Generalizing the breakdown of the maximum hardness and minimum polarizabilities principles for nontotally symmetric vibrations to non-pi-conjugated organic molecules

In previous works we have shown that certain pi-conjugated organic molecules possess nontotally symmetric vibrations that break the maximum hardness (MHP) and minimum polarizability principles (MPP). We have also derived a set of simple rules to determine a priori without calculations whether a particular pi-conjugated organic molecule violates these two principles. In the present work, we generalize these results, and we show that not only pi-conjugated organic molecules but also other molecules without pi-conjugated structure or even pi-bonds can exhibit nontotally symmetric molecular distortions that do not follow these two principles. We have also found that the breakdowns of the MHP and the MPP are not necessarily connected, since the polarizability is not always proportional to the softness. Finally, we also introduced a methodology based on the diagonalization of the hardness Hessian matrix with respect to the vibrational normal coordinates to determine the nontotally symmetric molecular displacements that do not follow the MHP.     

Complete basis set ab initio computational study of three-dimensional aromaticity in highly symmetric hydrogen clusters

The aromaticity of planar and highly symmetric three-dimensional hydrogen clusters were evaluated with the complete basis set ab initio computational method. The energy of formation of the hydrogen clusters from the hydrogen molecule and hydrogen molecular ions were used in comparison to their relative stabilities. The aromaticity of planar hydrogen clusters, as well as hydrogen clusters in the three dimensions, arranged as highly symmetric regular polyhedra (Plato's polyhedras), were discussed with respect to the Hückel and Möbius aromatic rules.     

Density functional theory study on anti-resonance in preresonance Raman scattering for naphthalene molecules

The anti-resonance phenomenon in preresonance Raman scattering is investigated on the basis of the direct Taylor expansion of the electric dipole transition moments in vibrational Raman tensors with respect to vibrational normal coordinates. A time-dependent density functional theory treatment is applied to compute the anti-resonance of a nontotally symmetric vibrational model for naphthalene molecules, and the model spectra agree favorably with experiment. This direct evaluation approach may provide a method of predicting anti-resonance and studying its origin.     

Theoretical determination of the vibrational Raman optical activity signatures of helical polypropylene chains.

Raman and vibrational Raman optical activity (VROA) spectra of helical conformers of polypropylene chains are simulated using ab initio methods to unravel the relationships between the vibrational signatures and the primary and secondary structures of the chains. For a polypropylene chain containing three units, conformational effects are shown to lead to more acute signatures for VROA than for Raman spectra. In addition to regular polypropylene chains, which can display right and left helicities with the same probability, chirality and therefore helicity are enforced by substituting one chain end with a phenyl group. The simulations predict that the threefold helical structures, which correspond to (TG)(N) conformations of the backbone, have a specific VROA backward signature in the form of an intense couplet around 1100 cm(-1). This couplet is associated with collective wagging and twisting motions, while most of its intensity comes from the anisotropic invariants combining normal coordinate derivatives of the electric dipole-electric dipole polarizability and of the electric dipole-magnetic dipole polarizability. A similar signature has already been found in model helical polyethylene chains, whereas it is very weak in forward VROA.     

Magic Clusters PtMg2,3H5− Facilitated by Local σ-Aromaticity

The concept of local aromaticity has been successfully utilized in understanding the stability of certain atomic clusters. However, all the skeleton atoms in these clusters are covered by at least one local aromatic feature, collectively making the multiple local aromaticities coexist globally. Herein we show the robustness of local aromaticity as a tool for the discovery of novel magic clusters: not all of the skeleton atoms need to be covered by an aromatic feature to make the cluster magic. In this study, the PtMg_2,3H₅⁻ cluster anions are generated by a unique high-current pulsed discharge ion source and found to be magic numbers using mass spectrometry. Photoelectron spectroscopy and calculations confirm that only the PtH₄²⁻ kernels in these clusters are locally aromatic. Based on these results, we propose that local aromaticity can be gainfully utilized as a new potential magic rule in the search for magic numbers.     

Intensity-carrying modes important for vibrational polarizabilities and hyperpolarizabilities of molecules: derivation from the algebraic properties of formulas and applications

The intensity-carrying mode (ICM) theory is developed for analyzing the vibrational motions that mainly contribute to vibrational polarizabilities and hyperpolarizabilities, which are important for describing intermolecular electrostatic interactions and nonlinear optical properties of molecules. The ICMs are derived from dipole derivatives, polarizability derivatives, and first hyperpolarizability derivatives by using algebraic properties of intensity formulas. The way to obtain explicit forms of ICMs, including the optimization method of the basis of the ICM vector space, is discussed in detail. One- and two-dimensional models are constructed on the basis of the ICMs. The theory is applied to three molecules (a push-pull type polyene, a streptocyanine dye cation, and a symmetric neutral polyene) taken as typical examples. It is shown that the ICM theory provides a reasonable picture on the vibrational polarization properties of these molecules. On the basis of this result, the validity of the valence-bond charge transfer (VB-CT) model, which is a one-dimensional model and is widely used to describe the electronic and vibrational properties of dye molecules, is also discussed.     

