Is the Conventional Interpretation of the Anisotropic Effects of CC Double Bonds and Aromatic Rings in NMR Spectra in Terms of the π‐Electron Shielding/Deshielding Contributions Correct?

Based on the nucleus‐independent chemical shift (NICS) concept, isotropic magnetic shielding values have been computed along the three Cartesian axes for ethene, cyclobutadiene, benzene, naphthalene, and benzocyclobutadiene, starting from the molecular/ring center up to 10 Å away. These through‐space NMR spectroscopic shielding (TSNMRS) values, which reflect the anisotropic effects, have been broken down into contributions from localized‐ and canonical molecular orbitals (LMOs and CMOs); these contributions revealed that the proton NMR spectroscopic chemical shifts of nuclei that are spatially close to the C?C double bond or the aromatic ring should not be explained in terms of the conventionally accepted π‐electron shielding/deshielding effects. In fact, these effects followed the predictions only for the antiaromatic cyclobutadiene ring.     

Method and basis set dependence of the NICS indexes of aromaticity for benzene

The role of theory level in prediction of benzene magnetic indexes of aromaticity is analysed and compared with calculated nuclear magnetic shieldings of ³He used as NMR probe. Three closely related nucleus‐independent chemical shift (NICS) based indexes were calculated for benzene at SCF‐HF, MP2, and DFT levels of theory and the impact of basis set on these quantities was studied. The changes of benzene NICS(0), NICS(1), and NICS(1)zz parameters calculated using SCF‐HF, MP2 and several density functionals were within 1 to 3 ppm. Similar deviations between magnetic indexes of aromaticity were observed for values calculated with selected basis sets. Only very small effect of polar solvent on benzene aromaticity was predicted. The ³He nuclear magnetic isotropic shielding (σ) and its zz‐components (σ_zz) of helium atom approaching the centre of benzene ring from above produced similar curves versus benzene‐He distance to NICS parameters calculated for similarly moving Bq ghost atom. We also propose an experimental verification of NICS calculations by designing the ³He NMR measurement for benzene saturated with helium gas or in low temperature matrices.     

Magnetic properties of conjugated molecules

An LCAO SCF perturbation theory is used to discuss the diamagnetic susceptibility and shielding constant contributions associated with ring currents in aromatic molecules. The proton shielding constants are calculated directly from the current density expression for benzene, naphthalene, anthracene and phenanthrene.     

A distributed multipole analysis of the charge densities of some aromatic hydrocarbons

SCF wavefunctions have been calculated for benzene, naphthalene, anthracene, phenanthrene, pyrene, triphenylene, perylene and coronene using a 3-21G basis set, and for benzene and naphthalene with a double-zeta basis set. A direct SCF method was used for the calculations on the three largest molecules. The distributed multipole analyses of these wavefunctions are used to comment on empirical models for the electrostatic interactions of these molecules.     

Density functional theoretical investigation of the aromatic nature of BN substituted benzene and four ring polyaromatic hydrocarbons

We have studied the topological and local aromaticity of BN-substituted benzene, pyrene, chrysene, triphenylene and tetracene molecules. The nucleus-independent chemical shielding (NICS), harmonic oscillator model of aromaticity (HOMA), para-delocalization index (PDI) and aromatic fluctuation index (FLU) have been calculated to quantify aromaticity in terms of magnetic and structural criteria. We find that charge separations due to the introduction of heteroatoms largely affect both the local and topological aromaticity of these molecules. Our studies show that the presence of any kind of heteroatom in the ring not only reduces the local delocalization in the six membered ring, but also affects strongly the topological aromaticity. In fact, the relative orders of the topological and local aromaticity depend strongly on the position of the heteroatoms in the structure. In general, more ring shared BN containing molecules are less aromatic than the less ring shared BN molecules. In addition our results provide evidence that the structural stability of the molecule is dominated by the σ bond rather than the π bond.     

