Information‐theoretic approach in density functional theory and its recent applications to chemical problems

Shannon entropy variation as a global indicator of electron density contraction at interatomic regions in chemical reactions

CONTEXT

The negative of the Shannon entropy derivative is proposed to account for electron density contraction as the chemical bonds are breaking and forming during a chemical reaction. We called this property the electron density contraction index, EDC, which allows identifying stages in a reaction that are dominated by electron contraction or expansion. Four different reactions were analyzed to show how the EDC index changes along the reaction coordinate. The results indicate that the rate of change of Shannon entropy is directly related to the rate of change of the electron density at the bond critical points between all the atomic pairs in the molecular systems. It is expected that EDC will complement the detailed analysis of reaction mechanisms that can be performed with the theoretical tools available to date.

METHODS

Density functional theory calculations at the B3LYP/6-31G(d,p) level of theory were carried out using Gaussian 16 to analyze the reaction mechanisms of the four reactions studied. The reaction paths were obtained via the intrinsic reaction coordinate method, which served as the reaction coordinate to obtain the reaction force and the EDC profiles in each case. Shannon entropy and electron density at the bond critical points were calculated using the Multiwfn 3.7 package.

Information-theoretic quantities as effective descriptors of electrophilicity and nucleophilicity in density functional theory

CONTEXT

Electrophilicity and nucleophilicity are two vastly important chemical concepts gauging the capability of atoms in molecules to accept and donate the maximal number of electrons. In our earlier studies, we proposed to simultaneously quantify them using the Kullback-Leibler divergence from the information-theoretic approach in density functional theory. However, several issues with this scheme remain to be clarified such as its general validity, predictability, and relationship with other information-theoretic quantities. In this work, we revisit the matter with bigger datasets and deeper theoretical insights. Five information-theoretic quantities including Kullback-Leibler divergence, Hirshfeld charge, Ghost-Berkowitz-Parr entropy, and second and third orders of relative Onicescu information energy are found to be reliable and robust descriptors of electrophilicity and nucleophilicity propensities. Employing these five descriptors, we design a list of new compounds and predict their electrophilicity and nucleophilicity scales. This work should markedly improve our confidence and capability in applying information-theoretic quantities to evaluate electrophilicity and nucleophilicity propensities and henceforth pave the route for more applications of these quantities from information-theoretic approach in density functional theory in the future.

METHODS

All structures were fully optimized at the M06-2X/6-311 + G(d) level of DFT functional using the Gaussian 16 package (version C01) with integration grids and tight self-consistent-field convergence. The solvent effect was taken into account by using the implicit solvent model (CPCM) in the CH2Cl2 solvent, and all 3D contour surfaces of Fukui function, local temperature, and ITA (information-theoretic approach) quantities were generated by GaussView. The Multiwfn 3.8 program was used to calculate the ITA indexes and atomic charges.

Density-based quantification of steric effects: validation by Taft steric parameters from acid-catalyzed hydrolysis of esters

The steric effect is one of the most widely used concepts for chemical understanding in publications and textbooks, yet a well-accepted formulation of this effect is still elusive. Experimentally, this concept was quantified by the acid-catalyzed hydrolysis of esters, yielding the so-called Taft steric parameter. Theoretically, we recently proposed a density-based scheme to quantify the effect from density functional theory. In this work, we directly compare these two schemes, one from theory and the other from experiment. To this end, we first establish the ester hydrolysis mechanism with multiple water molecules explicitly considered and then apply the energetic span model to represent the hydrolysis barrier height between the two schemes. Our results show that the barrier height of the reaction series is strongly correlated with both Taft steric parameters from experiment and steric quantification from theory. We also obtained strong correlations with steric potential, steric force, and steric charge from our theoretical scheme. Strong correlations with a few information-theoretic quantities are additionally unveiled. To the best of our knowledge, this is the first time in the literature that such a direct comparison between theoretical and experimental results is made. These results also suggest that our proposed two-water three-step mechanism for ester hydrolysis is effective, and our theoretical quantification of the steric effect is valid, robust, and experimentally comparable. In our view, this work should have satisfactorily addressed the issue of how the steric effect can be formulated and quantified, and thus it lays the groundwork for future applications.

A comprehensive electron wavefunction analysis toolbox for chemists, Multiwfn

Analysis of electron wavefunction is a key component of quantum chemistry investigations and is indispensable for the practical research of many chemical problems. After more than ten years of active development, the wavefunction analysis program Multiwfn has accumulated very rich functions, and its application scope has covered numerous aspects of theoretical chemical research, including charge distribution, chemical bond, electron localization and delocalization, aromaticity, intramolecular and intermolecular interactions, electronic excitation, and response property. This article systematically introduces the features and functions of the latest version of Multiwfn and provides many representative examples. Through this article, readers will be able to fully understand the characteristics and recognize the unique value of Multiwfn. The source code and precompiled executable files of Multiwfn, as well as the manual containing a detailed introduction to theoretical backgrounds and very rich tutorials, can all be downloaded for free from the Multiwfn website (http://sobereva.com/multiwfn).

