Aromatic pathways in mono- and bisphosphorous singly Möbius twisted [28] and [30]hexaphyrins

Magnetically induced current densities and strengths of currents passing through selected bonds have been calculated for monophosphorous [28]hexaphyrin ((PO)[28]hp) and for bisphosphorous [30]hexaphyrin ((PO)(2)[30]hp) at the density functional theory level using our gauge-including magnetically induced current (GIMIC) approach. The current-density calculations yield quantitative information about electron-delocalization pathways and aromatic properties of singly M?bius twisted hexaphyrins. The calculations confirm that (PO)[28]hp sustains a strong diatropic ring current (susceptibility) of 15 nA T(-1) and can be considered aromatic, whereas (PO)(2)[30]hp is antiaromatic as it sustains a paratropic ring current of -10 nA T(-1). Numerical integration of the current density passing through selected bonds shows that the current is generally split at the pyrroles into an outer and an inner pathway. For the pyrrole with the NH moiety pointing outwards, the diatropic ring current of (PO)[28]hp takes the outer route across the NH unit, whereas for (PO)(2)[30]hp, the paratropic ring current passes through the inner C(β)=C(β) double bond. The main diatropic ring current of (PO)[28]hp generally prefers the outer routes at the pyrroles, whereas the paratropic ring current of (PO)(2)[30]hp prefers the inner ones. In some cases, the ring current is rather equally split along the two pathways at the pyrroles. The calculated ring-current pathways do not agree with those deduced from measured (1)H NMR chemical shifts.     

Induced currents and electron counting in aromatic boron wheels: B8(2-) and B9-)

The newly discovered atom-centered polygonal wheels B8(2-) and B9- are predicted to show ring currents characteristic of aromatic systems. Ipsocentric mapping of induced current density for both molecules attributes a pi diatropic current to the four electrons of the doubly degenerate pi HOMO and a sigma diatropic current to the four electrons of the doubly degenerate sigma HOMO, each orbital pair having an available transition to corresponding LUMO orbitals in which the angular node count increases by one. Thus, on the magnetic criterion, B8(2-) and B9- are each both pi- and sigma-aromatic as a consequence of the nodal properties of the frontier orbitals of the pi- and sigma-stacks.     

Ring currents in tangentially p-p bonded sigma-aromatic systems

We report a theoretical study of ring systems that delocalize electrons in a cyclic array of p orbitals arranged tangentially in sigma-bonding fashion. Sigma-bonded arrays are compared to conventional pi-bonded analogues with respect to orbital symmetry and aromatic/antiaromatic behavior. In a one-to-one correspondence between pi and tangential molecular orbitals of a cycle, local rotation turns each pi to a tangential basis function, changing bonding interactions to antibonding and inverting the order of filling of molecular orbitals. The ipsocentric ring-current mapping approach is used to evaluate aromaticity on the magnetic criterion. As for conventional pi-ring currents, the sigma-ring current in tangential p-p bonded systems is dominated by the HOMO-LUMO transition, corresponding to circulation of four electrons in diatropic (4n + 2)-electron cycles but two in paratropic (4n)-electron cycles. The systems examined here utilize either C 2p or Si 3p orbitals for delocalization. Although interchangeable with C with respect to the fundamental orbital symmetry and ring-current rules, Si bonds at greater internuclear distances, a feature that allows easier design of potentially stable sigma-aromatic structures. Calculations show the wheel-like Si10C50H70 structure 6 as a stable, neutral aromatic molecule with a diatropic ring current following the sigma-bond path formed by Si 3p orbitals.     

Four- and two-electron rules for diatropic and paratropic ring currents in monocyclic pi systems

The pi ring current in an even-eletron monocycle is dominated by the HOMO-LUMO transition, and hence corresponds to circulation of four electrons in a diatropic (4n + 2)-electron, but two in a paratropic (4n)-electron cycle.     

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.     

