Magnetic Susceptibility Exaltation Research Articles

Total non-lewis structures: An application to predict the stability and reactivity of linear and angular polyacenes

In the present work, the total non-Lewis structure (TNLS) is introduced for describing the stability and reactivity of linear and angular polyacenes. TNLS of a molecule is derived from the natural bond orbital theory representing the antibonding orbitals and/or electron delocalization of π∗ orbitals. To verify this application, we obtained the TNLS values of thirteen linear and angular polyacenes and evaluated with other quantitative aromaticity probes based on reactivities, energetics, geometrics, and magnetic properties. Our results show that there is a remarkable second-order polynomial correlation between TNLS and seven popular global measures of aromaticity including hardness, resonance energy, aromatic stabilization energy, harmonic oscillator measure of aromaticity, magnetic susceptibility exaltation, global magnetic characteristics, and mean polarizability. By increasing the TNLS values of the systems the reactivity increases and stability decreases. It is worth mentioning that the angular polyacenes produce less TNLS values than the linear systems with the same number of benzene rings. Therefore, it can be stated that TNLS values confirmed with Clar’s rule which in general prove the angular polyacenes are more stable than linear ones.

Effect of Mono- and Poly-CH/P Exchange(s) on the Aromaticity of the Tropylium Ion

In view of the fact that the phosphorus atom in its low co-ordination state (coordination numbers 1 and 2) has been termed as the carbon copy, there have been attempts to investigate, theoretically as well as experimentally, the effect of the exchange(s) of CH- moiety with phosphorus atom(s) (CH/P) on the structural and other aspects of the classical carbocyclic and heterocyclic systems. Tropylium ion is a well-known non-benzenoid aromatic system and has been studied extensively for its aromatic character. We have now investigated the effect of mono- and poly-CH/P exchange(s) on the aromaticity of the tropylium ion. For this purpose, the parameters based on the geometry and magnetic properties, namely bond equalization, aromatic stabilization energies (ASE), Nucleus-Independent Chemical Shift (NICS) values, (NICS(0), NICS(1), NICS(1)zz), proton nucleus magnetic resonance (1H-NMR) chemical shifts, magnetic susceptibility exaltation and magnetic anisotropic values of mono-, di-, tri- and tetra-phosphatropylium ions have been determined at the Density Functional Theory (DFT) (B3LYP/6-31+G(d)) level. Geometry optimization reveals bond length equalization. ASEs range from −46.3 kcal/mol to −6.2 kcal/mol in mono- and diphospha-analogues which are planar. However, the ions having three and four phosphorus atoms lose planarity and their ASE values approach the values typical for non-aromatic structures. Of the three NICS values, the NICS(1)zz is consistently negative showing aromatic character of all the systems studied. It is also supported by the magnetic susceptibility exaltations and magnetic anisotropic values. Furthermore, 1H-NMR chemical shifts also fall in the aromatic region. The conclusion that mono-, di-, tri- and tetra-phosphatropylium ions are aromatic in nature has been further corroborated by determining the energy gap between the Highest Occupied Molecular Orbital (HOMO) and Lowest Unoccupied Molecular Orbital (LUMO) (HOMO − LUMO gap), which falls in the range, ca. 3 × 10−19–9 × 10−19 J. The systems having more than four phosphorus atoms are not able to sustain their monocyclic structure.

Aromaticity/antiaromaticity of phospha-analogues of carbocyclic ions: A DFT investigation

The aromaticity or antiaromaticity of mono- and polyphospha analogues of carbocyclic cations and anions, namely cyclopropenium, cyclopropenide, cyclopentadienium and cyclopentadienide ions has been investigated at the DFT (B3LYP/6-31+G∗) level on the basis of bond lengths equalization, aromatic stabilization energies, proton chemical shifts, NICS(0), NICS(1) and NICS(1)zz tensor component values and magnetic susceptibility exaltation criteria. The results reveal that the aromaticity is sustained on one or more CH/P exchange(s) in cyclopropenium and cyclopentadienide ions. However, as regards the antiaromatic systems, the results are not uniform. Furthermore, of all the criteria investigated, only magnetic susceptibility exaltation results are consistent, which have negative values for the aromatic systems and positive values for the antiaromatic ions.

