Some answers to frequently asked questions about the distortive tendencies of π-electronic system

The paper reviews briefly the various computational strategies, which have been devised by different groups to probe the symmetrizing vs distortive propensities of the π-bonding species of polyenes. All methods point to the same conclusion that the π-bonding components of benzene, allyl, aromatic annulenes and related species have intrinsic distortive tendencies; these species maintain bond-equalized geometries due to the symmetrizing driving force of the corresponding σ frames. Some frequently asked questions, that deal with the compatibility of the π-distortivity scenario with the greater body of experimental data regarding aromatic stability and π-delocalization, are addressed. Many of these questions are immediately answered, once the notion is accepted that delocalized π-systems possess a duality: their π-component is distortive and at the same time resonance stabilized relative to the localized structure with the same geometry. The notion of distortive π-electronic components of polyenes is shown to find a natural place in the wider context of a unified model of electronic delocalization that is valid for both conjugated π- and σ-electronic systems.     

AM1 studies of photoelectron spectra

Deep-lying π- and σ-orbitals of 10-alkylphenothiazines were studied by photoelectron spectroscopy and quantum-chemical AM1 calculations. It was demonstrated that in 10-ethylphenothiazine the lone electron pair of the S atom interacts with the π-system of the aromatic fragments. The π-MOs, whose energies are a function of the dihedral angle between the planes of the benzene rings of phenothiazines and are independent of the degree of pyramidality of the N atom, were found. The differences in the energy of these MOs were used for estimating equilibrium dihedral angles of tricyclic molecules in the gaseous phase. These values differ only slightly from those observed in the solid phase. The replacement of the hydrogen atom at position 10 by the methyl group leads to a decrease in the dihedral angle, leaving the orientation of the substituent unchanged. The orbital energies of phenothiazines, which were calculated by the AM1 method, adequately reflect the order of changes in the ionization potential. However, contributions of the two highest occupied π-MOs to the total charges on the N and S atoms are inconsistent with the experimental data. For Part 10, see Ref. 1. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1542–1548, August, 1998.     

Can five-membered Te<Subscript>2</Subscript>N<Subscript>2</Subscript>S rings be considered aromatic?

The structures and molecular properties of three cyclic tellurium species [Te₂N₂S]²⁺ (1 ²⁺ ), [Te₂N₂SCl]⁺ (1 ⁺ ), and Te₂N₂SCl₂ (1) were studied using Density Functional Theory (DFT) with the aim of analyzing and quantifying the degree of electron delocalization in the rings. The structural data for the AsF₆⁻ salt of the cation 1 ⁺ , as well as the experimental vibrational frequencies of 1 and 1 ⁺ , were compared to calculated structures and vibrational modes. While only the five-membered ring of 1 ²⁺ obeys the classic Hückel aromaticity criteria, reflected in the nature of the π orbitals and natural resonance structures, all the three species are magnetic aromatic according to nucleus-independent chemical shift (NICS). However, the out-of-plane component of the NICS tensor (NICS_zz) is able to provide a reliable characterization of the π aromatic character, by showing that successive binding of two chlorine atoms to the same tellurium atom disrupts the π electron delocalization, and that total NICS cannot always be trusted as an aromaticity indicator.     

Canonical orbital contributions to the magnetic fields induced by global and local diatropic and paratropic ring currents

The induced magnetic field (IMF) of naphthalene, biphenyl, biphenylene, benzocyclobutadiene, and pentalene is dissected to contributions from the total π system, canonical π‐molecular orbitals (CMO), and HOMO→π* excitations, to evaluate and interpret relative global and local diatropicity and paratropicity. Maps of the IMF of the total π system reveal its relative strength and topology that corresponds to global and local diatropic and paratropic ring currents. The total π magnetic response is determined by this of canonical HOMOs and particularly by paratropic contributions of rotational excitations from HOMOs to unoccupied π * orbitals. Low energy excitations and similar nodal structure of HOMO and π * induce strong paratropic fields that dominate on antiaromatic rings. High energy excitations and different nodal structures lead to weak paratropic contributions of canonical HOMOs, which are overwhelmed by diatropic response of lower energy canonical orbitals in aromatic rings. CMO‐IMF analysis is found in agreement with ring current analysis. © 2017 Wiley Periodicals, Inc.     

