Aromaticity and antiaromaticity in 4-, 6-, 8-, and 10-membered conjugated hydrocarbon rings

Recently, we presented a molecular orbital (MO) model of aromaticity that explains, in terms of simple orbital-overlap arguments, why benzene (C(6)H(6)) has a regular structure with delocalized double bonds whereas the geometry of 1,3-cyclobutadiene (C(4)H(4)) is distorted with localized double bonds. Here, we show that the same model and the same type of orbital-overlap arguments also account for the irregular and regular structures of 1,3,5,7-cyclooctatetraene (C(8)H(8)) and 1,3,5,7,9-cyclodecapentaene (C(10)H(10)), respectively. Our MO model is based on accurate Kohn-Sham DFT analyses of the bonding in C(4)H(4), C(6)H(6), C(8)H(8), and C(10)H(10) and how the bonding mechanism is affected if these molecules undergo geometrical deformations between regular, delocalized ring structures and distorted ones with localized double bonds. The propensity of the pi electrons is always to localize the double bonds, against the delocalizing force of the sigma electrons. Importantly, we show that the pi electrons nevertheless determine the localization (in C(4)H(4) and C(8)H(8)) or delocalization (in C(6)H(6) and C(10)H(10)) of the double bonds.     

Aromaticity: an ab initio evaluation of the properly cyclic delocalization energy and the pi-delocalization energy distortivity of benzene

A complete active space self-consistent field (CASSCF) calculation of the pi system of a conjugated molecule enables one to define optimal valence pi and pi* molecular orbitals (MOs). One may define from them a set of atom-centered orthogonal pi orbitals, one per carbon atom, and the resulting upper multiplet is used to define the pi-electron delocalization energy. This quantity is confirmed to be slightly distortive, i.e., to prefer bond-alternated geometries. One may also define strongly localized bond MOs corresponding to a Kekule structure and then perturb the associated strongly localized single determinant under the effect of the delocalization between the bonds and of the electronic correlation. The third order of perturbation introduces the contribution of the cyclic circulation of the electrons around the benzene ring, i.e. the aromatic energy contribution. Its value is about 1.5 eV. It is antidistortive, but remains important under bond alternation. The cyclic correlation effects are of minor importance.     

All-metal aromatic clusters M4(2-) (M = B, Al, and Ga). Are π-electrons distortive or not?

The π-electrons in benzene, the quintessential aromatic molecule, were previously shown to be distortive, i.e., they prefer localized double bonds alternating with single bonds. It is the σ-electrons that force the double bonds to delocalize, leading to a regular, D(6h) geometry. Herein, we computationally investigate the double-bond localizing or delocalizing propensities of σ- and π-electrons in the archetypal all-metal aromatic cluster Al(4)(2-) and its second- and fourth-period analogs B(4)(2-) and Ga(4)(2-), using Kohn-Sham molecular orbital (MO) theory at BP86/TZ2P in combination with quantitative bond energy decomposition analyses (EDA). We compare the three all-metal aromatic clusters with the structurally related organic species C(4)H(4)(2+), C(4)H(4), and C(4)H(4)(2-). Our analyses reveal that the π-electrons in the group-13 M(4)(2-) molecules have a weak preference for localizing the double bonds. Instead, the σ-electrons enforce the regular D(4h) equilibrium geometry with delocalized double bonds.     

