QTAIM N-center delocalization indices as descriptors of aromaticity in mono and poly heterocycles

The implementation of the n-center electron delocalization indices, n-DIs, and n-order electron localization indices, n-LIs, within the framework of the quantum theory of atoms in molecules, QTAIM, is performed. n-DIs are shown to be very useful to study the local aromaticity in monocyclic and polycyclic compounds. Total and pi n-DIs from n=4 to 7 were computed for a series of typical 4, 5, 6, and 7-center aromatic and antiaromatic rings. For n>or=5 the pi n-DI accounts for the 95% of the total n-DI and can be employed alone to measure the aromaticity. A scaling factor on the n-DIs is required in order to compare the aromaticity of [5c-6e] and [6c-6e] rings, the same correction allows to estimate the relative aromatic stabilization of polycyclic compounds using the sum of its values for individual rings. This is called Effective Scaled Electron Delocalization, ESED. The comparison with other aromaticity indices reflects a good correlation between ESED and both resonance energies, and HOMA indices. The most important differences between scaled pi n-DIs and NICS(0) indices are found for compounds that contain rings with different number of centers or pi electrons.     

Electronic structures, intramolecular interactions, and aromaticity of substituted 1-(2-iminoethylidene) silan amine: a density functional study

The intramolecular hydrogen bond, molecular structure, π electrons delocalization, and vibrational frequencies in 1-(2-iminoethylidene) silan amine and its derivatives have been investigated by means of density functional method with 6-311++G** basis set, in gas phase, water, and carbon tetrachloride solutions. The obtained results showed that the hydrogen bond strength is mainly governed by resonance variations inside the chelate ring induced by the substituent groups. Furthermore, the topological properties of the electron density distributions for N–H···N intramolecular hydrogen bond were analyzed in terms of the Bader's theory of atoms in molecules. On the other hand, the aromaticity of the ring formed is measured using several well-established indices of aromaticity such as nucleus-independent chemical shift, harmonic oscillator models of the aromaticity, para-delocalization index, average two-center indices, aromatic fluctuation index, and π-fluctuation aromatic index. Natural population analysis data, the electron density and Laplacian properties, as well as γ(NH) and ν(NH) were further used for estimation of the hydrogen bonding interactions and the forces driving their formation.     

σ Aromaticity Dominates in the Unsaturated Three‐Membered Ring of Cyclopropametallapentalenes from Groups 7–9: A DFT Study

Aromaticity, an old but still fantastic topic, has long attracted considerable interest of chemists. Generally, π aromaticity is described by π‐electron delocalization in closed circuits of unsaturated compounds whereas σ‐electron delocalization in saturated rings leads to σ aromaticity. Interestingly, our recent study shows that σ aromaticity can be dominating in an unsaturated three‐membered ring (3MR) of cyclopropaosmapentalene. An interesting question is raised: Can the σ aromaticity, which is dominant in the unsaturated 3MR, be extended to other cyclopropametallapentalenes? If so, how could the metal centers, ligands, and substituents affect the σ aromaticity? Here, we report a thorough theoretical study on these issues. The nucleus‐independent chemical shift calculations and the anisotropy of the current‐induced density plots reveal the dominant σ aromaticity in these unsaturated 3MRs. In addition, our calculations show that substituents on the 3MRs have significant effects on the σ aromaticity, whereas the ligand effect is particularly small.     

How Does Aromaticity Rule the Thermodynamic Stability of Hydroporphyrins?

Several measures of aromaticity including energetic, magnetic, and electron density criteria are employed to show how aromatic stabilization can explain the stability sequence of hydroporphyrins, ranging from porphin to octahydroporphin, and their preferred hydrogenation paths. The methods employed involve topological resonance energies and their circuit energy effects, bond resonance energies, multicenter delocalization indices, ring current maps, magnetic susceptibilities, and nuclear-independent chemical shifts. To compare the information obtained by the different methods, the results have been put in the same scale by using recently proposed approaches. It is found that all of them provide essentially the same information and lead to similar conclusions. Also, hydrogenation energies along different hydrogenation paths connecting porphin with octahydroporphin have been calculated with density functional theory. It is shown by using the methods mentioned above that the relative stability of different hydroporphyrin isomers and the observed inaccessibility of octahydroporphin both synthetically and in nature can be perfectly rationalized in terms of aromaticity.     

