Empirical force-field and ab initio calculations on delocalized open chain cations

Force-field calculations are reported for large delocalized cations. The results for the geometries, heats of formation, and π-electron densities agree well with MP2(full)/6–31G^* ab initio calculations. Both methods give similar results for the distortion of the carbon skeletons of unsubstituted cations by hyperconjugating methyl groups. Because of the SCF treatment of π-interactions, the MMP2 force-field technique enables calculations of resonance energies in delocalized cations. The additional resonance stabilization produced by extending conjugation is directly related to the π-charge on the carbon at which a vinyl group is substituted. The good agreement of MMP2 results for nonbonded resonance effects in large delocalized cationic π-systems with ab initio data suggests that MMP2 can be used to study the influence of these interactions in cationic π-systems too large to be calculated by correlated ab initio methods. © 1997 by John Wiley & Sons, Inc.     

Partition of <Emphasis Type="Italic">π</Emphasis>-electrons between faces of polyhedral carbon aggregates

We report for the trivalent regular and semiregular polyhedra (three Platonic and seven Archimedean carbon polyhedra) the π-electron partition between rings of various sizes based on considering all their resonance structures. It was found that small odd-membered (3-and 5-membered) faces are assigned a lower share of π-electrons than that corresponding to equipartition (i.e., 1/3 of an electron for carbon atoms shared between three rings). In contrast, 4-membered rings obtain a larger share of π-electrons than that corresponding to equipartition.     

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.     

Towards the self-assembly of polyrotaxanes

The self-assembly of a number of rotaxanes, pseudorotaxanes, and a pseudopolyrotaxane based on the π-electron deficient cyclobis(paraquat-p-phenylene)^d̊ and threads and dumbbell components composed of π-electron rich hydroquinone rings incorporated symmetrically within polyether chains terminated in the case of the rotaxanes by adamantoyl stoppers.     

Effect of methyl and hydroxyl substituents on the π-electronic spectra and ionization potential of p-benzoquinone

SCF -LCAO -MO -CI semi-empirical π-electron calculations have been made of the first two singlet transitions and ionization potentials of hydroxy-, methyl- and hydroxy-methyl substituted p-benzoquinone, using a modified Pariser-Parr-Pople method. The various molecules could be divided into two classes on the basis of their first π-electron transition, namely, those in which the 3-position was occupied and others where this position was vacant.     

π-Electron currents in fixed π-sextet aromatic benzenoids

In view of different patterns of π-electron density currents in benzenoid aromatic compounds it is of interest to investigate the pattern of ring currents in various classes of compounds. Recently such a study using a graph theoretical approach to calculating CC bond currents was reported for fully benzenoid hydrocarbons, that is, benzenoid hydrocarbons which have either π-sextets rings or “empty” rings in the terminology of Clar. In this contribution we consider π-electron currents in benzenoid hydrocarbons which have π-electron sextets and C=C bonds fully fixed. Our approach assumes that currents arise from contributions of individual conjugated circuits within the set of Kekulé valence structures of these molecules.     

Theoretical studies on the diazacyclopentadienylidenes: An analysis of aromatic versus nonaromatic systems and singlet versus triplet reactivity

Ab initio molecular orbital calculations have been carried out on the various electronic states of 2,3- ( 6 ), 2,4- ( 7 ), 2,5- ( 8 ), and 3,4-diazacyclopentadienylidene ( 9 ) at the fully geometry optimized 6–31G* level, with single point calculations being carried out at the MP2/6–31G* level. The calculated geometries are interpreted in terms of the degree of occupancy and the nature of the π and σ-nonbonded MO's. At the 6–31G* level the five π-electron, π,σ-triplet states were calculated to be considerably lower in energy. At the MP2/6–31G* level, however, with 7 the six π-electron singlet state is calculated to lie only slightly above the five π-electron triplet (0.4 kcal mole⁻¹), whereas with 8 and 9 the aromatic six π-electron singlet states are calculated to be lower in energy (9.0 and 8.1 kcal mole⁻¹). With 3 and 9 the aromatic six π-electron σ-triplet states lie only 3.6 and 5.5 kcal mole⁻¹ above the lowest energy states. It is concluded that, in general, the energy gained by having an electron in a lower energy σ-type MO instead of a higher energy π MO effectively offsets the energy gained by having an aromatic π system. The results are discussed in terms of the observed chemistry of 6–9 and their substituted systems.     

3J(HH)?Pμ,ν correlation for planar 7-membered cyclic π-systems—structural effects on 3J(HH)

It is shown that sterically unperturbed vicinal HH coupling constants in planar 7-membered π-systems correlate linearly with the HMO π-bond order: ³J(HH) = 20.91P_μ,_ν–3.85 (r.m.s. error 0.26 Hz, correlation coefficient =0.988). Systematic deviations from this relationship which most probably originate from valence angle changes are found for fused π-systems containing rings of different size. Model calculations using the CNDO/2 method as well as finite perturbation theory and INDO wave functions support the experimental findings. An improvement of existing ³J(HH)? P_μ,_ν correlations for planar 6-membered rings is possible if CNDO/2 π-bond orders are used instead of HMO or PPP-SCF data.     

