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  • Sundholm, Dage; Berger, Raphael J. F.; Fliegl, Heike (2016)
    Magnetically induced current susceptibilities and current pathways have been calculated for molecules consisting of two pentalene groups annelated with a benzene (1) or naphthalene (2) moiety. Current strength susceptibilities have been obtained by numerically integrating separately the diatropic and paratropic contributions to the current flow passing planes through chosen bonds of the molecules. The current density calculations provide novel and unambiguous current pathways for the unusual molecules with annelated aromatic and antiaromatic hydrocarbon moieties. The calculations show that the benzene and naphthalene moieties annelated with two pentalene units as in molecules 1 and 2, respectively, are unexpectedly antiaromatic sustaining only a local paratropic ring current around the ring, whereas a weak diatropic current flows around the C-H moiety of the benzene ring. For 1 and 2, the individual five-membered rings of the pentalenes are antiaromatic and a slightly weaker semilocal paratropic current flows around the two pentalene rings. Molecules 1 and 2 do not sustain any net global ring current. The naphthalene moiety of the molecule consisting of a naphthalene annelated with two pentalene units (3) does not sustain any strong ring current that is typical for naphthalene. Instead, half of the diatropic current passing the naphthalene moiety forms a zig-zag pattern along the C-C bonds of the naphthalene moiety that are not shared with the pentalene moieties and one third of the current continues around the whole molecule partially cancelling the very strong paratropic semilocal ring current of the pentalenes. For molecule 3, the pentalene moieties and the individual five-membered rings of the pentalenes are more antiaromatic than for 1 and 2. The calculated current patterns elucidate why the compounds with formally [4n + 2] p-electrons have unusual aromatic properties violating the Huckel pi-electron count rule. The current density calculations also provide valuable information for interpreting the measured H-1 NMR spectra.
  • Molina, V.; Rauhalahti, M.; Hurtado, J.; Fliegl, H.; Sundholm, D.; Munoz-Castro, A. (2017)
    [trans-Cu(mu-OH)(mu-dmpz)](6) (1) exhibits six Cu(II) centers effectively coupled through a ligand mediated mechanism leading to a diamagnetic ground state over a wide temperature range. Here we investigate further magneto-structural correlations based on the possible free electron precession along such a copper-based ring-like nanocoil mediated by bridging ligands. We find that in 1, mediated antiferro-magnetic coupling leads to characteristics that induce aromatic ring behavior through evaluation of both induced currents and shielding of cones from a relativistic density functional theory level. According to our gauge calculations including magnetically induced current densities and an induced magnetic field, a sizable ring current strength susceptibility is obtained for the cyclic Cu-N-N-Cu and Cu-O-Cu pathways, allowing a magnetic exchange between the copper centers. Our study suggests that [Cu-6(dmPz)(6)(OH)(6)] consisting of an aromatic ring structure displays aromaticity and superexchange along the Cu-O-Cu and Cu-N-N-Cu backbones, which accounts for 80% and 20% of the overall ring current strength susceptibility, respectively. This reveals the presence of particular aromatic ring characteristics in coordination compounds without a direct metal-metal bond, where several formally paramagnetic centers are antiferromagnetically-coupled through supporting ligands. We envisage that our findings can be extended to other examples depicting ligand-mediated interaction between metal centers.
  • Baryshnikov, Gleb V.; Valiev, Rashid R.; Karaush, Nataliya N.; Sundholm, Dage; Minaev, Boris F. (2016)
    Magnetically induced current densities and current pathways have been calculated for a series of fully annelated dicationic and dianionic tetraphenylenes, which are also named [8]circulenes. The gauge including magnetically induced current (GIMIC) method has been employed for calculating the current density susceptibilities. The aromatic character and current pathways are deduced from the calculated current density susceptibilities showing that the neutral [8]circulenes have two concentric pathways with aromatic and antiaromatic character, respectively. The inner octatetraene core (the hub) is found to sustain a paratropic (antiaromatic) ring current, whereas the ring current along the outer part of the macrocycle (the rim) is diatropic (aromatic). The neutral [8]circulenes can be considered nonaromatic, because the sum of the ring-current strengths of the hub and the rim almost vanishes. The aromatic character of the doubly charged [8]circulenes is completely different: the dianionic [8]circulenes and the OC-, CH-, CH2-, SiH-, GeH-, SiH2-, and GeH2-containing dicationic species sustain net diatropic ring currents i.e., they are aromatic, whereas the O-, S-, Se-, NH-, PH- and AsH-containing dicationic [8]circulenes are strongly antiaromatic. The present study also shows that GIMIC calculations on the [8]circulenes provide more accurate information about the aromatic character than that obtained using local indices such as nuclear-independent chemical shifts (NICSs) and H-1 NMR chemical shifts.
