Gauge-including Magnetically Induced Current Research Articles

In-Depth Theoretical Investigations of Borazine’s Aromaticity: Tailoring Electron Delocalization through Substituent Effects

The current study investigates the influence of several R substituents (e.g., Me, SiH3, F, Cl, Br, OH, NH2, etc.) on the aromaticity of borazine, also known as the “inorganic benzene”. By performing hybrid DFT methods, blended with several computational techniques, e.g., Natural Bond Orbital (NBO), Quantum Theory of Atoms in Molecules (QTAIM), Gauge-Including Magnetically Induced Current (GIMIC), Nucleus-Independent Chemical Shift (NICS), and following a simultaneous evaluation of four different aromaticity indices (para-delocalization index (PDI), multi-centre bond order (MCBO), ring current strength (RCS), and NICS parameters), it is emphasized that the aromatic character of B-substituted (B3R3N3H3) and N-substituted (B3H3N3R3) borazine derivatives can be tailored by modulating the electronic effects of R groups. It is also highlighted that the position of R substituents on the ring structure is crucial in tuning the aromaticity. Systematic comparisons of calculated aromaticity index values (i.e., via regression analyses and correlation matrices) ensure that the reported trends in aromaticity variation are accurately described, while the influence of different R groups on electron delocalization and related aromaticity phenomena is quantitatively assessed based on NBO analyses. The most relevant interactions impacting the aromatic character of investigated systems are (i) the electron conjugations occurring between the p lone pair electrons (LP) on the F, Cl, Br, O or N atoms, of R groups, and the π*(B=N) orbitals on the borazine ring (i.e., LP(R)→π*(B=N) donations), and (ii) the steric-exchange (Pauli) interactions between the same LP and the π(B=N) bonds (i.e., LP(R)↔π(B=N) repulsions), while inductive/field effects influence the aromaticity of the investigated trisubstituted borazine systems to a much lesser extent. This work highlights that although the aromatic character of borazine can be enhanced by grafting electron-donor substituents (F, OH, NH2, O−, NH−) on the N atoms, the stabilization due to aromaticity has only a moderate impact on these systems. By replacing the H substituents on the B atoms with similar R groups, the aromatic character of borazine is decreased due to strong exocyclic LP(R)→π*(B=N) donations affecting the delocalization of π-electrons on the borazine ring.

Electronic Structure, Aromaticity and Optical Properties of Dehydro[10]annulene.

Dehydro[10]annulene had been prepared experimentally recently, which is considered to be a highly rigid structure with planar configuration. In this paper, the electronic structure and bonding character of dehydro[10]annulene had been studied by means of molecular orbital (MO), density of states (DOS), bond order (BO) and interaction region indicator (IRI) analyses. The delocalization characters of out-of-plane and in-plane π-electrons (πout - and πin -electrons) of the bond regions were studied by using localized orbital locator (LOL). The anisotropy of the induced current density (AICD), iso-chemical shielding surface (ICSS) and anisotropy of the gauge-including magnetically induced current (GIMIC) were used to investigate the molecular response to external magnetic field, including the induced ring current and the magnetic shielding characteristic. The results showed that the electron delocalization of dehydro[10]annulene is mainly contributed by πout system. The apparent clockwise current in the πout system proved that dehydro[10]annulene is πout aromatic. Finally, the photophysical properties and (hyper)polarizability of dehydro[10]annulene were studied by TD-DFT calculation. The results showed that dehydro[10]annulene has strong local excitation characters. Its (hyper)polarizability decreases with the increase of frequency and has the characteristics of nonlinear anisotropy.

Benchmarking Magnetizabilities with Recent Density Functionals.

We have assessed the accuracy of the magnetic properties of a set of 51 density functional approximations, including both recently published and already established functionals. The accuracy assessment considers a series of 27 small molecules and is based on comparing the predicted magnetizabilities to literature reference values calculated using coupled-cluster theory with full singles and doubles and perturbative triples [CCSD(T)] employing large basis sets. The most accurate magnetizabilities, defined as the smallest mean absolute error, are obtained with the BHandHLYP functional. Three of the six studied Berkeley functionals and the three range-separated Florida functionals also yield accurate magnetizabilities. Also, some older functionals like CAM-B3LYP, KT1, BHLYP (BHandH), B3LYP, and PBE0 perform rather well. In contrast, unsatisfactory performance is generally obtained with Minnesota functionals, which are therefore not recommended for calculations of magnetically induced current density susceptibilities and related magnetic properties such as magnetizabilities and nuclear magnetic shieldings. We also demonstrate that magnetizabilities can be calculated by numerical integration of magnetizability density; we have implemented this approach as a new feature in the gauge-including magnetically induced current (GIMIC) method. Magnetizabilities can be calculated from magnetically induced current density susceptibilities within this approach even when analytical approaches for magnetizabilities as the second derivative of the energy have not been implemented. The magnetizability density can also be visualized, providing additional information that is not otherwise easily accessible on the spatial origin of magnetizabilities.