Fullerenes patched by flowers with octagonal core

AbstractThe aromatic character of three different flowers of general formula [n:(p i,p j)n/2], namely [8:(5,7)4], [8:(6,6)4] and [8:(5,6)4], has been evaluated by means of geometric (HOMA index), energetic (heats of formation) and magnetic criteria (NICS index, exaltation of magnetic susceptibility). Also, the reactivity descriptors within the DFT approach -absolute hardness, electrophilicity, Fukui functions — have been computed. All the different methods used for estimating the aromaticity led to a unitary conclusion. Two fullerene structures, patched by the most stable 8-Sumanene flower, have been designed and evaluated by means of ab initio computations

Computed NMR shielding of phosphorus-containing conjugated five-membered ring heterocycles as a measure of aromaticity

The GIAO–HF method in Gaussian 03 was used to calculate the isotropic shielding value of the proximal hydrogen of a diatomic hydrogen probe oriented perpendicular to the plane and moved in a square grid 2.5Å above the plane of conjugated five-membered ring heterocyclic compounds: pyrrole, furan, phosphole and thiophene and their phosphorus containing analogs. Subtraction of the calculated isotropic shielding value of diatomic hydrogen from each of these isotropic shielding values gave the shielding increment (Δσ) for each probe position. Plotting this value against Cartesian coordinates of the probe position allowed determination of the computed through-space shielding increment surfaces for these compounds. Substantial shielding was observed above the center of each ring, as expected for aromatic compounds. The magnitude of the shielding increment 2.5Å above the heterocyclic ring center correlated reasonably well with the other published methods of assessing aromaticity of these systems ASE (aromatic stabilization energy), Λ (exaltation of magnetic susceptibility) and NICS(1) (nucleus-independent chemical shift) values, both of which are magnetic criteria. The magnitude of the shielding increment also correlated with the number of phosphorus atoms in the ring. Greatest shielding (5.5ppm) was observed 2.5Å above 2,3,4,5-tetraphosphathiophene.

Reduction of Benzylidene Dibenzo[a,d]cycloheptenes: Over-Reduction of Antiaromatic Dianions to Aromatic Tetraanions

The antiaromaticity of a series of dianions of p-substituted benzylidene dibenzo[a,d]cycloheptenes was examined through calculated measures of antiaromaticity. The nucleus-independent chemical shifts (NICS) and magnetic susceptibility exaltation both showed substantial antiaromatic character in the benzannulated tropylium anion. When the antiaromaticity was normalized for the area of the ring, these tropylium anions were shown to be among the most antiaromatic anions in the chemical literature. Attempts to make the dianion through reduction with lithium or potassium gave the tetraanion as the only species observable in the (1)H NMR spectrum. Quench of the reaction mixture with trimethylsilyl chloride or D(2)O confirmed the presence of the tetraanion, but only as a small portion of the reaction mixture, with the major product being unreacted starting material. The failure to observe starting material was attributed to similarities in the structures of the starting material and anion radical (first reduction), allowing rapid electron transfer between them. The inability to see the dianion (second reduction) could be the result of the very small HOMO-LUMO gap anticipated for highly antiaromatic species, which would allow access to diradical species. The magnitude of the HOMO-LUMO gap was determined by the difference between the HOMO and LUMO energies from geometry optimization and the lowest energy transition from TD-DFT calculations. The HOMO-LUMO gap for the benzylidene dibenzocycloheptatriene dianions was shown to be much smaller than the HOMO-LUMO gap of species for which (1)H NMR spectra had been observed.

Chemical applications of neural networks: aromaticity of pyrimidine derivatives

Neural networks are computational tools able to apprehend non-linear relationships between different parameters, having the capacity to order a large amount of input data and transform them into a graphical pattern of output data. We have previously reported their use for the quantification of the aromaticity through the Euclidean distance between neurons. In this article, we apply the method to a variety of pyrimidine derivatives with electron-donor and electron-withdrawing groups as substituents, with capacity to produce push-pull compounds. We have calculated the aromaticity of benzene (as a reference molecule), parent pyrimidine and other 11 pyrimidine derivatives having amino, dimethylamino and tricyanovinyl substitution. The neural network has been generated using ASE, Λ, NICS(zz)(1) and HOMA as aromaticity descriptors, since our previous work showed that the combination of these indices provided the best performance of the network. On studying the influence of the substituent on the aromaticity of the molecule, we have found that, opposite to benzene derivatives, all the substituents decrease the aromaticity of the ring. The interplay between aromaticity, planarity and push-pull properties of all the substituted pyrimidines has also been addressed. An interesting feature of the neural network to quantify aromaticity is that the importance of the reference reaction used to evaluate energy stabilization and magnetic susceptibility exaltation is minimized.