Interplay of Hückel and Möbius Aromaticity in Metal-Metal Quintuple Bonded Complexes of Cr,Mo, and W with Amidinate Ligand: Ab initio DFT and Multireference Analysis**

The aromaticity of metal-metal quintuple bonded complexes of the type M₂L₂ (M=Cr, Mo, and W; L=amidinate) are studied employing gauge including magnetically induced ring current (GIMIC) analysis and electron density of delocalized bonds (EDDB). It is found that the complexes possess two types of aromaticity: i) Hückel aromaticity through delocalization of ligand π electrons with metal-metal δ-bond-forming 6 conjugated electrons (4π and 2δ) ring; ii) Craig-Möbius aromaticity through delocalization of π electrons of both the ligands with metal d-orbitals in Craig type orientation forming 10π electrons ring with a double twist. Extended transition state natural orbital chemical valence (ETS-NOCV) and canonical molecular orbital natural chemical shielding (CMO-NCS) analysis confirm the Craig-Möbius type arrangement of the orbitals. Furthermore, the unprecedented Hückel and Möbius type aromaticity is confirmed from the plot of the current pathways using 3D line integral convolution (3D-LIC) plots. The metal-metal bond order also increases down the group as justified from the complete active space self-consistent field (CASSCF) analysis. Due to an increase in the π and δ electron conjugation, both the Hückel and Möbius aromaticity increase down the group.     

Theoretical study of changes in pi-electron delocalization in the analogues of an ortho-hydroxy schiff base when the proton is replaced with Li+ or BeH+

Molecular geometries of ortho-hydroxy Schiff base in keto-enamine and enol-imine tautomeric forms, its anion, and their derivatives in which H+ was replaced with Li+ or BeH+ were optimized at the B3LYP/6-311+G level of theory. Isodesmic reactions for estimating delocalization due to H-bonding or cation chelating were calculated. Geometry-based aromaticity index HOMA and magnetism-based NICS1(zz) index were used to estimate pi-electron delocalization. Keto-enamine tautomer exhibits low aromaticity in the ring and a relatively high pi-electron delocalization in the quasi-ring. The reverse was found for enol-imine tautomer. The Li+ and BeH+ derivatives showed a relatively high pi-electron delocalization in the ring and in the quasi-ring. This may be interpreted by an extension of the electron delocalization path in the pi-electron system through low-lying unoccupied p-type orbitals of Li+ and BeH+ cations.     

High‐Field NMR Spectroscopy Reveals Aromaticity‐Modulated Hydrogen Bonding in Heterocycles

From DNA base pairs to drug–receptor binding, hydrogen (H‐)bonding and aromaticity are common features of heterocycles. Herein, the interplay of these bonding aspects is explored. H‐bond strength modulation due to enhancement or disruption of aromaticity of heterocycles is experimentally revealed by comparing homodimer H‐bond energies of aromatic heterocycles with analogs that have the same H‐bonding moieties but lack cyclic π‐conjugation. NMR studies of dimerization in C₆D₆ find aromaticity‐modulated H‐bonding (AMHB) energy effects of approximately ±30 %, depending on whether they enhance or weaken aromatic delocalization. The attendant ring current perturbations expected from such modulation are confirmed by chemical shift changes in both observed ring C−H and calculated nucleus‐independent sites. In silico modeling confirms that AMHB effects outweigh those of hybridization or dipole–dipole interaction.     

