The linear response kernel of conceptual DFT as a measure of aromaticity

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Aromaticity of six-membered nitro energetic compounds through molecular electrostatic potential, magnetic, electronic delocalization and reactivity-based indices

The electron density depletion associated with π-hole at the ring center typical of energetic compounds was clearly revealed by the molecular electrostatic potential (ESP). In addition, the spatial arrangement of NO2 groups appears to affect the ESP value in the ring center, and therefore sensitivity to detonation. Indeed, for monocyclic nitrobenzene compounds with the same number of NO2 groups, the ESP value in the ring center decreases as the NO2 groups are more closely spaced. As expected, the central rings become less aromatic as NO2 groups are added. The MCI, PDI, PLR, NICSzz(1), FLU indices are all strongly correlated with the ESP values observed in the ring center of the set of nitrobenzenes. Aromaticity indices based on electron delocalization criteria appear to be very sensitive to small variations in aromaticity. Among magnetic-based indices, only NICSzz(1) is capable to predict small changes in aromaticity. The PLR index derived from conceptual DFT is quite relevant for predicting small variations in aromaticity. According to our results, the most suitable aromaticity index is not based on a single criterion, and that selecting it is more subtle. Therefore, it is important to combine information from several criteria to obtain a more complete description of the aromaticity of the studied compounds.

Extending the Scope of Conceptual Density Functional Theory with Second Order Analytical Methodologies

In the context of the growing impact of conceptual density functional theory (DFT) as one of the most successful chemical reactivity theories, response functions up to second order have now been widely applied; in recent years, among others, particular attention has been focused on the linear response function and also extensions to higher order have been put forward. As the larger part of these studies have been carried using a finite difference approach to compute these concepts, we now embarked on (an extension of) an analytical approach to conceptual DFT. With the ultimate aim of providing a complete set of analytically computable second order properties, including the softness and hardness kernels, the hardness as the simplest second order response function is scrutinized again with numerical results highlighting the difference in nature between the analytical hardness (referred to as hardness condition) and the Parr-Pearson absolute chemical hardness. The hardness condition is investigated for its capability to gauge the (de)localization error of density functional approximations (DFAs). The analytical Fukui function, besides overcoming the difficulties in the finite difference approach in treating negatively charged systems, also showcases the errors of deviating from the straight-line behavior using fractional occupation number calculations. Subsequently, the softness kernel and its atom-condensed inverse, the hardness matrix, are accessed through the Berkowitz-Parr relation. Revisiting the softness kernel confirms and extends previous discussions on how Kohn's Nearsightedness of Electronic Matter principle can be retrieved and identified as the physicist's version of the chemist's "transferability of functional groups" concept. The accurate, analytical hardness matrix evaluation on the other hand provides further support for the basics of Nalewajski's charge sensitivity analysis. Based on Parr and Liu's functional expansion of the energy functional, a new energy decomposition is introduced with an order of magnitude analysis of the different terms for a series of simple molecules both at their equilibrium geometry and upon variation in bond length and dihedral angle. Finally, for the first time, the perturbation expansion of the energy functional is studied numerically up to second order now that all response functions and integration techniques are at hand. The perturbation expansion energies are in excellent agreement with those obtained directly from DFA calculations giving confidence in the convergence of the perturbation series and its use in judging the importance of the different terms in reactivity investigations.

Cyclo[n]carbons and catenanes from different perspectives: disentangling the molecular thread

All-carbon atomic rings, cyclo[n]carbons, have recently attracted vivid attention of experimentalists and theoreticians. Among them, cyclo[18]carbon is the most studied system. In this paper, we summarize and review various properties of cyclo[n]carbons, emphasising the aspects of their aromaticity/antiaromaticity. In the first part, the trends in bonding patterns and selected aromaticity indices with the increasing size of the rings are discussed. In the second part we explore the properties of catenane models based on interlocked cyclo[18]carbon rings from different perspectives and investigate their behaviour under the action of external force using computational experiments.