Corrigendum: Open‐Shell Characters, Aromaticities and Third‐Order Nonlinear Optical Properties of Carbon Nanobelts Composed of Five‐ and Six‐Membered Rings

In the original article,1 we reported that electronic structures and optical and magnetic response properties of an open-shell carbon nanobelt (IF-CNB) are evaluated by the spin-unrestricted density functional theory (U-DFT) method using the long-range corrected LC-BLYP exchange correlation functional, namely, at the LC-UBLYP/6-311+G** level. However, only in the calculations of magnetic response properties, we found that the results are obtained by the spin-restricted DFT (R-DFT) solution with <S2>=0. Therefore, the magnetically-induced current (MIC) density maps given in Figures 6 and S6 (in the Supporting Information) as well as the nucleus-independent chemical shift (NICS) values given in Figure S5 for the open-shell IF-CNB are found to be those evaluated at the LC-RBLYP/6-311+G** level. We sincerely apologize for this mistake. In a previous study,2 on the other hand, we compared the MIC density results from the R- and U-DFT solutions for oligoacenes and dicyclopenta-fused oligoacenes by using the gauge-including MIC (GIMIC) method. We found that the diatropic (aromatic) contributions of aromatic (4n+2)π systems with open-shell singlet electronic structures tend to be exaggerated when the R-DFT solution was employed primarily because of its very small energy gaps for the orbital transitions contributing to the diatropic current. Therefore, we have recalculated the MIC density map for IF-CNB at the LC-UBLYP/6-311+G** level of approximation and compared the result with that at the LC-RBLYP/6-311+G** level. The results are shown in Figure 1. Even though strong contributions of diatropic (aromatic) ring current were predicted everywhere around the belt at the LC-RBLYP level (Figure 1a), such strong aromatic contributions of ring current are found to be suppressed at the LC-UBLYP level (Figure 1b). In particular, paratropic (anti-aromatic) contributions are found to be predominant inside the belt whereas diatropic contributions are found to appear outside the belt at the LC-UBLYP level. Such paratropic/diatropic contributions inside/outside the hoop are similar to those of [6]annulene (benzene). However, the amplitudes of integrated MIC values of IF-CNB (1-3 nA/T) are found to be much smaller than that of the closed-shell [6]annulene (11.9 nA/T) evaluated at the LC-RBLYP/6-311+G** level [2]. Figure 2 shows the side-views of the MIC density map and the integrated values of MIC density for each bond calculated at the LC-RBLYP and LC-UBLYP levels. Even though the amplitudes of integrated MIC values are decreased, the net induced ring currents along the belt are predicted to flow clockwise at the LC-UBLYP level. Magnetically induced current (MIC) density vector plots of IF-CNB evaluated at the LC-RBLYP/6-311+G** (a) and LC-UBLYP/6-311+G** (b) levels on the plane perpendicular to the z-axis and 1 Å above the center of mass. Diatropic currents rotate clockwise, while the paratropic ones anticlockwise. The values in the color bar are given in a.u. The current vectors are scaled with a factor of 30 Å a.u.-1, where 1 a.u.=100.63 nA T−1 Å−2. Integrated MIC values [nA/T] of each bond with along with MIC maps for IF-CNB at the LC-RBLYP/6-311+G** (a) and LC-UBLYP/6-311+G** (b) levels. Positive and negative values represent clockwise (diatropic) and counter-clockwise (paratropic) contributions of ring current, respectively. Spatial integration of MIC densities was performed on the bisector plane of the bond with a width of 2.0 Å. The length of the plane is 8.0 Å from the center of the mass of the belt. Here, the current vectors are scaled with a factor of 20 Å a.u.−1. Figure 3 shows the results of NICS(0) values on the five- and six-membered rings, which characterize aromatic nature on each ring. In both R- and U-DFT cases, positive (negative) NICS values at the center of five- (six-) membered ring are obtained, whereas, the U-DFT results are found to exhibit more antiaromatic nature than the R-DFT results. This feature may be associated with the emergence of the odd electron density in the U-DFT solution. NICS(0) values [ppm] at the centers of five- and six-membered rings calculated at the LC-RBLYP/6-311+G** (a) and LC-UBLYP/6-311+G** levels. NICS(0) values of symmetry-independent positions are only shown. In summary, the MIC density map of IF-CNB in Figure 6 in the original article should be replaced by Figure 1b, the correct integrated MIC values corresponding to Figure S6 in the Supporting Information are shown in Figure 2b, and the NICS(0) values in Figure S5 (Supporting Information) are presented in Figure 3b. Judging from the results at the LC-UBLYP level, IF-CNB is expected to show not so strong, but fairly weak aromatic nature over the belt in the open-shell singlet state.

