Application of group theory formalisms to the solution of problems of chemical relevance (structure and reactivity). D1 - Knowledge and understanding
At the end of the course, the student must demonstrate knowledge of the fundamental concepts and tools used in molecular symmetry.
He/she possesses knowledge of molecular symmetry for the processing and analysis of scientific data. 
He is able to understand a scientific article describing the symmetry properties of molecules, derived from simulations.

D2 - Ability to apply knowledge and understanding
At the end of the course, the student must be able to correctly apply the concepts of molecular symmetry to realistic systems.

D3 - Autonomy of judgment
At the end of the course, the student must be able to critically analyze and apply the concepts of molecular symmetry.

 D4 - Communication skills
At the end of the course, the student will have to demonstrate that he/she is able to explain the concepts described in point D1

 D5 - Learning skills
At the end of the course, the student must demonstrate to be able to use molecular symmetry to interpret physical and chemical phenomena.

General chemistry

Introduction to group theory. Theorems and definitions. Molecular symmetry and point groups. Illustrative examples. Representations of a group. Reducible and irreducible representations. Reduction of reducible representations. Direct product representations. Group theory and quantum mechanics. Symmetry transformations of wave functions and quantum-mechanical operators. Eigenstates of the Hamiltonian and irreducibility. Selection Rules. Applications: Molecular Orbital theory, MO LCAO method, applications on organic, organometallic and inorganic systems. Molecular vibrations. Normal modes, normal coordinates and their symmetry properties. Selection rules for IR and Raman spectroscopies. Ligand field theory.

L. Dore, “Simmetria e chimica. Introduzione all'applicazione della teoria dei gruppi”, Editografica, 2023 F.A. Cotton, “Chemical applications of group theory”, 3rd Ed. Wiley, 1990.

Group theory, theorems and definitions. Properties and illustrative examples. Isomorphism and homomorphism. Subgroups. Conjugate elements and classes. Molecular symmetry and point groups. Symmetry elements and symmetry operations. Point groups and their notation. Molecular symmetry classification. Illustrative examples. Short introduction to linear algebra: vector spaces, subspaces, and invariant subspaces. Bases and orthonormal bases. Unitary and Hermitian operators. Unitary and Hermitian matrices. Algebraic eigenvalue problem. Group representations. Equivalent representations. Reducible and irreducible representations. Effect of symmetry transformation operators on functions. General representation theory, the Great Orthogonality Theorem. Characters. Reduction of reducible representations. Representation of a direct product group. Brief overview on the construction of character tables. Group theory and quantum mechanics. Symmetry transformations of wave functions and quantum mechanical operators. Eigenstates of the Hamiltonian and irreducibility. Selection rules. Construction and use of projection operators. Molecular orbital theory. Selected applications. Normal modes and normal coordinates. Symmetry classification of normal coordinates. Selection rules in IR and Raman spectroscopies.

In-person classes

The assessment of learning takes place through a final oral examination. At least three questions about the programme of the course. Score in the scale of thirties. Level of learning, appropriate language and ability of solving problems (by applying the theory on concrete examples) will be evaluated.

This course explores topics closely related to one or more goals of the United Nations 2030 Agenda for Sustainable Development (SDGs)