Electronic structure, geometry, and reactivity of arylsilenes: a quantum-chemical study

The geometry and electronic structure of 1,4-di(silaethen-1-yl)benzene (2), itsmeta- andbrtho-isomers (3 and4, respectively), and its carbon analog, 1,4-divinylbenzene (5), were studied by the semiempirical MNDO-PM3 method. Unlike5, two pairs of the frontier MOs in isomers2–4 are mainly π-orbitals of Si=C bonds, while the structure of the lowest occupied π-MO indicates delocalization of π-electrons of the entire system. The main characteristic features of the double Si=C bonds (the high polarity and narrow HOMO-LUMO energy gap, which favors the [2+2]-cycloaddition reaction) remain in arylsilenes2–4. The interaction between π-electrons of benzene fragment and the double Si=C bonds results in violation of the benzene ring symmetry, which is most pronounced in structure5. Weakening of the C−H bonds in theortho-positions of the aromatic nucleus in the compounds under study is observed. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 256–260, February, 1999.     

Sigma and pi contributions to the induced magnetic field: indicators for the mobility of electrons in molecules

The authors discuss the role of the sigma and pi contributions to the induced magnetic field for simple hydrocarbons containing a double or a triple bond, as well as for benzene and cyclobutadiene. While the magnetic field induced by the sigma electrons is short-ranged, the pi system is responsible for the formation of long-range cones. These cones influence the chemical shift of atoms by additional shielding (for aromatic) or deshielding (for antiaromatic molecules) contributions. While the hydrogen atoms of benzene are found to lie within the deshielded region of the magnetic field induced by the pi electrons, they are shielded by the total induced magnetic field. The induced magnetic field of the pi electrons support Pople's model on the basis of first-principles calculations.     

The first ionization potentials and conjugation in benzene derivatives containing organosilicon, organogermanium, organotin, and organolead substituents

The inductive and resonance effects of silicon-, germanium-, tin-, and lead-containing and some organic substituents on the HOMO energies (E _HOMO) for 43 monosubstituted andp-disubstituted benzene derivatives were analyzed in the Koopmans approximation. A linear dependence between the perturbation energy δE and the resonanceσ _R ⁺ parameters of the substituents was established. The Koopmans approximation is a rough approximation for the compounds studied, since to provide for its rigorous fulfilment, the δE values must depend on the σ _R ⁰ parameters of the substituents. The principal regularities of increasing the σ,π-conjugation between the organoelement substituents and the π-system caused by a positive charge on the benzene ring were established. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 70–75, January 1997.     

Effect on ring current of the Kekulé vibration in aromatic and antiaromatic rings

Derivative current-density maps are used to follow the changes in ring-current (and hence, on the magnetic criterion, the changes in aromaticity) with the Kekulé vibrations of the prototypical aromatic, antiaromatic, and nonaromatic systems of benzene, cyclooctatetraene (COT), and borazine. Maps are computed at the ipsocentric CHF/6-31G**//RHF/6-31G** level. The first-derivative map for benzene shows a growing-in of localized bond currents, and the second-derivative map shows a pure, paratropic "antiring-current", leading to the conclusion that vibrational motion along the Kekulé mode will reduce the net aromaticity of benzene, on average. For planar-constrained D(4h) COT, the Kekulé mode (positive for reduction of bond-length alternation) increases paratropicity at both first and second order, indicating an average increase in antiaromaticity with zero-point motion along this mode. On the ring-current criterion, breathing expansions of benzene and D(4h) COT reduce aromaticity and increase antiaromaticity, respectively.     

The ring current in cyclopropane

Mapping of induced current density using the coupled Hartree-Fock “ipsocentric” (CTOCD-DZ/ 6-31G**//RHF/6-31G**) method shows a ring current arising in the σ framework of cyclopropane that is intense, diatropic and annular, and hence is consistent with the numerous literature attributions of σ-aromaticity to this molecule. Localised orbital analysis shows that this current can be attributed to the set of three carbon–carbon bonds. In a similar analysis, the four carbon–carbon bonds of (planar constrained) cyclobutane are found to give rise to a central paratropic current. The maps are consistent with the view that cyclopropane is strongly σ-aromatic, cyclobutane is weakly σ-anti-aromatic, and the larger cycloalkane systems are essentially σ-non-aromatic. Contribution to the Fernando Bernardi Memorial Issue.     