Magnetically-induced current density investigation in carbohelicenes and azahelicenes.

A computational study of the magnetically-induced current (MIC) density has been carried out for a variety of ortho fused polycyclic aromatic molecules at the density functional theory level with the gauge including magnetically induced current (GIMIC) method. With this method, the aromatic character of each ring in a homologous series of carbohelicenes with an increasing number of fused benzene rings is assessed and compared with other aromaticity criteria such as the Nucleus Independent Chemical Shift [NICS(0), NICSzz(0)] and Bond Length Alternation (BLA) parameters. All criteria indicate that the two outer rings are the most aromatic ones [i.e. higher induced current, more negative NICS(0) and NICSzz(0) values, and smaller BLA values]. For the large helicenes (n > 10), the current drops along the following four rings and then rises again. Additionally, we have proven that this behavior is not due to a difference of the local magnetic field coming from a difference of orientation of the ring with respect to the external magnetic field (oriented along the helical axis). Upon fusing additional benzene rings to form hexa-peri-hexabenzo[7]helicene, some rings (B, D, and F) are a lot less aromatic (even non-aromatic) than the others. The NICS(0) and NICSzz(0) values exaggerate this behavior because they are all positive values, which is a signature of antiaromaticity. Then, when substituting one, three, or four benzene rings with pyrrole ones to form mono-aza-[7]-helicene, tri-aza-[7]-helicene, and tetra-aza-[7]-helicene, remarkable changes in the electronic structures of the helicenes are observed. Indeed, the induced currents are always smaller in the pyrrole rings than in the benzene ones. This has been further investigated using the streamline and the color map representations, which indicate that the diatropic current density passing through the plane cutting the C-N bonds in the pyrrole rings is stronger but is more localized than the current density passing through the plane cutting the C-C bonds in the benzene rings. This gives a positive but smaller total induced current for the pyrrole rings than for the benzene ones. For these systems, the NICS(0) and even more the NICSzz(0) values are not fully reliable to probe the local aromaticity, contrary to the induced current. Indeed, the NICSzz(0) values for the tri-aza-[7]-helicene molecule range from -14.23 to 1.14 ppm, which cannot lead to the same conclusion as the induced current values (10.03 to 12.87 nA T-1).

Aromatic Pathways in Porphycene Derivatives Based on Current-Density Calculations.

Magnetically induced current densities have been calculated for porphycenes at the density functional theory level using gauge-including atomic orbitals to ensure gauge-origin independence and a fast basis-set convergence of the current densities. The current densities have been analyzed by using the gauge-including magnetically induced current (GIMIC) method. The porphycenes are aromatic, sustaining strong diatropic ring currents. The ring-current pathways have been determined by integrating the strength of the current density passing selected bonds. The calculations show that the ring current of the porphycenes splits into an outer and inner branch at the pyrrolic rings implying that the ring current involves all 26 π electrons of the porphycenes, which is similar to the ring current of porphyrins. The pyrrolic rings of the aromatic porphycenes do not sustain any significant local ring currents. Dihydroporphycene with four inner hydrogens is antiaromatic with weakly aromatic pyrrolic rings. The annelated benzoic rings in benzoporphycene sustain local paratropic ring currents, whereas the global ring current of dibenzoporphycene splits into an outer and inner branch at the benzoic rings. Comparison of calculated1H NMR shieldings with ring-current strengths shows that interactions between the inner hydrogen and the neighbor nitrogen is more significant for differences in the 1H NMR shieldings than variations in global ring-current strengths. Calculated excitation energies show that the antiaromatic dihydroporphycene has a smaller optical gap than the aromatic porphycene, even though its HOMO-LUMO gap is larger.