The diatropic sigma ring currents of [pi2s + pi2s + pi2s] pericyclic transition states

Ab initio current-density maps for the (4n + 2)-electron transition states of two thermally allowed [pi2s + pi2s + pi2s] trimerisations, of ethyne to benzene (1), and of ethene to cyclohexane (2), show that both support sigma diatropic ring currents, dominated by four-electron sigma --> sigma* virtual excitation of HOMO electrons.     

Ring currents as probes of the aromaticity of inorganic monocycles : P5-, As5-, S2N2, S3N3-, S4N3+, S4N42+, S5N5+, S42+ and Se42+

Current-density maps were calculated by the ipsocentric CTOCD-DZ/6-311G** (CTOCD-DZ=continuous transformation of origin of current density-diamagnetic zero) approach for three sets of inorganic monocycles: S(4) (2+), Se(4) (2+), S(2)N(2), P(5) (-) and As(5) (-) with 6 pi electrons; S(3)N(3) (-), S(4)N(3) (+) and S(4)N(4) (2+) with 10 pi electrons; and S(5)N(5) (+) with 14 pi electrons. Ipsocentric orbital analysis was used to partition the currents into contributions from small groups of active electrons and to interpret the contributions in terms of symmetry- and energy-based selection rules. All nine systems were found to support diatropic pi currents, reinforced by sigma circulations in P(5) (-), As(5) (-), S(3)N(3) (-), S(4)N(3) (+), S(4)N(4) (2+) and S(5)N(5) (+), but opposed by them in S(4) (2+), Se(4) (2+) and S(2)N(2). The opposition of pi and sigma effects in the four-membered rings is compatible with height profiles of calculated NICS (nucleus-independent chemical shifts).     

The phenalenyl motif: a magnetic chameleon

The 12pi cation (3) and 14pi anion (4) derived from the phenalenyl radical (2) support diatropic ("aromatic") perimeter ring currents, but isoelectronic replacement of the central atom by either boron (5) or nitrogen (6) leads to paratropic ("antiaromatic") current; the ipsocentric approach to molecular magnetic response accounts for all four patterns in terms of competition between translationally and rotationally allowed virtual pi-pi* excitations.     

Aromaticity of ring carbo-mers of [N]annulenes and [N]cycloalkanes

Maps of current density induced by a perpendicular external magnetic field are calculated at the ipsocentric CTOCD-DZ/6-31G**//B3PW91/6-31G** level for ring carbo-mers of [N]-annulenes (closed-shell singlet states of C(3N)H, N = 3 to 7, with q = -1, 0, +1, 0, -1, respectively, and also the triplet ground state for N = 4) and of [N]-cycloalkanes (C(3N)H(qN), N = 3, 4, 5). Strong four-electron diatropic ring currents indicate conventional pi aromaticity for all the singlet and triplet carbo-[N]annulenes studied, with the exception of C(12)H(4), where instead the strong two-electron paratropic ring current is the signature of pi antiaromaticity. The carbo-[N]cycloalkanes (also known as [N]pericyclynes) show only localized pi currents, consistent with non-aromaticity. There is no indication of a 'homo-aromatic' ring current attributable to the in-plane pi orbitals of the inserted C2 units in any of the maps. Consequences for the interpretation of ELF (electron localisation function) populations are discussed.     

Do all-metal antiaromatic clusters exist?

As shown by detailed nucleus-independent chemical shift (NICS) analyses of the contributions of each molecular orbital, the very recently reported gas-phase all-metal Al4Li3- anion and its relatives (Kuznetsov, A.E.; Birch, K.A.; Boldyrev, A.I.; Li, X.; Zhai, A.I.; Wang, L.S. Science 2003, 300, 622) are aromatic rather than antiaromatic. The paratropic (antiaromatic) four-pi-electron contribution is overcome by the predominating diatropic effects of sigma aromaticity. However, true antiaromatic all-metal clusters, such as Sn62- (Schiemenz, B.; Huttner, G. Angew. Chem., Int. Ed. Engl. 1993, 32, 297), do exist.     

