From six to eight Π-electron bare rings of group-XIV elements and beyond: can planarity be deciphered from the “quasi-molecules” they embed?

Abstract

Ab initio molecular orbital theory is used to study the structures of six and eight π-electron bare rings of group-XIV elements, and even larger [n]annulenes up to C 18 H...

Can the quasi‐molecule concept help in deciphering planarity? The case of polycyclic aromatic hydrocarbons

“…Already expensive in many cases, no attempt is made to attain the highest affordable accuracy with the methods nowadays at our disposal [29–31] (and references therein). For the quasi‐tetratomics, that is required, and the sort of accuracy previously reported [2] is judged to be enough. In fact, even if some of the SR methods referred to above would be possible pointwise, the ones actually employed are deemed enough to support the conclusions.…”

“…For completeness, we reiterate next the concept of quasi‐molecule by recalling the two Lemmas [2], even if Lemma 1 is not here actually used:Lemma If all triads of points in a set are on a line, they are all on the same line (collinear in an Euclidean sense).Lemma If all tetrads of points in a set are on a plane, they are all on the same plane (coplanar in an Euclidean sense).…”

“…In fact, the proof of planarity may go as follows: first, form pairs of tetrads such as to have three points in common (e.g., 1234 and 2345); then, proceed sequentially over all tetrads. Since three points define a plane, all such tetrads sharing three atoms can be shown to share the same plane [2].…”

“…If need be, the same assumption may be extended to consider , with a small integer. Moreover, the radical is well known to be planar in its cyclic geometry, being more stable than its linear isomeric form [2, 16]. Additionally, the methyl radical is well known to have trigonal planar geometry [17] (and references therein) with bond angles 120°, although the energy cost for distortion to a pyramidal geometry is small.…”

“…Understanding a given molecule involves the analysis of its structure, stereochemistry, symmetry, shape, size, and similarity, commonly known as the six Ss, intricately related and interwoven [1]. Elsewhere [2], we introduced the concept of quasi‐molecule and highlighted its importance in explaining the shape of (real) molecules. Based on two Lemmas (1 and 2, the latter for planarity, and hence the only one of concern here), we have shown [2] that the quasi‐triatomics and quasi‐tetratomics embedded in the (parent) molecule are building blocks (tiles) that explain their linear and planar shapes, respectively.…”