Dr Peter Karadakov

01904 322555
Email: peter.karadakov@york.ac.uk

My research interests are in the area of molecular electronic structure theory and involve methodological work and code development, as well as theoretical studies of bonding, reactivity and other electronic properties of molecular systems in organic, inorganic chemistry and materials science.

Modern Valence-Bond Theory and Chemical Reactivity

The ability of a modern form of valence-bond (VB) theory, the spin-coupled (SC) method, to include a significant amount of electron correlation within a wavefunction, which remains easy-to-visualize and interpret, provides us with a powerful tool for studying not just bonding in isolated molecules, but also the bond-breaking and bond-formation processes that take place during chemical reaction. In a nutshell, our SC approach for interpreting chemical reaction mechanisms uses existing efficient implementations of high-level molecular orbital methods to obtain transition structures and sequences of geometries along the reaction path, which is followed by SC calculations at these geometries and a detailed analysis of the results.

This methodology is particularly suitable for describing the electronic mechanisms of pericyclic reactions, such as the Diels-Alder reaction between butadiene and ethene and the 1,3-dipolar cycloadditions between fulminic acid and ethyne. For each pericyclic reaction we have studied, it has been possible to obtain a very clear picture of the electronic rearrangements taking place as the system follows the reaction path from reactants, through the transition structure, to products. We can observe directly the evolution of the bonds being broken or formed during the reaction. During some reactions, for example, the Diels-Alder reaction, bonds break and reform in a homolytic way, the major recoupling of the spins of the active orbitals takes place at the transition structure and involves a resonance pattern very similar to that in benzene. This strongly suggests that these reactions involve aromatic transition structures. An entirely different rearrangement is observed for reactions involving more polar reactants, for example, the 1,3-dipolar cycloaddition between fulminic acid and ethyne: The bond breaking and formation now involve shifts of whole electron pairs rather that spin-recouplings. This indicates a heterolytic mechanism and a non-aromatic transition structure.

The amount of detail revealed by the SC interpretations of chemical reaction mechanisms has been providing us with insights into the changes in the electronic structure that take place during a wide range of chemical reactions which are not readily available from any other quantum-chemical approaches.

SC orbitals describing a C-H bond that will break
SC orbitals describing a C-H bond that will break [P. B. Karadakov, J. G. Hill and D. L. Cooper, The Unusual Electronic Mechanism of the [1,5] Hydrogen Shift in (Z)-1,3-Pentadiene Predicted by Modern Valence Bond Theory, Faraday Discuss. 2007, 135, 285-297].

Ab Initio Calculation of NMR Properties

Many calculations of NMR shielding tensors and indirect spin-spin coupling constants for larger molecules are still being carried out using uncorrelated Hartree-Fock (HF) wavefunctions. However, it is well known that the accurate ab initio prediction of NMR properties is not possible without inclusion of electron correlation effects. This requires the use of post-HF wavefunctions which, taken together with the fact that the NMR constants are second-order response properties and their evaluation has to be carried out through an appropriate stationary perturbation theory, suggests that the numerical effort required for calculations of this type should scale very unfavourably with the increase of the size of the molecule. Since the NMR shieldings and indirect spin-spin coupling constants are predominantly local properties, a high-level post-HF description is required only within the close neighbourhood of the nuclei of interest, while the remaining, normally much larger, part of the molecule can be described using a simpler and more efficient technique. We have formulated a systematic treatment of this type, which is based on the ONIOM (our own n-layer integrated molecular orbital and molecular mechanics) approach, in which a molecule is subdivided into n-layers, each of which can be described at a different level of theory. The corresponding NMR property is calculated as a combination of the NMR properties for the different layers. This allows highly accurate and efficient calculations on larger molecules, which would be inaccessible through conventional approaches.

The ONIOM Approach
P. B. Karadakov and K. Morokuma, ONIOM as an Efficient Tool for Calculating NMR Chemical Shielding Constants in Large Molecules, Chem. Phys. Lett. 2000, 317, 589-596.