Electrophilicity of Hoveyda-Grubbs Olefin Metathesis Catalysts as the Driving Force that Controls Initiation Rates

The dissociative mechanism of initiation for a series of Hoveyda-Grubbs type metathesis catalysts modified at the para and meta positions in the isopropoxybenzylidene ligand is investigated by means of DFT calculations. The electron donating/withdrawing capacity of the ligand was screened through the incorporation of various substituents such as halogens, nitro, alkoxides, ketones, esters, amines, and amides. Variations in structural parameters, energy barriers for the Ru-O bond dissociation, and Ru-O bond strength were examined as a function of the Hammett constant. It was found that electronic properties of the catalysts such as chemical potential, hardness, and electrophilicity correlate linearly with the dissociative energy barriers. These findings enable a systematic rationalization and prediction of rate of precatalyst initiation through the calculation of only the HOMO-LUMO gap of catalysts, as the faster the initiation, the more electrophilic the catalyst.

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.

Synthesis, characterization, and theoretical investigation of 4-chloro-6(phenylamino)-1,3,5-triazin-2-yl)asmino-4-(2,4-dichlorophenyl)thiazol-5-yl-diazenyl)phenyl as potential SARS-CoV-2 agent

The synthesis of 4-chloro-6(phenylamino)-1,3,5-triazin-2-yl)amino-4-(2,4 dichlorophenyl)thiazol-5-yl-diazenyl)phenyl is reported in this work with a detailed structural and molecular docking study on two SARS-COV-2 proteins: 3TNT and 6LU7. The studied compound has been synthesized by the condensation of cyanuric chloride with aniline and characterized with various spectroscopic techniques. The experimentally obtained spectroscopic data has been compared with theoretical calculated results achieved using high-level density functional theory (DFT) method. Stability, nature of bonding, and reactivity of the studied compound was evaluated at DFT/B3LYP/6-31 + (d) level of theory. Hyper-conjugative interaction persisting within the molecules which accounts for the bio-activity of the compound was evaluated from natural bond orbital (NBO) analysis. Adsorption, Distribution, Metabolism, Excretion and Toxicity (ADMET) properties of the experimentally synthesized compound was studied to evaluate the pharmacological as well as in silico molecular docking against SARS-CoV-2 receptors. The molecular docking result revealed that the investigated compound exhibited binding affinity of −9.3 and −8.8 for protein 3TNT and 6LU7 respectively. In conclusion, protein 3TNT with the best binding affinity for the ligand is the most suitable for treatment of SARS-CoV-2.

Olefin Metathesis Catalyzed by a Hoveyda-Grubbs-like Complex Chelated to Bis(2-mercaptoimidazolyl) Methane: A Predictive DFT Study

Although highly selective complexes for the cross-metathesis of olefins, particularly oriented toward the productive metathesis of Z-olefins, have been reported in recent years, there is a constant need to design and prepare new and improved catalysts for this challenging reaction. In this work, guided by density functional theory (DFT) calculations, the performance of a Ru-based catalyst chelated to a sulfurated pincer in the olefin metathesis was computationally assessed. The catalyst was designed based on the Hoveyda–Grubbs catalyst (SIMes)Cl₂Ru(=CH–o–OiPrC₆H₄) through the substitution of chlorides with the chelator bis(2-mercaptoimidazolyl)methane. The obtained thermodynamic and kinetic data of the initiation phase through side- and bottom-bound mechanisms suggest that this system is a versatile catalyst for olefin metathesis, as DFT predicts the highest energy barrier of the catalytic cycle of ca. 20 kcal/mol, which is comparable to those corresponding to the Hoveyda–Grubbs-type catalysts. Moreover, in terms of the stereoselectivity evaluated through the propagation phase in the metathesis of propene–propene to 2-butene, our study reveals that the Z isomer can be formed under a kinetic control. We believe that this is an interesting outcome in the context of future exploration of Ru-based catalysts with sulfurated chelates in the search for high stereoselectivity in selected reactions.

A straightforward method to quantify the electron-delocalizing ability of pi-conjugated molecules

Electronic delocalization is essential to the properties of pi-conjugated molecules. We introduce the inter-fragment delocalization index (IFDI) as an easy-to-use computational method for quantifying the electronic delocalization in pi-conjugated oligomers...