CuGBasis: High-performance CUDA/Python library for efficient computation of quantum chemistry density-based descriptors for larger systems

CuGBasis is a free and open-source CUDA®/Python library for efficient computation of scalar, vector, and matrix quantities crucial for the post-processing of electronic structure calculations. CuGBasis integrates high-performance Graphical Processing Unit (GPU) computing with the ease and flexibility of Python programming, making it compatible with a vast ecosystem of libraries. We showcase its utility as a Python library and demonstrate its seamless interoperability with existing Python software to gain chemical insight from quantum chemistry calculations. Leveraging GPU-accelerated code, cuGBasis exhibits remarkable performance, making it highly applicable to larger systems or large databases. Our benchmarks reveal a 100-fold performance gain compared to alternative software packages, including serial/multi-threaded Central Processing Unit and GPU implementations. This paper outlines various features and computational strategies that lead to cuGBasis's enhanced performance, guiding developers of GPU-accelerated code.

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

The Hohenberg-Kohn theorem of density functional theory (DFT) stipulates that energy is a universal functional of electron density in the ground state, so energy can be thought of having encoded essential information for the density. Based on this, we recently proposed to quantify energetic information within the framework of information-theoretic approach (ITA) of DFT (J. Chem. Phys. 2022, 157, 101103). In this study, we systematically apply energetic information to a variety of chemical phenomena to validate the use of energetic information as quantitative measures of physicochemical properties. To that end, we employed six ITA quantities such as Shannon entropy and Fisher information for five energetic densities, yielding twenty-six viable energetic information quantities. Then, they are applied to correlate with physicochemical properties of molecular systems, including chemical bonding, conformational stability, intermolecular interactions, acidity, aromaticity, cooperativity, electrophilicity, nucleophilicity, and reactivity. Our results show that different quantities of energetic information often behave differently for different properties but a few of them, such as Shannon entropy of the total kinetic energy density and information gain of the Pauli energy density, stand out and strongly correlate with several properties across different categories of molecular systems. These results suggest that they can be employed as quantitative measures of physicochemical properties. This work not only enriches the body of our knowledge about the relationship between energy and information, but also provides scores of newly introduced explicit density functionals to quantify physicochemical properties, which can serve as robust features for building machine learning models in future studies.

The Separability Problem in Molecular Quantum Systems: Information-Theoretic Framework for Atoms in Molecules

Even though molecules are fundamentally quantum entities, the concept of a molecule retains certain classical attributes concerning its constituents. This includes the empirical separability of a molecule into its three-dimensional, rigid structure in Euclidean space, a framework often obtained through experimental methods like X-Ray crystallography. In this work, we delve into the mathematical implications of partitioning a molecule into its constituent parts using the widely recognized Atoms-In-Molecules (AIM) schemes, aiming to establish their validity within the framework of Information Theory concepts. We have uncovered information-theoretical justifications for employing some of the most prevalent AIM schemes in the field of Chemistry, including Hirshfeld (stockholder partitioning), Bader's (topological dissection), and the quantum approach (Hilbert's space definition). In the first approach we have applied the generalized principle of minimum relative entropy derived from the Sharma-Mittal two-parameter functional, avoiding the need for an arbitrary selection of reference promolecular atoms. Within the ambit of topological-information partitioning, we have demonstrated that the Fisher information of Bader's atoms conform to a comprehensive theory based on the Principle of Extreme Physical Information avoiding the need of employing the Schwinger's principle, which has been proven to be problematic. For the quantum approach we have presented information-theoretic justifications for conducting Löwdin symmetric transformations on the density matrix to form atomic Hilbert spaces generating orthonormal atomic orbitals with maximum occupancy for a given wavefunction.

Bottom-Up Atomistic Descriptions of Top-Down Macroscopic Measurements: Computational Benchmarks for Hammett Electronic Parameters

The ability to relate substituent electronic effects to chemical reactivity is a cornerstone of physical organic chemistry and Linear Free Energy Relationships. The computation of electronic parameters is increasingly attractive since they can be obtained rapidly for structures and substituents without available experimental data and can be applied beyond aromatic substituents, for example, in studies of transition metal complexes and aliphatic and radical systems. Nevertheless, the description of "top-down" macroscopic observables, such as Hammett parameters using a "bottom-up" computational approach, poses several challenges for the practitioner. We have examined and benchmarked the performance of various computational charge schemes encompassing quantum mechanical methods that partition charge density, methods that fit charge to physical observables, and methods enhanced by semiempirical adjustments alongside NMR values. We study the locations of the atoms used to obtain these descriptors and their correlation with empirical Hammett parameters and rate differences resulting from electronic effects. These seemingly small choices have a much more significant impact than previously imagined, which outweighs the level of theory or basis set used. We observe a wide range of performance across the different computational protocols and observe stark and surprising differences in the ability of computational parameters to capture para- vs meta-electronic effects. In general, σm predictions fare much worse than σp. As a result, the choice of where to compute these descriptors-for the ring carbons or the attached H or other substituent atoms-affects their ability to capture experimental electronic differences. Density-based schemes, such as Hirshfeld charges, are more stable toward unphysical charge perturbations that result from nearby functional groups and outperform all other computational descriptors, including several commonly used basis set based schemes such as Natural Population Analysis. Using attached atoms also improves the statistical correlations. We obtained general linear relationships for the global prediction of experimental Hammett parameters from computed descriptors for use in statistical modeling studies.