Relativistic scalar and spin-orbit density functional calculations of the electronic structure, NICS index and ELF function of the [Re2(CO)8(μ-BiPh)2] and [Re2(CO)8(μ-BiPh2)2] clusters

Relativistic scalar and spin-orbit density functional calculations of the electronic structure, Nucleus-Independent Chemical Shift (NICS) index and ELF function of the [Re₂(CO)₈(μ-BiPh)₂] and [Re₂(CO)₈(μ-BiPh₂)₂] clusters are reported. We show here that the [Re₂(CO)₈(μ-BiPh)₂] cluster has large negative NICS values in the region defined by the Re-Bi-Re-Bi four-membered ring and the ELF function shows significant electron delocalization density in the center of the metallic ring, thus indicating an aromatic cluster. In contrast the Re-Bi-Re-Bi four-membered ring in the [Re₂(CO)₈(μ-BiPh₂)₂] cluster has negligible paratropic ring currents and the ELF function shows a low-density region within the metallic ring indicating that aromaticity is switched off. However, the phenyl ligands in both clusters show the expected aromatic character.     

Aromaticity of Rees-type hydrocarbons—a DFT computational study

The structure and aromatic properties of Rees hydrocarbons 7bH-cyclopent[cd]indene and its benzo-annelated derivative 1a and 2a, respectively, are examined by the B3LYP/6−31+G(d) calculations employing HOMA criterion of Krygowski and coworkers. It is shown that 1a possesses strong π-electron delocalization over the perimeter of the CC bonds, thus forming a quasi-[10]annulene pattern. Its aromatic character is determined to be 83%. In contrast, 2a is less convenient model system for [14]annulene. The reason behind is that the perimeter network of the potentially aromatic 14π-electrons is supplemented by two additional more local aromatic patterns involving 10π and 6π electrons. Consequently, the π-electron delocalization over the molecular rim is incomplete being thus diminished. The aromatic character of the peripheral bonds in both 1a ⁻ and 2a ⁻ anions formed upon deprotonation of the central C–H bond is decreased, since the role of the smaller rings in forming aromatic subsystems is increasing. Finally, polycyano substitution of 1a and 2a decreases aromaticity due to the price paid for the resonance effect taking place between the carbocyclic π-network and the double bonds of the CN groups. The resonance effect is particularly strong in anions derived by heterolytic cleavage of the C–H bond emanating from the central sp ³ carbon atom. Dedicated to Professor T. M. Krygowski for his outstanding scientific achievements on the occasion of his 70th birthday.     

Relativistic ring currents in metallabenzenes: an analysis in terms of contributions of localised orbitals

Ring currents calculated in the ipsocentric CTOCD-DZ formalism are presented for four representative metallabenzenes, compounds in which a benzene CH group is formally replaced by a transition metal atom with ligands. Aromaticity is probed using ring currents computed using non-relativistic and relativistic orbitals (derived with relativistic effective core potentials or ZORA). Maps computed at different levels of relativistic theory turn out to be similar, showing that orbital nodal character is the main determinant of ring current. Diatropic/paratropic global ring currents in these compounds, and also circulations localised on the metal centre, are interpreted in terms of contributions of localised π-type orbitals and metal d-orbitals, respectively. All four considered metallabenzenes should be regarded as 6π electron species, despite the fact that three support diatropic ('aromatic') ring currents and one a paratropic ('anti-aromatic') current. The current-density maps determine the correct way to count electrons in these species: differential occupation of d-orbitals of formal π-symmetry contributes to circulation on the metal centre, but not around the benzenoid ring. The overall trend from strongly diatropic to weakly paratropic ring currents along the series 1 to 4 is explained by the increasing strength of interaction between formally non-bonding orbitals on the metal centre and C(5)H(5) moiety, which together make up the six-membered ring.     

A theoretical study of the intramolecular interaction between proximal atoms in planar conformations of biphenyl and related systems

The nature of the interaction between proximal hydrogens in planar biphenyl has been recently a matter of debate as arguments in favor of and against the existence of “H–H” bonding have been recently put forward. This issue is addressed here through the study of both the electron density ρ(r) and the electron localization function (ELF) η(r) obtained in quantum calculations on molecular systems with F atoms replacing hydrogens in the moiety that presents this interaction. The analysis of geometries and properties of ρ(r) and η(r) at both planar and twisted equilibrium conformations of those systems along with biphenyl, permits to get information on this intramolecular interaction that is compared with the use of the traditional chemical concepts (steric hindrance and π-resonance effects) involved. It is shown that although the ELF gives information compatible with these classical terms, this does not preclude the existence of bonds between proximal atoms with features rather similar to those of well-established intramolecular hydrogen bonds.     