Polarisation of Electron Density and Electronic Effects: Revisiting the Carbon-Halogen Bonds

Electronic effects (inductive and mesomeric) are of fundamental importance to understand the reactivity and selectivity of a molecule. In this article, polarisation temperature is used as a principal index to describe how electronic effects propagate in halogeno-alkanes and halogeno-alkenes. It is found that as chain length increases, polarisation temperature decreases. As expected, polarisation is much larger for alkenes than for alkanes. Finally, the polarisation mode of the carbon-fluorine bond is found to be quite different and might explain the unusual reactivity of fluoride compounds.

Size-Dependent πg + πu Combination Band Intensities of Polyynes C2nH2 (n = 1-9) Analyzed by the Local CCH Bending and the Linear Response Functions

Polyynes (C_2nH₂) show the unusually strong π_g + π_u combination bands in the infrared absorption spectra. We calculated them as the first overtone of the local CCH bending; the strong intensities are interpreted as a consequence of the large-amplitude bending vibration of the acidic acetylenic hydrogen combined with the size-dependent π electron conjugation. Our theoretical calculations show that the absorption intensity increases steadily and their increase rate is gradually slowed down by increasing the number of acetylene units up to n = 9. However, the calculated vibrational wavenumber converges quickly in agreement with the experimental observation. The second-order electron density deformation caused by the local CCH bending was analyzed using the linear response functions, including the linear and nonlinear contributions, to explain the n dependence. The easily polarizable π electron density caused two kinds of deformation-dominant but dark δ_xx-yy type and minor but bright σ type. Both of them exhibit interesting zigzag sign alternations, consistent with the law of alternating polarity of Coulson and Longuet-Higgins. The electron density polarization in these intra- and interacetylene units induces a large axial component molecular dipole moment, contributing to the intensity that increases with n. The difference between the curvilinear and rectilinear bending coordinates is interpreted within the present theoretical scheme.

Zhang-Zhang Polynomials of Multiple Zigzag Chains Revisited: A Connection with the John-Sachs Theorem

Multiple zigzag chains Zm,n of length n and width m constitute an important class of regular graphene flakes of rectangular shape. The physical and chemical properties of these basic pericondensed benzenoids can be related to their various topological invariants, conveniently encoded as the coefficients of a combinatorial polynomial, usually referred to as the ZZ polynomial of multiple zigzag chains Zm,n. The current study reports a novel method for determination of these ZZ polynomials based on a hypothesized extension to John–Sachs theorem, used previously to enumerate Kekulé structures of various benzenoid hydrocarbons. We show that the ZZ polynomial of the Zm,n multiple zigzag chain can be conveniently expressed as a determinant of a Toeplitz (or almost Toeplitz) matrix of size m2×m2 consisting of simple hypergeometric polynomials. The presented analysis can be extended to generalized multiple zigzag chains Zkm,n, i.e., derivatives of Zm,n with a single attached polyacene chain of length k. All presented formulas are accompanied by formal proofs. The developed theoretical machinery is applied for predicting aromaticity distribution patterns in large and infinite multiple zigzag chains Zm,n and for computing the distribution of spin densities in biradical states of finite multiple zigzag chains Zm,n.

Graphical Transition Moment Decomposition and Conceptual Density Functional Theory Approaches to Study the Fundamental and Lower-Level Overtone Absorption Intensities of Some OH Stretching Vibrations

The investigation of electron density migrations caused by molecular structure changes is of central importance in various fields of chemistry. To address this topic in general and to study absorption intensities of vibrations, we analyze sensitive dipole moment functions (DMFs) of a molecule by combining the linear response function of conceptual DFT and bond dipoles separated by the quantum theory of atoms in molecules with a graphical transition moment decomposition scheme. The fundamental intensities of OH stretching vibrations depend strongly on the substituents but only weakly on the molecular conformations. Interestingly, in some alcohols, completely opposite trends have been observed for the lower-level overtone intensities: a weak substituent dependence but a stronger conformation dependence. It is well known that the formation of a hydrogen-bonded complex increases the OH stretching fundamental intensity, but less well known is the decrease in their overtone intensities. To investigate these characteristics comprehensively, we calculated their intensities (Δv = 1, 2, and 3) for conformers of ethanol and trifluoroethanol (TFE) and hydrogen-bonded phenol (PhOH) systems via the DFT method in the local mode model for the OH stretching coordinate ΔR. Their first and second derivatives of the electron density with respect to ΔR were calculated and interpreted using their bond moments. For ethanol and TFE, the OH, CC, and CH bond moments were found to make an important contribution to the molecular DMF derivatives parallel to the OH bond. The OH bond contributes only to the first derivative of DMF, and its conformational dependence is determined by the magnitude of the charge polarization of each structure. The electron density derivatives in the CC bond region were largely maintained during the internal rotation; thus, their conformation-dependent contributions were expressed by a geometrical factor of the CC bond direction. The CH bond at the antiperiplanar position of the OH bond was found to make a remarkably large contribution to the second derivative of DMF in the gauche conformer. The importance of electron density migration on substituents was also identified in the hydrogen-bonded phenol, in which the π-electron density change on the aromatic ring was clearly shown. This migration creates the DMF derivatives both perpendicular and parallel to the OH bond and strongly affects the absorption intensities. In all the cases, some bond moments on the substituents contribute to the first and second DMF derivatives in a structure-dependent manner, thus explaining their stereoelectronic effects.