Aromaticity of topological isomers of cyclazines and their [14] to [18] annulenes

The structures and magnetic properties of the parent cyclazines [2.2.2], [3.2.2], [3.3.2], [4.2.2], [3.3.3], [4.3.2], their topological isomers and the doubly bridged [14] to [18] annulenes were studied computationally at the B3LYP/6-311+G ** level of density functional theory (DFT). The magnetic criteria Λ (magnetic susceptibility exaltations, MSE), ∑NICS (the summation of nucleus-independent chemical shifts), and 1H NMR chemical shifts, geometry-based HOMA (harmonic oscillator model of aromaticity) index and HOMO–LUMO gaps were used to elucidate their aromatic and anti-aromatic properties. The excellent correlation between Λ and the summation of NICS(0) and NICS(1) demonstrates that these two originally proposed indices are still good indicators of the whole aromaticity of these polycyclic ring systems. The computed NMR chemical shifts are also in good agreement with available experimental data. In general, there is a good relationship between different criteria of aromaticity.

Are Thermodynamic and Kinetic Stabilities Correlated? A Topological Index of Reactivity toward Electrophiles Used as a Criterion of Aromaticity of Polycyclic Benzenoid Hydrocarbons

A topological index of reactivity (TIR) of benzenoid hydrocarbons is defined basing on an approximate value of the bicentric localization energies. TIR values correlate with all known (24) Hammett-Streitwieser position constants, based on kinetic data for electrophilic substitution in benzenoid hydrocarbons. The maximum value of the index, denoted by TIR(max), defines the stability of a molecule toward electrophiles. For all 35 nonisoarithmic molecules of benzenoid hydrocarbons for which Hess and Schaad data are known, TIR(max) values correlate with classical numerical characteristics of aromaticity: resonance energy per pi-electron (REPE), HOMO-LUMO gap, and geometry based aromaticity index HOMA. Correlation between TIR(max) and exaltation of magnetic susceptibility is also found for cata-condensed benzenoid hydrocarbons, whereas if the peri-condensed ones are included, no correlation is observed. This can be ascribed to the presence of both paratropic and diatropic rings in perifusenes.

Graph–topological approach to magnetic properties of benzenoid hydrocarbons

Application of topological properties and graph theory to benzenoid hydrocarbons allowed us to construct an effective approach interpreting ring current formation in molecules when exposed to an external magnetic field. Transformation of unexcited canonical structures for molecules of 34 benzenoid hydrocarbons into circuit structures and then to directed circuit structures allowed us to define global magnetic characteristics (GMC). GMC/n(2) values correlate very well with exaltation of magnetic susceptibility DeltaLambda/n(2) (computed at the CSGT/B3LYP/6-311G** level of theory by using optimized geometries at the B3LYP/6-311G** DFT level) with cc = 0.993. If the approach is applied to individual rings, then the correlation between local magnetic characteristics (LMC) for 129 various rings of 34 benzenoid hydrocarbons and NICS(1) works with cc = -0.975.

Interplay of π-Electron Delocalization and Strain in [n](2,7)Pyrenophanes

The geometries of a series of [n](2,7)pyrenophanes (n = 6-12) were optimized at the B3LYP/6-311G** DFT level. The X-ray crystal structures determined for the [9](2,7)- and [10](2,7)pyrenophanes agreed excellently with the computed structures. The degree of nonplanarity of the pyrene moiety depends on the number of CH2 groups in the aliphatic bridge and, as analyzed theoretically, influences the strain energy and the extent of pi-electron delocalization in the pyrene fragment. Various indices, e.g., the relative aromatic stabilization energies (DeltaASE), magnetic susceptibility exaltations (Lambda), nucleus-independent chemical shifts (NICS), and the harmonic oscillator model of aromaticity (HOMA) were used to quantify the change in aromatic character of the pyrene fragment. DeltaASE and relative Lambda values (with respect to planar pyrene) were evaluated by homodesmotic equations comparing the bent pyrene unit with its bent quinoid dimethylene-substituted analog. The bend angle, alpha, DeltaASE, and Lambda were linearly related. The aromaticity decreases smoothly and regularly over a wide range of bending, but the magnitude of the change is not large. The differences between planar pyrene (alpha = 0 degrees) and the most distorted pyrene unit (alpha = 39.7 degrees in [6](2,7)pyrenophane) are only 15.8 kcal/mol (DeltaASE) and 18.8 cgs-ppm (Lambda). Also, the geometry-based HOMA descriptor changes by only 0.07 unit. The local NICS descriptors of aromatic character also correlate very well with the global indices of aromaticity. In line with the known reactivity of pyrenophanes, the variations of NICS(1), a measure of pi-electron delocalization, were largest for the outer, biphenyl-type rings. The strain energies of the pyrene fragments were much larger and varied more than those evaluated for the bridge. Both strain energies were interrelated (correlation coefficient R = 0.979) and depend on the bend angle, alpha.

