Sigma-aromaticity and sigma-antiaromaticity in saturated inorganic rings

The magnetic properties of a series of inorganic saturated rings, (SiH2)n, (GeH2)n, (NH)n, (PH)n, (AsH)n, On, Sn, and Sen (n = 3-6), exhibit zigzag behavior with ring size resembling that of aromatic and antiaromatic Hückel pi-systems and (CH2)n rings. Computed GIAO-SCF nucleus-independent chemical shifts (NICS) and localized (LMO) NICS analysis indicate that the sigma-ring electrons are chiefly responsible for this zigzag behavior. This evidence for sigma-aromaticity is further supported by theoretical strain energy (TSE). The Hückel 4n + 2/4n aromaticity/antiaromaticity rule for pi-electron systems applies well to the smaller saturated rings.     

Violations of the Hückel (4n + 2) Rule

In polycyclic conjugated hydrocarbons the Hückel (4n + 2)-rule may be violated, so that certain (4n + 2)-membcred rings cause thermodynamic destabilization. The structural conditions for the occurrence of such an effect are analyze d. Eight examples (of which seven are new) of non-b enzenoid hydrocarbons are put forward, in which the Hückel rule is disobeyed.     

Quantum mechanical designs toward planar delocalized cyclooctatetraene: a new target for synthesis.

Ab initio and hybrid density functional quantum mechanical computation are applied to the structure and energetics of a series of annelated cyclooctatetraenes. Tetrakis-cyclobuteno, perfluorocyclobuteno or bicyclo[2.1.1]hexeno annelations result in planar structures with distinct exo and endo valence tautomers of the double bonded cycle. The contribution of each basic annelation to the exo/endo relative energy is estimated. An additivity scheme for approximating the energy of a mixed system is developed and compared to the quantum mechanical prediction. Bis bicyclic annelation to the a and d positions creates "valence tautomeric frustration" and strongly perturbs the molecular structure. This phenomenon leads to a general design for a planar cyclooctatetraenes where the "delocalized" diradicaloid state is the minimum energy form. These compounds are seen as excellent targets for chemical synthesis.     

A Nonaromatic Thiophene‐Fused Heptalene and Its Aromatic Dianion

Heptalene, a nonaromatic, bicyclic 12 π‐electron system with a twisted structure, is of great interest with regard to its potential Hückel aromaticity in the two‐electron oxidized or reduced forms. The synthesis of thiophene‐fused heptalene 5 from the reductive transannular cyclization of bisdehydro[12]annulene 4 , and its solid‐state structure, which was confirmed by X‐ray crystallographic analysis, is presented. Chemical reduction of 5 readily generated the corresponding dianion, which was successfully isolated as [(K[2.2.2]cryptand)⁺]₂ 5 ^2?. The X‐ray crystallographic analysis of the dianion revealed a shallower saddle structure for the heptalene moiety and a lesser degree of bond alternation relative to 5 . ¹H NMR spectroscopy exposed the effect of a diamagnetic ring current on dianion 5 ^2?, which was corroborated by nucleus‐independent chemical shift (NICS) calculations. These results demonstrate that the heptalene dianion, containing 14 π‐electrons, does indeed exhibit pronounced degrees of Hückel aromaticity.     

Quantitative approach to hückel rule the relations between the cycles of a molecular graph and the thermodynamic stability of a conjugated molecule

Contribution of the rings to the total π-electron energy (CE) is calculated for a number of polycyclic conjugated hydrocarbons. The Hückel 4m+2 rule is tested quantitatively in this way. It is shown that (4m)-membered rings always destabilize, while (4m + 2)-membered rings almost always stabilize the molecule. The magnitude of this effect is, however, subject to considerable variations. The main factors which determine the magnitude of CE are discussed. Examples of the alternant hydrocarbons are found for which the (4m + 2)-membered cycles have a destabilizing effect, and therefore violate the Hückel rule. The odd membered cycles are shown to have a negligibly small effect on the stability of the conjugated molecules.     