Captodative Substitution Enhances the Diradical Character of Compounds, Reduces Aromaticity, and Controls Single-Molecule Conductivity Patterns: A Valence Bond Study

The present contribution uses a valence bond (VB) perspective to consider the captodative substitution strategy, a method to enhance the diradical character of (potentially aromatic) compounds. We confirm the qualitative reasoning that has generally been used to rationalize the diradical-character-enhancing effect of captodative substitution: this type of substitution scheme disproportionally stabilizes specific Dewar/diradical(oid) VB structures, thus increasing their weight in the full ground-state wave function. Furthermore, we assess the effect of captodative substitution on the aromaticity of the considered compound. We observe a clear trade-off between diradical character and aromaticity for our model systems: as one of these properties increases, the other decreases. This finding is especially significant within the field of single-molecule electronics because it enables unification of the previously observed inverse proportionality between the aromaticity of a compound and the magnitude of conductance through that molecule, with the observed proportionality between diradical character and the magnitude of conductance associated with a compound. To some extent, both properties, i.e., aromaticity and diradical character, appear to be the flip-sides of the same coin.

Global and local aromaticity of acenes from the information-theoretic approach in density functional reactivity theory

In this work, we report a systematic study on the global and local aromaticity of acenes using a series of model structures from 2-acene to 11-acene. A recently developed ansatz, an information-theoretic approach coached into density functional reactivity theory has been employed, which essentially provides different density functionals characterizing the molecular electron density distribution. Based on the correlation analysis of six conventional aromaticity indices with eight information-theoretic quantities, we examined the aromaticity of acenes from both global and local perspectives. From the global aromaticity viewpoint, our results suggest that different descriptors based on various physicochemical properties are intrinsically dependent. A novel laminated feature ruling local aromaticity of acenes has been unveiled, from which we found that the distance from the terminal rings plays the critical role. Based on the shape of the correlation plots between the conventional aromaticity indices and information-theoretic quantities, the latter could be separated into three subgroups. The seemingly contradictory results from global and local aromaticity perspectives not only present us the uniqueness of the acene systems but all demonstrate the effectiveness of the information-theoretic approach from density functional reactivity theory. Besides strengthening the validity of a series of new aromaticity descriptors, our results should lead to more clear insights into the chemical significance of the information-theoretic quantities.

Quantifying aromaticity with electron delocalisation measures

Aromaticity cannot be measured directly by any physical or chemical experiment because it is not a well-defined magnitude. Its quantification is done indirectly from the measure of different properties that are usually found in aromatic compounds such as bond length equalisation, energetic stabilisation, and particular magnetic behaviour associated with induced ring currents. These properties have been used to set up the myriad of structural-, energetic-, and magnetic-based indices of aromaticity known to date. The cyclic delocalisation of mobile electrons in two or three dimensions is probably one of the key aspects that characterise aromatic compounds. However, it has not been until the last decade that electron delocalisation measures have been widely employed to quantify aromaticity. Some of these new indicators of aromaticity such as the PDI, FLU, ING, and INB were defined in our group. In this paper, we review the different existing descriptors of aromaticity that are based on electron delocalisation properties, we compare their performance with indices based on other properties, and we summarise a number of applications of electronic-based indices for the analysis of aromaticity in interesting chemical problems.