Antiaromatic Spacer-Bridged Bisfluorenyl Dications Generated by Superacid Induced Ionization

Derivatives of the dication of tetrabenzo[5.5]fulvalene were prepared with phenyl and ethynyl spacers through ionization of the appropriate bis-methylethers. The antiaromaticity shown by the parent dication was demonstrated for these dications with spacers, although it was attenuated by the presence of the spacer. It was substantially greater than that of fluorenyl monocations with similar substituents. Antiaromaticity was evaluated through comparison of (1)H NMR shifts with those of acyclic analogues, through nucleus independent chemical shifts, and through magnetic susceptibility exaltation. Although the fluorenyl systems are separated by spacers, the antiaromaticity of one system is affected by the other remote fluorenyl system. An explanation for this interaction may lie in the ability of a remote cationic substituent to attenuate delocalization in the spacer. The use of spacers is designed to prevent side reactions in less stable antiaromatic dications, allowing exploration of a number of species that have previously been inaccessible.

Variation of polarizability in the [4n + 2] annulene series: from [22]- to [66]-annulene

Using correlated ab initio methods, the polarizability of large [4n+2]-annulenes is determined, showing that there exists an almost linear relation between the exaltation of magnetic susceptibility (a measure of aromaticity) and an equivalent enlargement of polarizability.

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.

Brother versus brother: competitive stabilization of carbocationic centers by flanking cyclopropanes and π‐systems

AbstractB3LYP and MP2 quantum chemical calculations on cyclopropylcarbinyl cations fused to various cyclic and polycyclic architectures are described. ‘Competition’ for delocalization between the cyclopropane and other cyclopropanes and/or π‐systems incorporated into the (poly)cyclic framework to which it is fused was assessed, primarily through the use of characteristic geometric perturbations to the cyclopropane substructure. For example, a linear correlation between the orientation of the ‘empty p‐orbital’ at the carbocationic center, which is affected by the nature of the (poly)cyclic framework, and the magnitude of bond elongation in the cyclopropane was observed. Possible bis‐ and trishomoaromaticity of some systems was also evaluated using nucleus independent chemical shift (NICS) and magnetic susceptibility exaltation calculations. Copyright © 2007 John Wiley & Sons, Ltd.

Dications of 3-Phenylindenylidenefluorenes: Evaluation of Antiaromaticity of Indenyl and Fluorenyl Cations by Magnetic Measures

Dications of p-substituted 3-phenylindenylidenefluorenes were prepared to examine the response of the resulting indenyl and fluorenyl cationic systems to magnetic measures of antiaromaticity. All measures, (1)H NMR shifts, nucleus independent chemical shifts (NICS(1)(zz)), and magnetic susceptibility exaltation, Lambda, supported the antiaromaticity of the dications 3a-f2+. The 1H NMR shifts and NICS(1)(zz) showed that the indenyl ring system was less antiaromatic than the fluorenyl ring system, contrary to the antiaromaticity of indenyl monocations compared to fluorenyl monocations. The presence of a phenyl substituent in the 3-position was able to stabilize the indenylidene cation through resonance, decreasing its antiaromaticity, but even in the absence of the 3-phenyl substituent, the indenyl system of indenylidenefluorene dications was less antiaromatic than the fluorenyl system. The decreased antiaromaticity of the 3-phenylindenylidenefluorene dications over the unsubstituted indenylidenefluorene dication was supported by (anti)aromatic (de)stabilization energy calculations, ASE.

Super-Delocalized Valence Isomer of Coronene

Coronene (1) has been proposed to be "superaromatic", but energetic, geometric, and magnetic criteria of global and local aromaticity fail to support this proposal, and indeed, the calculated current-density map shows opposition of currents: diatropic on the 18-carbon rim and paratropic on the 6-carbon hub. However, [7,5,7,5,7,5]-isocoronene (2) ([7,5,7,5,7,5:6]-circulene, or isocoronene, for short), which is a valence isomer in which alternate pentagons and heptagons replace the hexagons surrounding the central ring, is predicted to have a single, unopposed, intense diatropic perimeter current arising from its four pi HOMO electrons, such as in the ipsocentric description of classically aromatic [4n + 2]-annulenes, hence, qualifying 2 as superaromatic on the magnetic criterion. This conclusion is in excellent agreement with anisotropy of magnetic susceptibility (359 cgs-ppm for isocoronene vs 247 cgs-ppm for coronene) and exaltation of magnetic susceptibility (isocoronene exceeds coronene by 51.4 cgs-ppm). Central and perimeter bond lengths suggest an increased aromaticity of isocoronene. In contrast, the energetic criterion shows that isocoronene is destabilized with respect to coronene by ca. 105 kcal/mol of which only ca. 30 kcal/mol can be attributed to differential strain.

