Some Observations on Triplet Ground-States in the Context of ‘Topological’ (HLPM) Ring-Currents in Conjugated Systems

Timothy K Dickens,Roger B Mallion

doi:10.5562/cca3538

Abstract

When the quasi graph-theoretical Hückel–London–Pople–McWeeny (HLPM) approach is used to calculate ‘topological’ π-electron ring-currents and bond-currents in conjugated hydrocarbons, a problem is identified that occurs whenever application of the Aufbau process gives rise to a π-electronic ground-state configuration that is a triplet. This circumstance seems to occur only occasionally and, even when it does, the generally somewhat outré molecular graphs in question appear unlikely to represent extant or viable conjugated systems. The molecular graphs of four examples are used to illustrate this ‘triplet ground-state problem’, only one of which represents a hydrocarbon that has actually been synthesised. It is pointed out that the ‘triplet ground-state problem’ does constitute an intrinsic limitation of the HLPM approach. It is, though, a limitation that is also necessarily inherent in other equivalent (though ostensibly different) methods of calculating magnetic properties due to π-electron ring-currents — methods that are likewise founded on the Hückel molecular-orbital conventions. When a triplet ground-state arises, topological ring-currents and bond-currents cannot be calculated by the HLPM method and its equivalents. Infinite paramagnetism is formally to be predicted in such situations.

Highlights

F OR a period of some 25 years, one of us (RBM) was privileged to work with the late Edward Cameron Kirby (1934–2019), the honorand of this Session of MATH/CHEM/COMP 31 (Dubrovnik, 2019)
A limitation that is necessarily inherent in other equivalent methods[13,14,15,33,34,35,36,37,38] of calculating magnetic properties due to π-electron ringcurrents — methods that are likewise founded on the Hückel molecular-orbital conventions.[11,12,39]
In this communication we have drawn attention to a difficulty that arises in the Hückel–London–Pople– McWeeny approach to calculating topological ring-currents and bond-currents in conjugated hydrocarbons. This happens whenever application of the Aufbau process to the eigenvalues/energy levels of the vertex-adjacency matrix of the hydrocarbon’s molecular graph results in a triplet π-electronic ground-state for the system. This difficulty has been illustrated by explicit appeal to four of only about half a dozen examples that the authors, over the years, have come across in the course of carrying out HLPM calculations on scores of different conjugated systems