Mathematics & Chemistry: Nuts, Knots and Vertex Spirals - Three Aspects of Fullerenes The Department of Mathematics and the Department of Chemistry of the University of Malta in collaboration with the Malta Chamber of Scientists will be hosting a lecture entitled  'Nuts, Knots and Vertex Spirals - Three Aspects of Fullerenes' delivered by Prof. Patrick W. Fowler, Professor of Theoretical Chemistry, University of Exeter, UK. This lecture should be of particular interest to chemists and mathematicians, as it will discuss how mathematics (in particularly spectral graph theory) can be applied to chemistry.

The lecture will be held on Tuesday, 1st March 2005, at 1pm in the Chemistry Lecture Room, Department of Chemistry, University of Malta. Chemists and mathematicians are particularly encouraged to attend. For further information please contact Dr. Irene Sciriha (Department of Mathematics, e-mail: or Dr Joseph N. Grima (Department of Chemistry, e-mail:

Fullerenes, discovered in 1985, when an arc was passed through carbon (C) vapour, are all-carbon 'sphere'-shaped molecules with trivalent polyhedral skeletons, having 12 faces pentagonal and all others hexagonal. They are a very important class of molecules and thousands of patents already exist for a broad range of pharmaceutical, electronic and other commercial applications, including anticancer and anti-HIV therapies, drugs for neurodegenerative diseases, drug delivery systems, and cosmetic preparations that retard the aging of skin. Potential industrial applications include superconductive materials, electrochemical systems, polymer and metal nano-composites, electrolyte separation membranes for fuel cells, gas storage and separation membranes, longer cell-life lithium ion batteries, highly functionalized coatings and ultra-fine crystalline artificial diamonds for drilling and industrial polishing.

The research of Professor Fowler aims to find an answer to some very important questions such as: How many fullerenes are there? Which fullerenes have a stable Pi-systems? Which have greatest overall stability? What are their likely patterns of reactivity? How might they interconvert? The methods used to answer these questions range from simple H_ckel theory and graph theory, to semi-empirical and ab initio molecular modelling simulations. In fact, many questions about their chemistry can be cast in graph-theoretical form, three sub-classes of which are Nut-graphs, Knot-graphs and V-spiral graphs.

This talk deals with fullerenes whose skeletons can be mathematically described as 'nut graphs'. (The notion of  nut-graph, conceived by Dr Irene Sciriha, has exactly one zero eigenvalue in its adjacency spectrum and no zero entries in the corresponding eigenvector.) In chemistry, a molecular nut graph has a non-bonding orbital with  implications for electron distribution and reactivity.  Some properties of and constructions for nut-fullerenes will be discussed.