Cyclic hydrocarbons: nanoscopic (π)-SQUIDs?

A nonperturbative method for calculating persistent currents in molecules and nanoscopic quantum rings is presented. Starting from the extended Hubbard model on a ring threaded by an Aharonov-Bohm flux, a feedback term through which the current can generate magnetic flux is added. Another extension of the Hamiltonian describes the energy stored in the internally generated field. This model is evaluated using exact diagonalization and an iterative scheme to find the minima of the free energy with respect to the current. The magnetic properties due to electron delocalization of conjugated hydrocarbons like benzene [magnetic anisotropy, magnetic susceptibility exaltation, nucleus-independent chemical shift (NICS)] — that have become important criteria for aromaticity — can be examined using this model. A possible novel mechanism for a permanent orbital magnetic moment in quantum rings analogous to the one in π-SQUIDs is found in the framework of the proposed model. The quantum rings must satisfy two conditions to exhibit this kind of permanent orbital magnetic moment: a negative Drude weight and an inductivity above the critical level.

10]Annulene: Bond Shifting and Conformational Mechanisms for Automerization

We report density-functional and coupled-cluster calculations on conformation change and degenerate bond shifting in [10]annulene isomers 1-5. At the CCSD(T)/cc-pVDZ//CCSD/6-31G level, conversion of the twist (1) to the heart (2) has a barrier of 10.1 kcal/mol, compared to Ea = 16.2 kcal/mol for degenerate "two-twist" bond shifting in 1. Pseudorotation in the all-cis boat isomer (3) proceeds with a negligible barrier. The naphthalene-like isomer 4 has a 3.9 kcal/mol barrier to degenerate bond shifting. The azulene-like isomer 5 is the only species for which the nature of the bond-equalized form (5-eq) depends on the method. At the CCSD(T)/cc-pVDZ//CCSD/6-31G level, 5-eq is 1.2 kcal/mol more stable than the bond-alternating form 5-alt. Conversion of 5-eq to 4 has a barrier of 12.6 kcal/mol. Despite being significantly nonplanar, both 5-eq and the transition state for bond shifting in 4 are highly aromatic based on magnetic susceptibility exaltations. On the basis of a detailed consideration of these mechanisms and barriers, we can now, with greater confidence, rule out 4 and 5 as candidates to explain the NMR spectra observed by Masamune. Our results support Masamune's original assignments for both isolated isomers.

The Aromaticity/Antiaromaticity Continuum. 1. Comparison of the Aromaticity of the Dianion and the Antiaromaticity of the Dication of Tetrabenzo[5.5]fulvalene via Magnetic Measures

The aromaticity of the dianion (2) and the antiaromaticity of the dication (3) of tetrabenzo[5.5]fulvalene have been evaluated through magnetic criteria, (1)H NMR shifts, nucleus-independent chemical shifts, NICS, and magnetic susceptibility exaltation, Lambda. The sum of the NICS values, using the GIAO (gauge-independent atomic orbital) method, for 2 is -35.2; that of 3 is +38.2, indicating the aromaticity of 2 and the antiaromaticity of 3. Calculation of magnetic susceptibility exaltation using the CSGT (continuous set of gauge transformations) method gives a similar result, with Lambda of -81.8 ppm cgs for 2 and 95.8 ppm cgs for 3. The general validity of these values is supported by excellent agreement between the NMR shifts calculated by the GIAO and CSGT methods with experimental shifts. Comparison of 1H NMR shifts with those of model compounds allows evaluation of the magnitude of the diatropic shift in 2 and paratropic shift in 3 and supports their assignment as aromatic/antiaromatic, respectively. The agreement between calculated and experimental 1H NMR shifts is excellent for 3 in the absence of counterions but much better for 2 when counterions are included. Inclusion of counterions in the evaluation of diatropic shift for 2 gave a smaller shift than in the absence of counterions, suggesting a decreased aromaticity. When counterions were included in the calculation of Lambda, the value was also decreased, suggesting a decreased aromaticity. This observation has important consequences in the use of experimental data for the evaluation of aromaticity, and presumably antiaromaticity, of anions since, in most cases, there will be close interaction with counterions.