Multidimensionality of delocalization indices and nucleus independent chemical shifts in polycyclic aromatic hydrocarbons

The aromaticity and local-aromaticity of a large set of polycyclic aromatic hydrocarbons (PAHs) is studied using multicenter delocalization indices from generalized population analysis and the popular nucleus independent chemical shift (NICS) index. A method for the fast computation of the NICS values is introduced, using the so-called pseudo-pi-method. A detailed examination is made of the multidimensional nature of aromaticity. The lack of a good correlation between the NICS and the multicenter delocalization indices is reported and the grounds discussed. It is shown through a thorough statistical analysis that the NICS values arise not only from local aromaticity of the benzenoid rings, but also from other circuits. It is shown that the NICS indices do not reveal the individual aromatic nature of a specific ring, contrary to the delocalization indices.     

Is Free Cyclooctatetraene Dianion an Aromatic System? A Quantum Chemistry Study

To investigate whether free cyclooctatetraene dianion (COT^2?) is aromatic, quantum chemistry methods were used to optimize its structure. Based on the optimized structures, the natural population analysis (NPA) charge, bond order, delocalization energy, nucleus‐independent chemical shift (NICS), and harmonic oscillator model of aromaticity (HOMA) values were computed by DFT‐B3LYP method with basis set 6‐311++G**, which shows that COT^2? is not aromatic as it is not planar and has different bond lengths and bond orders, smallest delocalization energy and positive NICS values. To further confirm the finding, the changes of NICS and energy against ring distortion angle were scanned. The COT^2? has positive NICS values all along the angle from 180° to 120° while other aromatic systems always have negative values. The energy scanning suggests that COT^2? should have the weakest capability to maintain its planar structure. All the calculations strongly indicate that COT^2? is not aromatic. This study also suggests that NICS scan might be a good approach to judge aromaticity.     

Probing the aromaticity in 2,3-pyrido-annulated N-heterocyclic carbene and its heavier analogues

The aromaticity in 2,3-pyrido-annulated 1,3,2λ²-diazatetroles C₅H₃N(NR)₂E^II (E^II = C, Si, Ge, Sn, Pb) was studied using a set of experimental and calculated criteria: UV-VIS, Raman, ISE, NICS, GIMIC and EDDB. The data obtained indicate either a slight decrease in aromaticity (NICS, GIMIC, ISE methods) or equal aromaticity (UV-VIS, ISE methods) compared to benzo-annulated analogues C₆H₄(NR)₂E. The π-aromaticity increases down the group from Si to Pb.     

Method and basis set dependence of the NICS indexes of aromaticity for benzene

The role of theory level in prediction of benzene magnetic indexes of aromaticity is analysed and compared with calculated nuclear magnetic shieldings of ³He used as NMR probe. Three closely related nucleus‐independent chemical shift (NICS) based indexes were calculated for benzene at SCF‐HF, MP2, and DFT levels of theory and the impact of basis set on these quantities was studied. The changes of benzene NICS(0), NICS(1), and NICS(1)zz parameters calculated using SCF‐HF, MP2 and several density functionals were within 1 to 3 ppm. Similar deviations between magnetic indexes of aromaticity were observed for values calculated with selected basis sets. Only very small effect of polar solvent on benzene aromaticity was predicted. The ³He nuclear magnetic isotropic shielding (σ) and its zz‐components (σ_zz) of helium atom approaching the centre of benzene ring from above produced similar curves versus benzene‐He distance to NICS parameters calculated for similarly moving Bq ghost atom. We also propose an experimental verification of NICS calculations by designing the ³He NMR measurement for benzene saturated with helium gas or in low temperature matrices.     

Local aromaticity in polyacenes manifested by individual proton and carbon shieldings: DFT mapping of aromaticity

Exponential dependencies between locally calculated geometric and magnetic indexes of aromaticity, harmonic oscillator model of aromaticity (HOMA) and nucleus independent chemical shifts (NICS)(0), NICS(1) and NICS(1)zz, and the number of conjugated benzene rings in linear acenes, from benzene to decacene were observed at B3LYP/6-311+G** level of theory. Correlations between HOMA and NICS indexes showed exponential dependencies and were fitted with simple three-parameter function. Similar correlations between both indexes of aromaticity and proton and carbon nuclear isotropic shieldings of individual acene rings were observed. Contrary to proton data, the predicted ¹³C nuclear isotropic shieldings of carbon atoms belonging to inner rings in polyacenes were less shielded, indicating lower aromaticity and therefore, higher reactivity.     

