Do the local softness and hardness indicate the softest and hardest regions of a molecule?

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.

Atoms-In-Molecules' Faces of Chemical Hardness by Conceptual Density Functional Theory

The chemical hardness concept and its realization within the conceptual density functional theory is approached with innovative perspectives, such as the electronegativity and hardness equalization of atoms in molecules connected with the softness kernel, in order to examine the structure-reactivity equalization ansatz between the electronic sharing index and the charge transfer either in the additive or geometrical mean picture of bonding. On the other hand, the maximum hardness principle presents a relation with the chemical stability of the hardness concept. In light of the inverse relation between hardness and polarizability, the minimum polarizability principle has been proposed. Additionally, this review includes important applications of the chemical hardness concept to solid-state chemistry. The mentioned applications support the validity of the electronic structure principles regarding chemical hardness and polarizability in solid-state chemistry.

Properties of the density functional response kernels and its implications on chemistry

An overview of mathematical properties of the non-local second order derivatives of the canonical, grand canonical, isomorphic, and grand isomorphic ensembles is given. The significance of their positive or negative semidefiniteness and the implications of these properties for atoms and molecules are discussed. Based on this property, many other interesting properties can be derived, such as the expansion in eigenfunctions, bounds on the diagonal and off-diagonal elements, and the eigenvalues of these kernels. We also prove Kato's theorem for the softness kernel and linear response and the dissociation limit of the linear responses as the sum of the linear responses of the individual fragments when dissociating a system into two non-interacting molecular fragments. Finally, strategies for the practical calculation of these kernels, their eigenfunctions, and their eigenvalues are discussed.

From Density Functional Theory to Conceptual Density Functional Theory and Biosystems

The position of conceptual density functional theory (CDFT) in the history of density functional theory (DFT) is sketched followed by a chronological report on the introduction of the various DFT descriptors such as the electronegativity, hardness, softness, Fukui function, local version of softness and hardness, dual descriptor, linear response function, and softness kernel. Through a perturbational approach they can all be characterized as response functions, reflecting the intrinsic reactivity of an atom or molecule upon perturbation by a different system, including recent extensions by external fields. Derived descriptors such as the electrophilicity or generalized philicity, derived from the nature of the energy vs. N behavior, complete this picture. These descriptors can be used as such or in the context of principles such as Sanderson’s electronegativity equalization principle, Pearson’s hard and soft acids and bases principle, the maximum hardness, and more recently, the minimum electrophilicity principle. CDFT has known an ever-growing use in various subdisciplines of chemistry: from organic to inorganic chemistry, from polymer to materials chemistry, and from catalysis to nanotechnology. The increasing size of the systems under study has been coped with thanks to methodological evolutions but also through the impressive evolution in software and hardware. In this flow, biosystems entered the application portfolio in the past twenty years with studies varying (among others) from enzymatic catalysis to biological activity and/or the toxicity of organic molecules and to computational peptidology. On the basis of this evolution, one can expect that “the best is yet to come”.

Energetics and J-coupling constants for Ala, Gly, and Val peptides demonstrated using ABEEM polarizable force field in vacuo and an aqueous solution

The development of an atom-bond electronegativity equalisation method at the σπ-level (ABEEM) polarisable force field (PFF) for peptides is presented. ABEEM PFF utilises a fluctuating charge model to explicitly describe...

Thermochemical and Quantum Descriptor Calculations for Gaining Insight into Ricin Toxin A (RTA) Inhibitors