Intermolecular interactions in solid benzene

The lattice dynamics and molecular vibrations of benzene and deuterated benzene crystals are calculated from force constants derived from density-functional theory (DFT) calculations and compared with measured inelastic neutron-scattering spectra. A very small change (0.5%) in lattice parameter is required to obtain real lattice-mode frequencies across the Brillouin zone. There is a strong coupling between wagging and breathing modes away from the zone center. This coupling and sensitivity to cell size arises from two basic interactions. Firstly, comparatively strong interactions that hold the benzene molecules together in layers. These include an intermolecular interaction in which H atoms of one molecule link to the center of the aromatic ring of a neighboring molecule. The layers are held to each other by weaker interactions, which also have components that hold molecules together within a layer. Small changes in the lattice parameters change this second type of interaction and account for the changes to the lattice dynamics. The calculations also reveal a small auxetic effect in that elongation of the crystal along the b axis leads to an increase in internal pressure in the ac plane, that is, elongation in the b direction induces expansion in the a and c directions.     

Ring current effects in crystals. Evidence from 13C chemical shift tensors for intermolecular shielding in 4,7-di-t-butylacenaphthene versus 4,7-di-t-butylacenaphthylene

13C chemical shift tensor data from 2D FIREMAT spectra are reported for 4,7-di-t-butylacenaphthene and 4,7-di-t-butylacenaphthylene. In addition, calculations of the chemical shielding tensors were completed at the B3LYP/6-311G** level of theory. While the experimental tensor data on 4,7-di-t-butylacenaphthylene are in agreement with theory and with previous data on polycyclic aromatic hydrocarbons, the experimental and theoretical data on 4,7-di-t-butylacenaphthene lack agreement. Instead, larger than usual differences are observed between the experimental chemical shift components and the chemical shielding tensor components calculated on a single molecule of 4,7-di-t-butylacenaphthene, with a root mean square (rms) error of +/-7.0 ppm. The greatest deviation is concentrated in the component perpendicular to the aromatic plane, with the largest value being a 23 ppm difference between experiment and theory for the 13CH2 carbon delta11 component. These differences are attributed to an intermolecular chemical shift that arises from the graphitelike, stacked arrangement of molecules found in the crystal structure of 4,7-di-t-butylacenaphthene. This conclusion is supported by a calculation on a trimer of molecules, which improves the agreement between experiment and theory for this component by 14 ppm and reduces the overall rms error between experiment and theory to 4.0 ppm. This intermolecular effect may be modeled with the use of nuclei independent chemical shieldings (NICS) calculations and is also observed in the isotropic 1H chemical shift of the CH2 protons as a 4.2 ppm difference between the solution value and the solid-state chemical shift measured via a 13C-1H heteronuclear correlation experiment.     

Beyond NICS: estimation of the magnetotropicity of inorganic unsaturated planar rings

A simple classical model of magnetic-field induced electron flow is used to evaluate the ring current strength for a few inorganic monocyclic compounds: B(3)H(3)N(3), B(3)H(3)O(3), P(6), N(6), Si(6)H(6), N, Al and H(6). It is shown that, for these neutral and charged systems, sustaining delocalized electron currents in the presence of a magnetic field B(ext) orthogonal to the σ(h) plane, the out-of-plane component of the nuclear magnetic shielding along the central axis is connected to the out-of-plane magnetizability by a simple equation, involving the radius of an average loop of current. A novel estimate of this effective radius is provided. Reliable ring current susceptibilities (that is, current strengths) can be evaluated by a simple relationship, using the out-of-plane components of nuclear shielding and magnetizability tensors. The accuracy of the current susceptibilities calculated by the classical model is established by comparison with corresponding ab initio estimates obtained by integrating the quantum mechanical current-density vector field. The out-of-plane components of nuclear shielding and magnetizability are both strongly biased by the molecular geometry. Their combined use to estimate the ring current susceptibility offers a quantifier of magnetotropicity more reliable than (i) the ξ(∥) out-of-plane component of magnetizability, (ii) the σ(∥)(CM) out-of-plane component of the magnetic shielding at the center of mass, widely reported as NICS(∥)(0) = -σ(∥)(CM). The inadequacy of these commonly adopted magnetotropicity measures is demonstrated by comparing a set of related molecules, C(6)H(6) and Si(6)H(6), N(6) and P(6).     

