Nucleus-independent chemical shifts (NICS): distance dependence and revised criteria for aromaticity and antiaromaticity

Nucleus-independent chemical shifts (NICS) have been used extensively for the identification of aromaticity properties of molecules, ions, intermediates, and transition states since their introduction in 1996 by Schleyer et al. Initially, probes (bq's) were placed at the centers of systems (NICS(0)) and later, 1A above the molecular planes (NICS(1)). However, contradicting assignments of aromaticity by NICS and other methods were found for some systems. In this article, an alternative NICS-based method is introduced. The method is based on scanning NICS values over a distance and separating them into in-plane and out-of plane contributions. The shapes of the plots of the chemical shifts and their components as a function of the distance of the NICS probe (bq) from the molecular plane give a clear indication of diamagnetic and paramagnetic ring currents. This method is applied to several (4n + 2)- and 4n pi-electron systems (molecules and ions) in the singlet and triplet electronic states, including some of the problematic systems mentioned above. It is also shown that relative aromaticities of rings in polycyclic systems (local aromaticities) cannot be estimated by comparing NICS or NICS-scan values.     

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.     

Local aromaticity of the six-membered rings in pyracylene. A difficult case for the NICS indicator of aromaticity

In this work, we have analyzed the local aromaticity of the six-membered rings (6-MRs) of planar and pyramidalized pyracylene species through the structurally based harmonic oscillator model of aromaticity (HOMA), the electronically based para-delocalization index (PDI), and the magnetic-based nucleus independent chemical shift (NICS) measurements, as well as with maps of ring current density. According to ring currents and PDI and HOMA indicators of aromaticity, there is a small reduction of local aromaticity in the 6-MRs of pyracylene with a bending of the molecule. In the case of NICS, the results depend on whether the NICS value is calculated at the center of the ring (NICS(0)) or at 1 A above (NICS(1)(out)) or below (NICS(1)(in)) the ring plane. While NICS(1)(out) values also indicate a slight decrease of aromaticity with bending, NICS(0) and NICS(1)(in) wrongly point out a large increase of aromaticity upon distortion. We have demonstrated that the NICS(0) reduction in the 6-MRs of pyracylene upon bending is due to (a) a strong reduction of the paratropic currents in 5-MRs and (b) the fact that, due to the distortion, the paratropic currents point their effects in other directions.     

Theoretical study of structure, bonding, and aromaticity of borazyne and B-substituted borazynes

The density functional theory (DFT) is used to study the geometries, and electronic structures of triplet and singlet of borazyne and B-substituted of borazyne. The aromaticity of these systems is analyzed in the light of nucleus-independent chemical shift (NICS), average of two-center indices (ATI). These methods show increasing of aromaticity in deactivating groups. The relation between electron density in ring critical point (RCP) and NICS(1.0) is observed. The most important interaction in these molecules has been investigated by natural bonding orbital method (NBO).     

Summation of nucleus independent chemical shifts as a measure of aromaticity

When the nucleus independent chemical shifts, NICS(1)zz, for a set of aromatic and antiaromatic hydrocarbons are summed, they show an excellent linear relationship with the magnetic susceptibility exaltation, Lambda, for neutral, cationic, and monoanionic species. Aromatic and antiaromatic dianions show a similar relationship but with a different slope. However, when both Lambda and the summation of NICS(1)zz are divided by the area of the ring squared, the vast majority of the aromatic and antiaromatic species fall on the same line, indicating that both NICS and Lambda are affected by the size of the ring. The species that deviate slightly from the line are a few of the anionic compounds, which may be a result of the difficulties of calculating magnetic properties of anions. This is the first report of the relationship of NICS to ring area. In addition, the excellent correlation between Lambda and the summation of NICS(1)zz demonstrates that summation of NICS(1)zz values for individual ring systems of polycyclic ring systems to give a measure of the aromaticity of the entire system is justified. By extension, the excellent correlation also serves to demonstrate that the NICS(1)zz values for individual ring systems are reliable measures of local aromaticity/antiaromaticity. Finally, the excellent correlation between experimental shifts and the 13C NMR shifts calculated with density functional theory, B3LYP/6-311+g(d,p), serves as an indirect validation of the accuracy of the NICS(1)zz calculated by the same method and basis set.     