Viability of Möbius Topologies in [26]‐ and [28]Hexaphyrins

Recently, hexaphyrins have emerged as a promising class of π‐conjugated molecules that display a range of interesting electronic, optical, and conformational properties, including the formation of stable Möbius aromatic systems. Besides the Möbius topology, hexaphyrins can adopt a variety of conformations with Hückel and twisted Hückel topologies, which can be interconverted under certain conditions. To determine the optimum conditions for viable Möbius topologies, the conformational preferences of [26]‐ and [28]hexaphyrins and the dynamic interconversion between the Möbius and Hückel topologies were investigated by density functional calculations. In the absence of meso substituents, [26]hexaphyrin prefers a planar dumbbell conformation, strongly aromatic and relatively strain free. The Möbius topology is highly improbable: the most stable tautomer is 33 kcal mol^?1 higher in energy than the global minimum. On the other hand, the Möbius conformer of [28]hexaphyrin is only 6.5 kcal mol^?1 higher in energy than the most stable dumbbell conformation. This marked difference is due to aromatic stabilization in the Möbius 4n electron macrocycle as opposed to antiaromatic destabilization in the 4n+2 electron system, as revealed by several energetic, magnetic, structural, and reactivity indices of aromaticity. For [28]hexaphyrins, the computed activation barrier for interconversion between the Möbius aromatic and Hückel antiaromatic conformers ranges from 7.2 to 10.2 kcal mol^?1, in very good agreement with the available experimental data. The conformation of the hexaphyrin macrocycle is strongly dependent on oxidation state and solvent, and this feature creates a promising platform for the development of molecular switches.     

Simple prediction of cycloaddition orientation: II—2+2 thermal cycloadditions. Scope and limitations of the method

In the accompanying paper, it has been suggested that, in a cycloaddition, the first σ bond to be formed is that corresponding to the greatest overlap stabilization. This rule has now been tested, successfully on over one hundred 2+2 cycloadditions.Comparisons of our method with other theoretical treatments are made and the reasons for the discrepancies pointed out.The choice of parameters (for Hückel calculations) or molecular geometries (for CNDO/2 calculations) is discussed. No particular advantage of CNDO/2 calculations over Hückel calculations has been observed.     

Momentum distribution of Hückel π electrons

The momentum distribution and related physical properties are examined for π molecular orbitals (MOs) of a conjugated hydrocarbon system obtained by the empirical Hückel method. Several general rules are derived and the momentum-space aspect of the Hückel π electron theory is clarified.     

Theoretical model for the polarization molecular and Hückel treatment of PhosphoCyclopentadiene in an external electric field: Hirschfeld study

In this study we relate the Hückel method and molecular polarization of PhosphoCyclopentadiene (P-cyclopentadiene) with respect to the Cyclopentadienyl, and its consequent separation of charges of particular set of conjugated diene systems. The Hückel method and Molecular Polarization of P-cyclopentadiene is expressed as a function of the induced polarizability of Cyclopentadienylin an external electric field, presenting a technique to express the molecular polarizabilities and Hückel method of diene systems as a function of another in an external electric field, using local quantum similarity index (LQSI) based on the Hirschfeld partitioning in the framework of conceptual density functional theory, this index was introduced in the molecular polarization of cyclopentadienyl in an external electric field and in the secular determinant of the Hückel method applied to the Cyclopentadienylin order to express the molecular polarization and Hückel method as a function of P-cyclopentadiene using six local similarity index: Overlap, Overlap-Interaction, Coulomb, Coulomb-Interaction, Overlap-Euclidian distance and Coulomb-Euclidian distance.The topo-geometrical superposition approach (TGSA) was used as method of alignment, which allows us to obtain high results in the proposed LQSIs, this method to be a straightforward procedure to cope with the problem of relative orientation of the molecules when evaluating, developing a new technique that will allow us to study structural systems that differ in one atom in its structure, and proposing methodologies for future studies on a much broader range of systems in which the Hückel method and molecular polarization of two species that differ only in one atom in its structure can be approximated in this way.     

Hückel theory applied to large linear and cyclic conjugated π-systems

By use of rotational symmetry (C_n-symmetry) a lower limit to the frontier orbital (HOMO-LUMO) gap in large molecules with linear and cyclic conjugated π-systems containing simple repetitive units has been calculated within the Hückel approxmation. The frontier orbitals are shown to be the same in series of cyclic oligomers and liner polymers containing the same repetitive units. The orbital gap is calculated from the repetitive units closed on themselves to give a ring of Hückel or, alternatively, Möbius topology depending on the number of conjugated π-electrons in a liner array between the ends of the repetitive unit. For 4n (4n+2) systems the small ring of Hückel (Möbius) topology will give the frontier orbitals.     