Enhancement of Antiaromatic Character via Additional Benzoannulation into Dibenzo[ a, f]pentalene: Syntheses and Properties of Benzo[ a]naphtho[2,1- f]pentalene and Dinaphtho[2,1- a, f]pentalene.

Understanding the structure-property relationships in antiaromatic molecules is crucial for controlling their electronic properties and designing new organic optoelectronic materials. Dibenzo[ a, f]pentalene, a structural isomer of dibenzopentalene, displays open-shell and antiaromatic character harmonization, which is not shared by the well-known isomer, dibenzo[ a, e]pentalene. The next questions of interest concern the topological effects of the π-extension on the harmonization of the open-shell and antiaromatic character in the dibenzo[ a, f]pentalene π-system. Herein, we describe the synthesis and characterization of the π-extended (bis)annulated analogues, benzo[ a]naphtho[2,1- f]pentalene 4 and dinaphtho[2,1- a, f]pentalene 5. The solid-state structures and the magnetic and optoelectronic properties characterized these π-extended analogues as closed-shell antiaromatic molecules, in sharp contrast with dibenzo[ a, f]pentalene 2. In these π-extended analogues, the open-shell character was annihilated whereas the antiaromatic character was retained. The fusion of additional hexagons into 2 shifted the main 4nπ-conjugated circuit from a global to a local system. Further investigations into magnetic ring currents using gauge-including magnetically induced current (GIMIC) calculations suggested that an enhanced local paratropic ring current appeared in the pentalene core of 5. The preservation of the benzenoid character in the additionally fused hexagons confined the paratropicity to the pentalene subunit, and the inherent presence of an o-quinoidal structure highlighted the 4nπ-electron delocalization on the pentalene unit. The antiaromaticity of 4 and 5 was characterized by their small HOMO-LUMO energy gap. Both experimental and computational results demonstrated that the [ a, f]-type ring fusion of the pentalene core effectively enhanced the antiaromatic character compared with the [ a, e]-type ring fusion in the reported bisannulated[ a, e]pentalenes. The findings of this study could potentially be used for the rational design of optoelectronic devices based on novel antiaromatic molecules.

Gauge-Origin Independent Calculations of the Anisotropy of the Magnetically Induced Current Densities.

Gauge-origin independent current density susceptibility tensors have been computed using the gauge-including magnetically induced current (GIMIC) method. The anisotropy of the magnetically induced current density (ACID) functions constructed from the current density susceptibility tensors are therefore gauge-origin independent. The ability of the gauge-origin independent ACID function to provide quantitative information about the current flow along chemical bonds has been assessed by integrating the cross-section area of the ACID function in the middle of chemical bonds. Analogously, the current strength susceptibility passing a given plane through the molecule is obtained by numerical integration of the current flow parallel to the normal vector of the integration plane. The cross-section area of the ACID function is found to be strongly dependent on the exact location of the integration plane, which is in sheer contrast to the calculated ring-current strength susceptibilities that are practically independent of the chosen position of the integration plane. The gauge-origin independent ACID functions plotted for different isosurface values show that a visual assessment of the current flow and degree of aromaticity depends on the chosen isosurface. The present study shows that ACID functions are not an unambiguous means to estimate the degree of molecular aromaticity according to the magnetic criterion and to determine the current pathway of complex molecular rings.

New insights into aromatic pathways of carbachlorins and carbaporphyrins based on calculations of magnetically induced current densities.

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 π-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 18π aromatic pathway. The aromatic pathways of the investigated carbaporphyrins and carbachlorins are very similar, since the current strength via the Cβ[double bond, length as m-dash]Cβ' bond of the cyclopentadienyl ring of the carbaporphyrins is almost as weak as the current density passing the corresponding saturated Cβ-Cβ' bond of the carbachlorins.

Aromaticity of the doubly charged [8]circulenes.

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 (1)H NMR chemical shifts.

Synthesis, aromaticity and photophysical behaviour of ferrocene- and ruthenocene-appended semisynthetic chlorin derivatives.