Can Substituted Cyclopentadiene Become Aromatic or Antiaromatic?

Cyclopentadiene derivatives with electronegative (F, Cl) or electropositive (H(3)Si, Me(3)Si) bis-5,5-substituents were studied at the B3LYP/6-311G* level of theory. It was found that there is no special stabilization or destabilization for any of the derivatives; the energetic effects that were previously attributed to aromatic stabilization or antiaromatic destabilization are the result of interactions in the reference systems. A nucleus-independent chemical shift (NICS) scan study at the HF-GIAO/6-311+G* theoretical level of these and similar derivatives suggest that they all show different magnitudes of diamagnetic ring current. None of the derivatives shows a paramagnetic ring current. Thus, cyclopentadienes are neither aromatic nor antiaromatic. It is also concluded that a diamagnetic ring current is perhaps necessary but certainly not a sufficient condition for aromaticity. The NICS scan procedure describes the type of ring current in the system, whereas a single isotropic NICS value (i.e., NICS(1)) may wrongly assign the type of ring current. It is shown that neither NICS(1) nor the NICS scan procedure can be used as a single aromaticity criterion.     

Sandwich Complexes of the As_4～(2-) Aromatic Ring with Some Transition Metals

The equilibrium geometries,energies,harmonic vibrational frequencies,and nucleus independent chemical shifts(NICS) of the new type sandwich structures [As4MAs4]n-(M = Fe,Co,Ni,Ru,Rh,Pd,Os,Ir and Pt;n = 0,1 or 2) are investigated at the B3LYP level.All the [As4MAs4]n-species adopt staggered(D4d) conformations as their stable structures and eclipsed(D4h) conformations as their transition states,and once the sandwich complexes are formed,the As42- square properties remain unchanged.The NICS calculation confirms that the complexes of Fe,Co,and Ni are aromatic with negative NICS values,and those of Ru,Rh,and Ir exhibit slight aromaticity,while those of Pd,Os,and Pt show slight antiaromaticity.     

全金属负离子团簇Ga42-、In42-芳香性的磁特征与多重芳香性

The optimized geometries, frequencies, and total electronic energies of two all-metal dianionic clusters Ga42- , In42- are calculated at the B3LYP, B3PW91, and MP2 levels of theory. There are two stable structures for each Ga42- , In42- species. For Ga42- , In42- species the square isomers are the most stable. On the basis of these computed stable structures we focus on two magnetic properties: magnetic susceptibility anisotropy and nucleus-independent chemical shift (NICS) for the square planar Ga42- , In42- isomers, which are calculated with B3LYP and HF methods. The computed results of NICS show that the square planar Ga42- , In42- isomers possess strong aromaticity. The detailed molecular orbital analysis for the two isomers further reveals that the two square planar Ga42- , In42- isomers have multiple-fold aromaticity: one delocalized π MOs and two delocalized σ MOs, which play important role in explaining the special stability of these all-metal square clusters.     

Application of AIM parameters at ring critical points for estimation of pi-electron delocalization in six-membered aromatic and quasi-aromatic rings

The AIM parameters at the ring critical point (the electron density and its Laplacian, the total electron energy density and both its components, potential and kinetic electron energy densities), have been intercorrelated with aromaticity indices: the geometry-based HOMA and the magnetism-based NICS, NICS(1), and NICS(1)(zz). A set of 33 phenylic rings having possibly a diversified aromatic character, and a set of 20 quasi-rings formed by intramolecular hydrogen and lithium bonds, have been taken into consideration. It has been found that the density of total electron energy, H, may serve as a new quantitative characteristic of pi-electron delocalization. The dependences between H values and aromaticity indices are correlated (cc(H/HOMA)=0.99, cc(H/NICS(1)zz)=0.95).     

