the quantitative effects of molecular electronic environments on the O-methylation kinetic of substituted phenols has been investigated. QTMS theory produces for each molecule a matrix of descriptors, containing bond (or structure) information in one dimension and electronic effects in another dimension, instead of other methods producing a vector of descriptors for each molecule. A collection of chemometrics tools including principal component analysis (PCA), partial least squares (PLS), and genetic algorithms (GA) were used to model the structure-kinetic data. PCA separated the bond and descriptor effects, and PLS modeled the effects of these parameters on the rate constant data, and GA selected the most relevant subset of variables. The model performances were validated by both cross-validation and external validation. The results indicated that the proposed models could explain about 95% of variances in the rate constant data. The significant effects of variables on the reaction kinetic were identified by calculating variable important in projection (VIP). It was found that the rate constant of esterification of phenols is highly influenced by the electronic properties of the C2--C1--O--H fragment of the parent molecule. Indeed, the C2--X and C4--X bonds (corresponding to ortho and para substituents) were found as highly influential parameters. All of the eight calculated QTMS indices were found significant however, lambda1, lambda2, lambda3, epsilon, and K(r) were detected as highly influential parameters.

The cytotoxicity of ortho alkyl substituted 4-X-phenols: A QSAR based on theoretical bond lengths and electron densities

A new method called quantum topological molecular similarity (QTMS) was recently proposed [O'Brien, S. E.; Popelier, P. L. A. J. Chem. Inf. Comp. Sci.2001, 41, 764] and has been shown to be successful in a variety of medicinal, ecological and physical organic QSAR/QSPRs. QTMS method uses electronic descriptors drawn from ab initio wavefunctions of geometry-optimized molecules. We investigated a remarkable and unusual set of ortho alkyl-substituted phenols [Selassie, C. D.; Verma, R. P.; Kapur, S.; Shusterman, A. J.; Hansch, C. J. Chem. Soc., Perkin2002, II, 1112], recently studied by the Hansch group. Our results do not support their proposal that a steric factor is important in the determination of the cytotoxicity of this set of substituted phenols. Thus, we conclude that the cytotoxicity of these sterically encumbered phenols is dependent primarily on electronic and radical effects, and that steric issues do not appear to be a critical distinguishing factor.