1°) Perform the essential operations of linear algebra such as a scalar product, orthonormalization of vectors, diagonalization of a matrix, matrix inversion, calculation of eigenvalues and eigenvectors of a Hermitian matrix. 2°) Determine the point group of a molecule and the characteristics of this group 3°) Master the central notions of group theory (classes, commutativity, multiplication tables, character tables, labels, ...) 4°) Use group theory in vibrational spectroscopy, UV/visible electronic absorption spectroscopy and quantum chemistry (symmetry of molecular orbitals).
To introduce the essential notions of group theory and to show the implications of symmetry on molecular properties, in particular their signatures in vibrational and UV/visible absorption spectroscopies. Therefore, as a prerequisite to the group theory course, the essential basics of linear algebra will be introduced.
Part A: Linear Algebra I. Vectors A. Definition; B. Addition and subtraction; C. Scalar product; D. Norm of a vector; E. Vector space; F. The Gram-Schmidt orthogonalization procedure II. Operators and matrices A. Definition; B. The matrix product for operators; C. General aspects of matrices; D. The determinant; E. Changes of basis to vectors and matrices; F. Eigenvalue problems Part B: Elements of group theory I. Introduction II. Sets, ordered pairs and groups III. Subgroups, cyclic groups and group generators IV. Isomorphism V. The classes VI. Euclidean symmetry operations VII. Point symmetry groups VIII. Group representations A. Applications; B. Representations derived from basis vectors; C. Equivalent and reducible representations; D. Characters; E. The orthogonality theorem and the orthogonality of characters; F. Character tables; G. Reduction of reducible representations; H. The group of Hamiltonian IX. Use of Group Theory in vibrational spectroscopy A. Degrees of freedom; B. Notions of IR and Raman spectroscopy; C. IR and Raman intensities; D. Vibrational modes as a basis for point group representations X. Group theory, electronic structures and optical transitions A. Transitional electric dipole moment and representations; B. Optical transitions; C. Atomic orbitals as a basis for representations; D. Molecular orbitals and symmetry
Written exam (2H00) followed by an oral exam (15 min)
D.M. Bishop, Group Theory and Chemistry, Dover. P.H. Walton, Chemistry and Group Theory, De Boeck, 2001 N.Y. Öhrn, Elements of Molecular Symmetry, Wiley, 2000.
| Training | Study programme | Block | Credits | Mandatory |
|---|---|---|---|---|
| Bachelier en sciences chimiques | Standard | 0 | 5 | |
| Bachelier en sciences chimiques | Standard | 2 | 5 |