Nucleus Independent Chemical Shift (NICS) at Small Distances from the Molecular Plane: The Effect of Electron Density

When close to the molecular plane, the behavior of nucleus independent chemical shift (NICS) as a function of the distance from the molecular plane deviates from its behavior at larger distances. By using a dense grid of NICS-probes (BQs) it is shown that, when close to the molecular plane, maximal (absolute) NICS values are obtained above the atoms. These maxima move towards the center as the grid is elevated until the (absolute) maximum NICS is obtained at the center and stay there when the grid is further elevated. It is shown that this behavior is a result of the current density, which is influenced by the electron density, according to the Biot-Savart law, which, in turn, causes the induced magnetic field measured by the NICS. It is thus concluded that if magnetic aromaticity is studied, the NICS calculations should be carried out at a large enough distance so that only the π-ring current affects the NICS. At distances ≥2 Å, NICS(r)_π,zz=A+B*C^r. Using non-linear correlation for obtaining A, B and C and extrapolate to NICS(1)_π,zz and NICS(1.7)_π,zz is recommended as measures for aromaticity.     

The delocalization index as an electronic aromaticity criterion: application to a series of planar polycyclic aromatic hydrocarbons

This work introduces a new local aromaticity measure, defined as the mean of Bader's electron delocalization index (DI) of para-related carbon atoms in six-membered rings. This new electronic criterion of aromaticity is based on the fact that aromaticity is related to the cyclic delocalized distribution of pi-electrons. We have found that this DI and the harmonic oscillator model of aromaticity (HOMA) index are strongly correlated for a series of six-membered rings in eleven planar polycyclic aromatic hydrocarbons. The correlation between the DI and the nucleus-independent chemical shift (NICS) values is less remarkable, although in general six-membered rings with larger DI values also have more negative NICS indices. We have shown that this index can also be applied, with some modifications, to study of the aromaticity in five-membered rings.     

Sandwich Complexes of the As42-Aromatic Ring with Some Transition Metals

The equilibrium geometries, energies, harmonic vibrational frequencies, and nuc- leus independent chemical shifts (NICS) of the new type sandwich structures [As4MAs4]n- (M = Fe, Co, Ni, Ru, Rh, Pd, Os, Ir and Pt; n = 0, 1 or 2) are investigated at the B3LYP level.All the [As4MAs4]n- species adopt staggered (D4d) conformations as their stable structures and eclipsed (D4h) conformations as their transition states, and once the sandwich complexes are formed, the As42- square properties remain unchanged.The NICS calculation confirms that the complexes of Fe, Co, and Ni are aromatic with negative NICS values, and those of Ru, Rh, and Ir exhibit slight aromaticity, while those of Pd, Os, and Pt show slight antiaromaticity.     

Local aromaticity in polycyclic aromatic hydrocarbons: electron delocalization versus magnetic indices

The local aromaticity of benzenoid rings is examined by means of the Polansky index (P) and generalized population analysis (GPA). The results are found to agree very well with recently published circuit-condensed ring currents and magnetic-energetic aromaticity indices, but no correlation is found with nucleus independent chemical shifts (NICS). This is usually seen as a manifestation of the more general multidimensional nature of aromaticity. This paper examines the sources for the observed correlations, showing that some indices give conflicting results because they inherently reflect different phenomena.     

Theoretical studies on the structures,properties, and aromaticities of fluorinated arsabenzenes

The electronic structures and properties of the fluorinated arsabenzenes series have been investigated using the basis set 6–311+G(d,p) and hybrid density functional theory. The basic measures of aromatic character derived from molecular orbitals and magnetic criteria (anisotropic susceptibilities and nucleus-independent chemical shifts) are considered. The energy criteria suggest that the F3, F36, H36, and H3 isomers are the most stable isomers in the mono-, di-, tri-, and tetrafluorinated species, respectively. Analysis of χ_aniso and the HOMO-LUMO gaps showed that these were not compatible with NICS data. The NICS values show that aromaticity is greater in the fluorinated derivatives.     

四同芳香性转烯及其羰基硼衍生物

运用G03W程序, 在高精度理论水平(B3P86/6-311＋G**)下, 对母体转烯(Hypostrophene)及其BCO衍生物的单态、三态、开壳层单态的Cope重排体系进行了理论研究: 对体系进行了相应的结构优化和频率计算, 并进一步计算了体系的重排势垒、反应能量、核独立化学位移值等理论参数. 文中首次提出具有四同芳香性的实例: 转烯的Cope重排过渡态. 计算同时表明BCO取代CH的行为使得进行Cope重排的反应物和过渡态的离域性、芳香性以及稳定性都得到很大的促进, 这可以从前线轨道的成键以及延伸方面得到合理的解释. 所得结果进一步验证了BCO基团的稳定性效应.     