Electron affinities of Al(n) clusters and multiple-fold aromaticity of the square Al4(2-) structure

The concept of aromaticity was first invented to account for the unusual stability of planar organic molecules with 4n + 2 delocalized pi electrons. Recent photoelectron spectroscopy experiments on all-metal MAl(4)(-) systems with an approximate square planar Al(4)(2-) unit and an alkali metal led to the suggestion that Al(4)(2-) is aromatic. The square Al(4)(2-) structure was recognized as the prototype of a new family of aromatic molecules. High-level ab initio calculations based on extrapolating CCSD(T)/aug-cc-pVxZ (x = D, T, and Q) to the complete basis set limit were used to calculate the first electron affinities of Al(n)(), n = 0-4. The calculated electron affinities, 0.41 eV (n = 0), 1.51 eV (n = 1), 1.89 eV (n = 3), and 2.18 eV (n = 4), are all in excellent agreement with available experimental data. On the basis of the high-level ab initio quantum chemical calculations, we can estimate the resonance energy and show that it is quite large, large enough to stabilize Al(4)(2-) with respect to Al(4). Analysis of the calculated results shows that the aromaticity of Al(4)(2-) is unusual and different from that of C(6)H(6). Particularly, compared to the usual (1-fold) pi aromaticity in C(6)H(6), which may be represented by two Kekulé structures sharing a common sigma bond framework, the square Al(4)(2-) structure has an unusual "multiple-fold" aromaticity determined by three independent delocalized (pi and sigma) bonding systems, each of which satisfies the 4n + 2 electron counting rule, leading to a total of 4 x 4 x 4 = 64 potential resonating Kekulé-like structures without a common sigma frame. We also discuss the 2-fold aromaticity (pi plus sigma) of the Al(3)(-) anion, which can be represented by 3 x 3 = 9 potential resonating Kekulé-like structures, each with two localized chemical bonds. These results lead us to suggest a general approach (applicable to both organic and inorganic molecules) for examining delocalized chemical bonding. The possible electronic contribution to the aromaticity of a molecule should not be limited to only one particular delocalized bonding system satisfying a certain electron counting rule of aromaticity. More than one independent delocalized bonding system can simultaneously satisfy the electron counting rule of aromaticity, and therefore, a molecular structure could have multiple-fold aromaticity.     

Tetradehydroadamantane-1,3,5,7-di- and tetracations and their helium and hydride inclusion complexes: spherical aromaticity and evidence for a bonding interaction between carbon and helium

The unusual stability of the experimentally known 1,3-dehydro-5,7-adamantyl dication was previously explained by four-center two-electron aromaticity with three-dimensional (tetrahedral) topology. Magnetic criteria (ACID and ring-current analysis) now demonstrate that there is also a very strong contribution from hyperconjugation with all six methylene bridges. The delocalized system of electrons thus includes all valence electrons, and the structure, therefore, should rather be described as a spherically aromatic 50-electron system. The corresponding Td-symmetric tetracation with 48 electrons is antiaromatic and not a minimum structure. With a He atom or a hydride ion at the center of the cage, the tetracation is predicted to form a kinetically stable complex. Magnetic criteria demonstrate that the antiaromaticity is greatly reduced, and a bond analysis hints at bonding interactions between He (and H-) and the carbon atoms of the adamantane cage.     

Quantification of the (anti)aromaticity of fulvalenes subjected to pi-electron cross-delocalization

Fulvalenes 3-12 were theoretically studied at the ab initio level of theory. For the global minima structures, the occupation of the bonding (pi)C=C orbital of the interring C=C double bond obtained by NBO analysis quantitatively proves pi-electron cross-delocalization resulting in, at least partially, 2- or 6pi-electron aromaticity and 8pi-electron antiaromaticity for appropriate moieties. The cross-conjugation was quantified by the corresponding occupation numbers and lengths of the interring C=C double bonds, while the aromaticity or antiaromaticity due to cross-delocalization of the pi-electrons was visualized and quantified by through-space NMR shielding surfaces.     