Tuning the Structure and Properties of N-doped Positively Charged Polycyclic Aromatic Hydrocarbons

A detailed study of the geometry, aromatic character, electronic and magnetic properties for a series of positively charged N-doped polycyclic aromatic hydrocarbons (PAHs) was performed. Magnetic properties of the examined molecules were analyzed by means of the magnetically induced current density calculated using the diamagnetic-zero version of the continuous transformation of origin of current density (CTOCD-DZ) method. The comparative study of the local aromaticity of the studied molecules was performed using several different indices: energy effect (ef), harmonic oscillator model of aromaticity (HOMA) index, six centre delocalization index (SCI) and nucleus independent chemical shifts (NICS). The presence of N-atoms in the inner rings was found to cause a planarity distortion in the studied N-doped systems. The geometric changes and charged nature of the studied N-doped systems do not significantly influence the current density and the local aromaticity distribution in comparison with the corresponding parent benzenoid hydrocarbons. The present study demonstrates how quantum chemical calculations can be used for rational design of novel PAHs and for fine tuning of their properties.     

Aromaticity: molecular-orbital picture of an intuitive concept

Geometry is one of the primary and most direct indicators of aromaticity and antiaromaticity: a regular structure with delocalized double bonds (e.g., benzene) is symptomatic of aromaticity, whereas a distorted geometry with localized double bonds (e.g., 1,3-cyclobutadiene) is characteristic of antiaromaticity. Here, we present a molecular-orbital (MO) model of aromaticity that explains, in terms of simple orbital-overlap arguments, why this is so. Our MO model is based on accurate Kohn-Sham DFT analyses of the bonding in benzene, 1,3-cyclobutadiene, cyclohexane, and cyclobutane, and how the bonding mechanism is affected if these molecules undergo geometrical deformations between regular, delocalized ring structures, and distorted ones with localized double bonds. We show that the propensity of the pi electrons is always, that is, in both the aromatic and antiaromatic molecules, to localize the double bonds, against the delocalizing force of the sigma electrons. More importantly, we show that the pi electrons nevertheless decide about the localization or delocalization of the double bonds. A key component of our model for uncovering and resolving this seemingly contradictory situation is to analyze the bonding in the various model systems in terms of two interpenetrating fragments that preserve, in good approximation, their geometry along the localization/delocalization modes.     

On the correlation between the bifurcation values of the electron localization function and the nuclear independent chemical shift in aromatic and heteroaromatic compounds

In this work, for a representative set of 24 aromatic molecules, that includes hydrocarbons, hetero and charged rings, we explore the correlations between two aromaticity indexes. One of these indexes is based on the bifurcation values of the σ and π electron localization function (ELF), while the other one is the nuclear independent chemical shift (NICS). We observe that the quality of the possible correlations between these two kinds of indexes strongly depends on the kind of rings and on the particular indexes that are considered.     

A DFT Study of the Modulation of the Antiaromatic and Open-Shell Character of Dibenzo[a,f]pentalene by Employing Three Strategies: Additional Benzoannulation,BN/CC Isosterism,and Substitution

Dibenzo[a,f]pentalene ( [a , f ]DBP ) is a highly antiaromatic molecule having appreciable open-shell singlet character in its ground state. In this work, DFT calculations at the B3LYP/6-311+G(d,p) level of theory were performed to explore the efficiency of three strategies, that is, BN/CC isosterism, substitution, and (di)benzoannulation of [a , f ]DBP , in controlling its electronic state and (anti)aromaticity. To evaluate the type and extent of the latter, the harmonic oscillator model of aromaticity (HOMA) and aromatic fluctuation (FLU) indices were used, along with the nucleus-independent chemical shift NICS-XY-scan procedure. The results suggest that all three strategies could be employed to produce either the closed-shell system or open-shell species, which may be in the singlet or triplet ground state. Triplet states have been characterized as aromatic, which is in accordance with Baird's rule. All the singlet states were found to have weaker global paratropicity than [a , f ]DBP . Additional (di)benzo fusion adds local aromatic subunit(s) and mainly retains the topology of the paratropic ring currents of the basic molecule. The substitution of two carbon atoms by the isoelectronic BN pair, or the introduction of substituents, results either in the same type and very similar topology of ring currents as in the parent compound, or leads to (anti)aromatic and nonaromatic subunits. The triplet states of all the examined compounds are also discussed.     