High-resolution electron spectroscopy, preferential metal-binding sites, and thermochemistry of lithium complexes of polycyclic aromatic hydrocarbons

Polycyclic aromatic hydrocarbons are model systems for studying the mechanisms of lithium storage in carbonaceous materials. In this work, Li complexes of naphthalene, pyrene, perylene, and coronene were synthesized in a supersonic metal-cluster beam source and studied by zero-electron-kinetic-energy (ZEKE) electron spectroscopy and density functional theory calculations. The adiabatic ionization energies of the neutral complexes and frequencies of up to nine vibrational modes in the singly charged cations were determined from the ZEKE spectra. The metal-ligand bond energies of the neutral complexes were obtained from a thermodynamic cycle. Preferred Li∕Li(+) binding sites with the aromatic molecules were determined by comparing the measured spectra with theoretical calculations. Li and Li(+) prefer the ring-over binding to the benzene ring with a higher π-electron content and aromaticity. Although the ionization energies of the Li complexes show no clear correlation with the size of the aromatic molecules, the metal-ligand bond energies increase with the extension of the π-electron network up to perylene, then decrease from perylene to coronene. The trends in the ionization and metal-ligand bond dissociation energies of the complexes are discussed in terms of the orbital energies, local quadrupole moments, and polarizabilities of the free ligands and the charge transfer between the metal atom and aromatic molecules.     

Diatropicity of tetraazanaphthalenes

Tetraazanaphthalenes are diatropic molecules, whose magnetic response to a magnetic field perpendicular to the molecular plane closely resembles that of naphthalene. The out-of-plane component of the magnetic susceptibility tensor and its strong anisotropy can be used as quantifiers of magnetic aromaticity. Maps showing streamlines and modulus of the current density field provide clear evidence for diatropicity of these systems. They also explain the strong anisotropy of carbon and nitrogen magnetic shielding, which is determined by the big out-of-plane component of the nuclear shielding tensor. The electronic ring currents observed in the map deshield the nuclei of ring hydrogens by enforcing the local magnetic field and diminishing the out-of-plane component of proton shielding.     

Borazine: to be or not to be aromatic

Aromaticity of borazine, which has been subject of controversial discussions, is addressed. Beside a short review on aromaticity of borazine we report a detailed analysis of two molecular fields, the induced magnetic field (B ^ind) and the electron localization function (ELF). The induced magnetic field of borazine shows a long-range shielding cone perpendicular to the molecular plane, as in benzene, but lower in magnitude. Contrary to benzene, borazine shows two weakly paratropic regions, one of them inside the ring, and the second one enveloping the boron atoms. It is necessary to separate σ and π contributions to identify whether borazine exhibits π-aromatic character comparable to benzene. Nucleus-independent chemical shift (NICS) isolines show that the σ electrons are much stronger localized than π electrons, their local paramagnetic contributions generate a short-range response and a paratropic (deshielding) region in the ring center (similar to an anti-aromatic response). Three regions can be identified as chemically meaningful domains exhibiting an internally strong electron delocalization (ELF = 0.823). Borazine may be described as a π aromatic compound, but it is not a globally aromatic species, as the electronic system is not as delocalized as in benzene. Dedicated to the 70th birthday of Prof. Tadeusz Marek Krygowski.     