Guanidinium-Type resonance stabilization and its biological implications. I. the guanidine and extended-guanidine series

An unusual type of π-electron delocalization in Y-shaped molecules related to guanidine and its protonated form, the guanidinium ion, has been studied by ab initio methods at the STO -3G and 3-21G levels. Results are reported for tautomeric, rotameric, and protonated forms of the oxygen-substituted guanidine series (urea, carbamic, and carbonic acids); “extended-guanidine” (aminomethylene guanidine) including pseudocyclic forms; and simple ring systems in which the extended-guanidine group is incorporated (3-amino-1,2,4-triazole, 2,4-diaminopyrimidine). Both the guanidine and guanidinium type stabilizations have been characterized in terms of a number of structural and energetic parameters: degree of single/double bond character from bond lengths and π-bond orders, electron distributions, and protonation energies. The major finding is that the structural and energetic properties of the isolated extended-guanidinium group resemble those of the group when incorporated within 6-membered heterocyclic or heterobicyclic rings, although the details vary with the nature of the ring and possibility of reinforcement or interference with the substructure resonance from overall ring delocalization. The implications for stabilization of the protonated forms of some biologically important pteridines is discussed.     

Hydrogen bonding in simple π-electron systems II. Pyridine–pyrrol

Previous work in this laboratory concerning the properties of hydrogen bonds in the base pairs of DNA [1–6] has led to considerable interest in the properties of hydrogen bonds in π-electron systems. The first paper in this series [7] has investigated the usefulness of the LCAO –MO –SCF method and the Pariser–Parr–Pople approximation as applied to this problem, by calculation on the ideal pyridine–pyridinium complex. In this paper, a relation with experiment will be established by comparison of the results obtained from this method of calculation with the properties of the experimentally observable pyridine–pyrrol system.     

Wellenmechanische behandlung der protonisierung des äthylens unter berücksichtigung aller elektronen

The system C₂H₅⁺ has been investigated as ethyl cation and as protonated ethylene using the SCF –MO –LC (LCGO ) method. Equilibrium distances and angles have been estimated by different potential curves. No difference in total energy was found between the π- and the σ-complex.     

Synthesis and properties of azobenzocrown ethers with π-electron donor, or π-electron donor and π-electron acceptor group(s) on benzene ring(s)

New azobenzocrown ethers of differentiated size and with substituted benzene residues have been synthesized. These crown ethers possess π-electron donor, or π-electron donor-π-electron acceptor pair of functional group(s) in benzene ring(s) in the para position to azo-grouping. Their metal ion complexation abilities in solution were studied using UV-vis spectrophotometry. The X-ray structure of a 19-membered crown ether with 4-dimethylamino-4′-nitroazobenzene fragment has been solved.     

Molecular orbital calculations for f-orbital complexes: The dicyclooctatetraenylcerium(III) anion

INDO SCF calculations on the title complex indicate that, although the single f-electron is essentially localised on the metal, the metal 5d (e_1g and e_2g) orbitals interact significantly with the ligands and play a major role in determining the total energy.     

A Triply Negatively Charged Nanographene Bilayer with Spin Frustration

We report on the largest open-shell graphenic bilayer and also the first example of triply negatively charged radical π-dimer. Upon three-electron reduction, bilayer nanographene fragment molecule (C₉₆H₂₄Ar₆)₂ (Ar=2,6-dimethylphenyl) ( 1 ₂) was transformed to a triply negatively charged species 1 ₂^3.−, which has been characterized by single-crystal X-ray diffraction, electron paramagnetic resonance (EPR) spectroscopy and magnetic properties on a superconducting quantum interference device (SQUID). 1 ₂^3.− features a 96-center-3-electron (96c/3e) pancake bond with a doublet ground state, which can be thermally excited to a quartet state. It consists of 34 π-fused rings with 96 conjugated sp² carbon atoms. Spin frustration is observed with the frustration parameter f>31.8 at low temperatures in 1 ₂^3.−, which indicates graphene upon reduction doping may behave as a quantum spin liquid.     

The origin of global and macrocyclic aromaticity in porphyrinoids

The global and macrocyclic aromaticity of porphyrinoids was characterized using our graph theory of aromaticity. The sequential line plots of topological resonance energy (TRE) against the number of π-electrons (N(π)) for different porphyrinoids are similar with four major extrema to those for five-membered heterocycles. This supports the view that five-membered rings are the main origin of global aromaticity in porphyrinoids. Macrocyclic circuits contribute significantly to macrocyclic π-circulation but modestly to global aromaticity. Macrocyclic aromaticity/antiaromaticity in oligopyrrolic macrocycles can be predicted by formally applying Hückel's [4n + 2] rule to an annulene-like main macrocyclic conjugation pathway (MMCP). This bridged annulene model can be justified by examining the contribution of individual macrocyclic circuits to macrocyclic aromaticity. A Hückel-like rule of macrocyclic aromaticity was found for porphyrinoid species.     