The Laplacian of electron density versus NICSzz scan: measuring magnetic aromaticity among molecules with different atom types

The electron density versus NICS(zz) (the out-of-plane component of nucleus-independent chemical shifts (NICS)) scan for assessing magnetic aromaticity among similar molecules with different ring sizes is improved by scanning the Laplacian of electron density versus NICS(zz) to include molecules containing different types of atoms. It is demonstrated that the new approach not only reproduces the results of the previous method but also surpasses that in the case of species with different atom types. The relative positions of curves in the plots of the Laplacian of electron density versus NICS(zz) correlate well with the ring current intensities of these molecules both near and far from the ring planes of the considered molecules. Accordingly, relative magnetic aromaticity of a number of planar hydrocarbons and a group of double aromatic metallic/semimetallic species are studied and discussed.     

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.     

Transannular pi-pi interactions in janusenes and in related rigid systems with cofacial aromatic rings; gauging aromaticity in the hydrocarbons and in model carbocations; a DFT study

The utility of NICS (nuclear independent chemical shift) as a probe for detecting/sensing variation in aromaticity due to transannular pi-pi interactions in janusene , a [3.3]orthocyclophane having two cofacial benzene rings within van der Waals distance, its tetrafluoro- and octafluoro-derivatives and , and in tropiliojanusene was studied by DFT at the B3LYP/6-31G(d) level. The related hydrocarbons and with a buried double-bond and their carbocations were also included in this study. Whereas NICS(0) and NICS(1) are rather insensitive to transannular interactions, computed NICS(1)(zz), values are larger and more negative for both pi-decks in the interannular space and this is consistent with increased transannular pi-pi interactions in the cofacial rings, previously shown in these systems via spectroscopic studies (UV and NMR), and by electrophilic chemistry. Transannular effects in , , and were also probed by examining the forms of HOMO-LUMOs. Attempts to measure donor-accepter interactions between electron rich/electron poor cofacial decks via NICS (1)(zz) through substituent effects proved unsuccessful, resulting in only very small changes. Protonation of the double-bond buried in between the two pi-decks in and results in internally pi-stabilized carbocations that exhibit more negative NICS(1) and NICS(1)(zz) values in the interannular space. GIAO NMR data were computed for the neutral hydrocarbons and their derived carbocations, as a guiding tool for planned experimental studies.     

An insight on the aromatic changes in closed shell icosagen,tetrel, and pnictogen phenalenyl derivatives

A computational study of the aromatic and antiaromatic characteristics of closed shell charged phenalenyl (PLY⁺¹ and PLY^?1) upon replacement of the central carbon atom by icosagen (B, Al and Ga), tetrel (Si and Ge) and pnictogen (N, P and As) atoms comprising systems in which the icosagen and pnictogen derivatives considered are neutral while the tetrel ones are anions or cations, has been carried out at the B3LYP/6–311++G(d,p) computational level. By substitution, two different kinds of structures have been obtained, one planar (N and B) and another one bowl-shaped depending on the size of the central atom. In terms of aromaticity, the substitution of the central C atom causes a loss of the aromatic character in all cases as indicated by nucleus-independent chemical shifts (NICS) profiles and NICS values on the 0.001 au isosurface. Regarding the charge, PLY⁺¹ presents larger electron delocalisation than PLY^?1, phenomenon associated with aromaticity. Furthermore, the current density maps for those planar systems corroborate NICS findings, showing anticlockwise currents in PLY⁺¹ (like in benzene) but clockwise in PLY-N⁰ and PLY-B⁰, indicating aromatic and antiaromatic behaviour, respectively.     

Development of the cyclic cluster model formalism for Kohn-Sham auxiliary density functional theory methods

The development of the cyclic cluster model (CCM) formalism for Kohn-Sham auxiliary density functional theory (KS-ADFT) methods is presented. The CCM is a direct space approach for the calculation of perfect and defective systems under periodic boundary conditions. Translational symmetry is introduced in the CCM by integral weighting. A consistent weighting scheme for all two-center and three-center interactions appearing in the KS-ADFT method is presented. For the first time, an approach for the numerical integration of the exchange-correlation potential within the cyclic cluster formalism is derived. The presented KS-ADFT CCM implementation was applied to covalent periodic systems. The results of cyclic and molecular cluster model (MCM) calculations for trans-polyacetylene, graphene, and diamond are discussed as examples for systems periodic in one, two, and three dimensions, respectively. All structures were optimized. It is shown that the CCM results represent the results of MCM calculations in the limit of infinite molecular clusters. By analyzing the electronic structure, we demonstrate that the symmetry of the corresponding periodic systems is retained in CCM calculations. The obtained geometric and electronic structures are compared with available data from the literature.     

