Although quantum chemistry is now accepted as a useful partner to experimental chemistry, the link between the abstract mathematics of quantum mechanics and the practical chemical concepts that characterize the structure and reactivity of atoms, molecules and solids remains problematic. The powerful computational methods needed to obtain quantitative agreement with experiment diverge from the simplified interpretations familiar to most chemists. Refining old concepts - and finding new ones - that are also applicable to state-of-the-art quantum chemistry methods is the overarching goal of this project.
The approach I follow is based on a framework for chemical reactivity indices called Conceptual Density Functional Theory (CDFT) (sometimes also called DFT reactivity theory, chemical DFT or Chemical Reactivity Theory). In CDFT, chemical concepts and reactivity indices are identified with the response of the energy of the chemical system, E, to perturbations in its number of electrons, N, and its external potential, v(r). (For an isolated system, v(r) is just the potential due to the atomic nuclei.) Many concepts that are commonly used by chemists, but often vaguely defined, have been reformulated using these response functions.
The motivation for this work is the significant progress made in accurately calculating the wave function and energy. Modern computer technology makes traditional high-level ab initio methods like Complete Active Space Self Consistent Field (CASSCF), Full Configuration Interaction (Full-CI) and multi-reference Configuration-Interaction (MRCI) calculations more feasible.
Accurate computation of the energy does not imply an understanding of the reaction considered. This is especially true for many of these high-level wavefunction methods, since they give accurate results but are not readily interpretable with classical orbital-based chemical concepts. The CDFT concepts are, however, defined in a universal manner, and are thus applicable at all levels of modern electronic structure theory.
To obtain qualitative insight into the chemical reactions of molecules using the above mentioned high-level methods, I combined the best of these two worlds by analytically calculating the Fukui function and linear response, two important reactivity indices known from CDFT, using accurate wave function methods, more specifically Full-CI and MRCI. In the frame of this project, I have derived the equations of these response functions, together with Prof. Paul W. Ayers (McMaster University, Canada), an expert in CDFT, high-level ab initio methods. These equations have been implemented using the open-source HORTON (Helpful Open-source Research TOol for N-fermion systems) software and CHEMTOOLS (
https://chemtools.org(odnośnik otworzy się w nowym oknie)) packages. As such we provide conceptual tools and the software to interpret accurate multideterminantal wavefunctions within the framework of CDFT.
The equations ant the implementation have been tested and benchmarked on small molecules and test-systems and this method and the code can now be applied to systems which cannot be accurately described with single Slated determinant methods, like certain transition states, biradicals and carbenes. Extending the CDFT framework to these high-level ab initio methods opens new collaboration opportunities, with both experimentalists (e.g. groups doing catalysis with transition and main group metals with carbene ligands) and theoreticians (e.g. groups specializing in accurate wave function methods).
The complexity of the calculation of these CDFT concepts for multi-reference wavefunctions, however, increases significantly, making the routine calculations of them hard and only reserved for special cases where the single slater determinant is known of suspected to be incorrect.