Harvesting Chemical Understanding with Machine Learning and Quantum Computers

It is tenable to argue that nobody can predict the future with certainty, yet one can learn from the past and make informed projections for the years ahead. In this Perspective, we overview the status of how theory and computation can be exploited to obtain chemical understanding from wave function theory and density functional theory, and then outlook the likely impact of machine learning (ML) and quantum computers (QC) to appreciate traditional chemical concepts in decades to come. It is maintained that the development and maturation of ML and QC methods in theoretical and computational chemistry represent two paradigm shifts about how the Schrödinger equation can be solved. New chemical understanding can be harnessed in these two new paradigms by making respective use of ML features and QC qubits. Before that happens, however, we still have hurdles to face and obstacles to overcome in both ML and QC arenas. Possible pathways to tackle these challenges are proposed. We anticipate that hierarchical modeling, in contrast to multiscale modeling, will emerge and thrive, becoming the workhorse of in silico simulations in the next few decades.

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

Simultaneous prediction of the molecular response properties, such as polarizability and the NMR shielding constant, at a low computational cost is an unresolved issue. We propose to combine a linear-scaling generalized energy-based fragmentation (GEBF) method and deep learning (DL) with both molecular and atomic information-theoretic approach (ITA) quantities as effective descriptors. In GEBF, the total molecular polarizability can be assembled as a linear combination of the corresponding quantities calculated from a set of small embedded subsystems in GEBF. In the new GEBF-DL(ITA) protocol, one can predict subsystem polarizabilities based on the corresponding molecular wave function (thus electron density and ITA quantities) and DL model rather than calculate them from the computationally intensive coupled-perturbed Hartree-Fock or Kohn-Sham equations and finally obtain the total molecular polarizability via a linear combination equation. As a proof-of-concept application, we predict the molecular polarizabilities of large proteins and protein aggregates. GEBF-DL(ITA) is shown to be as accurate enough as GEBF, with mean absolute percentage error <1%. For the largest protein aggregate (>4000 atoms), GEBF-DL(ITA) gains a speedup ratio of 3 compared with GEBF. It is anticipated that when more advanced electronic structure methods are used, this advantage will be more appealing. Moreover, one can also predict the NMR chemical shieldings of proteins with reasonably good accuracy. Overall, the cost-efficient GEBF-DL(ITA) protocol should be a robust theoretical tool for simultaneously predicting polarizabilities and NMR shieldings of large systems.

Some Recent Advances in Density-Based Reactivity Theory

Establishing a chemical reactivity theory in density functional theory (DFT) language has been our intense research interest in the past two decades, exemplified by the determination of steric effect and stereoselectivity, evaluation of electrophilicity and nucleophilicity, identification of strong and weak interactions, and formulation of cooperativity, frustration, and principle of chirality hierarchy. In this Featured Article, we first overview the four density-based frameworks in DFT to appreciate chemical understanding, including conceptual DFT, use of density associated quantities, information-theoretic approach, and orbital-free DFT, and then present a few recent advances of these frameworks as well as new applications from our studies. To that end, we will introduce the relationship among these frameworks, determining the entire spectrum of interactions with Pauli energy derivatives, performing topological analyses with information-theoretic quantities, and extending the density-based frameworks to excited states. Applications to examine physiochemical properties in external electric fields and to evaluate polarizability for proteins and crystals are discussed. A few possible directions for future development are followed, with the special emphasis on its merger with machine learning.

Entropic Density Functional Theory

A formulation of density functional theory (DFT) is constructed as an application of the method of maximum entropy for an inhomogeneous fluid in thermal equilibrium. The use of entropy as a systematic method to generate optimal approximations is extended from the classical to the quantum domain. This process introduces a family of trial density operators that are parameterized by the particle density. The optimal density operator is that which maximizes the quantum entropy relative to the exact canonical density operator. This approach reproduces the variational principle of DFT and allows a simple proof of the Hohenberg-Kohn theorem at finite temperature. Finally, as an illustration, we discuss the Kohn-Sham approximation scheme at finite temperature.

Simultaneous identification of strong and weak interactions with Pauli energy, Pauli potential, Pauli force, and Pauli charge

Strong and weak interatomic interactions in chemical and biological systems are ubiquitous, yet how to identify them on a unified theoretical foundation is still not well established. Recently, we proposed employing Pauli energy-based indexes, such as strong covalent interaction and bonding and noncovalent interaction indexes, in the framework of density functional theory for the purpose. In this work, we extend our previous theoretical work by directly employing Pauli energy, Pauli potential, Pauli force, and Pauli charge to simultaneously identify both strong covalent bonding and weak noncovalent interactions. Our results from this work elucidate that using their signature isosurfaces, we can identify different types of interactions, either strong or weak, including single, double, triple, and quadruple covalent bonds, ionic bond, metallic bond, hydrogen bonding, and van der Waals interaction. We also discovered strong linear correlations between Pauli energy derived quantities and different covalent bond orders. These qualitative and quantitative results from our present study solidify the viewpoint that a unified approach to simultaneously identify both strong and weak interactions is possible. In our view, this work signifies one step forward towards the goal of establishing a density-based theory of chemical reactivity in density functional theory.