Valence bond descriptions of benzene and cyclobutadiene and their counterparts with localized bonds

Geometry optimizations have been performed for benzene and cyclobutadiene and for the corresponding moieties with nonresonating double bonds, viz. 1,3,5‐cyclohexatriene and 1,3‐cyclobutadiene. The calculations were done using the valence bond self‐consistent field method including orbital optimization. Both strictly local and delocalized p‐like orbitals were used for the π system, which influences the strengths of the π bonds. The calculations result in geometries and resonance and stabilization energies for benzene and cyclobutadiene, which are compared with theoretical models of aromaticity. The importance of resonance is discussed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Symmetry breaking in benzene and larger aromatic molecules within generalized valence bond coupled cluster methods

The origin of symmetry breaking (SB) in benzene in generalized valence bond methods is investigated within a coupled cluster formalism that correlates all valence electrons. Retention of a limited number of pair correlation amplitudes (as in the perfect- and imperfect-pairing models) that incompletely describes interpair correlations leads to symmetry breaking as the orbitals and amplitudes are optimized. Local correlation models that are exact for one, two, and three interacting pairs at the doubles excitation level are compared against the exact pair correlation treatment, which correlates four interacting pairs at once in the connected double substitution operator. For simplicity, this comparison is performed with a second-order model of electron correlation, which is reasonably faithful to the infinite-order result. The significant SB known for the one-pair model (perfect pairing) is not eliminated at the two-pair level, but is virtually eliminated at the three-pair level. Therefore, a tractable hybrid model is proposed, which combines three-pair correlations at the second-order level and infinite-order treatment for the strong imperfect-pairing correlations involving one and two-pair correlations. This model greatly reduces SB in benzene and larger delocalized pi systems such as naphthalene and the phenalenyl cation and anion. The resulting optimized orbitals are localized in the sigma space but exhibit significant delocalization in the pi space. This means that correlation effects associated with different resonance structures are treated in a more balanced way than if the pi orbitals localize, leading to reduced SB.     

Predicting an Antiaromatic Benzene Ring in the Ground State Caused by Hyperconjugation

Benzene, the prototype of aromatics, has six equivalent C?C bonds (1.397 Å), which are intermediate between a C?C double bond and a C?C single bond. For over 80 years, chemists have spent much effort on freezing a localized structure to obtain a distorted bond‐length alternating benzene ring in the ground state, leading to various localized trisannelated benzene rings. However, most of the central benzene rings are still aromatic or nonaromatic. Here we report an antiaromatic benzene ring caused by hyperconjugation. Specifically, symmetric annulation of 5,5‐difluorocyclopentadiene results in an antiaromatic benzene ring, which is supported by various aromaticity indices, including nucleus‐independent chemical shift, anisotropy of the induced current density, π‐separated electron‐localization function and heat of hydrogenation. Our findings highlight a strong power of hyperconjugation, a “weak” interaction in organic chemistry, paving the way for designing and realizing more novel (anti)aromatics.     

New procedure to evaluate aromaticity at the density functional theory,Hartree–Fock,and post‐self‐consistent field levels

The spatial exchange interaction, arising from the exchange‐type two‐electron integrals ( ) between two different groups P and Q, is another driving force for the delocalization of π‐electrons besides orbital charge‐transfer and exchange interactions. We have developed a new combination program for restricted geometry optimization, in which all of the orbital and spatial interactions among isolated groups were excluded from the localized geometry of a conjugated molecule. This was achieved by deleting particular Fock elements and the 15 types of exchange‐type two‐electron integrals, ensuring that the corresponding π‐electrons are completely localized within their respective groups and the π‐orbitals are fully localized. The extra stabilization energy (ESE) of benzene is ?36.3 kcal/mol (B3LYP/6‐31G*), and the level of density functional theory, Hartree–Fock, and post‐self‐consistent field (Møller–Plesset 2, configuration interaction singles and doubles, and singles and doubles coupled‐cluster) and the basis sets have slight effect on the ESE. Based on the comparisons between our procedure, Morokuma's energy decomposition analysis and the block‐localized wave function method, it was confirmed that our program calculates reliable results. The nonaromaticity of acyclic polyenes and antiaromaticity of cyclobutadiene and planar cyclooctatetraene were also estimated. Comparison of the C? C single bond lengths in the ground state with its π‐localized geometries showed that shortening of the single bonds in acyclic polyenes and butadiyne should be attributed to different hybridization, demonstrating that the effect of π‐delocalization on single bonds is so small as to be negligible. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Femtosecond laser ionization of organic amines with very low ionization potentials: relatively small suppressed ionization features