Theoretical study on structures and aromaticities of P5(-) anion, [Ti (eta(5)-P5)]- and sandwich complex [Ti(eta(5)-P5)2]2-

The equilibrium geometries, energies, harmonic vibrational frequencies, and nucleus independent chemical shifts (NICSs) of the ground state of P5(-) (D(5h)) anion, the [Ti (eta(5)-P5)]- fragment (C(5v)), and the sandwich complex [Ti(eta(5)-P5)2]2- (D(5h) and D(5d)) are calculated by the three-parameter fit of the exchange-correlation potential suggested by Becke in conjunction with the LYP exchange potential (B3LYP) with basis sets 6-311+G(2d) (for P) and 6-311+G(2df) (for Ti). In each of the three molecules, the P-P and Ti-P bond distances are perfectly equal: five P atoms in block P5(-) lie in the same plane; the P-P bond distance increases and the Ti-P bond distance decreases with the order P5(-), [Ti(eta(5)-P5)2]2-, and [Ti (eta(5)-P5)]-. The binding energy analysis, which is carried out according to the energy change of hypothetic reactions of the three species, predicts that the three species are all very stable, and [Ti (eta(5)-P5)]- (C(5v)), more stable than P5(-) and [Ti(eta(5)-P5)2]2- synthesized in the experiment, could be synthesized. NICS values, computed for the anion and moiety of the three species with GIAO-B3LYP, reveal that the three species all have a larger aromaticity, and NICS (0) of moiety, NICS (1) of moiety, and minimum NICS of the inner side of ring P5 plane in magnitude increase with the order P5(-), [Ti(eta(5)-P5)2]2-, and [Ti (eta(5)-P5)]-. By analysis of the binding energetic and the molecular orbital (MO) and qualitative MO correlation diagram, and the dissection of total NICS, dissected as NICS contributions of various bonds, it is the main reason for P5(-) (D(5h)) having the larger aromaticity that the P-P sigma bonds, and pi bonds have the larger diatropic ring currents in which NICS contribution are negative, especially the P-P sigma bond. However, in [Ti (eta(5)-P5)]- (C(5v)) and [Ti(eta(5)-P5)2]2- (D(5h), and D(5d)), the reason is the larger and more negative diatropic ring currents in which the NICS contributions of P-P pi bonds and P5-Ti bonds including pi, delta, and sigma bonds, especially P5-Ti bonds, are much more negative and canceled the NICS contributions of P and Ti core and lone pair electrons.     

Sigma-antiaromaticity in cyclobutane,cubane, and other molecules with saturated four-membered rings

Dissected nucleus-independent chemical shift (NICS) analyses of cycloalkanes and cage hydrocarbons reveal contrasting ring current effects, diatropic in three- and five-membered and paratropic in four-membered ring systems. The large shielding effects of the C-C bonds of the archetypal sigma-aromatic, cyclopropane, are magnified in tetrahedrane and related structures. The remarkable deshielding effect of the cyclobutane C-C(sigma) bonds is general: cubane and cages with four-membered rings are strongly deshielding (i.e., sigma-antiaromatic).[structure--see text]     

Diamagnetic and paramagnetic ring currents in expanded porphyrins

Ipsocentric current density maps are computed at the coupled Hartree-Fock level in the 6-31G** basis set for the planar C(2v) B3LYP geometries of the expanded porphyrins, sapphyrin and orangarin. Both give clearly dominant global macrocyclic ring currents, but with opposite senses of circulation: in 22[small pi] sapphyrin, a diatropic current runs, with some bifurcation, around the conventional 22-centre delocalisation pathway; in 20[small pi] orangarin, a paratropic current runs around the inner 17-atom pathway. In agreement with the annulene analogy for these macrocycles, analysis of orbital contributions shows that in each case topology, energy and symmetry of the frontier orbitals together determine the macrocyclic ring current. In sapphryrin, 4-electron diamagnetism (aromaticity) arises from translationally allowed HOMO-LUMO excitations as in benzene itself; in orangarin, 2-electron paramagnetism (antiaromaticity) arises from rotationally allowed HOMO-LUMO excitations as in planarised cyclooctatetraene. The active orbitals invoked in the explanation of ring currents are those involved in the longstanding four-orbital model of porphyrin electronic spectra.     