  • Orozco-Ic, Mesias; Celaya, Christian A.; Sundholm, Dage (2020)
    Magnetic response properties of 1,2,3,5-tetrazine derivatives including the newly synthesized 4,6-diphenyl-1,2,3,5-tetrazine have been studied computationally at the density functional theory (DFT) level. Calculations of magnetically induced current densities and induced magnetic fields show that the unsubstituted 1,2,3,5-tetrazine is almost as aromatic as benzene. Separating the magnetic shielding functions into molecular orbital components provided additional insights into the magnetic response. The aromatic character estimated from magnetically induced current densities and induced magnetic fields shows that NICS pi zz(0) values and ring-current strengths yield about the same degree of aromaticity, whereas NICSzz(0) and NICSzz(1) values are contaminated by sigma electron contributions. The studied 1,2,3,5-tetrazine derivatives are less aromatic than the unsubstituted one. Calculations of magnetic response properties of 4,6-diphenyl-1,2,3,5-tetrazine showed that it is the least aromatic among the studied molecules according to the ring-current criterion, while 4,6-[1,2,3,5]-ditetrazinyl-1,2,3,5-tetrazine is as aromatic as 4,6-dimethyl-1,2,3,5-tetrazine and slightly less aromatic than the unsubstituted 1,2,3,5-tetrazine.
  • Benkyi, Isaac; Staszewska-Krajewska, Olga; Gryko, Daniel T.; Jaszuński, Michał; Stanger, Amnon; Sundholm, Dage (2020)
    The aromaticity of three nonplanar, fully conjugated aza-nanographenes built around a pyrrolo[3,2-b]pyrrole core is assessed through the application of two different computational procedures—GIMIC and NICS. We examine the calculated magnetically induced current densities (GIMIC) and nucleus-independent chemical shifts (NICS). The structural differences between these three apparently similar molecules lead to significantly different aromatic properties. GIMIC analysis indicates that the peripheral diatropic ring current of 3.9 nA/T for the studied bowl-shaped diaza-nanographene is the strongest, followed by the double [6]helicene which lacks seven-membered rings, and is practically nonexistent for the double [5]helicene possessing seven-membered rings. The biggest difference however is that in the two not-fully-fused molecules, the central pyrrole rings possess a significant diatropic current of about 4.1 nA/T, whereas there is no such current in the diaza-nanographene. Moreover, the antiaromaticity of the seven-membered rings is increasing while moving from double [5]helicene to diaza-nanographene (from −2.4 to −6.0 nA/T). The induced currents derived from NICSπ,zz-XY-scan analysis for all of the studied systems are in qualitative agreement with the GIMIC results. Subtle differences may originate from σ-electron currents in GIMIC or inaccuracy of NICSπ,zz values due to the nonplanarity of the systems, but the general picture is similar.
  • Rauhalahti, Markus; Sundholm, Dage; Johansson, Mikael P. (2021)
    The magnetically induced current density of an intriguing naphthalene-fused heteroporphyrin has been studied, using the quantum-chemical, gauge-including magnetically induced currents (GIMIC) method. The ring-current strengths and current-density pathways for the heteroporphyrin, its Pd complex, and the analogous quinoline-fused heteroporphyrin provide detailed information about their aromatic properties. The three porphyrinoids have similar current-density pathways and are almost as aromatic as free-base porphyrin. Notably, we show that the global ring current makes a branch at three specific points. Thus, the global current is composed of a total of eight pathways that include 22 pi-electrons, with no contributions from 18-electron pathways.
  • Benkyi, Isaac; Fliegl, Heike; Valiev, Rashid R.; Sundholm, Dage (2016)
    Magnetically induced current densities have been calculated and analyzed for a number of synthesized carbachlorins and carbaporphyrins using density functional theory and the gauge including magnetically induced current (GIMIC) method. Aromatic properties have been determined by using accurate numerical integration of the current flow yielding reliable current strengths and pathways that are related to the degree of aromaticity and the aromatic character of the studied molecules. All investigated compounds are found to be aromatic. However, the obtained aromatic pathways differ from those previously deduced from spectroscopic data and magnetic shielding calculations. For all studied compounds, the ring current divides into an outer and an inner branch at each pyrrolic subring, showing that all pi-electrons of the pyrrolic rings take part in the delocalization pathway. The calculations do not support the common notion that the main share of the current takes the inner route at the pyrrolic rings without an inner hydrogen and follows an 18 pi aromatic pathway. The aromatic pathways of the investigated carbaporphyrins and carbachlorins are very similar, since the current strength via the C-beta=C-beta' bond of the cyclopentadienyl ring of the carbaporphyrins is almost as weak as the current density passing the corresponding saturated C beta-C-beta' bond of the carbachlorins.