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

To accurately and efficiently predict the molecular response properties (such as polarizability) at post-Hartree-Fock levels for condensed-phase systems under periodic boundary conditions (PBC) is still an unaccomplished and ongoing task. We demonstrate that static isotropic polarizabilities can be cost-effectively predicted at post-Hartree-Fock levels by combining the linear-scaling generalized energy-based fragmentation (GEBF) and information-theoretic approach (ITA) quantities. In PBC-GEBF, the total molecular polarizability of an extended system is obtained as a linear combination of the corresponding quantities of a series of small embedded subsystems of several monomers. Here, we show that in the PBC-GEBF-ITA framework, one can obtain the molecular polarizabilities and establish linear relations to ITA quantities. Once these relations are established for smaller subsystems, one can predict the polarizabilities of larger subsystems directly from the molecular wavefunction (or electron density) via ITA quantities. Alternatively, one can determine the total molecular polarizability via a linear combination equation in PBC-GEBF. We have corroborated that this newly proposed PBC-GEBF-ITA protocol is much more efficient than the original PBC-GEBF approach but is not much less accurate and that this conclusion holds for both many-body perturbation theory and the coupled cluster calculations. Good efficiency and transferability of the PBC-GEBF-ITA protocol are demonstrated for periodic systems with several hundred atoms in a unit cell.

Topological analysis of information-theoretic quantities in density functional theory

We have witnessed considerable research interest in the recent literature about the development and applications of quantities from the information-theoretic approach (ITA) in density functional theory. These ITA quantities are explicit density functionals, whose local distributions in real space are continuous and well-behaved. In this work, we further develop ITA by systematically analyzing the topological behavior of its four representative quantities, Shannon entropy, two forms of Fisher information, and relative Shannon entropy (also called information gain or Kullback-Leibler divergence). Our results from their topological analyses for 103 molecular systems provide new insights into bonding interactions and physiochemical properties, such as electrophilicity, nucleophilicity, acidity, and aromaticity. We also compare our results with those from the electron density, electron localization function, localized orbital locator, and Laplacian functions. Our results offer a new methodological approach and practical tool for applications that are especially promising for elucidating chemical bonding and reactivity propensity.

Mechanistic Study and Conceptual Chemical Reactivity Analysis of Hydroboration of Carbon Dioxide Catalyzed by a Manganese(I)-PNP-Pincer Complex

Designing efficient and selective catalysts for carbon dioxide reduction is an intensive research area in the recent literature on homogeneous catalysis. In this work, we study the catalytic activity of a newly reported Mn(I)-PNP-pincer catalyst with an embedded aromatic ring. First, we systematically examine its capability to yield different products and highlight the importance of ligand aromaticity and steric effects on metal-ligand cooperativity. We then further conceptually probe its reactivity with descriptors from both conceptual density functional theory and an information-theoretic approach, thereby proposing a novel partitioning of the reaction coordinate into three relevant regions. Our results show that the reactivity in these different regions is governed by different properties such as steric effects, electrophilicity/nucleophilicity, or aromaticity. We anticipate that this methodology, with the analytical tools employed in this study, can be generalized and extended to other catalytic systems and find applications in designing better catalysts.

Excited-State Polarizabilities: A Combined Density Functional Theory and Information-Theoretic Approach Study

Accurate and efficient determination of excited-state polarizabilities (α) is an open problem both experimentally and computationally. Following our previous work, (Phys. Chem. Chem. Phys. 2023, 25, 2131−2141), in which we employed simple ground-state (S0) density-related functions from the information-theoretic approach (ITA) to accurately and efficiently evaluate the macromolecular polarizabilities, in this work we aimed to predict the lowest excited-state (S1) polarizabilities. The philosophy is to use density-based functions to depict excited-state polarizabilities. As a proof-of-principle application, employing 2-(2′-hydroxyphenyl)benzimidazole (HBI), its substituents, and some other commonly used ESIPT (excited-state intramolecular proton transfer) fluorophores as model systems, we verified that either with S0 or S1 densities as an input, ITA quantities can be strongly correlated with the excited-state polarizabilities. When transition densities are considered, both S0 and S1 polarizabilities are in good relationships with some ITA quantities. The transferability of the linear regression model is further verified for a series of molecules with little or no similarity to those molecules in the training set. Furthermore, the excitation energies can be predicted based on multivariant linear regression equations of ITA quantities. This study also found that the nature of both the ground-state and excited-state polarizabilities of these species are due to the spatial delocalization of the electron density.

