Metallaantiaromaticity of 10-Platinacorrole Complexes.

The aromaticity of cyclic π-conjugated organometallic compounds is known as metallaaromaticity. π-Conjugated metallacycles, such as metallabenzenes and metallapentalenes, have been investigated in order to understand the involvement of the d electrons from the metal center in the π-conjugated systems of the organic ligands. Here, we report the synthesis of Pd(II) 10-platinacorrole complexes with cyclooctadiene (COD) and norbornadiene (NBD) ligands. While the Pd(II) 10-platinacorrole COD complex adopts a distorted structure without showing appreciable antiaromaticity, the corresponding NBD complex exhibits a distinct antiaromatic character due to its highly planar conformation. Detailed density functional theory (DFT) calculations revealed that two d orbitals are involved in macrocyclic π-conjugation. We furthermore demonstrated that Craig-Möbius antiaromaticity is not present in the studied system. The synthesis of 10-platinacorroles enables a systematic comparison of the antiaromaticity and aromaticity of closely related porphyrin analogues, providing a better understanding of π-conjugation that involves d orbitals.

Determinant Factors of Three-Dimensional Aromaticity in Antiaromatic Cyclophanes.

Three-dimensional aromaticity arising from the close stacking of two antiaromatic π-conjugated macrocycles has recently received considerable attention. Here, a cyclophane consisting of two antiaromatic Ni(II) norcorrole units tethered with two flexible alkyl chains was synthesized. The norcorrole cyclophane showed crystal polymorphism providing three different solid-state structures. Surprisingly, one of them adopted an aligned face-to-face stacking arrangement with negligible displacement along the slipping axis. Although the exchange repulsion between two π-clouds should be maximized in this orientation, the π-π distance is remarkably close (3.258 Å). Three-dimensional aromaticity in this conformation has been supported experimentally and theoretically as evidenced by small bond length alternations as well as the presence of a diatropic ring current. An analogous cyclophane with two aromatic Ni(II) porphyrin units was prepared for comparison. The porphyrin cyclophane exhibited a slipped-stacking conformation with a larger displacement (2.9 Å) and a larger interplanar distance (3.402 Å) without noticeable change of the aromaticity of each porphyrin unit. In solution, the norcorrole cyclophane forms a twist stacking arrangement with effective interplanar orbital overlap and exists in an equilibrium between stacked and nonstacked structures. Thermodynamic parameters of the stacking process were estimated, revealing an inherently large attractive interaction operating between two norcorrole units, which has been further supported by energy decomposition analysis.

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.

Spatial Contributions to Nuclear Magnetic Shieldings.

We develop a methodology for calculating, analyzing, and visualizing nuclear magnetic shielding densities which are calculated from the current density via the Biot-Savart relation. Atomic contributions to nuclear magnetic shielding constants can be estimated within our framework with a Becke partitioning scheme. The new features have been implemented in the GIMIC program and are applied in this work to the study of the 1H and 13C nuclear magnetic shieldings in benzene (C6H6) and cyclobutadiene (C4H4). The new methodology allows a visual inspection of the spatial origins of the positive (shielding) and negative (deshielding) contributions to the nuclear magnetic shielding constant of a single nucleus, something which has not been hitherto easily accomplished. Analysis of the shielding densities shows that diatropic and paratropic current-density fluxes yield both shielding and deshielding contributions, as the shielding or deshielding is determined by the direction of the current-density flux with respect to the studied nucleus instead of the tropicity. Becke partitioning of the magnetic shieldings shows that the magnetic shielding contributions mainly originate from the studied atom and its nearest neighbors, confirming the localized character of nuclear magnetic shieldings.

Calculation of vibrationally resolved absorption spectra of acenes and pyrene.

The absorption spectra of naphthalene, anthracene, pentacene and pyrene in the ultraviolet-visible (UV-Vis) range have been simulated by using an efficient real-time generating function method that combines calculated adiabatic electronic excitation energies with vibrational energies of the excited states. The vertical electronic excitation energies have been calculated at the density functional theory level using the PBE0 functional and at the second-order approximate coupled-cluster level (CC2). The absorption spectra have been calculated at the PBE0 level for the studied molecules and at the CC2 level for naphthalene. The transition probabilities between vibrationally resolved states were calculated by using the real-time generating function method employing the full Duschinsky formalism. The absorption spectrum for naphthalene calculated at the PBE0 and CC2 levels agrees well with the experimental one after the simulated spectra have been blue-shifted by 0.48 eV and 0.12 eV at the PBE0 and CC2 level, respectively. The absorption spectra for anthracene, pentacene and pyrene simulated at the PBE0 level agree well with the experimental ones when they are shifted by 0.49 eV, 0.57 eV and 0.46 eV, respectively. The strongest transitions of the main vibrational bands have been assigned.