A theoretical study of cation--π interactions: Li+, Na+, K+, Be2+, Mg2+ and Ca2+ complexation with mono- and bicyclic ring-fused benzene derivatives

DFT (B3LYP functional) and MP2 methods using 6-311+G(2d,2p) basis set have been employed to examine the effect of ring fusion to benzene on the cation--π interactions involving alkali metal ions (Li⁺, Na⁺, and K⁺) and alkaline earth metal ions (Be²⁺, Mg²⁺ and Ca²⁺). Our present study indicates that modification of benzene (π-electron source) by fusion of monocyclic or bicyclic (or mixture of these two kinds of rings) strengthens the binding affinity of both alkali and alkaline earth metal cations. The strength of interaction decreases in the following order: Be²⁺ > Mg²⁺ > Ca²⁺ > Li⁺ > Na⁺ > K⁺ for any considered aromatic ligand. The interaction energies for the complexes formed by divalent cations are 4–6 times larger than those for the complexes involving monovalent cations. The structural changes in the ring wherein metal ion binds are examined. The distance between ring centroid and the metal ion is calculated for all of the complexes. Strained bicyclo[2.1.1]hexene ring fusion has substantially larger effect on the strength of cation--π interactions than the monocyclic ring fusion for all of the cations due to the π-electron localization at the central benzene ring.     

Magnetic euripi in corannulene

Ab initio current densities induced by an external magnetic field have been computed for corannulene dianion, dication, and tetraanion. The pi-ring currents are found to be large with respect to benzene and to undergo remarkable changes in response to variations in the oxidation state. According to the results obtained here, the three corannulene ions plus the neutral species constitute a very special set that spans all of the possible patterns of rim and hub circulations: diatropic/hub-paratropic/rim (the dianion), paratropic/hub-paratropic/rim (the dication, assuming conformationally averaged current density), diatropic/hub-diatropic/rim (the tetraanion), and paratropic/hub-diatropic/rim (the neutral, as already reported by other authors). Orbital contributions and their breakdown into explicit contributions from virtual excitations have been analyzed. It is shown that the dianion and dication are both (2p) systems characterized by a single highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) rotationally allowed transition. For the dianion, this transition is responsible not only for the outer paratropic circulation but also for the inner diatropic circulation, a behavior that requires an extension of the few electron model based on orbital contributions to be fully rationalized. For the dication, the HOMO-LUMO transition provides a paratropic circulation localized on one indene subunit. However, because of the fast exchange of conformers, it is sensible to calculate an averaged current density field, which is characterized by con-rotating paratropic inner and outer ring currents. For the tetraanion, the calculated current pattern is in agreement with a previous indication, while the orbital analysis reveals that the HOMO and the HOMO - 1 contribute to both inner and outer circulations. Despite the small 6-31G** basis set employed to calculate current densities and magnetic properties, a satisfactory agreement between computed and available experimental (1)H and (13)C chemical shifts is found, providing a firm basis for the above conclusions. Remarkably, the "diamagnetic" corannulene dianion observed in NMR at low temperature is predicted to be a paramagnetic closed-shell species.     

Revisiting Aromaticity and Chemical Bonding of Fluorinated Benzene Derivatives

The electron delocalization of benzene (C₆H₆) and hexafluorobenzene (C₆F₆) was analyzed in terms of the induced magnetic field, nucleus-independent chemical shift (NICS), and ring current strength (RCS). The computed out-of-plane component of the induced magnetic field at a distance (r) greater than or equal to 1.0 Å above the ring center correlates well (R²>0.99) with the RCS value. According to these criteria, fluorination has two effects on the C₆ skeleton; concomitantly, the resonant effects diminish the π electron delocalization and the inductive effects decrease the charge density at the ring center and therefore reduce the magnitude of the paratropic current generated in this region. The equilibrium between both effects decreases aromaticity in the fluorinated benzene derivatives. These results can be extrapolated to determine the aromaticity of any derivative within the series of fluorinated benzene derivatives (C₆H_(6−n)F_n, where n=1–5).     

