Alex Borgoo

Postdoctoral Research Assistant VUB


Quantum similarity indices (QSI) (eqn (23) and (24)) for noble
gases, using the Dirac delta function as separation operator. Each
noble gas corresponds to a curve comprising of similarity indices with
all other atoms.


The approach in this thesis is situated on the border between atomic physics and quantum chemistry. It starts with a short introduction, which sketches an overview of the work and indicates the links between the themed chapters. Next follows a chapter where the general theoretical background is given. In a first part atomic electronic structure methods are covered, from Hartree–Fock to modern multi-configuration methods and relativistic Dirac–Hartree–Fock methods. The second part is concerned with methods for investigating molecules. Furthermore in the same chapter, density functional theory and the Hohenberg–Kohn theorems are highlighted as the central motivation for the investigation of atomic and molecular density functions. The theoretical chapter ends with a brief treatment of molecular similarity and the shape function, two topics from contemporary research in quantum chemistry.

The first research related chapter reports on the formal development of a density operator for atoms, written in second quantization and using spherical tensor operators. A computer code to evaluate the density function for atoms is also discussed. After elaborating on the construction and the evaluation of atomic density functions, with particular attention to the spherical symmetry, these density functions are investigated in the spirit of the Hohenberg–Kohn theorems, i.e. trying to establish how chemical information should be read from the density functions. Several studies were made, employing the ideas from molecular similarity. The results indicate that i) the LS-term dependency of the density function is small, that ii) similarity indices mask the periodicity in Mendeleev’s table, that iii) the influence of relativistic effects can be estimated from the density function. The chapter ends with the construction of a similarity measure, regaining concepts from conceptual density functional theory.

The search for the recovery of the periodicity in the table of elements is continued in the next chapter. After treating the relevant background, information measures (functionals which express the amount of information present in a probability distribution) are employed to investigate atoms. The periodicity of Mendeleev’s table was regained, using a particular form of the Kullback–Leibler information and a newly constructed quantum similarity index. The influence of relativistic effects on the density function was indicated by the evaluation of the Fisher information measure and the LMC complexity measure. In the last part of the information theoretical chapter, the Kullback–Leibler form is adopted to investigate molecules in a selection of benchmark chemical processes. The results reveal interesting reaction profiles, which are in agreement with Hammond’s postulate. The application of Hirshfeld’s partitioning scheme for atoms in molecules indicates the site with the largest electron reorganizing during the investigated processes.

The last chapter covers an investigation of the influence of spatial confinement on the chemical reactivity of atoms and molecules. It is argued that by placing atoms or molecules inside a potential cavity with a large barrier, the effect of the size of the cavity can be isolated from other effects for instance in the cavity of a zeolite cage. The results indicate that the chemical hardness of confined atoms and molecules increases in comparison with the free, isolated system and consistent with this, excitation energies are found to increase when the cavity is reduced in size. The investigation of the Fukui function and the molecular electrostatic potential also indicates that the regio-selectivity of chemical reactions is influenced by the confinement, related to the binding of the extra electron of the anion inside the potential well.

Poster Gallery


Selected Talks

EGAS APS09 phd_presentation

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