  • Kumar, Chandan; Fliegl, Heike; Sundholm, Dage (2017)
    Magnetically induced ring-current strength susceptibilities and nucleus independent chemical shifts (NICS) have been studied for 15 single-ring aromatic, antiaromatic, and nonaromatic molecules. The current densities have been calculated at the density functional theory (DFT), Hartree-Fock (HF) theory, and second-order Moller-Plesset perturbation theory (MP2) levels using the gauge-including magnetically induced current method (GIMIC). The ring-current strength susceptibilities have been obtained by numerical integration of the current density flowing around the molecular ring. The calculated ring-current strength susceptibilities are almost independent of the level of theory. The relative degree of aromaticity deduced from the magnetic properties has been compared with the ones deduced from hydrogenation enthalpies that are considered to be proportional to aromatic stabilization energies (ASE). For the studied single-ring molecules, GIMIC, NICS, and ASE calculations yield similar trends. The study shows that there is a linear correlation between the magnetic and energetic criteria of aromaticity. The largest uncertainty originates from the accuracy of the energy data, because they are much more dependent on the employed computational level than the calculated magnetic properties. Thus, ring-current strength susceptibilities can be used for assessing the degree of aromaticity.
  • Dimitrova, Maria; Sundholm, Dage (2018)
    We have investigated the aromatic properties of seven low-lying isomers of [10]annulene and of the recently synthesized dicupra[10]annulene compounds that were crystallised with two or four lithium counterions (Wei et al., J. Am. Chem. Soc., 2016, 138, 60-63). The molecular structures of the [10]annulene conformers and the dicupra[10]annulenes with bulky trimethylsilyl (TMS) and phenyl groups, as well as the corresponding unsubstituted dicupra[10]annulenes were optimised using density functional theory, employing a semiempirical dispersion correction to consider van der Waals interactions. The structures of the hydrocarbon annulenes were subsequently optimised at the SCS-MP2/def2-QZVPD level. Single-point coupled-cluster calculations with explicit treatment of the electron correlation CCSD(F12)(T) were performed to obtain the relative energies of the hydrocarbon annulenes. Four of the conformations lie close in energy relative to each other. Three substituted and three unsubstituted dicupra[10]annulene structures with either four, two or no Li+ counterions were investigated. Magnetically induced current densities calculated using the GIMIC program were used for the assessment of the aromatic properties of the studied molecules. The conformations of [10] annulene with lowest energies are non-aromatic. The calculations revealed that the electron donation of the lithium atoms to the dicupra[10]annulene core significantly affects the electronic and molecular structures of the dicupra[10]annulenes. The annulene ring is non-planar for all studied dicupra[10]annulenes except for the unsubstituted one with four Li+ counterions, which was also found to be the only molecule that sustains a strong diatropic ring current around the dicupra[10]annulene ring. The other five dicupra[10]annulenes sustain very weak net ring currents and can be considered non-aromatic.
  • Dimitrova, Maria; Fliegl, Heike; Sundholm, Dage (2017)
    Four polycyclic molecules have been investigated at the DFT B3LYP/def2-TZVP level of theory using calculated magnetically induced current densities as an indicator of their (anti)aromaticity. Complicated current pathways were found in dibenzo[a,e]pentalene and its three heterocyclic analogues each containing two boron and two nitrogen atoms. The antiaromatic character of the pentalene moiety is weaker in the hydrocarbon molecule and in 5,11-dihydrobenzo[d]benzo[4,5][1,2,3]azadiborolo[3,2-b][1,2,3]azadiborole as compared to the pentalene molecule. The antiaromatic character of the pentalene moiety is completely absent in the other two heterocyclic structures. In 6,12-dihydrobenzo[d]benzo[4,5][1,2,3]diazaborolo[2,1-a][1,2,3]diazaborole all four molecular rings are aromatic according to the ring-current criterion, and in 6,12-dihydrobenzo[d]benzo[3,4][1,2,5]azadiborolo[1,2-a][1,3,2]diazaborole, the diazaborole ring is aromatic, while the azadiborole ring is antiaromatic. In all four molecules the six-membered rings are aromatic sustaining a weaker ring current than benzene does.