Molecular structures of amino and nitro derivatives of 1,3-di(morpholin-4-yl)benzene

The 4,6-diamino-1,3-di(morpholin-4-yl)- and 5-amino-2,4-di(morpholin-4-yl)-1-nitro derivatives of benzene, which serve as model compounds in studies of spatial structures and reactivities of monomer units of many polymers of practical importance, have been studied by X-ray diffraction analysis. The morpholine rings are twisted so that they are virtually perpendicular to the benzene ring. According to the results of AM1 calculations, the hydrogen atoms of the methylene groups of these substituents carry noticeable positive charges. The introduction of different substituents into the benzene ring has no substantial effect on the charge distribution in the morpholine rings due to the absence of conjugation between the lone electron pairs of the nitrogen atoms of the ring and the π-system of the benzene ring. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 444–449, March, 1998.     

A unified orbital model of delocalised and localised currents in monocycles, from annulenes to azabora-heterocycles

Why are some (4n+2)π systems aromatic, and some not? The ipsocentric approach to the calculation of the current density induced in a molecule by an external magnetic field predicts a four‐electron diatropic (aromatic) ring current for (4n+2)π carbocycles and a two‐electron paratropic (antiaromatic) current for (4n)π carbocycles. With the inclusion of an electronegativity parameter, an ipsocentric frontier‐orbital model also predicts the transition from delocalised currents in carbocycles to nitrogen‐localised currents in alternating azabora‐heterocycles, which rationalises the differences in (magnetic) aromaticity between these isoelectronic π‐conjugated systems. Ab initio valence‐bond calculations confirm the localisation predicted by the naïve model, and coupled‐Hartree–Fock calculations give current‐density maps that exhibit the predicted delocalised‐to‐localised/carbocycle–heterocycle transition.     

Conjugation in radical cations of benzene, ethylene, and acetylene derivatives. Nonuniversality of the resonance parameters of group 14 organoelement substituents

The first vertical ionization potentialsl ₁ of molecules R_πX (X=Ph, H₂C=CH, and HC≡C) depend on the joint influence of the inductive, resonance, and polarizability effects of substituents X, which are characterized by parameters σ₁, σ_R+, and σ_α, respectively. The mechanism of conjugation in radical cations formed upon ionization of R_πX is changed as compared to neutral R_πX molecules, while the substituent X becomes polarized. The conjugation and polarizability effects are strenthened in the sequence Ph < H₂C=CH <HC≡C as R_π changes from Ph to H₂C=CH and HC≡C. The σ_R+ parameters of Si-, Ge-, and Sn-containing substituents X are dependent on the type of R_π but are connected by linear dependences in the series of benzene, ethylene, and acetylene derivatives. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1481–1486, August, 1998.     

Synthesis characterization and hydroformylation activity of new mononuclear rhodium(I) compounds incorporated with polar-group functionalized phosphines

A first effort employing a range of polar-group functionalized phosphines (L ₁ –L ₇ ) to design mononuclear Rh(I) compounds of [Rh(quin-8-O)(CO)(L)] (quin-8-O = 8-hydroxy quinolate) is described. The reaction of a Rh(I) precursor [Rh(μ-Cl)(CO)₂]₂ with 8-hydroxyquinoline in the presence of a base followed by phosphines (L ₁ –L ₇ ) produced only a single isomer of [Rh(quin-8-O)(CO)(L)] compounds (1–7) with pendant, i.e. non-bonded, polar-groups (includes carboxyl, hydroxyl and formyl). A relationship between Δgd³¹P chemical shifts and the ν(C≡O) was derived to evaluate and explain the σ-donor properties of these phosphines with respect to the electronic properties of the polar groups and the extent of π-back-bonding to the CO group. These mononuclear Rh(I)-Phosphines were investigated as catalysts in the hydroformylation of 1-hexene and cyclohexene in aqueous two-phase and single-phase solvent systems. The Rh(I) catalysts with strong σ-donor and hydrophilic phosphines provided better yields and selectivities for the hydroformylation products, which is a reverse trend compared to literature reports. When the Rh(I) compounds contained strong σ-donor phosphines, the π-acceptor properties of the pyridine ring of 8-hydroxyquinolate were found to be beneficial for the facile cleavage of the CO group during hydroformylation, and additionally, to improve the kinetic stability of catalysts.