Two novel synthetic strategies to covalently link a metallocene electron-donor unit to a chlorin ring are presented. In one approach, pyropheophorbide a is readily converted into its 13(1) -ferrocenyl dehydro derivative by nucleophilic addition of the ferrocenyl anion to the 13(1) -carbonyl group. In another approach, the corresponding 13(1) -pentamethylruthenocenyl derivative is synthesised from 13(1) -fulvenylchlorin by a facile ligand exchange/deprotonation reaction with the [RuCp*(cod)Cl] (Cp*=pentamethylcyclopentadienyl; cod=1,5-cyclooctadiene) complex. The resulting metallocene-chlorins exhibit reduced aromaticity, which was unequivocally supported by ring-current calculations based on the gauge-including magnetically induced current (GIMIC) method and by calculated nucleus-independent chemical shift (NICS) values. The negative ring current in the isocyclic E ring suggests the antiaromatic character of this moiety and also clarifies the spontaneous reactivity of the complexes with oxygen. The oxidation products were isolated and their electrochemical and photophysical properties were studied. The ruthenocene derivatives turned out to be stable under light irradiation and showed photoinduced charge transfer with charge-separation lifetimes of 152-1029 ps.

Evaluating Shielding‐Based Ring‐Current Models by Using the Gauge‐Including Magnetically Induced Current Method

AbstractMagnetically induced current densities and integrated ring‐current strength susceptibilities have been calculated at the density functional theory (DFT) level for a test set consisting of 17 ring‐shaped molecules using the gauge‐including magnetically induced current (GIMIC) method. Reliable values for the ring‐current strengths have been obtained by performing numerical integration of the current‐density susceptibility passing a cut plane perpendicularly to the molecular ring. The current densities and ring current strengths were calculated at the DFT level using the B3LYP functional and def2‐TZVP basis sets. Current densities and ring‐current strengths have also been calculated at the Hartree‐Fock self‐consistent field (HF‐SCF) level using Dunning’s aug‐cc‐pVTZ basis sets, which allow a direct comparison with ring‐current strengths that have previously been estimated using ring‐current models based on magnetic shielding calculations. Current density calculations at both levels of theory show that the magnetic shielding based ring‐current models are not a very accurate means to estimate the magnetically induced ring current strengths, whereas they provide qualitatively the correct aromaticity trends for the studied molecules.

Aromatic pathways in carbathiaporphyrins.

Magnetically induced current densities and current pathways have been calculated for carbaporphyrins and carbathiaporphyrins using the gauge including magnetically induced current (GIMIC) method. The aromatic character and current pathways are obtained from the calculated current density susceptibilities. The current-density calculations show that five of the studied carbaporphyrinoids are aromatic, two are antiaromatic, and one is nonaromatic. The analysis of the current pathways of the investigated molecules reveals some general trends for the current flow in carbaporphyrinoids. Insertion of a CH2 group into the all-carbon ring generally cuts or restricts the current flow, leading to a stronger current of the alternative pathway of the ring. No obvious trends regarding the current strengths and pathways of the thiophene and cyclopentadienyl rings were obtained. The present study shows that it is indeed difficult to predict the electron delocalization pathways of general carbaporphyrinoids. Thus, a careful analysis of the current density is necessary for determining their electron delocalization pathways.

Predicting the degree of aromaticity of novel carbaporphyrinoids.

Magnetically induced current densities have been calculated for dioxaporphyrin, dithiaporphyrin, true carbaporphyrins, and N-confused porphyrins using the gauge-including magnetically induced current (GIMIC) method. The current-strength susceptibilities (current strengths) have been obtained by numerically integrating the current flow passing selected chemical bonds. The current strength calculations yield very detailed information about the electron delocalization pathways of the molecules. The strength of the ring-current that circles around the porphyrinoid macroring is used to estimate the degree of molecular aromaticity. The studied porphyrinoid structures have been obtained by replacing the NH and N groups of porphin with formally isoelectronic moieties such as O, S, CH and CH2. Replacing an NH moiety of trans-porphin with isoelectronic O and S does not significantly change the current strengths and pathways, whereas substitution of N with an isoelectronic CH group leads to significant changes in the current pathway and current strengths. CH2 groups cut the flow of diatropic currents, whereas in strongly antiaromatic molecules a significant fraction of the paratropic ring-current is able to pass the sp(3) hybridized inner carbons. N-confused porphyrinoids sustain a ring current whose strength is about half the ring-current strength of porphin with the dominating current flow along the outer pathway via the NH moiety. When no hydrogen is attached to the inner carbon of the inverted pyrrolic ring, the current prefers the inner route at that ring.