Three-dimensional aromaticity in an antiaromatic cyclophane.

Understanding of interactions among molecules is essential to elucidate the binding of pharmaceuticals on receptors, the mechanism of protein folding and self-assembling of organic molecules. While interactions between two aromatic molecules have been examined extensively, little is known about the interactions between two antiaromatic molecules. Theoretical investigations have predicted that antiaromatic molecules should be stabilized when they stack with each other by attractive intermolecular interactions. Here, we report the synthesis of a cyclophane, in which two antiaromatic porphyrin moieties adopt a stacked face-to-face geometry with a distance shorter than the sum of the van der Waals radii of the atoms involved. The aromaticity in this cyclophane has been examined experimentally and theoretically. This cyclophane exhibits three-dimensional spatial current channels between the two subunits, which corroborates the existence of attractive interactions between two antiaromatic π-systems.

Absorption shifts of diastereotopically ligated chlorophyll dimers of photosystem I.

The light-harvesting chlorophyll (Chl) molecules of photosynthetic systems form the basis for light-driven energy conversion. In biological environments, the Chl chromophores occur in two distinct diastereotopic configurations, where the α and ß configurations have a magnesium-ligating histidine residue and a 17-propionic acid moiety on the opposite side or on the same side of the Chl ring, respectively. Although ß-ligated Chl dimers occupy conserved positions around the reaction center of photosystem I (PSI), the functional relevance of the α/ß configuration of the ligation is poorly understood. We employ here correlated ab initio calculations using the algebraic-diagrammatic construction through second order (ADC(2)) and the approximate second-order coupled cluster (CC2) methods in combination with the reduced virtual space (RVS) approach in studies of the intrinsic excited-state properties of α-ligated and ß-ligated Chl dimers of PSI. Our ab initio calculations suggest that the absorption of the α-ligated reaction-center Chl dimer of PSI is redshifted by 0.13-0.14 eV in comparison to the ß-ligated dimers due to combined excitonic coupling and strain effects. We also show that time-dependent density functional theory (TDDFT) calculations using range-separated density functionals underestimate the absorption shift between the α- and ß-ligated dimers. Our findings may provide a molecular starting point for understanding the energy flow in natural photosynthetic systems, as well as a blueprint for developing new molecules that convert sunlight into other forms of energy.

Ni(II) 10-Phosphacorrole: A Porphyrin Analogue Containing Phosphorus at the Meso Position.

Ni(II) 10-Phosphacorrole, a porphyrinoid containing phosphorus at the meso position, was synthesized from a bis(α,α'-dibromodipyrrin) Ni(II) complex and a phosphine anion via the palladium-catalyzed formation of a C-C and two C-P bonds. The optoelectronic properties of Ni(II) 10-phosphacorrole can be modulated effectively by oxidation or coordination of a metal to the phosphorus center. While Ni(II) 10-phosphacorrole exhibits a distinctly aromatic character due to the cyclic conjugation of 18 π-electrons, its oxide exhibited weak antiaromaticity, which was confirmed experimentally and theoretically.

Four-component relativistic 31P NMR calculations for trans-platinum(ii) complexes: importance of the solvent and dynamics in spectral simulations.

We report a combined experimental-theoretical study on the 31P NMR chemical shift for a number of trans-platinum(ii) complexes. Validity and reliability of the 31P NMR chemical shift calculations are examined by comparing with the experimental data. A successful computational protocol for the accurate prediction of the 31P NMR chemical shifts was established for trans-[PtCl2(dma)PPh3] (dma = dimethylamine) complexes. The reliability of the computed values is shown to be critically dependent on the level of relativistic effects (two-component vs. four component), choice of density functionals, dynamical averaging, and solvation effects. Snapshots obtained from ab initio molecular dynamics simulations were used to identify those solvent molecules which show the largest interactions with the platinum complex, through inspection by using the non-covalent interaction program. We observe satisfactory accuracy from the full four-component matrix Dirac-Kohn-Sham method (mDKS) based on the Dirac-Coulomb Hamiltonian, in conjunction with the KT2 density functional, and dynamical averaging with explicit solvent molecules.