We examined the femtosecond nonresonant ionization of organic amines with vertical ionization potentials as low as 5.95 eV. The quantitative evaluation of suppressed ionization relative to the single active electron approximation model was done by comparing the saturation intensity, I(sat), in experiments and theory. ADK theory was found to be useful in predicting the ionization yield in the I(sat) scale within a factor of 2, even for molecules with very low ionization potentials. The degree of suppression was, however, smaller than that of benzene. The localization of electrons on the nitrogen atom was found to affect the ionization behavior under the strong laser field. The delocalized pi electrons in benzene could not follow the laser field adiabatically, while those in localized molecular orbitals could. In addition, the growth of a tunneling barrier due to the screening effect in amines may be relatively smaller than that in benzene.     

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.     

Borazine: to be or not to be aromatic

Aromaticity of borazine, which has been subject of controversial discussions, is addressed. Beside a short review on aromaticity of borazine we report a detailed analysis of two molecular fields, the induced magnetic field (B ^ind) and the electron localization function (ELF). The induced magnetic field of borazine shows a long-range shielding cone perpendicular to the molecular plane, as in benzene, but lower in magnitude. Contrary to benzene, borazine shows two weakly paratropic regions, one of them inside the ring, and the second one enveloping the boron atoms. It is necessary to separate σ and π contributions to identify whether borazine exhibits π-aromatic character comparable to benzene. Nucleus-independent chemical shift (NICS) isolines show that the σ electrons are much stronger localized than π electrons, their local paramagnetic contributions generate a short-range response and a paratropic (deshielding) region in the ring center (similar to an anti-aromatic response). Three regions can be identified as chemically meaningful domains exhibiting an internally strong electron delocalization (ELF = 0.823). Borazine may be described as a π aromatic compound, but it is not a globally aromatic species, as the electronic system is not as delocalized as in benzene. Dedicated to the 70th birthday of Prof. Tadeusz Marek Krygowski.     

Chemical graph theory and n-center electron delocalization indices: a study on polycyclic aromatic hydrocarbons

Relations between aromaticity indices derived from chemical graph theory and those based on 6-center electron delocalization are investigated for a series of polybenzenoid hydrocarbons. Aromatic stabilization obtained by means of the effective scaled electron delocalization is highly correlated to the resonance energy, RE, obtained both from SCF MO calculations and conjugated ring circuits model. Local aromaticity of benzene rings is discussed using two different criteria, in one of them aromaticity is just given by the cyclic pi-electron conjugation of the ring, whereas terms involving more than one ring are also considered in the other one. Indices derived from chemical graph theory and those obtained from the 6-center electron delocalization give rise to the same local aromaticity. Moreover, 6-center electron delocalization provides more quantitative information.     

A simple computational scheme for obtaining localized bonding schemes and their weights from a CASSCF wave function

We devise and apply a simple computational scheme for obtaining localized bonding schemes and their weights from a CASSCF wave function. These bonding schemes are close to resonance structures drawn by chemists. Firstly, a CASSCF wave function is computed. Secondly, the CASSCF computation is repeated but now the delocalized complete active space MOs are substituted by Weinhold's localized natural atomic orbitals. In this way the original CASSCF wave function is represented by a sequence of Slater determinants composed of localized natural atomic orbitals. Thus, a standard CASSCF wave function can be reinterpreted in terms of a local picture. To test the method we obtain localized bonding schemes and their weights for the ground and the pi-pi* excited state of ethylene. Moreover, bonding schemes and their weights are derived for the ground, the 1(1)B(u), and the 2(1)Ag pi-pi* excited states of trans-butadiene. The large weight bonding schemes are shown to be a qualitative indicator for the known photochemistry of butadiene. The remarkable stability of the Arduengo carbene is discussed by obtaining bonding schemes that indicate a stabilizing delocalization of the pi electrons. We illustrate that the large weight bonding schemes are in line with the observed reactivity of the Arduengo carbene.     