σ‐Aromaticity in an Unsaturated Ring: Osmapentalene Derivatives Containing a Metallacyclopropene Unit

In general, aromaticity can be clarified as π‐ and σ‐aromaticity according to the type of electrons with major contributions. The traditional π‐aromaticity generally describes the π‐conjugation in fully unsaturated rings whereas σ‐aromaticity may stabilize fully saturated rings with delocalization caused by σ‐electron conjugation. Reported herein is an example of σ‐aromaticity in an unsaturated three‐membered ring (3 MR), which is supported by experimental observations and theoretical calculations. Specifically, when the 3 MR in cyclopropaosmapentalene is cleaved by ethane through two isodesmic reactions, both of them are highly endothermic (+29.7 and +35.0 kcal mol^?1). These positive values are in sharp contrast to the expected exothermicity, thus indicating aromaticity in the 3 MR. Further nucleus‐independent chemical shift and anisotropy of the current‐induced density calculations reveal the nature of σ‐aromaticity in the unsaturated 3 MR.     

Aromaticity and stability going in opposite directions: An energetic,structural, magnetic and electronic study of aminopyrimidines

The relation between molecular energetics and aromaticity was investigated for the interaction between the amino functional group and the nitrogen atoms of the pyridine and pyrimidine rings, using experimental thermodynamic techniques and computational geometries, enthalpies, chemical shifts, atomic charges and the Quantum Theory of Atoms in Molecules. 2,4-diaminopyrimidine and 2,4,6-triaminopyrimidine were studied by static bomb combustion calorimetry and Knudsen effusion technique. The derived gaseous-phase enthalpies of formation together with the enthalpies of formation of the three isomers of aminopyridine reported in the literature, were compared with the calculated computationally ones and extended to other diamino- and triaminopyrimidine isomers using the MP2/6-311++G(d,p) level of theory.The results were analyzed in terms of enthalpy of interaction between substituents and, due to the absence of meaningful stereochemical hindrance, strong inductive effects, or intramolecular hydrogen bonds according to QTAIM results, the resonance electron delocalization plays an almost exclusive role in the very exothermic enthalpies obtained. Therefore, this enthalpy of interaction was used as an experimental energetic measure of resonance effects and analyzed in terms of aromaticity. It was found that more conjugation between substituents means less aromaticity according to the magnetic (NICS) and electronic (Shannon) criteria, but more aromaticity according to the geometric (HOMA) criterion.     

Interplay between hydrogen-bond formation and multicenter pi-electron delocalization: intramolecular hydrogen bonds

The specific case of intramolecular hydrogen bonds assisted by pi-electron delocalization is thoroughly investigated using multicenter delocalization analysis. The effect of the pi-electron delocalization on the intramolecular hydrogen-bond strength is determined by means of the relative molecular energies of "open" and "closed" structures, calculated at the B3LYP/6-311++G(d,p) level of theory. These relative energies are compared to variations in the multicenter electron delocalization indices and covalent hydrogen-bond indices, which are shown to correlate very well with the relative strength of the intramolecular hydrogen bonds studied. The multicenter electron delocalization indices and covalent bond indices have been computed using the quantum theory of atoms in molecules approach. The hydrogen bonds are formed with oxygen, nitrogen, or sulfur as acceptor atom, which are also the atoms considered to be bonded to the donor hydrogen. Malonaldehyde is taken as reference; the substitution of oxygen by other atoms at the acceptor and donor positions and the effect of the aromaticity have been studied. The results shown here match perfectly with the qualitative expectations derived from the resonance models. In addition, they provide a quantitative picture of the role played by the pi-electron delocalization on the relative strength of intramolecular hydrogen bonds.     

Characterization of pericyclic reactions using multicenter electron delocalization analysis.

This work investigates the applicability of multicenter delocalization analysis to the characterization of pericyclic reactions. The results indicate that multicenter delocalization indices are a powerful tool for studying concerted processes, allowing the characterization of aromatic transition states with a significant increase in the electron delocalization. Moreover, an advantage over magnetic-based indices is that multicenter delocalization indices are not influenced by local electron currents but by the electron delocalization along the multiple (n) centers, and provide, in a quantitative sense, more reliable results. A thorough comparison with magnetic-based indices is carried out for the trimerization reaction of acetylene. Tracking the values of multicenter delocalization indices along the reaction path allows investigation of the nature of concerted mechanisms. Six-center electron delocalization displays a maximum at the transition state of the Diels-Alder reaction, whereas a similar maximum of four-center electron delocalization is slightly displaced to butadiene for the ring opening of cyclobutene. The profile of multicenter electron delocalization indices along the reaction path of [2+2] cycloaddition of ketene to ethene shows the presence of the two independent mechanisms that agree with the two HOMO/LUMO orbital interactions previously proposed to dominate this reaction.     