Explaining the High Catalytic Activity in Bis(indenyl)methyl Zirconium Cation Using Combined EDA-NOCV/QTAIM Approach

The main purpose of this study is to elucidate some discrepancies already observed in the catalytic activity values of some zirconocene methyl cations. The EDA-NOCV scheme was employed for a theoretical description of the interactions between an ethylene molecule and five catalysts of zirconocene methyl cation. The nature of the chemical interactions has been elucidated through the QTAIM topological analysis. The steric hindrance due to the ligands was evaluated qualitatively by means of an IRI-based analysis and quantitively through Fisher information. The findings prove that the indenyl ligand seems to favor the orbital interaction between the ethylene molecule and the metal centre of zirconocene methyl cation. Both electrostatic and orbital contributions play a crucial role in stabilising the studied complexes. Based on the NOCV deformation density contributions, the strongest orbital interaction is reached with the bis(indenyl)methyl zirconium cation, which is the only one exhibiting covalent interactions. Especially, the strong contribution of π-back donation (occurring from the occupied orbitals of the zirconium atom to the π* anti-bonding orbital of ethylene) may be a key to understand why this catalyst has a higher polymerisation yield than the other studied catalysts. This work suggests a perspective for predicting values of catalytic activity when theoretically designing novel catalysts of zirconocene type.

Development and Applications of the Density-Based Theory of Chemical Reactivity

Density functional theory, which is well-recognized for its accuracy and efficiency, has become the workhorse for modeling the electronic structure of molecules and extended materials in recent decades. Nevertheless, establishing a density-based conceptual framework to appreciate bonding, stability, function, reactivity, and other physicochemical properties is still an unaccomplished task. In this Perspective, we at first provide an overview of the four pathways currently available in the literature to tackle the matter, including orbital-free density functional theory, conceptual density functional theory, direct use of density-associated quantities, and the information-theoretic approach. Then, we highlight several recent advances of employing these approaches to realize new understandings for chemical concepts such as covalent bonding, noncovalent interactions, cooperation, frustration, homochirality, chirality hierarchy, electrophilicity, nucleophilicity, regioselectivity, and stereoselectivity. Finally, we provide a few possibilities for the future development of this relatively uncharted territory. Opportunities are abundant, and they are all ours for the taking.

A Density Functional Theory and Information-Theoretic Approach Study of Interaction Energy and Polarizability for Base Pairs and Peptides

Using density functional theory (DFT) and the information-theoretic approach (ITA) quantities to appreciate the energetics and properties of biopolymers is still an unaccomplished and ongoing task. To this end, we studied the building blocks of nucleic acid base pairs and small peptides. For base pairs, we have dissected the relative importance of energetic components by using two energy partition schemes in DFT. Our results convincingly show that the exchange-correlation effect predominantly governs the molecular stability of base pairs while the electrostatic potential plays a minor but indispensable role, and the steric effect is trivial. Furthermore, we have revealed that simple density-based ITA functions are in good relationships with molecular polarizabilities for a series of 30 hydrogen-bonded base pairs and all 20 natural α-amino acids, 400 dipeptides, and 8000 tripeptides. Based on these lines, one can easily predict the molecular polarizabilities of larger peptides, even proteins as long as the total molecular wavefunction is available, rather than solving the computationally demanding coupled-perturbed Hartree–Fock (CPHF) equation or its DFT counterpart coupled-perturbed Kohn–Sham (CPKS) equation.

Evaluation of Slight Changes in Aromaticity through Electronic and Density Functional Reactivity Theory-Based Descriptors

Aromaticity is a useful tool to rationalize the structure, stability, and reactivity in several compounds. Although aromaticity is not directly an observable, it is well accepted that electronic delocalization around the molecular ring is a key stabilizing feature of aromatic compounds. This contribution presents a systematic evaluation of the capability of delocalization and reactivity criteria to describe aromaticity in a set of fluorinated benzenes. The aromaticity indices are compared with quantities obtained from the magnetic criteria of aromaticity, i.e., the strength of the ring current induced by an external magnetic field and the popular NICS _zz (1) index. In this evaluation, the indices based on delocalization criteria used are aromatic fluctuation index (FLU), para-delocalization index (PDI), PDI_π, and the multicenter delocalization index (MCI). In addition, indices based on the bifurcation values of scalar functions are derived from electron density such as electron localization function (the π contribution, ELF_π) and the π contribution of the localized orbital locator (LOL_π). Furthermore, reactivity indices based on chemical reactivity and the information-theoretic (reactivity) approach are para-linear response (PLR), Shannon entropy, Fisher information, and Ghosh-Berkowitz-Parr (GBP) entropy. The results obtained show that the delocalization-based indicators present a high sensitivity to slight changes in aromaticity and that the reactivity criterion can be considered as a complementary tool for the study of this phenomenon, even when these changes are minimal. These results encourage the use of multiple indicators for a complete understanding of aromaticity in various chemical compounds.

Relative rates of alkylation for B-substituted triarylphosphines: an ortho-Boron group enhances reactivity on phosphorus

Advancements in main-group catalysis are contingent on our ability to quantify effects that enhance reactivity in these systems. Herein we report the rates of alkylation for several substituted phosphines. We report that by incorporating a single pinacol boronic ester group in the ortho-position on triphenylphosphine, the rate of substitution with benzyl bromide is approximately 4.7 times faster than the parent compound as measured by initial rates. The corresponding meta- and para-isomers are only 1.3 and 1.5 times as fast, respectively. Using X-ray crystallographic data and quantum chemical calculations, we propose this rate acceleration occurs from an O to P electrostatic interaction that stabilizes the transition state.