In this work, we performed a study to assess the interactions between the ricin toxin A (RTA) subunit of ricin and some of its inhibitors using modern semiempirical quantum chemistry and ONIOM quantum mechanics/molecular mechanics (QM/MM) methods. Two approaches were followed (calculation of binding enthalpies, ΔH _bind, and reactivity quantum chemical descriptors) and compared with the respective half-maximal inhibitory concentration (IC₅₀) experimental data, to gain insight into RTA inhibitors and verify which quantum chemical method would better describe RTA-ligand interactions. The geometries for all RTA-ligand complexes were obtained after running classical molecular dynamics simulations in aqueous media. We found that single-point energy calculations of ΔH _bind with the PM6-DH+, PM6-D3H4, and PM7 semiempirical methods and ONIOM QM/MM presented a good correlation with the IC₅₀ data. We also observed, however, that the correlation decreased significantly when we calculated ΔH _bind after full-atom geometry optimization with all semiempirical methods. Based on the results from reactivity descriptors calculations for the cases studied, we noted that both types of interactions, molecular overlap and electrostatic interactions, play significant roles in the overall affinity of these ligands for the RTA binding pocket.

Unifying Conceptual Density Functional and Valence Bond Theory: The Hardness-Softness Conundrum Associated with Protonation Reactions and Uncovering Complementary Reactivity Modes

In this study, we address the long-standing issue-arising prominently from conceptual density functional theory (CDFT)-of the relative importance of electrostatic, i.e., "hard-hard", versus spin-pairing, i.e., "soft-soft", interactions in determining regiochemical preferences. We do so from a valence bond (VB) perspective and demonstrate that VB theory readily enables a clear-cut resolution of both of these contributions to the bond formation/breaking process. Our calculations indicate that appropriate local reactivity descriptors can be used to gauge the magnitude of both interactions individually, e.g., Fukui functions or HOMO/LUMO orbitals for the spin-pairing/(frontier) orbital interactions and molecular electrostatic potentials (and/or partial charges) for the electrostatic interactions. In contrast to previous reports, we find that protonation reactions cannot generally be classified as either charge- or frontier orbital-controlled; instead, our results indicate that these two bonding contributions generally interplay in more subtle patterns, only giving the impression of a clear-cut dichotomy. Finally, we demonstrate that important covalent, i.e., spin pairing, reactivity modes can be missed when only a single spin-pairing/orbital interaction descriptor is considered. This study constitutes an important step in the unification of CDFT and VB theory.

Competition between N and O: use of diazine N-oxides as a test case for the Marcus theory rationale for ambident reactivity

The preferred site of alkylation of diazine N-oxides by representative hard and soft alkylating agents was established conclusively using the 1H-15N HMBC NMR technique in combination with other NMR spectroscopic methods. Alkylation of pyrazine N-oxides (1 and 2) occurs preferentially on nitrogen regardless of the alkylating agent employed, while O-methylation of pyrimidine N-oxide (3) is favoured in its reaction with MeOTf. As these outcomes cannot be explained in the context of the hard/soft acid/base (HSAB) principle, we have instead turned to Marcus theory to rationalise these results. Marcus intrinsic barriers (ΔG ‡ 0) and Δr G° values were calculated at the DLPNO-CCSD(T)/def2-TZVPPD/SMD//M06-2X-D3/6-311+G(d,p)/SMD level of theory for methylation reactions of 1 and 3 by MeI and MeOTf, and used to derive Gibbs energies of activation (ΔG ‡) for the processes of N- and O-methylation, respectively. These values, as well as those derived directly from the DFT calculations, closely reproduce the observed experimental N- vs. O-alkylation selectivities for methylation reactions of 1 and 3, indicating that Marcus theory can be used in a semi-quantitative manner to understand how the activation barriers for these reactions are constructed. It was found that N-alkylation of 1 is favoured due to the dominant contribution of Δr G° to the activation barrier in this case, while O-alkylation of 3 is favoured due to the dominant contribution of the intrinsic barrier (ΔG ‡ 0) for this process. These results are of profound significance in understanding the outcomes of reactions of ambident reactants in general.

