Our research resides within the area of computational chemistry, which was summarised in a 3500-page encyclopedia in 1998. Starting from a coherent and novel theory called Quantum Chemical Topology(QCT) we have branched out to a variety of subareas, contributing to both the interpretation and the prediction of chemical structure and properties.
According to complexity theory chemistry can be regarded as a science that emerges from physics. Chemistry describes patterns and rules that occur at a more complex level than the physics that govern them. However these patterns and rules are rooted in physics and can be predicted from it via powerful equations such as the Schrödinger equation. Sophisticated algorithms have been developed to produce accurate solutions of this equation efficiently. However the methods behind these algorithms are often remote from the crude but insightful ideas that chemists use and teach. A central question is how many of these ideas survive the scrutiny of modern knowledge about wave functions. In other words, can we rigorously show how chemistry emerges from physics? Of course this is an ambitious research program that has already been accomplished to some extent. Nevertheless it warrants the continued attention of research community in order to keep conceptual chemistry “healthy”. It is important that we explain the right things for the right reasons. QCT is a serious attempt to bridge the growing gap between conceptual chemistry and modern computational data.
In our quest for chemical insight from modern wave functions we use advanced mathematical tools such as topology, vector calculus and differential geometry. We seek to recover chemical concepts that are compatible with modern wave functions. An important aspect of obtaining chemical insight is to be able to partition molecular systems. The relationship between the whole and its parts is another significant theme of complexity theory. A central premise of our research is to work in real space rather than the Hilbert space of basis functions. We look at scalar fields such as the electron density, its Laplacian, the Electron Localisation Function(ELF), etc. and their gradient vector fields. These real space gradient vector fields enable an understanding of molecules in terms of shape, distortion, curvature, finite boundaries and catastrophic change.
Our research is rooted in the theory of “Atoms in Molecules (AIM)” pioneered by Richard Bader’s group at McMaster University, Canada. This theory originates in the late sixties emerging from careful analyses of the then available computer-generated electron densities of small molecules. A brief review of the AIM literature from its inception to 1998 can be found in , which reports on AIM based research from June 1998 to May 1999. A subsequent report summarises the literature between June 1999 and May 2001 . A book aimed at advanced undergraduates was written  in an attempt to make the “chemical quantum topological” approach more accessible and available to students. A more general introductory book  was co-authored with Ron Gillespie.
As QCT rigorously defines atoms in molecules it can be used to transfer accurate information from small molecules to proteins, carbohydrates, lipids and DNA. We want to design a new biomolecular force field from scratch, an ambitious undertaking. There is a need for a new generation of force fields based on sounder principles. Our projected force field could also be incorporated in the active field of QM/MM to model enzymatic reactions.
With an eye on the emerging field of proteomics, there is a need for more reliable fragmentation rules in modern peptide mass spectrometry. Ab initio calculations (in the gas phase) will provide a solid basis to establish new selective cleavage rules and scrutinise old ones.
We continue our work on the bulk properties of liquid water, the solvent of Life. This ubiquitous and most important liquid is still not fully understood, and its modeling will benefit from our polarisation potential based on artificial intelligence (neural networks, genetic algorithms). Our accurate potential will be transferable to biomolecular solvation problems.
Understanding non-covalent interactions is vital to make progress in molecular recognition and supramolecular chemistry. Rules beyond hydrogen bonding, Jorgensen’s secondary interaction hypothesis, and Sanders’ π-π interaction need to be strongly rooted in modern ab initio quantum chemistry.