Dinickelaferrocene: A Ferrocene Analogue with Two Aromatic Nickeloles Realized by Electron Back-Donation from Iron

The first example of ferrocene analogues with two transition-metal metallole ligands of the general formula (η⁵-C₄R₄M)₂Fe in a sandwich structure are reported. Specifically, dinickelaferrocene 2 , a type of dimetallametallocene, is efficiently synthesized from the reaction of dilithionickelole 1 with FeBr₂ or FeCl₂, presumably via a redox process, and is subjected to detailed experimental (single-crystal X-ray structural analysis, ICP-OES, magnetometry, ⁵⁷Fe Mössbauer, XPS) and theoretical (MOs, CDA, NICS, ICSS, and AICD) characterizations. Unlike ferrocene and its Cp ligands, the aromaticity of dinickelaferrocene and its nickelole ligands is accomplished by electron back-donation from the Fe 3d orbitals to the π* orbitals of nickelole. Taken together, this work describes a new class of metallaferrocene sandwich complexes and provides a novel approach to effect aromaticity that will contribute to further development of metallocene chemistry.     

The NICS‐XY‐Scan: Identification of Local and Global Ring Currents in Multi‐Ring Systems

Nucleus‐independent chemical shift (NICS)‐based methods are very popular for the determination of the induced magnetic field under an external magnetic field. These methods are used mostly (but not only) for the determination of the aromaticity and antiaromaticity of molecules and ions, both qualitatively and quantitatively. The ghost atom that serves as the NICS probe senses the induced magnetic field and reports it in the form of an NMR chemical shift. However, the source of the field cannot be determined by NICS. Thus, in a multi‐ring system that may contain more than one induced current circuit (and therefore more than one source of the induced magnetic field) the NICS value may represent the sum of many induced magnetic fields. This may lead to wrong assignments of the aromaticity (and antiaromaticity) of the systems under study. In this paper, we present a NICS‐based method for the determination of local and global ring currents in conjugated multi‐ring systems. The method involves placing the NICS probes along the X axis, and if needed, along the Y axis, at a constant height above the system under study. Following the change in the induced field along these axes allows the identification of global and local induced currents. The best NICS type to use for these scans is NICS_πZZ, but it is shown that at a height of 1.7 Å above the molecular plane, NICS_ZZ provides the same qualitative picture. This method, namely the NICS‐XY‐scan, gives information equivalent to that obtained through current density analysis methods, and in some cases, provides even more details.     

Neural networks as a tool to classify compounds according to aromaticity criteria

Aromaticity is a fundamental concept in chemistry, with many theoretical and practical implications. Although most organic compounds can be categorized as aromatic, non-aromatic, or antiaromatic, it is often difficult to classify borderline compounds as well as to quantify this property. Many aromaticity criteria have been proposed, although none of them gives an entirely satisfactory solution. The inability to fully arrange organic compounds according to a single criterion arises from the fact that aromaticity is a multidimensional phenomenon. Neural networks are computational techniques that allow one to treat a large amount of data, thereby reducing the dimensionality of the input set to a bidimensional output. We present the successful applications of Kohonen's self-organizing maps to classify organic compounds according to aromaticity criteria, showing a good correlation between the aromaticity of a compound and its placement in a particular neuron. Although the input data for the training of the network were different aromaticity criteria (stabilization energy, diamagnetic susceptibility, NICS, NICS(1), and HOMA) for five-membered heterocycles, the method can be extended to other organic compounds. Some useful features of this method are: 1) it is very fast, requiring less than one minute of computational time to place a new compound in the map; 2) the placement of the different compounds in the map is conveniently visualized; 3) the position of a compound in the map depends on its aromatic character, thus allowing us to establish a quantitative scale of aromaticity, based on Euclidean distances between neurons, 4) it has predictive power. Overall, the results reported herein constitute a significant contribution to the longstanding debate on the quantitative treatment of aromaticity.     

Extended Bis(benzothia)quinodimethanes and Their Dications: From Singlet Diradicaloids to Isoelectronic Structures of Long Acenes

Extended bis(benzothia)quinodimethanes and their dications were synthesized as stable species. The neutral compounds mainly have a quinoidal structure in the ground state but show increased diradical character with extension of the central quinodimethane unit. The dications exhibit similar electronic absorption spectra, NMR spectra, NICS values, and diatropic ring currents to their aromatic all‐carbon acene analogues and thus can be regarded as genuine isoelectronic structures of pentacene, hexacene, and heptacene, respectively. Our research gave some insights into the design and synthesis of stable longer acene analogues.