ABEEM/MM OH- Models for OH-(H2O)n Clusters and Aqueous OH-: Structures, Charge Distributions, and Binding Energies

Based on the atom-bond electronegativity equalization method fused into molecular mechanics (ABEEM/MM), two fluctuating charge models of OH^--water system were proposed. The difference between these two models is whether there is charge transfer between OH^- and its first-shell water molecules. The structures, charge distributions, charge transfer, and binding energies of the OH^-(H₂O)_n (n = 1-8, 10, 15, 23) clusters were studied by these two ABEEM/MM models, the OPLS/AA force field, the OPLS-SMOOTH/AA force field, and the QM methods. The results demonstrate that two ABEEM/MM models can search out all stable structures just as the QM methods, and the structures and charge distributions agree well with those from the QM calculations. The structures, the charge transfer, and the strength of hydrogen bonds in the first hydration shell are closely related to the coordination number of OH^-. Molecular dynamics simulations on the aqueous OH^- solution are performed at 298 and 278 K using ABEEM/MM-I model. The MD results show that the populations of three-, four-, and five-coordinated OH^- are 29.6%, 67.1%, and 3.4% at 298 K, respectively, and those of two-, three-, four-, and five-coordinated OH^- are 10.8%, 44.9%, 39.2%, and 4.9% at 278 K, respectively; the average hydrogen bond lengths and the hydrogen bond angle in the first shell increase with the temperature decreasing.

The hunt for reactive alkynes in bio-orthogonal click reactions: insights from mechanochemical and conceptual DFT calculations

In our effort to implement the mechanical force used to activate single molecules in mechanochemistry in the context of conceptual density functional theory, we present a theoretical investigation of strained alkynes for rationalizing structural trends as well as the reactivity of cyclic alkynes that are of great importance in in vivo click reactions. The strain on the triple bond in cyclic alkynes is modeled by angular constraints in a 2-butyne fragment and the corresponding bending force is calculated by means of an extended COGEF (constrained geometries simulate external forces) model. In general, the force required to bend the triple bond is smaller with electron-withdrawing groups on the propargylic C-atom, which elegantly results in smaller angles around the triple bond in cyclic alkynes with such substitution pattern. By means of conceptual DFT descriptors, the electrophilic and nucleophilic character of bent triple bonds was investigated revealing moderate activation for small distortions from the linear geometry (0° to 15°) and a drastically more reactive π-space if the triple bond is bent further. This analysis of the intrinsic reactivity of the triple bond is in line with experimental observations, explaining the reactive nature of cyclooctynes and cycloheptynes, whereas larger cyclic systems do not drastically activate the triple bond.

Quantum chemical determination of molecular geometries and spectral investigation of 4-ethoxy-2, 3-difluoro benzamide

The present work reports the application of density functional theory (DFT) at B3LYP with various basis sets which provide the relationship between the structural and spectral properties of 4-ethoxy-2, 3-difluoro benzamide (4EDFB). A Complete vibrational analysis has been performed at the density functional theory (DFT) method with various basis sets in the ground state. The results of vibrational wave numbers are in good agreement with the experimental spectra (Infrared and Raman). Energy gap of the molecule is evaluated using frontier molecular orbital energies (HOMO-LUMO). The frontier energy gap value reveals the chemical reactivity and intermolecular charge transfer occur within the molecule. Global chemical descriptors provide the local and global softness and local reactivity parameters used to identify the nucleophilic and electrophilic behavior of a specific site within the compound. The dimer structure is performed to evaluate the intermolecular hydrogen bond (O-H-O). The title molecule is capable of receiving second harmonic generation (SHG) is due to high value of hyperpolarizability indicates the NLO activity of the molecule. Apart from NLO entities, aromaticity and the molecular electrostatic potential surface (MEP) explain the hydrogen bonding and provide the reactive behavior of the molecule. The Mulliken population analysis leads to redistribution of electron density in the ring.

