LEARNING OUTCOMES

The Theoretical Chemistry course aims to impart to the learner the fundamental concepts and techniques of quantum mechanics for their application to chemical problems (electronic structure of atoms, molecules or solid state).  Standard methods of approximate resolution of the polyelectronic problem, starting from the Hartree-Fock model to get to provide hints relating to more sophisticated modern methodologies (for example the theory of density functional) and the corresponding quantum chemical calculation software. The student will have the opportunity to acquire knowledge and familiarity with the methods quantum mechanics treated in their correct and rigorous mathematical and physical description, through examples/exercises.

AIMS AND LEARNING OUTCOMES

The teaching of theoretical chemistry aims to provide the student with the methodological tools and the language necessary to tackle quantum mechanical issues in medium-advanced level of chemistry, in order to be able to critically discuss concepts and techniques of quantum mechanics. Knowing apply this knowledge to chemical problems relating to the electronic structure of the systems studied.
At the end of the proposed didactic path, the student will have acquired:
- the knowledge and understanding of the main aspects of quantum mechanics, in the chemical field, and the correct physical-mathematical formalism to set up and solve the corresponding problems of the electronic properties of the studied systems.
- the ability to apply previous knowledge in solving problems related to the electronic structure of atoms or molecules or of the solid state.
- autonomy and critical judgment in applying the models introduced in teaching for the resolution of the polyelectronic problem in the chemical field.
- identify the fundamental aspects in the description of a quantum mechanical problem applied to atoms or molecules.
- the ability to describe the general problems of quantum chemistry and its fundamental paradigms with a correct language and correct approach, identifying its potential and limits.
- the ability to deal with advanced texts or scientific articles on topics concerning methods and / or applications of quantum chemistry.

PREREQUISITES

For a successful attendance, a review of the skills and abilities achieved in the teachings of: Institutions of Mathematics, Numerical Computing, General Physics and Physical Chemistry 3 of the three-year degree course in Chemistry and Chemical Technologies or equivalent is recommended.

TEACHING METHODS

The teaching corresponds to 32 hours of frontal lessons held in Italian (please note that there is also an effective and effective individual study commitment of 68 hours)

Lessons will take place in the traditional way with extensive use of the blackboard, any handouts will be available on the AulaWeb page dedicated to teaching.

Furthermore, in this context, at the discretion of the teacher self-test and/or auxiliary material, both interactive and non-interactive, will be made available to assist/facilitate the students' individual study.

This material will be made available on the AulaWeb website.

SYLLABUS/CONTENT

The syllabus of the teaching, synoptically, can be traced back to:
- Basics of mathematics: complex numbers, differential equations, vector spaces and eigenvalue equation.
- Review of quantum mechanics: axiomatic formulation of quantum mechanics and related aspects (concept of wave function, electron density, operator...).

- Review of quantum systems that can be solved exactly; potential hole / barrier, hydrogen atom ...

Note: on the part relating to reminders, at the request of the students, additional lessons may be provided aimed at facilitating the student in deepening the arguments proposed therein.
• Elements of linear algebra, properties of (Hermitian) operators and approximate methods for solving quantum mechanical problems (variational and perturbative).
• Effective operators; example with the Kronig-Penney model for the treatment of a particle in a periodic potential, derivation of the concept of band electronics and its physical implications.
• The polyelectronic problem; application of variational theorems, the treatment of the spin problem and definition of the polyelectronic wave function through determined by Slater.
• The Hartree-Fock method; derivation and meaning of Hartree-Fock equations (polyelectronic atom or molecule case), concept of molecular orbital, field self-consistent, basic set, molecular properties.
• Post-Hartree-Fock methods; treatment of the problem of electronic correlation approach based on the method of the interaction of configurations and / or on theory of the density functional.
• Topic chosen on the basis of students' interests which may be oriented to theoretical aspects related to the treatment of atomic / molecular problems or related to the description of the solid state or to modeling-computational aspects.

RECOMMENDED READING/BIBLIOGRAPHY

Reference texts:

Modern quantum chemistry: introduction to advanced electronic structure theory. Attila Szabo, Neil S.Ostlund, Dover Pubns, 1996

Elementary methods of molecular quantum mechanics: mathematical methods and applications. Valerio Magnasco, Elsevier, 2013.

Any further didactic material can be provided by the teacher.