Abstract
Systematic scrutiny is carried out of the ability of multicentre bond indices and the NOEL-based similarity index dAB to serve as excited-state aromaticity criteria. These indices were calculated using state-optimized complete active-space self-consistent field wavefunctions for several low-lying singlet and triplet states of the paradigmatic molecules of benzene and square cyclobutadiene and the inorganic ring S2N2. The comparison of the excited-state indices with aromaticity trends for individual excited states suggested by the values of magnetic aromaticity criteria show that whereas the indices work well for aromaticity reversals between the ground singlet and first triplet electronic states, addressed by Baird’s rule, there are no straightforward parallels between the two sets of data for singlet excited states. The problems experienced while applying multicentre bond indices and dAB to singlet excited states are explained by the loss of the information inherently present in wavefunctions and/or pair densities when calculating the first-order density matrix.
Highlights
IntroductionDespite its somewhat vaguely defined qualitative nature, the concept of aromaticity has had huge impacts on organic chemistry, starting with the formulation of the Hückel aromaticity rules [1,2] and encompassing a broad research area including the elucidation of the link between cyclic delocalization and energetic stabilization of conjugated (poly)cyclic hydrocarbons [3,4,5,6,7,8,9,10], the role of cyclic conjugation in inducing the ring currents [11,12,13,14,15,16,17,18,19] responsible for the special magnetic properties of aromatic compounds, and revealing the links between electron counts, orbital topology and selection rules in pericyclic reactions [20,21,22,23]
One such example is provided by attempts to correlate the extents of cyclic delocalization in the individual benzene rings in polycyclic aromatic hydrocarbons (PAHs), as given by multicentre bond indices, with the values of nucleus-independent chemical
In view of the potential problems mentioned in the previous section, the use of quantities based on the first-order density matrix might not always be a completely satisfactory approach: This matrix is not able to reflect all of the features of a more complicated wavefunction and, in certain cases, the features not carried over could be of crucial importance
Summary
Despite its somewhat vaguely defined qualitative nature, the concept of aromaticity has had huge impacts on organic chemistry, starting with the formulation of the Hückel aromaticity rules [1,2] and encompassing a broad research area including the elucidation of the link between cyclic delocalization and energetic stabilization of conjugated (poly)cyclic hydrocarbons [3,4,5,6,7,8,9,10], the role of cyclic conjugation in inducing the ring currents [11,12,13,14,15,16,17,18,19] responsible for the special magnetic properties of aromatic compounds, and revealing the links between electron counts, orbital topology and selection rules in pericyclic reactions [20,21,22,23]. The fact that the phenomenon of aromaticity can be associated with a very wide range of structural, energetic, and magnetic properties [3,4,5,6,7,8,9,10,11,12,13,14,16,17,18,24,25] has given impetus to numerous attempts to define measures or indices that are intended to characterize the “extent” of aromaticity in quantitative terms [16,17,18,19,24,25,26,27,28,29,30,31,32,33] Such efforts have often been plagued by discrepancies between the various types of indices; these have led to the postulation of a multidimensional character for this phenomenon [34,35,36], even implying “orthogonality”. This fails not least because of the incompatibility between the strictly local character of multicentre indices and the fact that the NICS value for an individual ring is “contaminated”
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