Latin American contributions to quantum chemical topology

We survey the contributions from Latin American theoretical chemists to the field of quantum chemical topology (QCT) over nearly the last 30 years with emphasis on the developments and applications of the quantum theory of atoms in molecules (QTAIM). Applications of QCT in the fields of excited states, electron delocalization, chemical bond, aromaticity, conformational analysis, spectroscopic properties, and chemical reactivity are presented. We also consider the coupling of QTAIM with time-dependent density functional theory, the virial theorem in the Kohn-Sham method and the inclusion of electron dynamical correlation in the interacting quantum atoms method using coupled cluster and multi-configurational densities. Additionally, we describe the development of efficient algorithms for the calculation of topological properties derived from the electron density. This review is aimed not only at providing an account of the contributions to QCT in Latin America but also at stimulating guides for further progress in the field.     

Ab initio and DFT studies on 1-(thionitrosomethylene) hydrazine: conformers, energies, and intramolecular hydrogen-bond strength

In the current study, we present an intramolecular HB, molecular structure, π-electrons delocalization and vibrational frequencies analysis of 25 possible conformers of 1-(thionitrosomethylene) hydrazine by means of DFT (B3LYP), MP2 methods in conjunction with the 6-311++G** and augmented correlation-consistent polarized-valence triple-zeta basis sets and G2MP2 theoretical level. The influence of the solvent on the stability order of conformers and the strength of intramolecular hydrogen-bonding was considered using the Tomasi’s polarized continuum model. Statistical analyses of quantitative definitions of aromaticity, nucleus independent chemical shift, harmonic oscillator model of aromaticity, aromatic fluctuation index, and the π-electron delocalization parameter (Q) as a geometrical indicator of a local aromaticity, evaluated for this conformers. Further verification of the obtained transition state structures were implemented via intrinsic reaction coordinate (IRC) analysis. Calculations of the ¹H NMR chemical shift at GIAO/B3LYP/6-311++G** levels of theory are also presented. The calculated highest occupied molecular orbital (MO) and lowest unoccupied MO energies show that charge transfer occur within the molecule. Hydrogen-bond energies for H-bonded conformers were obtained from Espinosa method and the natural bond orbital theory and the atoms in molecules theory were also applied to get a more precise insight into the nature of such H-bond interactions.     

Comparison of the AIM delocalization index and the Mayer and fuzzy atom bond orders

In this paper the behavior of three well-known electron-sharing indexes, namely, the AIM delocalization index and the Mayer and fuzzy atom bond orders are studied at the Hartree-Fock level. A large number of five-membered ring molecules, containing several types of bonding, constitute the training set chosen for such purpose. A detailed analysis of the results obtained shows that the three indexes studied exhibit strong correlations, especially for homonuclear bonds. The correlation is somewhat poorer but still significant for polar bonds. In this case, the bond orders obtained with the Mayer and fuzzy atom approaches are normally closer to the formally predicted bond orders than those given by the AIM delocalization indexes, which are usually smaller than those expected from chemical intuition. In some particular cases, the use of diffuse functions in the calculation of Mayer bond orders leads to unrealistic results. In particular, noticeable trends are found for C-C bonds, encouraging the substitution of the delocalization index by the cheaper fuzzy atom or even the Mayer bond orders in the calculation of aromaticity indexes based on the delocalization index such as the para-delocalization index and the aromatic fluctuation index.     