Bicycloaromaticity and Baird-type bicycloaromaticity of dithienothiophene-bridged [34]octaphyrins.

Aromatic properties of two recently synthesized dithienothiophene-bridged (DTT) [34]octaphyrins have been investigated by calculating magnetically induced current densities and vertical excitation energies. These intriguing molecules have been proposed to be the first synthesized neutral bicycloaromatic compounds. The triplet state of their dications was even suggested to be Baird-type bicycloaromatic rendering them very interesting as a new prototype of molecules possessing simultaneously the two rare types of aromaticity. Here, we investigate computationally the aromatic properties of the neutral as well as the singly and doubly charged DTT-bridged [34]octaphyrins. Our study provides unambiguous information about changes in the aromatic properties of the DTT-bridged [34]octaphyrins upon oxidation. The calculations identify two independent diatropic ring currents in the neutral DTT-bridged [34]octaphyrins, showing that they are indeed bicycloaromatic. The current-density flow of the two independent ring currents of the bicycloaromatic compounds are visualized and individual aromatic pathways are quantified by performing numerical integration. The calculations show that two independent diatropic ring currents can indeed be sustained by molecules consisting of two aromatic rings that share a common set of π electrons. The current density calculations on the singly charged DTT-bridged [34]octaphyrins show that they are weakly antiaromatic, which does not agree with the suggested aromatic character deduced from spectroscopical studies. The triplet state of the two DTT-bridged [34]octaphyrin cations with very similar molecular structures have unexpectedly different aromatic character. One of them is Baird-type bicycloaromatic, whereas the triplet state of the other dication has one aromatic and one nonaromatic ring, which could not be resolved from available spectroscopical data. Calculations of excitation energies reveal that a simple model cannot be employed for interpreting the electronic excitation spectra of the present molecules, because more than 20 excited states contribute to the spectra above 2.5 eV (500 nm) showing the importance of computations. The present work illustrates how detailed information about molecular aromaticity can nowadays be obtained by scrutinizing calculated current densities.

Rational Synthesis of Antiaromatic 5,15-Dioxaporphyrin and Oxidation into ß,ß-Linked Dimers.

5,15-Dioxaporphyrin was synthesized for the first time by a nucleophilic aromatic substitution reaction of a nickel bis(α,α'-dibromodipyrrin) complex with benzaldoxime, followed by an intramolecular annulation of the α-hydroxy-substituted intermediate. This unprecedented molecule is a 20π-electron antiaromatic system, in terms of Hückel's rule of aromaticity, because lone pair electrons of oxygen atoms are incorporated into the 18π-electron conjugated system of the porphyrin. A theoretical analysis based on the gauge-including magnetically induced current method confirmed its antiaromaticity and a dominant inner ring pathway for the ring current. The unique reactivity of 5,15-dioxaporphyrin forming a ß,ß-linked dimer upon oxidation was also revealed.

Computational Studies of Aromatic and Photophysical Properties of Expanded Porphyrins.

Magnetically induced current densities and ring-current pathways have been calculated at density functional theory (DFT) and second-order Møller-Plesset perturbation theory (MP2) levels of theory for a set of expanded porphyrins consisting of five or six pyrrolic rings. The studied molecules are sapphyrin, cyclo[6]pyrrole, rubyrin, orangarin, rosarin, and amethyrin. Different functionals have been employed to assess the functional dependence of the ring-current strength susceptibility. Vertical singlet and triplet excitation energies have been calculated at the second-order approximate coupled cluster (CC2), expanded multiconfigurational quasi-degenerate perturbation theory (XMC-DPT2), and time-dependent density functional theory levels. The lowest electronic transition of the antiaromatic molecules was found to be pure magnetic transitions providing an explanation for the large paratropic contribution to the total current density. Rate constants for different nonradiative deactivation channels of the lowest excited states have been calculated yielding lifetimes and quantum yields of the lowest excited singlet and triplet states. The calculations show that the spin-orbit interaction between the lowest singlet ( S0) and triplet ( T1) states of the antiaromatic molecules is strong, whereas for the aromatic molecule the spin-orbit coupling vanishes. The experimentally detected fluorescence from S2 to S0 of amethyrin has been explained. The study shows that there are correlations between the aromatic character and optical properties of the investigated expanded porphyrins.