Local aromaticity mapping in the vicinity of planar and nonplanar molecules

We report on nucleus-independent magnetic shielding (NICS) scans over the centers of six- and five-membered rings in selected metal phthalocyanines (MPc) and fullerene C60 for more accurate characterization of local aromaticity in these compounds. Detailed tests were conducted on model aromatic molecules including benzene, pyrrole, indole, isoindole, and carbazole and subsequently applied to H₂Pc, ZnPc, Al(OH)Pc, and CuPc. Similar behavior of three selected magnetic probes, Bq, ³He, and ⁷Li⁺, approaching perpendicularly the ring centers, was observed. For better visualization of shielding zone over the centers of aromatic rings, we introduced a simple mathematical procedure: the first and second derivatives of scan curves with respect to magnetic probe position enabled their additional examination. It allowed an easier localization of curve minimum and discrimination between areas in space varying by the magnetic field magnitude and to illustrate local aromaticity of two different kinds of rings in MPc with better resolution. Our results supported earlier reports on very low aromaticity indexes of pyrrole ring incorporated into MPc and significant aromaticity of the central macrocycle. No direct dependence between harmonic oscillator model of aromaticity and NICS was observed. Instead, a correlation between position of scan curve minimum and its magnitude were observed. In addition, the NICS values and ³He chemical shifts in the middle of neutral C60 and C60⁶⁻ anion agreed well with the reported experimental NMR values for He@C60 and He@C60⁶⁻.     

Accurate description of van der Waals complexes by density functional theory including empirical corrections

An empirical method to account for van der Waals interactions in practical calculations with the density functional theory (termed DFT-D) is tested for a wide variety of molecular complexes. As in previous schemes, the dispersive energy is described by damped interatomic potentials of the form C6R(-6). The use of pure, gradient-corrected density functionals (BLYP and PBE), together with the resolution-of-the-identity (RI) approximation for the Coulomb operator, allows very efficient computations for large systems. Opposed to previous work, extended AO basis sets of polarized TZV or QZV quality are employed, which reduces the basis set superposition error to a negligible extend. By using a global scaling factor for the atomic C6 coefficients, the functional dependence of the results could be strongly reduced. The "double counting" of correlation effects for strongly bound complexes is found to be insignificant if steep damping functions are employed. The method is applied to a total of 29 complexes of atoms and small molecules (Ne, CH4, NH3, H2O, CH3F, N2, F2, formic acid, ethene, and ethine) with each other and with benzene, to benzene, naphthalene, pyrene, and coronene dimers, the naphthalene trimer, coronene. H2O and four H-bonded and stacked DNA base pairs (AT and GC). In almost all cases, very good agreement with reliable theoretical or experimental results for binding energies and intermolecular distances is obtained. For stacked aromatic systems and the important base pairs, the DFT-D-BLYP model seems to be even superior to standard MP2 treatments that systematically overbind. The good results obtained suggest the approach as a practical tool to describe the properties of many important van der Waals systems in chemistry. Furthermore, the DFT-D data may either be used to calibrate much simpler (e.g., force-field) potentials or the optimized structures can be used as input for more accurate ab initio calculations of the interaction energies.     

The NICS‐XY‐Scan: Identification of Local and Global Ring Currents in Multi‐Ring Systems

Nucleus‐independent chemical shift (NICS)‐based methods are very popular for the determination of the induced magnetic field under an external magnetic field. These methods are used mostly (but not only) for the determination of the aromaticity and antiaromaticity of molecules and ions, both qualitatively and quantitatively. The ghost atom that serves as the NICS probe senses the induced magnetic field and reports it in the form of an NMR chemical shift. However, the source of the field cannot be determined by NICS. Thus, in a multi‐ring system that may contain more than one induced current circuit (and therefore more than one source of the induced magnetic field) the NICS value may represent the sum of many induced magnetic fields. This may lead to wrong assignments of the aromaticity (and antiaromaticity) of the systems under study. In this paper, we present a NICS‐based method for the determination of local and global ring currents in conjugated multi‐ring systems. The method involves placing the NICS probes along the X axis, and if needed, along the Y axis, at a constant height above the system under study. Following the change in the induced field along these axes allows the identification of global and local induced currents. The best NICS type to use for these scans is NICS_πZZ, but it is shown that at a height of 1.7 Å above the molecular plane, NICS_ZZ provides the same qualitative picture. This method, namely the NICS‐XY‐scan, gives information equivalent to that obtained through current density analysis methods, and in some cases, provides even more details.     