Reaction mechanism of NO with hydrolysates of NAMI-A: an MD simulation by combining the QM/MM(ABEEM) with the MD-FEP method

Nitrosylation reaction mechanisms of the hydrolysates of NAMI-A and hydrolysis reactions of ruthenium nitrosyl complexes were investigated in the triplet state and the singlet state. Activation free energies were calculated by combining the QM/MM(ABEEM) method with free energy perturbation theory, and the explicit solvent environment was simulated by an ABEEMσπ polarizable force field. Our results demonstrate that nitrosylation reactions of the hydrolysates of NAMI-A occur in both the triplet and the singlet states. The Ru-N-O angle of the triplet ruthenium nitrosyl complexes is in the range of 132.0°-138.2°. However, all the ruthenium nitrosyl complexes at the singlet state show an almost linear Ru-N-O angle. The nitrosylation reaction happens prior to the hydrolysis reaction for the first-step hydrolysates. The activation free energies of the nitrosylation reactions show that the H₂ O-NO exchange reaction of [RuCl₄ (Im)(H₂ O)] in the singlet spin sate is the most likely one. Comparing with the activation free energies of the hydrolysis reactions of the ruthenium nitrosyl complexes, the results indicate that the rate of the DMSO-H₂ O exchange reaction of [RuCl₃ (NO)(Im)(DMSO)] is faster than that of [RuCl₃ (H₂ O)(Im)(DMSO)] in both the triplet spin state and the singlet spin state. © 2018 Wiley Periodicals, Inc.

Electronic and optical properties of metalloporphyrins of zinc on TiO2 cluster in dye-sensitized solar-cells (DSSC). A quantum chemistry study

Dye-sensitized solar-cell (DSSC) systems have been investigated by calculating light-absorption and electron-injection processes of zinc-porphyrin-dye based sensitizers adsorbed on a TiO₂ cluster simulating the semiconductor.

Local chemical potential, local hardness, and dual descriptors in temperature dependent chemical reactivity theory

From the definition of a local chemical potential, well-behaved expressions for the local hardness and the dual descriptors are derived.

Revisiting the definition of local hardness and hardness kernel

Local hardness is redefined following similar rules to those of local softness. The new concept describes chemical trends correctly.

Improvement of photovoltaic performance by substituent effect of donor and acceptor structure of TPA-based dye-sensitized solar cells

We report a computational study of a series of organic dyes built with triphenylamine (TPA) as an electron donor group. We designed a set of six dyes called (TPA-n, where n = 0-5). In order to enhance the electron-injection process, the electron-donor effect of some specific substituent was studied. Thus, we gave insights into the rational design of organic TPA-based chromophores for use in dye-sensitized solar cells (DSSCs). In addition, we report the HOMO, LUMO, the calculated excited state oxidized potential E(dye*)(eV) and the free energy change for electron-injection ΔGinject(eV), and the UV-visible absorption bands for TPA-n dyes by a time-dependent density functional theory (TDDFT) procedure at the B3LYP and CAM-B3LYP levels with solvent effect. The results demonstrate that the introduction of the electron-acceptor groups produces an intramolecular charge transfer showing a shift of the absorption wavelengths of TPA-n under studies. Graphical Abstract Several organic dyes TPA-n with different donors and acceptors are modeled. A strong conjugation acrros the donor and anchoring groips (TPA-n) bas been studied. Candidate TPA-3 shows a promising results.

Investigation of electron density changes at the onset of a chemical reaction using the state-specific dual descriptor from conceptual density functional theory

The electron density changes from reactants towards the transition state of a chemical reaction is expressed as a linear combination of the state-specific dual descriptors (SSDD) of the corresponding reactant complexes.

On the trends of Fukui potential and hardness potential derivatives in isolated atoms vs. atoms in molecules