Constrained iterative Hirshfeld charges: A variational approach

We develop a variational procedure for the iterative Hirshfeld (HI) partitioning scheme. The main practical advantage of having a variational framework is that it provides a formal and straightforward approach for imposing constraints (e.g., fixed charges on certain atoms or molecular fragments) when computing HI atoms and their properties. Unlike many other variants of the Hirshfeld partitioning scheme, HI charges do not arise naturally from the information-theoretic framework, but only as a reverse-engineered construction of the objective function. However, the procedure we use is quite general and could be applied to other problems as well. We also prove that there is always at least one solution to the HI equations, but we could not prove that its self-consistent equations would always converge for any given initial pro-atom charges. Our numerical assessment of the constrained iterative Hirshfeld method shows that it satisfies many desirable traits of atoms in molecules and has the potential to surpass existing approaches for adding constraints when computing atomic properties.

Toward Density-Based and Simultaneous Description of Chemical Bonding and Noncovalent Interactions with Pauli Energy

Chemical bonds and noncovalent interactions are extraordinarily important concepts in chemistry and beyond. Using density-based quantities to describe them has a long history in the literature, yet none can satisfactorily describe the entire spectrum of interactions from strong chemical bonds to weak van der Waals forces. In this work, employing Pauli energy as the theoretical foundation, we fill in that knowledge gap. Our results show that the newly established density-based index can describe single and multiple covalent bonds, ionic bonds, metallic bonds, and different kinds of noncovalent interactions, all with unique and readily identifiable signature shapes. Two new descriptors, BNI (bonding and noncovalent interaction) index and USI (ultra-strong interaction) index, have been introduced in this work. Together with NCI (noncovalent interaction) and SCI (strong covalent interaction) indexes already available in the literature, a density-based description of both chemical bonds and noncovalent interactions is accomplished.

Electron Donor-Acceptor Properties of Different Muscarinic Ligands: On the Road to Control Schizophrenia

Schizophrenia is a severe neuropsychiatric disorder that deteriorates perception, affection, and cognitive mental functions. The current treatments are mainly focused on the dopamine system, but the so-named dopamine hypothesis of schizophrenia fails to explain all the symptoms. Previous studies have shown that there is a reciprocal relationship between muscarinic acetylcholine receptors and dopamine receptor function. Some muscarinic ligands show antidopaminergic activity, and therefore, they should have some antipsychotic efficacy. In this work, conceptual density functional theory is employed to analyze the properties of acetylcholine's agonists, partial agonists, or antagonists. The aim is to establish a classification of the antipsychotic-like or pro-psychotic activities of these molecules based on the electron-donor and electron-acceptor properties. Most of the agonists and antagonists are better electron donors and worse electron acceptors than partial agonists. We found that acetylcholine antagonists that clinically promote psychotic symptoms are good electron-donor molecules, and acetylcholine agonists that clinically relieve symptoms of psychosis are good electron donors. These results represent a further advance on the road to understanding the charge-transfer properties of drugs used as possible treatments for schizophrenia.

Principle of Chirality Hierarchy in Three-Blade Propeller Systems

There are different kinds of molecular chirality, such as zero-dimensional point chirality, one-dimensional axial chirality, 2D planar chirality, and 3D chirality. When they coexist in one system, such as in helical structures of proteins and DNA, they form a chirality hierarchy. Earlier, we showed that the chirality propensity of a lower level in a hierarchy is dictated by that of a higher level and henceforth proposed the Principle of Chirality Hierarchy. In this work, we confirm the validity of this principle in the three-blade propeller molecular system. Our results show that the preference of the 0D chirality of a functional group in the propeller system is determined by the 1D chirality, and homochirality is also a remarkable feature for this system. The establishment and confirmation of the Principle of Chirality Hierarchy from this work should find important applications in asymmetric synthesis, macromolecular assembly, and many others.

Systematic Investigation of Error Distribution in Machine Learning Algorithms Applied to the Quantum-Chemistry QM9 Data Set Using the Bias and Variance Decomposition

Most machine learning applications in quantum-chemistry (QC) data sets rely on a single statistical error parameter such as the mean square error (MSE) to evaluate their performance. However, this approach has limitations or can even yield incorrect interpretations. Here, we report a systematic investigation of the two components of the MSE, i.e., the bias and variance, using the QM9 data set. To this end, we experiment with three descriptors, namely (i) symmetry functions (SF, with two-body and three-body functions), (ii) many-body tensor representation (MBTR, with two- and three-body terms), and (iii) smooth overlap of atomic positions (SOAP), to evaluate the prediction process's performance using different numbers of molecules in training samples and the effect of bias and variance on the final MSE. Overall, low sample sizes are related to higher MSE. Moreover, the bias component strongly influences the larger MSEs. Furthermore, there is little agreement among molecules with higher errors (outliers) across different descriptors. However, there is a high prevalence among the outliers intersection set and the convex hull volume of geometric coordinates (VCH). According to the obtained results with the distribution of MSE (and its components bias and variance) and the appearance of outliers, it is suggested to use ensembles of models with a low bias to minimize the MSE, more specifically when using a small number of molecules in the training set.

Density Functional Theory of Highly Excited States of Coulomb Systems

The density functional theory proposed earlier for excited states of Coulomb systems is discussed. The localized Hartree–Fock (LHF) and the Krieger, Li, and Iafrate (KLI) methods combined with correlation are generalized for excited states. Illustrative examples include some highly excited states of Li and Na atoms.