Using three major criteria to evaluate aromaticity of five-member C-containing rings and their Si-, N-, and P-substituted aromatic heterocyclics

In this paper, we used bond-length equalization, aromatic stabilization energies (ASE) and nucleus-independent chemical shifts (NICS), calculated with (density functional theory) B3LYP levels at the 6-311+G^** basis set, to evaluate the aromaticity of a set of 38 five-member planar π-electron aromatic systems: sila-, aza- and phospha- derivatives and their parent systems. The result revealed statistically significant correlations among the above three criteria, and the order of aromaticity of the whole set was: Aza- derivatives rings > Phospha- derivatives rings > Sila- derivatives rings > Carbon-containing rings; NICS(0.6) and NICS(0.8) had the same results in evaluating the order of aromaticity in our case.     

Probing the aromaticity of the [(H(t)Ac)3(μ2-H)6], [(H(t)Th)3(μ2-H)6],(+), and [(H(t)Pa)3(μ2-H)6] clusters

In this study we report about the aromaticity of the prototypical [(H(t)Ac)(3)(μ(2)-H)(6)], [(H(t)Th)(3)(μ(2)-H)(6)](+), and [(H(t)Pa)(3)(μ(2)-H)(6)] clusters via two magnetic criteria: nucleus-independent chemical shifts (NICS) and the magnetically induced current density. All-electron density functional theory calculations were carried out using the two-component zeroth-order regular approach and the four-component Dirac-Coulomb Hamiltonian, including scalar and spin-orbit relativistic effects. Four-component current density maps and the integration of induced ring-current susceptibilities clearly show that the clusters [(H(t)Ac)(3)(μ(2)-H)(6)] and [(H(t)Th)(3)(μ(2)-H)(6)](+) are non-aromatic whereas [(H(t)Pa)(3)(μ(2)-H)(6)] is anti-aromatic. However, for the thorium cluster we find a discrepancy between the current density plots and the classification through the NICS index. Our results also demonstrate the increasing influence of f orbitals, on bonding and magnetic properties, with increasing atomic number in these clusters. We think that the enhanced electron mobility in [(H(t)Pa)(3)(μ(2)-H)(6)] is due the significant 5f character of its valence shell. Also the participation of f orbitals in bonding is the reason why the protactinium cluster has the shortest bond lengths of the three clusters. This study provides another example showing that the magnetically induced current density approach can give more reliable results than the NICS index.     

Is nucleus-independent chemical shift scan a reliable aromaticity index for planar heteroatomic ring systems?

Density functional theoretical investigation has been performed to explore the reliability of the nucleus-independent chemical shift (NICS) scheme in assessing aromatic behavior of some planar six-membered heteroatomic systems. It has been observed that the NICS scan and the diamagnetic and paramagnetic contributions of the in-plane and out-of-plane components are quite reliable in assessing any aromatic or antiaromatic behavior in borazine. However, for boraphosphabenzene, the aromatic stabilization energy is too small to consider it as an aromatic system but the NICS scans and the homodesmotic reactions suggest an opposite trend. Interestingly, in the case of alumazene, a very shallow minimum is observed for the out-of-plane component, which suggests the presence of weak diamagnetic ring current. However, the diamagnetic and paramagnetic contribution curves to the out-of-plane component for alumazene clearly reveal a net paramagnetic contribution. Thus we may surmise that apart from the single NICS value, the NICS scan also is not a very authentic tool for the assessment of aromaticity of planar six-membered heteroatomic systems.     

Efficient and accurate three-dimensional Poisson solver for surface problems

We present a method that gives highly accurate electrostatic potentials for systems where we have periodic boundary conditions in two spatial directions but free boundary conditions in the third direction. These boundary conditions are needed for all kinds of surface problems. Our method has an O(N log N) computational cost, where N is the number of grid points, with a very small prefactor. This Poisson solver is primarily intended for real space methods where the charge density and the potential are given on a uniform grid.     

