*)N.B. if there are students who do not speak Portuguese the language is English.
The student should get an in-depth knowledge about the electronic structure of atoms, molecules and solids and become familiar with the most common techniques for ab-initio calculations - and be aware of the approximations involved in such calculations.
He/she should be able to solve specific problems involving electronic structure calculations using modern computational tools (such as GAMMESS and OCTOPUS codes)
This student should be able to search, with guidance, for relevant bibliographic references and become familiar with the state of the art theoretical and computational techniques for electronic structure calculations.
The student should develop analytical and problem solving skills, and critical reasoning while tackling specific problems. He/she should be able to organize and plan the best strategies and apply the most appropriate analytical or computational tools, in a creative way, to problems and analyse the results.
Molecular orbitals. Huckel's molecular orbital method.
Linear combination of atomic orbitals (LCAO).
Minimum energy principle, variational methods.
Interpretation of molecular orbitals.
The Hartree-Fock method. Roothan equations.
The H2 molecule.
Density functional theory.
Exchange and correlation functionals.
Electronic structure of atoms. Pseudopotentials.
Electronic structure calculations.
Electronic structure of crystals, methods using reciprocal space calculations: plane wave methods.
Calculations in real space: grid methods.
The tight binding method.
Solution of Kohn-Sham equations using a basis set of localised functions.
APW, MTO and KKR methods.
LAPW and LMTO methods.
Basic knowledge in Quantum Mechanics and Atomic Physics
Generic skills to reach
. Competence in analysis and synthesis; . Competence to solve problems; . Critical thinking; . Competence in autonomous learning; . Competence in applying theoretical knowledge in practice; . Competence in organization and planning; . Competence in oral and written communication; . Competence in information management; . Competence to communicate with people who are not experts in the field; . Creativity; (by decreasing order of importance)
Teaching hours per semester
total of teaching hours
Laboratory or field work
Bibliography of reference
Modern Quantum Chemistry, Introduction to advanced electronic structure theory, A. Szabo & N .S. Ostlund, 1996, Dover ISBN: 0486691861
Electronic Structure, Basic Theory and Practical Methods, R.M. Martin, Cambridge University Press, 2004 ISBN: 0521534402
C. Fiolhais et al. (eds.), A Primer in Density Functional Theory, Springer, 2003 ISBN: 978-3-540-37072-7
During the lectures, the main theory topics will be presented to the student, that will be illustrated, whenever possible, with practical examples. A few mathematical demonstration will not be made during the lectures but will be left for the student to complete at home, following recommended bibliography. These small theory problems will count for the student evaluation, in addition to the assigned computational problems.