π-Systems in three dimensions

Highly symmetric, three-connected carbon clusters are treated as three-dimensional π-systems, using spherical harmonics to classify the orbitals. Simple Hückel calculations predict stable closed shells for neutral C₆₀ and C₇₀, in agreement with recent experimental observations. A previously proposed C₁₂₀ structure is unstable with respect to two C₆₀ clusters. Neutral C₂₀ and C₈₀ are not closed-shell in icosahedral symmetry. Inclusion of interaction between the exo π-systems and skeletal edge bonding does not change the predicted electron count.     

ESI‐MS/MS of expanded porphyrins: a look into their structure and aromaticity

Electrospray mass spectrometry/mass spectrometry was used to investigate the gas‐phase properties of protonated expanded porphyrins, in order to correlate those with their structure and conformation. We have selected five expanded meso‐pentafluorophenyl porphyrins, respectively, a pair of oxidized/reduced fused pentaphyrins (22 and 24 π electrons), a pair of oxidized/reduced regular hexaphyrins (26 and 28 π electrons) and a regular doubly N‐fused hexaphyrin (28 π electrons). The gas‐phase behavior of the protonated species of oxidized and reduced expanded porphyrins is different. The oxidized species (aromatic Hückel systems) fragment more extensively, mainly by the loss of two HF molecules. The reduced species (Möbius aromatic or Möbius‐like aromatic systems) fragment less than their oxidized counterparts because of their increased flexibility. The protonated regular doubly fused hexaphyrin (non‐aromatic Hückel system) shows the least fragmentation even at higher collision energies. In general, cyclization through losses of HF molecules decreases from the aromatic Hückel systems to Möbius aromatic or Möbius‐like aromatic systems to non‐aromatic Hückel systems and is related to an increase in conformational distortion. Copyright © 2016 John Wiley & Sons, Ltd.     

Interaction of the t-butylcalix[4]arene Anion with Ammonium Cations in Acetonitrile: Host–Guest Complexes or exo Counterions? A Molecular Dynamics Investigation

We report a theoretical study of the NR4+salts (R = H; Me; Et) of the t-butylcalix[4]arenemonooxyanion L- inacetonitrile solution, to compare the endocomplexes NR4+ inside the cone of thehost) with the exo ones. For a given cation, wefind that the complexes display structures of similartype in the gas phase and in acetonitrile solution.Intrinsically, the endo forms are more stablethan exo ones, but they are less well solvated.As a result, exo complexes are predicted to bemore stable than the endo ones in acetonitrile.In the gas phase and in solution, the exocomplexes of NMe4+ and NEt4+display interesting examples of fluctional intimateion pairs, where the cation oscillates between theoxygen lower rim region of L- and exo stacking with the phenolic rings ofL-. Based on free energy perturbation calculations,we compare endo NH4+/NMe4+complexes and find that the hypotheticalNH4+ complex is more stable in acetonitrile solution.     

Spectra of Conic Carbon Radicals

Conic carbon radicals with non-trivial automorphism groups are topologically possible when the curvature originates from 1, 3 or 5 pentagons in the otherwise hexagonal graphene sheet. By splitting determinants of quotient graphs, we determine the bonding nature of the last occupied and first unoccupied Hückel orbitals of the radicals constituting the three infinite series with the most plausible topologies. Each member of the series with three pentagons at the tip has one electron in the first anti-bonding orbital, each member of the series with one or five pentagons at the tip has one vacancy in the last bonding orbital, and none of the radicals have any un-bonding orbital. Within the limits of the Hückel model, this implies, respectively, stable conic cations and anions. The quotient graphs also give the collected Hückel energy for each of the one-dimensional irreducible representations of the point groups.     

Electron-rich bonding and the importance of s,p mixing as one moves across a period: a lesson from the LiSn system.