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 Möbius 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.

Aromatic Pathways in Twisted Hexaphyrins

The aromatic pathways and the degree of aromaticity of expanded porphyrins have been determined by explicit calculations of the routes and strengths of the magnetically induced currents using the gauge-including magnetically induced current (GIMIC) approach. Density functional theory calculations show that the doubly twisted hexaphyrins fulfilling Hückel's (4n + 2) pi-electron rule for aromaticity and those obeying the 4n pi-electron rule for antiaromaticity are aromatic and antiaromatic, respectively. The investigated [26]hexaphyrin (2) and (3) and [30]hexaphyrin (5) isomers are aromatic, and [28]hexaphyrin (4) is antiaromatic. The formally antiaromatic [24]hexaphyrin (1) does not sustain any strong ring current and must be considered nonaromatic. A detailed analysis of the current pathways of the hexaphyrins is presented. It was found that the current pathways of the investigated aromatic hexaphyrins are not always dominated by the flow along the inner route through the non-hydrogenated C-N-C moieties, as previously proposed. The current flow is often split into two branches at the pyrrole rings, but sometimes it takes the outer route via the C=C bond of the pyrrole. The current pathway of the weak paratropic ring current of [24]hexaphyrin is dominated by the outer C=C route. The calculations show that the routes of the current transport cannot be assessed merely by inspection or from nucleus independent chemical shifts; explicit calculations of the current pathways are compulsory. The current-density studies also show that the pyrrole rings do not sustain any strong ring currents of their own.

Magnetically Induced Currents in Bianthraquinodimethane-Stabilized Möbius and Hückel [16]Annulenes

The ring currents, NMR chemical shifts, topology of the chemical bonding, and UV-vis spectra of bianthraquinodimethane-stabilized [16]annulenes possessing Möbius and Hückel topology are investigated. The aromatic character of the title compounds is discussed on the basis of the magnetically induced current density obtained using the gauge-including magnetically induced current (GIMIC) approach. Numerical integration of the current density circling around the [16]annulene ring shows that both the Hückel and the Möbius isomers are non-aromatic. The [16]annulene ring of both isomers sustains a net ring current whose strength is only 0.3 nA/T. The ring current consists of a diamagnetic flow on the outside of the [16]annulene ring and a paramagnetic current inside it. Since the net ring-current strength of the [16]annulene is less than 5% of the ring current strength for benzene, both isomers must be considered non-aromatic by the ring current criterion. The similar bond length alternation of the [16]annulene rings also points to a similarity in aromatic character of the two isomers. The shape of the ring current of the Möbius isomer shows that the current density is somewhat more outspread than that of the Hückel isomer. Spatially separated diatropic and paratropic currents of equal strength follow the annulene bonds. The atoms-in-molecules (AIM) analysis reveals a cage critical point in the region of the outspread current density of the Möbius isomer. Intramolecular CH...pi and pi-pi interactions identified by AIM analysis, in combination with the outspread current density, stabilizes the Möbius isomer relative to the Hückel one. The molecule is characterized by calculating the (13)C and (1)H NMR chemical shifts and the UV-vis spectrum and comparing these to experimental spectra. The (13)C NMR and (1)H NMR chemical shifts are rather similar for the two isomers. The UV-vis spectra are compared with the excitation energies calculated at the time-dependent density functional theory (TDDFT) level using Becke's three-parameter hybrid functional together with the LYP correlation functional (B3LYP), as well as at the approximate coupled cluster singles (CCS) and at the approximate coupled cluster singles and doubles (CC2) levels of theory. The CC2 calculations yield excitation energies in fairly good agreement with experimental data.

