OVERVIEW

Theoretical chemistry is a peculiar subject. It is based on an equation that can hardly be solved.   -Patrick William Fowler-

The course aims to be a deepening of the knowledge of physical chemistry, with particular reference to the theoretical foundations in the description of the atomic/molecular properties.

AIMS AND CONTENT

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

1. Complex Numbers

General definitions, addition, multiplication, powers, roots of complex numbers.

2. Probability and Statistics

First and second moment of a distribution, standard deviation, continuous distributions, gaussian distributions, examples

3. Postulates and general principles of quantum mechanics

Classical dynamical variables and comparison with quantum mechanics, well-behaved functions, Postulate 1, behavior of the wavefunction for a discontinuous potential, Postulates 2-4, examples of commutator of two operators, its relation with the uncertainty principle, Hermitian operators, Dirac Notation, orthogonality of eigenfunctions of Hermitian operators, Gram-Schmidt orthogonalization, Fourier series, probability of obtaining a given value for an observable, time-dependent Schroedinger equation and its plausibility, quantum measurement for a particle in a box.

4. The hydrogen atom

Schroedinger for the hydrogen atom, s and p orbitals, Zeeman effect, spin-orbit interaction, atomic term symbols, helium atom.

5. Approximation methods

Variational method, trial wavefunctions linearly dependent on variational parameters trial wavefunctions not linearly dependent on variational parameters, perturbation theory at the first and second order, examples

6. Multi-electron atoms

Atomic units, helium atom, Hartree-Fock equations, anti-symmetry of the electron wavefunction, Slater determinants, derivation of the Hartree-Fock equations, the Hartree-Fock-Rothaan method and results for atoms, correlation energy, multielectron atomic term symbols.

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.

LESSONS

LESSONS START

From October 16, 2023

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam is oral, lasts about 45 minutes and is conducted by two tenured teachers.
The test is structured to ascertain the assimilation of the teaching contents and their re-elaboration criticism.

The test is considered insufficient if the student does not show the minimum required knowledge of the course contents.

ASSESSMENT METHODS

The exam is aimed at verifying the achievement of an adequate level of knowledge of the topics covered in the teaching and their adequate exposure with the correct terminology of the discipline (see examination methods).

In this context the student must:
- identify the correct context of the question and rigorously develop the related concepts, demonstrating the mastery of the mathematical tools available and their correspondence/discussion according to the physics of the system.

- recognize the limits, approximations and potentials of the various models for the description of the electronic structure and consequently choose the most suitable ones for the description of the proposed problem.

- to be able to correctly describe the basic concepts of quantum mechanics and to correlate the electronic structure of the studied system with its main chemical-physical properties.

- show adequate language properties.

FURTHER INFORMATION

Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Sergio Di Domizio (sergio.didomizio@unige.it), the Department’s disability liaison.