Evidence for d orbital aromaticity in square planar coinage metal clusters

Quantitative evidence for the existence of aromaticity involving the d orbitals of transition metals is provided for the first time. The doubly bridged square planar (D(4)(h)()) coinage metal clusters (M(4)Li(2), M = Cu (1), Ag (2), and Au (3)) are characterized as aromatic by their substantial nucleus independent chemical shifts (NICS) values in the centers (-14.5, -14.1, and -18.6, respectively). Nevertheless, the participation of p orbitals in the bonding (and cyclic electron delocalization) of 1-3 is negligible. Instead, these clusters benefit strongly from the delocalization of d and to some extent s orbitals. The same conclusion applies to Tsipis and Tsipis' H-bridged D(4)(h)() Cu(4)H(4) ring (4). Canonical MO-NICS analysis of structures 1-3 shows the total diatropic d orbital contributions to the total NICS to be substantial, although the individual contributions of the five sets of filled d orbitals vary. The d orbital aromaticity of Cu(4)Li(2) also is indicated by its atomization energy, 243.2 kcal/mol, which is larger than Boldyrev's doubly (sigma and pi) aromatic Al(4)Li(2) (215.9 kcal/mol).     

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.     

Stable transition metal complexes of an all-metal antiaromatic molecule (Al4Li4): role of complexations

We propose for the first time a few examples of stable transition metal complexes of an all-metal antiaromatic molecule Al4Li4. We demonstrate that these all-metal species can be stabilized by complexation with 3d transition metals very similar to their organic counterpart, C4H4. Complexation to transition metal ions reduces the frontier orbital energies and introduces aromatic charactersitics. We consider a series of such complexes: [eta4-(Al4Li4)-Fe(CO)3, eta2,sigma2-(Al4Li4)-Ni, and (Al4Li4)2Ni] and compare and contrast their energetics with their organometallic counterparts. Fragmentation energy, orbital correlation energy analysis, and the nucleus-independent chemical shift (NICS) values support the complexation-induced stabilities in these systems.     

Aromatic pathways of porphins, chlorins, and bacteriochlorins

Magnetically induced current densities have been calculated for free-base porphynoids using the gauge including magnetically induce current (GIMIC) method. Numerical integration of the current density passing selected chemical bonds yields current pathways and the degree of aromaticity according to the magnetic criterion. The ring-current strengths of the porphins, chlorins, and bacteriochlorins are 1.5-2.5 times stronger than for benzene. The calculations show that the 18π [16]annulene inner cross is not the correct picture of the aromatic pathway for porphyrins. All conjugated chemical bonds participate in the current transport independently of the formal number of π electrons. The ring current branches at the pyrrolic rings taking both the outer and the inner route. The NH unit of the pyrrolic rings has a larger resistance and a weaker current strength than the pyrroles without inner hydrogens. The traditional 18π [18]annulene with inactive NH bridges is not how the ring-current flows around the macroring. The porphins have the strongest ring current of ca. 27 nA/T among the investigated porphynoids. The current strengths of the chlorins and bacteriochlorins are 19-24 nA/T depending on whether the ring current is forced to pass an NH unit or not. The current strengths of the 3-fold and 4-fold β-saturated porphynoids are 13-17 nA/T, showing that the inner-cross 18π [16]annulene pathway is not a preferred current route.