Conceptual DFT: chemistry from the linear response function

Within the context of reactivity descriptors known in conceptual DFT, the linear response function (χ(r,r')) remained nearly unexploited. Although well known, in its time dependent form, in the solid state physics and time-dependent DFT communities the study of the "chemistry" present in the kernel was, until recently, relatively unexplored. The evaluation of the linear response function as such and its study in the time independent form are highlighted in the present review. On the fundamental side, the focus is on the approaches of increasing complexity to compute and represent χ(r,r'), its visualisation going from plots of the unintegrated χ(r,r') to an atom condensed matrix. The study on atoms reveals its physical significance, retrieving atomic shell structure, while the results on molecules illustrate that a variety of chemical concepts are retrieved: inductive and mesomeric effects, electron delocalisation, aromaticity and anti-aromaticity, σ and π aromaticity,…. The applications show that the chemistry of aliphatic (saturated and unsaturated) chains, saturated and aromatic/anti-aromatic rings, organic, inorganic or metallic in nature, can be retrieved via the linear response function, including the variation of the electronic structure of the reagents along a reaction path. The connection of the linear response function with the concept of nearsightedness and the alchemical derivatives is also highlighted.

Exploring Chemical Space with the Alchemical Derivatives

In this paper, we verify the usefulness of the alchemical derivatives in the prediction of chemical properties. We concentrate on the stability of the transmutation products, where the term "transmutation" means the change of the nuclear charge at an atomic site at constant number of electrons. As illustrative transmutations showing the potential of the method in exploring chemical space, we present some examples of increasing complexity starting with the deprotonation, continuing with the transmutation of the nitrogen molecule, and ending with the substitution of isoelectronic B-N units for C-C units and N units for C-H units in carbocyclic systems. The basis set influence on the qualitative and quantitative accuracies of the alchemical predictions was investigated. The alchemical deprotonation energy (from the second order Taylor expansion) correlates well with the vertical deprotonation energy and can be used as a preliminary indicator for the experimental deprotonation energy. The results of calculations for the BN derivatives of benzene and pyrene show that this method has great potential for efficient and accurate scanning of chemical space.

Charge sensitivity approach to mutual polarization of reactants: molecular mechanics perspective

Charge sensitivity analysis (CSA) in force-field atoms resolution was applied to describe the mutual polarization of reactants as well as charge-transfer (CT) effects. An inclusion complex of β-cyclodextrin with salicylic acid was used as a model system. Three CSA models were taken into account and verified on a Born–Oppenheimer molecular dynamics (BOMD) trajectory. The models differed in terms of the equilibrium conditions imposed on the system. It was demonstrated that mutual polarization is an important source of stabilization, in contrast to the results obtained from static charge calculations. The energy lowering induced by CT was small and comparable to the CT stabilization that occurs in hydrogen-bonded systems. All models correctly described the main topological features of the BOMD energy surface. CSA in force-field atoms resolution qualitatively reproduced the charge reorganization accompanying hydrogen-bond formation. It was shown that CSA parameters are very sensitive to the bond formation process, which suggests that they could be applied in reactive force fields as detectors of newly formed chemical bonds.

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σ, π aromaticity and anti-aromaticity as retrieved by the linear response kernel

The chemical importance of the linear response kernel from conceptual Density Functional Theory (DFT) is investigated for some σ and π aromatic and anti-aromatic systems. The effect of the ring size is studied by looking at some well known aromatic and anti-aromatic molecules of different sizes, showing that the linear response is capable of correctly classifying and quantifying the aromaticity for five- to eight-membered aromatic and anti-aromatic molecules. The splitting of the linear response in σ and π contributions is introduced and its significance is illustrated using some σ-aromatic molecules. The linear response also correctly predicts the aromatic transition states of the Diels-Alder reaction and the acetylene trimerisation and shows the expected behavior along the reaction coordinate, proving that the method is accurate not only at the minimum of the potential energy surface, but also in non-equilibrium states. Finally, the reason for the close correlation between the linear response and the Para Delocalisation Index (PDI), found in previous and the present study, is proven mathematically. These results show the linear response to be a reliable DFT-index to probe the σ and π aromaticity or anti-aromaticity of a broad range of molecules.