Pros and cons of σ -aromaticity

A discussion of σ-aromaticity requires a distinction between σ-conjugation, σ-electron delocalization, and σ-bond delocalization, all of which can be considered as prerequisites of σ-aromatic character. All molecules with three or more atoms encounter σ-conjugative interactions. Also, all σ-electrons are delocalized if the term delocalization is taken in its quantum theoretical meaning. However, σ-conjugation and σ-electron delocalization do not necessarily imply σ-bond delocalization. - One can distinguish between three different modes of σ-delocalization: ribbon delocalization in acyclic molecules and larger rings, surface delocalization in small rings, and volume delocalization in cage compounds. Surface delocalization of σ-electrons is found to lead to σ-bond delocalization. An example is cyclopropane. Bonding in cyclopropane can only be described in terms of nonclassical 2-electron 3-center and 4-electron 3-center bonds. Application of the criteria used to define π-aromaticity reveals that the properties of cyclopropane are in line with these criteria and that the term σ-aromaticity cannot be rejected on the grounds that aromaticity is restricted to π-electrons. The pros and cons of using the term σ-aromaticity in chemical discussions are presented.     

Electron delocalization and aromaticity variations in the stacked nucleic acid base pairs

A newly developed exchange-correlation functional (MPWB1K) in density functional theory has been applied to evaluate the electron delocalization of individual fragments in the stacking interaction between nucleic acid bases (NABs). Electronically and structural-based indices have been employed to investigate the aromaticity variation during stacking interaction. A quantitative study of NABs in their isolated and stacked forms reveals that stacking interaction causes a decrease in bond delocalization. It is shown that the decrease in the aromaticity is accompanied by local decrease in two-center delocalization indices within the pyrimidine rings. We found that the aromaticity exhibits a similar trend for NABs in both their isolated and stacked forms. Moreover, it is indicated that aromatic fluctuation index is more sensible index to delineate the aromaticity variation during stacking interaction.

     

Local aromaticity of [n]acenes, [n]phenacenes, and [n]helicenes (n = 1-9)

The local aromaticity of the six-membered rings in three series of benzenoid compounds, namely, the [n]acenes, [n]phenacenes, and [n]helicenes for n = 1-9, has been assessed by means of three probes of local aromaticity based on structural, magnetic, and electron delocalization properties. For [n]acenes our analysis shows that the more reactive inner rings are more aromatic than the outer rings. For [n]phenacenes, all indicators of aromaticity show that the external rings are the most aromatic. From the external to the central ring, the local aromaticity varies in a damped alternate way. The trends for the [n]helicene series are the same as those found for [n]phenacenes. Despite the departure from planarity in [n]helicenes, only a very slight loss of aromaticity is detected in [n]helicenes as compared to the corresponding [n]phenacenes. Finally, because of magnetic couplings between superimposed six-membered rings in the higher members of the [n]helicenes series, we have demonstrated that the NICS indicator of aromaticity artificially increases the local aromaticity of their most external rings.     

Enhanced aromaticity of the transition structures for the diels-alder reactions of quinodimethanes: evidence from ab initio and DFT computations

The Diels-Alder reactions of various quinodimethanes with ethylene are studied by means of ab initio molecular orbital and density functional theory (DFT) to show the effect of aromaticity on the reaction path. The calculations reveal that these reactions are both kinetically and thermodynamically much more favored than the prototype butadiene-ethylene Diels-Alder reaction due to the aromatization process in the transition state (TS) and product. A progressive aromaticity gain is noticed during the reaction, and hence the partial pi-delocalized peripheral diene ring function is coupled with the six-electron sigma,pi-delocalized cyclic unit resulting in an enhanced aromaticity of the TS. The magnetic criteria such as magnetic susceptibility exaltation and nucleus independent chemical shift provide definitive evidence for and fully support the aromatization process and the aromaticity of the TS. The extent of sigma-pi delocalization and the bond make-break at the TS are consistent with each other, and this is strongly influenced by the adjacent pi-aromatization process. Moreover, the aromaticity trends in the resulting TSs and products parallel the activation and reaction energies; the extent of aromatization increases with increasing reaction rate and exothermicity. This confirms that aromaticity is the driving factor governing cycloadditions involving quinodimethanes.