Non-classical aromaticity

The molecular orbitals of boron flakes follow the particle on a disk model. This gives rise to a new set of closed shell magic numbers. The figure below illustrates this correspondence for B₁₉^- and B₂₀^2- clusters. The project will focus on development of extended particle models for several continuous  symmetries and topologies.

Applications to hollow and solid clusters will  mainly concentrate on boron allotropes, viz. the core-shell solid boron clusters. Focus is on the use of group theory. The project also involves a computational part in collaboration with Prof. Minh Tho Nguyen.

 Shapes of π-orbitals in boron flakes, as compared to wavefunctions of a circular disk.

 From: Truong, Ceulemans, Nguyen, Chemistry A European Journal, 2012, 18, 4510-4512

The inverse London problem

In 1937 London solved the problem of the Zeeman effect of a magnetic field on a cyclic molecule.  This involves induced ring currents and is at the basis of current NMR spectroscopy. The inverse London problem is defined as finding the ring currents that resolve electronic degeneracies in polycyclic aromats. This is the complex analogue of the Jahn-Teller theorem.

The project requires the study of group theory and graph theory. Ring current calculations are carried out in collaboration with the University of Groningen.

 The phenalenyl radical, and its Jahn-Teller distortion surface.

 From Ceulemans, et al, Proceedings Royal Society (London), 2012

The Madelung problem

Together with PhD student Pieter Thyssen a book project was launched on the Lie algebra of the periodic table.

The Madelung rule predicts that the Aufbau principle of the elements follows diagonal sequences through the hydrogenic levels, comparable to Regge sequences in hadron spectroscopy.

The purpose is to embed this rule in the covering SO(4,2) algebra of the hydrogen spectrum,

Corresponding to the baruton, named after Asim Barut.

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