Local Temperature as a Chemical Reactivity Descriptor

Using the electron density and its associated quantities in a molecular system to quantify chemical reactivity in density functional theory is of considerable recent interest. Local temperature based on the kinetic energy density is an intrinsic property of a molecular system, which can be employed for this purpose. In this work, we explore such a possibility. To this end, we examine the local behavior of local temperature with a few choices of the kinetic energy density, apply it to determine regioselectivity of nucleophilic and electrophilic compounds, and then investigate its performance in appreciating reactions along the intrinsic reaction pathway for exothermic, endothermic, and thermoneutral transformations. Our results confirm that local temperature can be used as an effective descriptor of molecular reactivity.

Quantifying Frustrations for Molecular Complexes with Noncovalent Interactions

Molecular systems bound together through noncovalent interactions are involved in a lot of life-essential processes such as molecular recognition, signal transduction, and allosteric regulation. While cooperation as an important effect discovered in these systems focuses on the behavior of system's entirety, we need also examine the behavior of individual parts. In this work, using the distortion energy as the descriptor, we quantify frustration as the energetic loss of individual parts due to the formation of nonadditive molecular complexes. The applicability of our approach has been illustrated by a few simple clusters. Our results show that the frustration effect is smaller than the cooperation effect, but same as cooperativity, it can be both positive and negative. The ultimate benefit of a system made of multiple parts is dictated by the balance between the cooperative behavior among parts and the sacrifice from its individuals. This conflicting yet complementary conceptual pair of cooperation and frustration provides us with a different perspective from the systems' viewpoint for molecular complexes. This new angle of appreciating molecular complexes can be applied in conformational changes, enzymatic catalysis, and many more.

Quantifications and Applications of Relative Fisher Information in Density Functional Theory

Though density functional theory is widely accepted as one of the most successful developments in theoretical chemistry in the past few decades, the knowledge of how to apply this new electronic structure theory, to help us better understand chemical processes and transformations, is still an unaccomplished task. The information-theoretic approach is emerging as a viable option for that purpose in the recent literature, providing new insights about steric effect, cooperativity, electrophilicity, nucleophilicity, stereoselectivity, homochirality, etc. In this work, based on the result from a recent paper by one of us [ J. Chem. Phys, 2019, 151, 141103], we present two quantifications of the relative Fisher information and discuss their physiochemical properties and possible applications. To that end, their analytical properties have been elucidated. They have also been applied to six categories of systems to illustrate their applicability. A better descriptor to quantify the single bond rotation barrier has been obtained. The relative Fisher information can also simultaneously determine electrophilicity and nucleophilicity, and effectively describe helical structures with different homochiral and heterochiral propensities. As integral parts of the information-theoretic approach, these newly introduced quantities will provide us with more analytical tools toward the long-term goal of crafting a chemical reactivity theory in the density-based language.

Using Bases as Initiators to Isomerize Allylic Alcohols: Insights from Density Functional Theory Studies

Allylic alcohols, as common and readily available building blocks, could be converted into many widely used carbonyl compounds through isomerization reactions. However, these processes often involve expensive transition metal (TM) complexes as the catalyst. What is the bottleneck in the mechanism when no TM is used? In this study, density functional theory (DFT) was employed to explore the mechanistic patterns of allylic alcohols catalyzed using bases, such as KOH, NaOH, LiOH, tBuOK, tBuONa, tBuOLi, 1,5,7-triazabicyclo[4.4.0]dec-5-ene, 1,3,4,6,7,8-hexahydro-1-methyl-2H-pyrimido[1,2-a]pyrimidine, and 1,8-diazabicyclo[5.4.0]undec-7-ene. Our results show that bases containing metal cations follow the metal cation-assisted (MCA) mechanism, whereas organic bases without metal cations follow the ion pair-assisted (IPA) mechanism. The catalytic efficiency of bases containing metal cations is higher than that of bases without metal cations, indicating that metal cations play an important role in the reaction. Additionally, the modulation of substituents R₁ and R₂ in the substrate reveals that electron-withdrawing groups are favorable for C-H bond cleavage, and electron-donating groups are favorable for hydrogen transfer. To better understand these patterns, we applied the DFT and information-theoretic approach (ITA) to examine the impact of bases and substrate substituents on the reactivity of allylic alcohol isomerization. This work should provide a much-needed theoretical guidance to design better non-TM catalysts for the isomerization of allylic alcohols and their derivatives.

Density Functional Theory and Information-Theoretic Approach Study on the Origin of Homochirality in Helical Structures

Homochirality of macromolecules such as proteins and DNA is one of the most striking features in nature; yet, there is still no convincing theory to explain its origin. In a recent work by one of the present authors (J. Phys. Chem. Lett. 2020, 11, 8690-8696), a general proposal from the viewpoint of thermodynamics has been put forward. It proposes that it is the handedness of helices ubiquitous in biological macromolecules that plays the decisive role. It also unveiled that there exist strong cooperativity effects dominated by favorable electrostatic interactions in the homochiral conformer. In this work, making use of analytical tools, we recently developed a density functional theory and an information-theoretic approach and through four sets of helical structures we designed for the present study, we examine these systems to provide new insights about these properties. We found that the 3₁₀-helix and the α-helix are markedly different in cooperativity from the viewpoint of both the total energy and its three components. The electrostatic dominance of homochiral species is manifested by both the electron charge distribution and information gain. At the atomic level, different elements behave significantly differently because they play different roles in the systems. Our results from this work validate that these analytical tools can be applied to homochiral systems, which can be further extended to others with potential interest in asymmetric synthesis and macromolecular assembly where the Principle of Homochirality Hierarchy comes into play.