The electronic structure of an unusual LiSn phase (computed using band structure calculations in the framework of the extended Hückel tight binding theory) is the starting point for a general analysis of the variation of electron-rich multicenter bonding across a period. The LiSn crystal structure of Müller and Sch?fer in question contains 2D slabs of Sn atoms arranged as microscopic stairs and intercalated by Li atoms. Discrepancies between an electron count derived from a recent extension of the Zintl-Klemm rules to electron-rich systems (5(2/3) electrons) and the experimental one (5 electrons for the Sn sublattice) and other failures of chemical "common sense" emerge in the analysis. The key for interpretation of a series of puzzling results was found in the comparative analysis of the Sn net with other main group element hypervalent slabs. Increasing s,p-mixing as one moves from the right to the left side of the same row of the periodic table is responsible for these effects. The result is that a lower electron count is found in the Sn slabs relative to the one expected from the extended Zintl-Klemm theory. The effect should also occur in discrete molecules. We also showed that the Li atoms have a role in the determination of the final structure, not only because of their small size but also through the degree of the electron transfer to the Sn sublattice.     

On the shell structure and geometry of monovalent metal clusters

The Hückel model is used to study the electronic structure of monovalent metal clusters. In an fcc cluster the Hückel model gives an estimate to the electronic structure of a free electron cluster. It is shown that the surface faceting of the fcc cluster can destroy the electronic shell structure already when the cluster has about 100 electrons. In the Hückel model the icosahedral structure has smaller total energy than the fcc structures, from which the Wulff construction has the smallest energy already when the cluster has 600 atoms.     

The Nowotny chimney ladder phases: whence the 14 electron rule?

The late transition metal Nowotny chimney ladder phases (NCLs, T(t)E(m); T, groups 7-9; E, groups 13 and 14) follow a 14 electron rule: the total number of valence electrons per T atom is 14. In this paper, we extract a chemical explanation for this rule from extended Hückel calculations; we focus on RuGa(2), the parent NCL structure. A gap between filled and unfilled bands arises from the occupation of two Ga-Ga bonding/Ru-Ga nonbonding orbitals per RuGa(2), independent of k-point. In addition, the five Ru d levels are filled. Together this makes for 7 filled bands at each k-point, or 14 electrons per Ru. We discuss the connections between this 14 electron rule and the 18 electron rule of organometallic complexes.     

An Unusually Small Singlet–Triplet Gap in a Quinoidal 1,6‐Methano[10]annulene Resulting from Baird’s 4n π‐Electron Triplet Stabilization

Within the continuum of π‐extended quinoidal electronic structures exist molecules that by design can support open‐shell diradical structures. The prevailing molecular design criteria for such structures involve proaromatic nature that evolves aromaticity in open‐shell diradical resonance structures. A new diradical species built upon a quinoidal methano[10]annulene unit is synthesized and spectroscopically evaluated. The requisite intersystem crossing in the open‐shell structure is accompanied by structural reorganization from a contorted Möbius aromatic‐like shape in S₀ to a more planar shape in the Hückel aromatic‐like T₁. This stability was attributed to Baird’s Rule which dictates the aromaticity of 4n π‐electron triplet excited states.     

Debye–Hückel Contributions to the Gibbs Energy Interaction Parameters for Ternary Electrolyte + Non-Electrolyte + Water Systems

The Debye–Hückel and non-Debye–Hückel contributions to the Gibbs energy interaction parameters are investigated for electrolyte (E) + non-electrolyte (N) + water (W) systems. A method is proposed for calculating the interaction parameters, C _n ^DH,C _n ^N, and C _n ^T, which represent the Debye–Hückel, non-Debye–Hückel, and total contributions, respectively. Four ternary E + N + W systems are chosen and the interaction parameters are computed with different forms of the Debye–Hückel equation. Results show that: (1) the Gibbs energy interaction parameters between E and N can be divided into two parts: the Debye–Hückel contribution and the non-Debye–Hückel contribution, C _n ^T=C _n ^DH+C _n ^N; (2) the signs and magnitudes of the Debye–Hückel contribution to the interaction parameters, C _n ^DH, depend mainly on the change in the dielectric constant of the solvent due to the addition of the non-electrolyte into the solvent; and (3) when the addition of the non-electrolyte only affects slightly the dielectric constant of the solvent, C ₁^DH (indicating the Debye–Hückel contribution to the interaction parameter for E + N) has a very small value and consequently can be neglected. In general, C ₁^DH is large, even larger than C ₁^N. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.