Method/basis set dependence of NICS values among metallic nano-clusters and hydrocarbons

The influence of various all-electron basis sets and effective core potentials employed along with several DFT functionals (B3LYP, B3PW91, BLYP, BP86 and M06) on the magnitude of nucleus independent chemical shift (NICS) values in different metallic nano-clusters and hydrocarbons is studied. In general, it is demonstrated that the NICS values are very sensitive to the applied method/basis set; however, the method/basis set dependence is more prominent for computed NICS values in transition metal clusters. In hydrocarbons, medium-size basis sets perform roughly similar to large basis sets in most cases. It is also found that NICS(0) values are more sensitive to the method/basis set variation compared to the NICS values computed at 1 or 2 ? above the ring plane. However, in many cases, no broad-spectrum regulation is found for the effect of basis set/method on the magnitude of NICS values. A detailed study showed that bond length alternation in a molecule has an insignificant effect on the magnitude of NICS values so the influence of method/basis sets on the magnitude of NICS values mostly arises from the different predicted ring current intensities at various computational levels.     

A theoretical and experimental scale of aromaticity. The first nucleus-independent chemical shifts (NICS) study of the dimethyldihydropyrene nucleus

Nucleus-independent chemical shift (NICS) values were calculated at several locations for a series of dimethyldihydropyrenes (DDPs). These NICS values were used to assess the relative aromaticities of the dimethyldihydropyrene nucleus (DDPN) of these DDPs and to construct a NICS scale of aromaticity. The NICS and experimentally determined relative aromaticities of these DDPNs are in complete agreement, verifying that NICS can be used not only to classify a compound as aromatic but also to determine the degrees of aromaticity of structurally related systems.     

Isotropic periodic sum: a method for the calculation of long-range interactions

This work presents an accurate and efficient approach to the calculation of long-range interactions for molecular modeling and simulation. This method defines a local region for each particle and describes the remaining region as images of the local region statistically distributed in an isotropic and periodic way, which we call isotropic periodic images. Different from lattice sum methods that sum over discrete lattice images generated by periodic boundary conditions, this method sums over the isotropic periodic images to calculate long-range interactions, and is referred to as the isotropic periodic sum (IPS) method. The IPS method is not a lattice sum method and eliminates the need for a reciprocal space sum. Several analytic solutions of IPS for commonly used potentials are presented. It is demonstrated that the IPS method produces results very similar to that of Ewald summation, but with three major advantages, (1) it eliminates unwanted symmetry artifacts raised from periodic boundary conditions, (2) it can be applied to potentials of any functional form and to fully and partially homogenous systems as well as finite systems, and (3) it is more computationally efficient and can be easily parallelized for multiprocessor computers. Therefore, this method provides a general approach to an efficient calculation of long-range interactions for various kinds of molecular systems.     

Substitution Effect in NICS Values in Tropylium Ion Derivatives: An Ab Initio Study

Hartree–Fock (HF) and hybrid density functional theory (B3LYP) calculations were performed on tropylium ion and 19 of its mono- and diheteroatomic derivatives. The aromaticity in this class of compounds is evaluated based on the nucleus independent chemical shift (NICS) values. The NICS values are calculated at the center of the rings NICS (0) and at 1Å above the molecular plane NICS (1). The geometry optimization and NICS calculations were carried out at the HF/6–311+G?? and at the B3LYP/6–311+G (2d, p) density functional level, respectively. These calculations in the effects of heteroatoms such as N, B, P, and Si are considered on aromaticity, molecular properties, NICS values, and structural parameters.     

Theoretical study on platinabenzene and mono- and difluorinated platinabenzenes: Structure, properties, and aromaticity

The electronic structures and properties of the platinabenzene and mono- and difluorinated platinabenzenes isomers have been investigated using hybrid density functional B3LYP theory. Basic measures of aromatic character were derived from structure, molecular orbital, and nuclear independent chemical shift (NICS). An energetic criterion suggests that ortho isomer of monofluorinated and F15 isomer of difluorinated platinabenzenes enjoy conspicuous stabilization. The polarizability and molecular orbital analysis are compatible with this result. NICS values calculated at several points above the ring center fail to give the result consistent with that based on relative energy, polarizability, and molecular orbital analysis. The atoms in molecules analysis indicates a correlation between NICS (1.0) and the electron density of the ring critical point (ρ_rcp) in monofluorinated platinabenzenes. There is a similar correlation in difluorinated platinabenzenes (except for F12 and F24 isomers) between NICS (0.5) and ρ_rcp.