Magnetically Induced Ring-Current Strengths in Möbius Twisted Annulenes.

The topology of twisted molecular rings is characterized by the linking number, which is equal to the sum of the twist-a local property of the molecular frame-and the writhe-a global parameter, which represents the bending of the molecular ring. In this work, we investigate a number of cyclic all- trans C40H40 annulenes with varying twisting numbers for a given linking number and their dications. The aromatic character is assessed by calculating ring-current strength susceptibilities using the gauge-including magnetically induced currents (GIMIC) method, which makes it possible to conduct a systematic study of the relation between the topology and aromaticity of twisted molecules. We found that the aromatic properties of the investigated Möbius twisted molecules are not only dependent on the linking number as previously suggested but also depend strongly on the partitioning of the linking number into the twist and writhe contributions.

Optical and magnetic properties of antiaromatic porphyrinoids.

Magnetic and spectroscopic properties of a number of formally antiaromatic carbaporphyrins, carbathiaporphyrins and isophlorins with 4n π electrons have been investigated at density functional theory and ab initio levels of theory. The calculations show that the paratropic contribution to the magnetically induced ring-current strength susceptibility and the magnetic dipole-transition moment between the ground and the lowest excited state are related. The vertical excitation energy (VEE) of the first excited state decreases with increasing ring-current strength susceptibility, whereas the VEE of the studied higher-lying excited states are almost independent of the size of the ring-current strength susceptibility. Strong antiaromatic porphyrinoids, based on the magnitude of the paratropic ring-current strength susceptibility, have small energy gaps between the highest occupied and lowest unoccupied molecular orbitals and a small VEE of the first excited state. The calculations show that only the lowest S0 → S1 transition contributes signficantly to the magnetically induced ring-current strength susceptibility of the antiaromatic porphyrinoids. The decreasing optical gap combined with a large angular momentum contribution to the magnetic transition moment from the first excited state explains why molecules III-VII are antiaromatic with very strong paratropic ring-current strength susceptibilities. The S0 → S1 transition is a magnetic dipole-allowed electronic transition that is typical for antiaromatic porphyrinoids with 4n π electrons.

Closed-shell paramagnetic porphyrinoids.

Magnetizabilities and magnetically induced ring-current strength susceptibilities have been calculated at the Hartree-Fock, density functional theory and second order Møller-Plesset levels for a number of antiaromatic closed-shell carbaporphyrins, carbathiaporphyrins and isophlorins. The calculations yield a linear relation between magnetizabilities and ring-current strength susceptibilities. The calculations show that the porphyrinoids with the largest ring-current strength susceptibility are closed-shell paramagnetic molecules with positive magnetizabilities. The closed-shell paramagnetism is due to the large paramagnetic contribution to the magnetizability originating from the strong paratropic ring current in the antiaromatic porphyrinoids.

Relation Between Ring Currents and Hydrogenation Enthalpies for Assessing the Degree of Aromaticity.

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 Møller-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.

The influence of heteroatoms on the aromatic character and the current pathways of B2N2-dibenzo[a,e]pentalenes.

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.

Nuclei-selected atomic-orbital response-theory formulation for the calculation of NMR shielding tensors using density-fitting.

An atomic orbital density matrix based response formulation of the nuclei-selected approach of Beer, Kussmann, and Ochsenfeld [J. Chem. Phys. 134, 074102 (2011)] to calculate nuclear magnetic resonance (NMR) shielding tensors has been developed and implemented into LSDalton allowing for a simultaneous solution of the response equations, which significantly improves the performance. The response formulation to calculate nuclei-selected NMR shielding tensors can be used together with the density-fitting approximation that allows efficient calculation of Coulomb integrals. It is shown that using density-fitting does not lead to a significant loss in accuracy for both the nuclei-selected and the conventional ways to calculate NMR shielding constants and should thus be used for applications with LSDalton.

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.