Aims

The principle aim of this course is to elaborate further than an elementary course in quantum chemistry or inorganic chemistry into the electronic structure of atomic systems. In doing so, the student acquires detailed knowledge of the ladder-operator method, Clebsch-Gordon coefficients, perturbation theory for degenerate systems, and spin-orbit coupling as a relativistic effect. Also the student is able to place the time-independent Schrödinger equation in the broader context of time-dependent quantum mechanics. He/she  also recognizes how spectroscopic selection rules are derived as an application of time-dependent perturbation theory. The students know how to apply various kinds of operators, such as ladder operators and projection operators.

In preparation of a detailed description of multiplet theory, the Condon-Slater rules for calculating matrix elements between Slater determinants are introduced. Students are able to derive these rules in general for the one-electron operators and for specific cases (e.g. three electron systems) for electron repulsion. The student recognizes spherical harmonics as the corner stone for the description of the electronic wavefunctions of atomic systems and knows their detailed origin as solutions of differential equations by applying the appropriate boundary conditions. He/she can describe the relationship with the ladder operator approach and the Clebsch-Gordon coefficients, and can apply them.

The student understands the need for perturbation theory for degenerate systems, its derivation, and how to solve the secular equations in practice. The student can derive formulas for calculating matrix elements of various kinds of one-electron operators (many electron systems) between Slater determinants. He/she can describe the origin of the Condon-Shortley parameters as applied in the semi-empirical approach to multiplet theory, and can apply them to specific configurations.

The student knows and appreciates the necessity and origin of the spin-orbit quantum numbers and recognizes which other quantum numbers are to which degree still applicable. He/she can describe the origin of the spin-orbit coupling constants (one and many-electron case) and knows how to use them to calculate the energy levels and the corresponding semi-empirical values for hydrogenic and many-electron atomic systems. He/she can construct projection operators of various kinds as an alternative for deriving wavefunctions. The difference between (pure) Russell-Saunders and j-j coupling is understood.

Previous knowledge

The course is based on the knowledge acquired in the introductory course of computational chemistry.

Is included in these courses of study

• Erasmus Mundus Master of Science in Theoretical Chemistry and Computational Modelling (Leuven et al) 120 ects.
• Courses for Exchange Students Faculty of Science (Leuven)
• Master of Chemistry (Leuven) 120 ects.