Calculation of Magnetically Induced Currents in Hydrocarbon Nanorings

Magnetically induced current densities, nuclear magnetic shieldings, and electric polarizabilities of planar ring-shaped hydrocarbons have been studied at the density-functional theory level using the Becke-Perdew (BP86) functional. The current densities were calculated using the Gauge-Including Magnetically Induced Current (GIMIC) method employing gauge-including atomic orbitals. The GIMIC calculations yield rules to estimate the global and local ring-current strengths as well as the current pathways for the hydrocarbon nanorings. For the overall antiaromatic molecules, aromatic groups such as benzene, naphthalene, anthracene, and pyrene moieties localize the ring current making the global ring currents vanish. The ability of the edge groups to localize the currents is related to the aromatic character of the molecule as a whole. The local ring current prefers to follow the edges of the group. Phenalenyl corner moieties are found to introduce strong global ring currents, whereas with fused benzene and pyrene corner groups the global ring current vanishes. Fused benzene rings in the corner or along the edge of overall antiaromatic molecules sustain local ring currents of about the same size as for a free benzene molecule. For the overall aromatic molecules, the global ring current is split along the bonds of the edge moieties, but the detailed division fulfilling Kirchhoff's current law is not easily predictable and must be calculated for each individual bond. At the phenalenyl corner moieties, the global ring current follows the innermost route isolating the rest of the group from the main delocalization pathway. A hydrocarbon nanoring sustaining strong ring currents should be large and formally aromatic with many and large aromatic moieties along the edges. A clear correlation between the strength of the global ring currents and the size of the electric polarizabilities is obtained. The calculated 1H NMR shieldings of a proton in immediate contact to the global ring current vary between 22 ppm and 67 ppm in the studied molecules. The trend correlates well with the global ring-current strengths, which are in the range of 0-88 nA/T. The 13C NMR shieldings are also sensitive to the strength of the global ring current, but they vary less systematically and are not as good an indicator of the current strength as the hydrogen shieldings.

On the Aromaticity of the Planar Hydrogen-Bonded (HF)3 Trimer.

The nuclear magnetic shieldings and magnetically induced ring currents have been calculated for the planar ring-shaped hydrogen fluoride trimer (HF)3 at correlated ab initio and density functional theory levels. Calculations of the magnetically induced current densities using the gauge-including magnetically induced current (GIMIC) method show that, contrary to a recent suggestion, (HF)3 has, at the MP2/TZVPP level, a very small ring-current susceptibility of 0.37 nA/T. Thus, only a weak net current is passing across the H···F hydrogen bond. An external magnetic field perpendicular to the ring plane induces strong edge currents circling around each HF molecule giving rise to a nonvanishing magnetic shielding at the center of the ring. The GIMIC results are supported by calculations of the long-range magnetic shielding function; the long-range magnetic shielding is very small, indicating that the magnetically induced ring-current is very weak. The surprisingly large nucleus-independent chemical shift (NICS) value for (HF)3 was recently taken as an indication of "H-bonded aromaticity". The NICS value calculated at the CCSD/QZ2P level is 2.77 ppm. The present GIMIC and aromatic ring-current shielding study shows that some care has to be taken when using NICS values as aromaticity indices.

Experimental and Computational Studies of Alkali-Metal Coinage-Metal Clusters

Coinage and alkali metal mixed clusters, M4Na- (M = Cu, Au) have been investigated experimentally using photoelectron spectroscopy and computationally at correlated ab initio levels. The related Cu4Li-, Ag4Li-, Ag4Na-, and Au4Li- clusters as well as the neutral Cu4Li2 and Cu4Na2 clusters have also been studied computationally. The calculations show that the two lowest isomers of the negatively charged clusters include a pyramidal C4v structure and a planar C2v species. For Cu4Li- and Cu4Na-, the C4v structure is calculated at correlated ab initio level to be 30.9 and 16.9 kJ/mol below the planar C2v isomer, whereas the planar isomers of Au4Li- and Au4Na- are found to be 29.7 and 49.4 kJ/mol below the pyramidal ones. For Ag4Li- and Ag4Na-, the pyramidal isomers are the lowest ones. Comparison of the calculated and measured photoelectron spectra of Cu4Na- and Au4Na- shows that the pyramidal Cu4Na- cluster of C4v symmetry and the planar Au4Na- of C2v symmetry are detected experimentally. Calculations of the magnetically induced current density in Cu4Li- and Cu4Li2 using the Gauge-Including Magnetically Induced Current (GIMIC) method show that strong ring currents are sustained mainly by the highest-occupied molecular orbital primarily derived from the Cu 4s. The GIMIC calculations thus show that the Cu4(2-) ring is -aromatic and that the d orbitals do not play any significant role for the electron delocalization effects. The present study does not support the notion that the square-planar Cu4(2-) is the first example of d-orbital aromatic molecules.