OVERVIEW

This course completes the physical chemistry training of the Bachelor’s Degree in Chemistry and Chemical Technologies by introducing the fundamentals of quantum mechanics and their applications in chemistry. The course provides the conceptual and formal tools required to describe atomic and molecular structure, the electronic properties of matter and the main spectroscopic phenomena, integrating the knowledge acquired in previous basic courses.

If quantum physics doesn't confuse you, then you don't understand it.
Niels Bohr

AIMS AND CONTENT

LEARNING OUTCOMES

The teaching, in relation to the acquisition of knowledge relating to the chemical-physical field, intends to provide the basic tools of quantum mechanics and its applications in the chemical field (for example in molecular spectroscopy). The methodological tools and the basic language of quantum chemistry will be provided, which will enable the student to understand and reinterpret, in a formal way, the basic chemical knowledge (chemical bond, wave function, radiation/matter interaction, etc. ..). Furthermore, the course aims to develop the student's skills and competences, enabling him to elaborate connections between the concepts acquired with the basic knowledge in the chemical field, and the ability to tackle problems using the formal tools of quantum mechanics.

AIMS AND LEARNING OUTCOMES

Attendance and active participation in lectures, self‑assessment activities and possible exercises, together with individual study, will enable students to acquire the following knowledge, skills and competences.

At the end of the course, the student will be able to:

1. Describe and critically analyse the fundamental experiments that led to the crisis of classical physics (photoelectric effect, Compton effect, matter waves, double‑slit experiment, black‑body radiation), identifying their role in the development of quantum mechanics.

2. Understand and apply the postulates of quantum mechanics, the concepts of state and wave function, the operator formalism, and the meaning of the measurement process, including the limits imposed by the uncertainty principle.

3. Set up and solve simple quantum‑mechanical problems related to model systems (particle in a potential well or barrier, harmonic oscillator, rotor), constructing the Hamiltonian operator and physically interpreting the solutions of the Schrödinger equation.

4. Understand and use the main approximate methods of quantum mechanics, in particular the variational method and perturbation theory, applying them to simple physical and chemical systems.

5. Describe and interpret the electronic structure of hydrogen‑like and multi‑electron atoms, including atomic orbitals, spin, Slater determinants, effective potential, spectroscopic notation and electron correlation, and solve simple related exercises.

6. Analyse and describe the electronic structure of molecules using the MO‑LCAO method, understanding the evolution from atomic to molecular systems, the nature of the covalent bond and the main chemical‑physical implications, also through the construction of molecular orbital diagrams.

7. Understand and apply the fundamental principles of radiation–matter interaction and molecular spectroscopy (rotational, vibrational and electronic spectroscopy), interpreting simple spectra and solving basic application exercises.

Furthermore, at the end of the course the student will have developed:

• communication skills, being able to clearly, rigorously and coherently present the concepts of quantum mechanics using appropriate scientific terminology;
• integration skills and autonomous judgement, connecting previously acquired chemical knowledge with the new conceptual and formal tools introduced in the course;
• autonomous learning skills, useful for advanced courses in physical chemistry and related disciplines.
• for each conceptual block, optional handouts are provided for further study to complement the topics covered.

PREREQUISITES

For a fruitful frequency it is recommended to have acquired the knowledge related to the teachings of:

- Mathematics Institutions,

- Numerical Calculus,

- General physics with laboratory,

- General and Inorganic Chemistry.

TEACHING METHODS

The teaching methods are designed in coherence with the expected learning outcomes and aim to promote not only the acquisition of theoretical knowledge, but also its application to problem solving, as well as the development of critical analysis and scientific communication skills.

The course corresponds to 6 CFU, equivalent to 150 hours of total student workload, divided into 48 hours of lectures and 102 hours of individual study.
Individual study includes iterative learning activities such as self‑assessment quizzes, discussion forums and supplementary learning materials (videos, articles, etc.).

Lecture notes are normally made available on the AulaWeb platform in coordination with classroom activities.

The course, in order to meet specific needs such as student workers, has a one-to-one correspondence with a related website (made available by the University - AulaWeb service) where it is possible, through a substantially diachronic method, to access the teaching material provided: handouts, auxiliary material (optional) for in-depth study of an iterative and/or non-iterative type, discussion forum (student-teacher, student-student) for the topics associated with each lesson, self-assessment tests/quizzes.

SYLLABUS/CONTENT

• Introduction to Quantum Mechanics.