Modelling the structural and reactivity landscapes of tucatinib with special reference to its wavefunction-dependent properties and screening for potential antiviral activity

HER-2 type breast cancer is one of the most aggressive malignancies found in women. Tucatinib is recently developed and approved as a potential medicine to fight this disease. In this manuscript, we present the gross structural features of this compound and its reactivity and wave function properties using computational simulations. Density functional theory was used to optimise the ground state geometry of the molecule and molecular docking was used to predict biological activity. As the electrons interact with electromagnetic radiations, electronic excitations between different energy levels are analysed in detail using time-dependent density functional theory. Various intermolecular and intermolecular interactions are analysed and reaction sites for attacking electrophiles and nucleophiles identified. Information entropy calculations show that the compound is inherently stable. Docking with COVID-19 proteins show docking score of - 9.42, - 8.93, - 8.45 and - 8.32 kcal/mol respectively indicating high interaction between the drug and proteins. Hence, this is an ideal candidate to study repurposing of existing drugs to combat the pandemic.

Structural investigations, quantum mechanical studies on proton and metal affinity and biological activity predictions of selpercatinib

Cancer of the lungs and thyroid is particularly difficult to manage and treat. Notably, selpercatinib has recently been suggested as an effective drug to combat these diseases. The entire world is currently tackling the pandemic caused by the SARS-CoV-19 virus. Numerous pharmaceuticals have been evaluated for the management of the disease caused by SARS-CoV-19 (i.e., COVID-19). In this study, selpercatinib was proposed as a potential inhibitor of different SARS-CoV-19 proteins. Several intriguing effects of the molecule were found during the conducted computational investigations. Selpercatinib could effectively act as a proton sponge and exhibited high proton affinity in solution. Moreover, it was able to form complexes with metal ions in aqueous solutions. Specifically, the compound displayed high affinity towards zinc ions, which are important for the prevention of virus multiplication inside human cells. However, due to their charge, zinc ions are not able to pass the lipid bilayer and enter the cell. Thus, it was determined that selpercatinib could act as an ionophore, effectively transporting active zinc ions into cells. Furthermore, various quantum mechanical analyses, including energy studies, evaluation of the reactivity parameters, examination of the electron localisation and delocalisation properties, as well as assessment of the nonlinear optical (NLO) properties and information entropy, were conducted herein. The performed docking studies (docking scores -9.3169, -9.1002, -8.1853 and -8.1222 kcal mol^-1) demonstrated that selpercatinib strongly bound with four isolated SARS-CoV-2 proteins.

Theoretical prediction of the impact sensitivities of energetic C-nitro compounds

In order to design high-energetic and insensitive explosives, the frontier orbital energy gaps, surface electrostatic potentials, nitro group charges, bond dissociation energies (BDEs) of the C-NO₂ trigger bonds, and intermolecular interactions obtained by the M06-2X/6-311++G(2d,p) method were quantitatively correlated with the experimental drop hammer potential energies of 10 typical C-nitro explosives. The changes of several information-theoretic quantities (ITQs) in the density functional reactivity theory were discussed upon the formation of complexes. The BDEs in the explosives with six-membered ring are larger than those with five-membered ring. The frontier orbital energy gaps of the compounds with benzene ring are larger than those with N-heterocycle. The models involving the intermolecular interaction energies and the energy gaps could be used to predict the impact sensitivity of the C-nitro explosives, while those involving ΔS_S, ΔI_F, and ΔS_GBP are invalid. With the more and more ITQs, the further studies are needed to seek for a good correlation between impact sensitivity measurements and ITQs for the energetic C-nitro compounds. The origin of sensitivity was revealed by the reduced density gradient method.

Changes in Structure and Reactivity of Ng2 Encapsulated in Fullerenes: A Density Functional Theory Study

Noble gas can be no noble in certain situations from the perspective of structure, bonding, and reactivity. These situations could be extreme experimental conditions or others. In this contribution, we systematically investigate the impact of fullerene encapsulation on molecular structure and chemical reactivity of noble gas dimers (Ng2) in a few fullerene molecules. To that end, we consider He2, Ne2, and Ar2 dimers encapsulated in C50, C60, and C70 fullerenes. We unveil that bond distances of Ng2 inside fullerene become substantially smaller and noble gas atoms become more electrophilic. In return, these noble gas dimers make fullerene molecules more nucleophilic. Using analytical tools from density functional theory, conceptual density functional theory, and information-theoretic approach, we appreciate the nature and origin of these structure and reactivity changes. The results and conclusions from this work should provide more new insights from the viewpoint of changing the perspectives of noble gas reactivity.