Do large polycyclic aromatic hydrocarbons and graphene bend? : How popular theoretical methods complicate finding the answer to this question

Theoretical studies of the vibrational frequencies of C6n 2H6n (n =2-12) coronenes, show that, despite full conjugation, delocalization and aromaticity, the stability of the planar geometry rapidly decreases with size. A switch to a nonplanar geometry can be expected at around n =9-12; any larger gas-phase coronene, including graphene, should be nonplanar. When applied to coronenes, popular quantum chemical methods, including Hartree-Fock and density functional theory, are shown to produce anomalous imaginary frequencies suggesting unrealistic geometry distortions; this reveals a serious methodological problem in calculations on extended systems which needs to be resolved through further basis set development

The atomic orbitals of the topological atom

The effective atomic orbitals have been realized in the framework of Bader’s atoms in molecules theory for a general wavefunction. This formalism can be used to retrieve from any type of calculation a proper set of orthonormalized numerical atomic orbitals, with occupation numbers that sum up to the respective Quantum Theory of Atoms in Molecules (QTAIM) atomic populations. Experience shows that only a limited number of effective atomic orbitals exhibit significant occupation numbers. These correspond to atomic hybrids that closely resemble the core and valence shells of the atom. The occupation numbers of the remaining effective orbitals are almost negligible, except for atoms with hypervalent character. In addition, the molecular orbitals of a calculation can be exactly expressed as a linear combination of this orthonormalized set of numerical atomic orbitals, and the Mulliken population analysis carried out on this basis set exactly reproduces the original QTAIM atomic populations of the atoms. Approximate expansion of the molecular orbitals over a much reduced set of orthogonal atomic basis functions can also be accomplished to a very good accuracy with a singular value decomposition procedure

Modern Valence-Bond Description of Homoaromaticity

Spin-coupled (SC) theory is used to obtain modern valence-bond descriptions of the electronic structures of local minimum and transition-state geometries of three species that have been considered to exhibit homoconjugation and homoaromaticity: the homotropenylium ion, C8H9+, the cycloheptatriene neutral ring, C7H8, and the 1,3-bishomotropenylium ion, C9H11+. The resulting compact SC wave functions are of comparable quality to complete-active-space self-consistent field constructions that are based on the same “N electrons in M orbitals” active spaces, but they are much easier to interpret directly. Analysis of the forms of the SC orbitals and of the overlaps between them, as well as an examination of the compositions of the associated resonance patterns, strongly suggest that both of the homotropenylium and 1,3-bishomotropenylium ions are homoaromatic at their local minimum geometries, with all of the other cases that were considered being nonaromatic. The SC results also show that the differences between “no-bond” and “bond” homoconjugated systems are very likely to be much smaller than previously thought

Magnetic Shielding, Aromaticity, Antiaromaticity and Bonding in the Low-Lying Electronic States of Benzene and Cyclobutadiene

Aromaticity, antiaromaticity, and their effects on chemical bonding in the ground states (S 0), lowest triplet states (T 1), and the first and second singlet excited states (S 1 and S 2) of benzene (C 6H 6) and square cyclobutadiene (C 4H 4) are investigated by analyzing the variations in isotropic magnetic shielding around these molecules in each electronic state. All shieldings are calculated using state-optimized π-space complete-active-space self-consistent field (CASSCF) wave functions constructed from gauge-including atomic orbitals (GIAOs), in the 6-311++G(2d,2p) basis. It is shown that the profoundly different shielding distributions in the S 0 states of C 6H 6 and C 4H 4 represent aromaticity and antiaromaticity "fingerprints" which are reproduced in other electronic states of the two molecules and allow classification of these states as aromatic (S 0 and S 2 for C 6H 6, T 1 and S 1 for C 4H 4) or antiaromatic (S 0 and S 2 for C 4H 4, T 1 and S 1 for C 6H 6). S 2 C 6H 6 is predicted to be even more aromatic than S 0 C 6H 6. As isotropic shielding isosurfaces and contour plots show very clearly the effects of aromaticity and antiaromaticity on chemical bonding, these can be viewed, arguably, as the most succinct visual definitions of the two phenomena currently available

Magnetic shielding study of bonding and aromaticity in corannulene and coronene

Bonding and aromaticity in the bowl-shaped C5v and planar D5h geometries of corannulene and the planar D6h geometry of coronene are investigated using 3D isosurfaces and 2D contour plots of the isotropic magnetic shielding σiso(r) and, for planar geometries, of the out-of-plane component of the shielding tensor σzz(r). Corannulene and coronene both feature conjoined shielded “doughnuts” around a peripheral six-membered carbon ring, suggesting strong bonding interactions and aromatic stability; a deshielded region inside the hub ring of corannulene indicates that this ring is antiaromatic, more so in planar corannulene. The switch from the planar to the bowl-shaped geometry of corannulene is shown to enhance both bonding and the local aromaticities of the five- and six-membered rings; these factors, in addition to ring strain reduction, favour the bowl-shaped geometry. The most and least shielded bonds in both corannulene and coronene turn out to be the spoke and hub bonds, respectively. The higher π electron activity over spoke bonds in planar corannulene and coronene is supported by σzz(r) contour plots in planes 1 Å above the respective molecular planes; these findings about spoke bonds are somewhat unexpected, given that ring current studies indicate next to no currents over spoke bonds

Excited State Aromaticity Reversals in Naphthalene and Anthracene

Aromaticity reversals between the electronic ground (S0) and low-lying singlet (S1, S2) and triplet (T1, T2, T3) states of naphthalene and anthracene are investigated by calculating the respective off-nucleus isotropic magnetic shielding distributions using complete-active-space self-consistent field (CASSCF) wavefunctions involving gauge-including atomic orbitals (GIAOs). The shielding distributions around the aromatic S0, antiaromatic S1 (1Lb), and aromatic S2 (1La) states in naphthalene are found to resemble the outcomes of fusing together the respective S0, S1, and S2 shielding distributions of two benzene rings. In anthracene, 1La is lower in energy than 1Lb, and as a result, the S1 state becomes aromatic, and the S2 state becomes antiaromatic; the corresponding shielding distributions are found to resemble extensions by one ring of those around the S2 and S1 states in naphthalene. The lowest antiaromatic singlet state of either molecule is found to be significantly more antiaromatic than the respective T1 state, which shows that it would be incorrect to assume that the similarity between the (anti)aromaticities of the S1 and T1 states in benzene, cyclobutadiene, and cyclooctatetraene would be maintained in polycyclic aromatic hydrocarbons