1. Crisis of Classical Physics (Illustrated and discussed some of the basic experiments chosen from: atomic model, photoelectric effect, Compton effect, material waves - Davison-Germer experiment, the two-slit experiment, black body and specific heats).
2. The Schrödinger equation and postulates of quantum mechanics (the concept of: state of a system, wave function, operator will be introduced. In axiomatic form, the postulates of quantum mechanics will be discussed).
   •  Introduction to the concept of measurement (hint) and the uncertainty principle.
   •  Introduction to the Schrödinger equation and analysis of its implications.
3. Quantum mechanics applied to simple systems.
   •  Particle in a potential hole/barrier (hint tunnel effect).
   •  Particle with rotational motion.
   •  Harmonic oscillator.
4.     Approximate methods for solving the Schrödinger equation.
   • Variational method (general discussion of the concept, simple applications).
   •  Perturbative methods (hint).
5.  Atomic structure (hydrogen atom case, spin, polyelectron atoms, Slater determinants, vector model, spectroscopic notation).
   •  Hydrogen model and its extension to multi-electron atoms.
   •  Atomic orbitals.
6.  Molecular structure (case of diatomic, polyatomic molecules, basic concepts on the nature of bonding, walsh diagram construction, general considerations).
   •  MO-LCAO method for constructing the polyelectron wave function.
   •  The covalent bond.
7. Applications of quantum mechanics in molecular spectroscopy.
   • Radiation/matter interaction.
   • Rotational spectroscopy.
   • Vibrational spectroscopy.
   •  Electron spectroscopy.

RECOMMENDED READING/BIBLIOGRAPHY

P. W. Atkins, J. De Paula, Chimica Fisica, Zanichelli, Bologna, 2004.

P. W. Atkins, R. Friedman, Molecular Quantum Mechanics, Oxford University Press, 2007.

Optional:

James R. Barrante, Applied Mathematics for Physical Chemistry

Donald A. McQuarrie, Mathematics for Physical Chemistry

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

According to the timetable reported here 

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The oral exam lasts at least 45 minutes and is administered by two tenured professors.

Attention! In a change to the standard practice adopted at the CCS, for this course (for better organizational management), registration must be completed 5 working days before the exam date.

The oral exam typically includes four questions to assess the student's understanding of the concepts covered in the course, summarized below:

a) General aspects of quantum mechanics and the transition from classical to quantum physics (corresponding to the first four points of the syllabus).

b) Hydrogen-like atom and/or polyelectronic atom (corresponding to the fifth point of the syllabus).

c) Molecules (corresponding to the sixth point of the syllabus).

d) Spectroscopy (corresponding to the seventh point of the syllabus).
​
For Erasmus students, upon request, the exam format may be adapted (written test in English followed by discussion of the paper), while maintaining the evaluation criteria unchanged.

ASSESSMENT METHODS

Assessment methods are designed to be consistent with the expected learning outcomes. Specifically, the oral exam assesses: knowledge and understanding of the theoretical foundations of quantum mechanics; the ability to apply this knowledge to solve simple problems related to atomic, molecular, and spectroscopic systems; independent judgment in the critical analysis of the models covered; and communication skills through the appropriate use of scientific language.

At the beginning of the course and on the corresponding AulaWeb website, students are provided with a graded score table (expressed in thirtieths) indicating the assessment criteria for the acquisition of knowledge, skills, and abilities related to the course, and the corresponding score that can be achieved.

The oral exam is designed to assess the achievement of an adequate level of knowledge of the topics developed/discussed during the lessons and the ability to use correct terminology combined with coherent presentation of concepts.

Specifically, the following will be assessed through discussion of topics covered in the program and/or the solution of exercises: the depth and coherence of the acquired knowledge of quantum chemical methodologies; the ability to apply this knowledge to the description of atomic and/or molecular systems; and the ability to use the acquired knowledge and skills to critically describe specific cases of chemical-physical systems.

The initial question of the exam involves the selection of a postulate of quantum mechanics to critically discuss (also in connection with the transition from classical to quantum physics).

The assessment also takes into account the formal correctness of the logical and mathematical steps and the ability to connect theoretical models and real chemical-physical phenomena.

FURTHER INFORMATION

For students with DSA, please refer to what is regulated by the University, on the dedicated pages of the website.

The course is delivered in Italian. Teaching materials and support activities may be available in English.

For any further information not included in this documents, please contact the teacher.