Hirshfeld‐based intrinsic polarizability density representations as a tool to analyze molecular polarizability

In this work, a general scheme to visualize polarizability density distributions is proposed and implemented in a Hirshfeld‐based partitioning scheme. This allows us to obtain easy‐to‐interpret pictorial representations of both total and intrinsic polarizabilities where each point of the density is formed by the contribution of any atom or group of atoms in the molecule. In addition, the procedure used here permits the possibility of removing the size dependence of the electric‐dipole polarizability. Such a development opens new horizons in exploring new applications for the analysis of the molecular polarizability tensor. For instance, this visualization shows which atoms or regions are more polarizable distinguishing, moreover, the fine structure of atoms affected by the vicinity, and might extend the dipole polarizability as a tool for aromaticity studies in polycyclic aromatic hydrocarbons. Additionally, this approach can serve us to assess the methods performance in describing the interaction of electric fields with a molecule and local electron correlation effects in intrinsic polarizabilities. © 2015 Wiley Periodicals, Inc.     

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.     

Neural networks as a tool to classify compounds according to aromaticity criteria

Aromaticity is a fundamental concept in chemistry, with many theoretical and practical implications. Although most organic compounds can be categorized as aromatic, non-aromatic, or antiaromatic, it is often difficult to classify borderline compounds as well as to quantify this property. Many aromaticity criteria have been proposed, although none of them gives an entirely satisfactory solution. The inability to fully arrange organic compounds according to a single criterion arises from the fact that aromaticity is a multidimensional phenomenon. Neural networks are computational techniques that allow one to treat a large amount of data, thereby reducing the dimensionality of the input set to a bidimensional output. We present the successful applications of Kohonen's self-organizing maps to classify organic compounds according to aromaticity criteria, showing a good correlation between the aromaticity of a compound and its placement in a particular neuron. Although the input data for the training of the network were different aromaticity criteria (stabilization energy, diamagnetic susceptibility, NICS, NICS(1), and HOMA) for five-membered heterocycles, the method can be extended to other organic compounds. Some useful features of this method are: 1) it is very fast, requiring less than one minute of computational time to place a new compound in the map; 2) the placement of the different compounds in the map is conveniently visualized; 3) the position of a compound in the map depends on its aromatic character, thus allowing us to establish a quantitative scale of aromaticity, based on Euclidean distances between neurons, 4) it has predictive power. Overall, the results reported herein constitute a significant contribution to the longstanding debate on the quantitative treatment of aromaticity.     

Does aromaticity in a reaction product increase or decrease the intrinsic barrier? Kinetics of the reversible deprotonation of benzofuran-3(2H)-one and benzothiophene-3(2H)-one

A kinetic study of the reversible deprotonation of benzofuran-3(2H)-one (3H-O) and benzothiophene-3(2H)-one (3H-S) by amines and hydroxide ion in water at 25 degrees C is reported. The respective conjugate bases, 3--O and 3--S, represent benzofuran and benzothiophene derivatives, respectively, and thus are aromatic. The main question addressed in this paper is whether this aromaticity has the effect of enhancing or lowering intrinsic barriers to proton transfer. These intrinsic barriers were either determined from Br?nsted plots for the reactions with amines or calculated on the basis of the Marcus equation for the reaction with OH-; they were found to be lower for the more highly aromatic benzothiophene derivative, indicating that aromaticity lowers the intrinsic barrier. It is shown that the reduction in the intrinsic barrier is not an artifact of other factors such as inductive, steric, resonance, polarizability, and pi-donor effects, although these factors affect the intrinsic barriers in a major way. Our results imply that aromatic stabilization of the transition state is ahead of proton transfer; this contrasts with simple resonance effects, which typically lag behind proton transfer at the transition state, thereby increasing intrinsic barriers.     

Symmetrization of operator matrix elements

The method of Dupuis and King for generating matrix elements of a totally symmetric one-electron operator in terms of symmetry-distinct integrals only is generalized to the case of nontotally symmetric operators. For operators constructed from two-electron integrals, explicit reduction of integral processing to permutationally inequivalent symmetry-distinct integrals only is described, while for one-electron operators further reductions are derived using double coset decompositions. Finally, some computational consequences of this approach are briefly discussed.     

Stability and reactivity of all-metal aromatic and antiaromatic systems in light of the principles of maximum hardness and minimum polarizability

It is demonstrated that among various possible isomers of all-metal aromatic compounds such as Al(4)(2-) and their complexes the most stable isomer with the minimum energy is the hardest and the least polarizable. A similar situation is observed for different isomers of all-metal antiaromatic compounds such as Al(4)(4-) and their complexes. It is shown that linear Al(4)(4-) is energetically more stable than its cyclic isomer. The reaction energies associated with the complexation processes highlight the stability of those complexes. The difference in energy, hardness, and polarizability between a cyclic molecule and its linear counterpart convincingly shows that an aromatic molecule exhibits negative changes in energy and polarizability but positive changes in hardness as expected from the principles of minimum energy, minimum polarizability, and maximum hardness. Although the aromaticity of Al(4)(2-) is unequivocally established through this study, the antiaromaticity picture in the case of Al(4)(4-) is shown to be poorly understood;however, the present analysis sheds light on this controversy.     

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.