In the present study, trends of electronic contribution to molecular electrostatic potential [Vel(r¯)(r=0)], Fukui potential [v(+)f|(r=0) and v(-)f|(r=0)] and hardness potential derivatives [Δ(+)h(k) and Δ(-)h(k)] for isolated atoms as well as atoms in molecules are investigated. The generated numerical values of these three reactivity descriptors in these two electronically different situations are critically analyzed through the relevant formalism. Values of Vel(r¯) (when r → 0, i.e., on the nucleus) are higher for atoms in molecules than that of isolated atoms. In contrast, higher values of v(+)|(r=0) and v(-)|(r=0) are observed for isolated atoms compared to the values for atoms in a molecule. However, no such regular trend is observed for the Δ(+)h(k) and Δ(-)h(k) values, which is attributed to the uncertainty in the Fukui function values of atoms in molecules. The sum of Fukui potential and the sum of hardness potential derivatives in molecules are also critically analyzed, which shows the efficacy of orbital relaxation effects in quantifying the values of these parameters. The chemical consequence of the observed trends of these descriptors in interpreting electron delocalization, electronic relaxation and non-negativity of atomic Fukui function indices is also touched upon. Several commonly used molecules containing carbon as well as heteroatoms are chosen to make the investigation more insightful.

An information-theoretic resolution of the ambiguity in the local hardness

A definition of the local hardness, suitable for application in the local hard/soft acid/base principle, is derived by applying information theory.

Intermolecular interactions in organic crystals: gaining insight from electronic structure analysis by density functional theory

Conceptual density functional theory is exploited to extend the HSAB (hard and soft acids and bases) principle for investigating the locality and regioselectivity of intermolecular interactions in organic crystals.

Farewell to the HSAB treatment of ambident reactivity

The concept of hard and soft acids and bases (HSAB) proved to be useful for rationalizing stability constants of metal complexes. Its application to organic reactions, particularly ambident reactivity, has led to exotic blossoms. By attempting to rationalize all the observed regioselectivities by favorable soft-soft and hard-hard as well as unfavorable hard-soft interactions, older treatments of ambident reactivity, which correctly differentiated between thermodynamic and kinetic control as well as between different coordination states of ionic substrates, have been replaced. By ignoring conflicting experimental results and even referring to untraceable experimental data, the HSAB treatment of ambident reactivity has gained undeserved popularity. In this Review we demonstrate that the HSAB as well as the related Klopman-Salem model do not even correctly predict the behavior of the prototypes of ambident nucleophiles and, therefore, are rather misleading instead of useful guides. An alternative treatment of ambident reactivity based on Marcus theory will be presented.

Application of the electron density force to chemical reactivity

In this paper the concept of force experienced by the electron density is applied to chemical reactivity. The force is based upon the gradient of a local chemical potential. Closely related concepts such as force field lines and local electron flux are defined to provide insight in chemical reactivity. The time evolution of a molecular site density is also proposed. From the divergence of the force, the nucleophilic and electrophilic behaviour of atomic sites are characterized. Finally, the relations between the force and local conceptual DFT descriptors are also given.

Opposite regiospecific ring opening of 2-(cyanomethyl)aziridines by hydrogen bromide and benzyl bromide: experimental study and theoretical rationalization

Ring opening of 1-arylmethyl-2-(cyanomethyl)aziridines with HBr afforded 3-(arylmethyl)amino-4-bromobutyronitriles via regiospecific ring opening at the unsubstituted aziridine carbon. Previous experimental and theoretical reports show treatment of the same compounds with benzyl bromide to furnish 4-amino-3-bromobutanenitriles through ring opening at the substituted aziridine carbon. To gain insights into the regioselective preference with HBr, reaction paths have been analyzed with computational methods. The effect of solvation was taken into account by the use of explicit solvent molecules. Geometries were determined at the B3LYP/6-31++G(d,p) level of theory, and a Grimme-type correction term was included for long-range dispersion interactions; relative energies were refined with the meta-hybrid MPW1B95 functional. Activation barriers confirm preference for ring opening at the unsubstituted ring carbon for HBr. HBr versus benzyl bromide ring opening was analyzed through comparison of the electronic structure of corresponding aziridinium intermediates. Although the electrostatic picture fails to explain the opposite regiospecific nature of the reaction, frontier molecular orbital analysis of LUMOs and nucleophilic Fukui functions show a clear preference of attack for the substituted aziridine carbon in the benzyl bromide case and for the unsubstituted aziridine carbon in the HBr case, successfully rationalizing the experimentally observed regioselectivity.