NMR studies of conformations and dynamic processes—III : Cyclophanes with unsaturated bridges

Three cyclophanes, each displaying a different type of dynamic process, have been studied by NMR methods. The barriers to these processes are attributed mainly to the decrease in π-electron overlap between the benzene rings and adjacent double bonds which occurs in the transition state for each process. In [5₂] paracyclophanetetraene, two successive flippings of the benzene rings interconvert the two hydrogens in the methylene groups (Scheme 1). In tetramethyl [2₄] paracyclophanetetraene, the passage of one methyl group through the central cavity of the molecule interconverts two conformations of similar, but not equal, free energy (Scheme 2). In [2₆] orthoparacyclophanehexaene, the orthosubstituted rings change sides by passing through the centre of the cyclophane (Scheme 3).     

Effects of annulation on the mass spectral behaviour of bicyclo[4.3.0]-3-nonene derivatives: Keto esters and ketones

The fragmentation patterns of the title compounds are shown to depend on the nature of the ring annulation. On ionization the cis-annulated isomers lose a molecule of benzene in contrast to the corresponding trans isomers which do not. A mechanism involving a participation of the π-electron system in the cleavage of the 5-membered ring is suggested to explain the observed differences.     

A multi-configuration LCAO–MO study for complex unsaturated molecules. II. Application to the benzene cation

The method of the MC –LCAO –MO approach, described in the preceding paper, is further applied to the benzene cation. Through the iteration process the π-electron energies and the molecular shapes are computed for the ground and two lowest excited states of the cation in both D_6h and D_2h geometries. A remarkable fact obtained is that a comparatively small variation of the geometrical structure (c. 0.010 – 0.013 Å bond length difference) brings about a considerable change of the energy value (c. 0.85 – 1.25 eV). The π-electronic excitation energies obtained from the iteration process are compared with the transition energies calculated from the usual method in which the structures of the excited states are assumed to be the same as the corresponding ground state structures. The difference in the excitation energy between the cation and the anion, and the CI effect on the excited states, are discussed. It is found that the doubly excited configurations play an important role in CI , which is somewhat different from that of the singly excited configurations. The stabilization energy due to the Jahn–Teller distortion is estimated for the ground state of the cation.     

Macrocyclic Tetraethynylethene Molecular Scaffolding: Perethynylated aromatic dodecadehydro[18]annulenes,antiaromatic octadehydro[12]annulenes,and expanded radialenes

Tetraethynylethene (3,4-diethynylhex-3-ene-1,5-diyne) molecular scaffolding provided access to novel macrocyclic nanometer-sized C-rich molecules with unusual structural and electronic properties. Starting from cis-bis-deprotected cis-bis(trialkylsilyl)protected tetraethynylethenes, the per(silylethynyl)ated octadehydro[12]annulenes 1 and 2 and the corresponding dodecadehydro[18]annulenes 4 and 5 were prepared by oxidative Hay coupling. X-Ray crystal-structure analyses of (i-Pr)₃Si-protected 2 and Me₃Si-protected 4 showed that both annulene perimeters are perfectly planar. Electronic absorption spectral comparisons provided strong evidence that the macro rings in the deep-purple-colored 1 and 2 are antiaromatic (4n π-electrons), whereas those in yellow 4 and 5 are aromatic ((4n + 2) π-electrons). Although unstable in solution, the antiaromatic compound 2 gave high-melting crystals in which the individual octadehydro[12]annulene chromophores are isolated and stabilized in a matrix-type environment formed by the bulky (i-Pr)₃Si groups. Electrochemical studies demonstrated that the antiaromatic octadehydro[12]annulene 2 undergoes two stepwise one-electron reductions more readily that the aromatic chromophore 5 . This redox behavior is best explained by the formation of an aromatic (4n + 2) π-electron dianion from 2 , whereas 5 loses its aromaticity upon reduction. The Me₃Si derivative 4 was deprotected with borax in MeOH/THF to give the highly unstable hexaethynyl-dodecadehydro[18]annulene 6 , a C₃₀H₆ isomer and macrocyclic precursor to a two-dimensional all-C-network. Deprotection of 2 did not give isolable amounts of tetraethynyl-octadehydro[12]annulene 3 due to the extreme instability of the latter. Starting from dimeric and trimeric acyclic tetraethynylethene oligomers, a series of expanded radialenes were obtained. They possess large C-cores with silylethynyl-protected peripheral valences and can be viewed as persilylated C₄₀ ( 7 ), C₅₀ ( 8 ), and C₆₀ ( 9 ) isomers. These expanded C-sheets are high-melting, highly stable, soluble materials which were readily characterized by laser-desorption time-of-flight (LD-TOF) mass spectrometry. Due to inefficient macrocyclic cross-conjugation and/or non-planarity, the extent of π-electron delocalization in 7 – 9 is limited to the longest linearly conjugated π-electron fragment. In agreement with these properties, all three expanded radialenes exhibited similar redox behavior; they are difficult to oxidize but undergo several reversible one-electron reductions in similar potential ranges. Presumably, the reduced π-electron delocalization is also at the origin of the particularly high stability of 7 – 9 .