Nucleus Independent Chemical Shift (NICS) at Small Distances from the Molecular Plane: The Effect of Electron Density

When close to the molecular plane, the behavior of nucleus independent chemical shift (NICS) as a function of the distance from the molecular plane deviates from its behavior at larger distances. By using a dense grid of NICS-probes (BQs) it is shown that, when close to the molecular plane, maximal (absolute) NICS values are obtained above the atoms. These maxima move towards the center as the grid is elevated until the (absolute) maximum NICS is obtained at the center and stay there when the grid is further elevated. It is shown that this behavior is a result of the current density, which is influenced by the electron density, according to the Biot-Savart law, which, in turn, causes the induced magnetic field measured by the NICS. It is thus concluded that if magnetic aromaticity is studied, the NICS calculations should be carried out at a large enough distance so that only the π-ring current affects the NICS. At distances ≥2 Å, NICS(r)_π,zz=A+B*C^r. Using non-linear correlation for obtaining A, B and C and extrapolate to NICS(1)_π,zz and NICS(1.7)_π,zz is recommended as measures for aromaticity.     

The theoretical study of aromaticity in N-heteroatom compounds

In this article, we used nucleus-independent chemical shifts (NICS), aromatic stabilization energies (ASE), and magnetic susceptibility isotropic, calculated with (density functional theory) B3LYP levels at the 6-311+G (d, p) basis set, to evaluate the aromaticity of a set of 12 six-member planar π-electron aromatic systems: mono- and multi-substituted benzenes by nitrogen atoms. NICS were calculated at the center of the rings, 0.5 Å and 1 Å above the molecular plane, and in order to reflect the π-electron effects, we compare the values of NICS(0.5). The result statistically revealed significant correlations among the above three criteria. The comparison result was obtained as benzene > mono-nitrogen benzene > di-nitrogen benzene > tri-nitrogen benzene > tetra-nitrogen benzene > penta-nitrogen benzene.     

Effect of collision interactions on 13C nuclear magnetic shielding in monosubstituted benzenes in halogen-containing solvents

The ¹³C nuclear magnetic shielding in benzene and ten monosubstituted benzenes was studied when these compounds were dissolved in cyclohexane, carbon tetrachloride, tetrachloroethylene, methylene bromide and methylene iodide. The results revealed that the observed changes of ¹³C magnetic shielding are dependent on both the solute and solvent molecular properties, although the dependence on the solvent is much more significant. It was also shown that the solvent effects for aromatic carbons are independent of the π electron density distribution in an aromatic ring. The observed ¹³C deshielding was attributed mainly to overlap effects which take place during molecular collisions.     

Magnetic criteria of aromaticity in a benzene cation and anion: how does the Jahn–Teller effect influence the aromaticity?

The aromatic/antiaromatic behavior of the Jahn–Teller (JT) active benzene cation and anion has been investigated using Density Functional Theory (DFT) calculations of Nuclear Independent Chemical Shifts (NICS) and magnetic susceptibility. NICS parameters have been scanned along the Intrinsic Distortion Path (IDP) for the benzene cation showing antiaromaticity which decreases with increasing deviation from D_6h to D_2h symmetry. Changes in NICS values along the IDP from D_6h to C_2v in the benzene anion revealed non-aromatic character.     

Aromatic behavior of three membered rings

The aromatic behavior of three membered ring compounds has been analyzed by mean of GAUSSIAN94 theoretical calculations at B3LYP//6-311++G(2d,p) level. Diamagnetic exaltation values obtained from magnetic susceptibilities as well as NICS show the expected aromatic character of the cyclopropyl cation, but the correspondent anion also shows aromatic behavior. This unexpected result is analyzed as well as the character of the other three membered ring derivatives.     

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

Magnetically 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.