Comprehensive analysis of chemical bonding in boron clusters

We present a comprehensive analysis of chemical bonding in pure boron clusters. It is now established in joint experimental and theoretical studies that pure boron clusters are planar or quasi-planar at least up to twenty atoms. Their planarity or quasi-planarity was usually discussed in terms of pi-delocalization or pi-aromaticity. In the current article, we demonstrated that one cannot ignore sigma-electrons and that the presence of two-center two-electron (2c--2e) peripheral B--B bonds together with the globally delocalized sigma-electrons must be taken into consideration when the shape of pure boron cluster is discussed. The global aromaticity (or global antiaromaticity) can be assigned on the basis of the 4n+2 (or 4n) electron counting rule for either pi- or sigma-electrons in the planar structures. We showed that pure boron clusters could have double (sigma- and pi-) aromaticity (B3-, B4, B5+, B6(2+), B7+, B7-, B8, B(8)2-, B9-, B10, B11+, B12, and B13+), double (sigma- and pi-) antiaromaticity (B6(2-), B15), or conflicting aromaticity (B5-,sigma-antiaromatic and pi-aromatic and B14, sigma-aromatic and pi-antiaromatic). Appropriate geometric fit is also an essential factor, which determines the shape of the most stable structures. In all the boron clusters considered here, the peripheral atoms form planar cycles. Peripheral 2c--2e B--B bonds are built up from s to p hybrid atomic orbitals and this enforces the planarity of the cycle. If the given number of central atoms (1, 2, 3, or 4) can perfectly fit the central cavity then the overall structure is planar. Otherwise, central atoms come out of the plane of the cycle and the overall structure is quasi-planar.     

Symmetry restrictions as starting point for the determination of geometric representations and the dynamics of cyclic π systems

A quasiclassical‐state approach was developed for probing π bonding and delocalization energies focused on benzene. A more general picture is now given for neutral n π‐conjugated cyclic systems with a geometry distortion from D_nh into D_1/2nh (n=4,6,8,…,16), which results in a new aromaticity‐antiaromaticity criterion. For n=6 and 8 the corresponding divalent charged systems were studied in relation to zero‐field splittings of the triplet ground state and geometry, respectively. Attention is also given to antiaromatic π‐conjugated systems focused on the cyclopropenyl anion, the cyclopentadienyl cation, and the cycloheptatrienyl anion and their relaxed states. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 641–650, 2000     

Contrast of Bonding and Characters for C6, B3N3, C6H6 and B3N3H6 Molecules

Through integrative consideration of NICS, MO, MOC and NBO, we precisely investigated delocalization and bonding characters of C₆, C₆H₆, B₃N₃ and B₃N₃H₆ molecules. Firstly, we originally discovered and testified that C₆ cluster was sp² hybridization. Negative NICS values in 0 and 1 Å indicated that C₆ had δ and Π aromaticity. Secondly, B₃N₃ with sp² hybridization had obvious δ aromaticity. Finally, WBI values approved that there were delocalization in C₆, C₆H₆ and B₃N₃ molecules, but B₃N₃H₆ structure did not have delocalization with the WBI 1.0. Moreover, total WBI values of carbon, boron and nitrogen atoms were four, three and three, respectively. Namely, the electrons of B₃N₃H₆ and B₃N₃ were localized in nitrogen atoms and they did not form delocalized bonding. In a word, bonding characters of carbon, boron and nitrogen atoms were dissimilar although the molecules composed of carbon, boron and nitrogen were regarded as isoelectronic structures.