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

Teaching corresponds to 4 CFU equivalent to 100 hours of "effective" student commitment and is divided as follows: 32 hours of lectures and 68 hours of personal study. The latter include iterative teaching activities such as: self-assessment quizzes, discussion forums, in-depth materials (videos, articles, etc.), which are strongly recommended and can be chosen independently by the student.

Any lesson handouts are usually available (where possible with adequate advance notice) on the AulaWeb page dedicated to teaching at the same time as the relative contents are taught in the classroom (lectures).

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

The teaching syllabus, synoptic, can be traced back to:

• A first part of conceptual reminders on basic topics of quantum mechanics
  1. Mathematics: complex numbers, differential equations, vector spaces and eigenvalue equations;
  2. Quantum mechanics: basic postulates (according to the Copenhagen school);
  3. Quantum mechanics: systems that can be exactly solved;
  4. Quantum mechanics: approximate methods.

Note: on the part relating to the reminders, upon request of the students, supplementary lessons may be provided aimed at facilitating the student in re-examining the topics proposed therein (essentially attributable to the teaching of Physical Chemistry 3 of the three-year degree).

• Elements of linear algebra: properties of operators (Hermitian) and in-depth analysis of approximate methods for solving quantum mechanical problems (variational and perturbative method).
• Reworking of the treatment of the hydrogen atom.
• Effective operators; example with the Kronig-Penney model for the treatment of a particle in a periodic potential, derivation of the concept of electronic band and its physical implications.
• The polyelectronic problem; application of variational theorems, treatment of the spin problem and definition of the polyelectronic wave function through Slater's determinants.
• The Hartree-Fock method; in-depth analysis of the model with derivation and meaning of the Hartree-Fock equations (polyelectronic atom or molecule case), concept of molecular orbital, self-consistent field, basis set, molecular properties.
• Post-Hartree-Fock methods; treatment of the electronic correlation problem, approach based on the configuration interaction method and/or on the density functional theory.
• Optional, depending on the time available: topic of choice, based on the students' interests, which may be oriented towards theoretical aspects relating to the treatment of atomic/molecular problems or relating to the description of the solid state or to modelling-computational aspects.

RECOMMENDED READING/BIBLIOGRAPHY

Reference texts:

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

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

Any further didactic material can be provided by the teacher.

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

The start of the lessons is specified in the course programme and will take place according to the timetable indicated here. 

Class schedule

The timetable for this course is available here: EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam is oral, lasts about 45 minutes and is conducted by two tenured professors.

Attention!
In variation to the normal practice adopted in the CCS, for this teaching (in order to improve organizational management) registration for the exam must be done 5 working days before the exam date.

The test consists of at least three questions and is structured to ascertain the assimilation of the teaching contents and their critical re-elaboration.

The evaluation criteria of the exam can be synoptically traced back to:

• 18-20/30: Basic understanding and poor mastery of the topics covered in the teaching, sufficient command of language, poor ability to apply the knowledge/skills acquired;
• 21-23/30: Sufficient understanding but not full mastery of the topics covered in the teaching, sufficient command of language, limited ability to apply the knowledge/skills acquired;
• 24-25/30: Fair understanding of the main topics covered in the teaching and basic for the others, fair command of language, fair ability to apply the knowledge and limited ability to apply the skills acquired;
• 26-29/30: Good mastery of the topics covered in the teaching, full command of language, good ability to apply the knowledge and skills acquired;
• 30/30: Excellent knowledge of the topics covered in the teaching, brilliant command of language, excellent analytical ability to apply the knowledge and skills acquired;
• 30/30 cum laude: in addition to the criteria for obtaining 30/30, the student must have demonstrated a strong interest in the teaching that ranges across all its aspects, not necessarily related to the program, on which there has been an ability to independently rework/critical understand.

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

For students with disabilities or DSA, please refer to the Further Information section.

ASSESSMENT METHODS

The exam is aimed at verifying the achievement of an adequate level of knowledge of the topics covered in the course and their adequate exposition with the correct terminology of the discipline.

In this context, the student must:

• Frame the correct context of the question and rigorously develop the related concepts, demonstrating mastery of the mathematical tools available and their correspondence/discussion as a function of the physics of the system.
• Recognize the limits, approximations and potential of the various models for the description of the electronic structure and consequently choose the most appropriate ones for the treatment of the proposed problem.
• Know how to correctly describe the basic concepts of quantum mechanics and correlate the electronic structure of the system studied with its main chemical-physical properties.
• Show adequate language skills.

FURTHER INFORMATION

Erasum students are given the opportunity, upon request, to take the exam in English and, at the discretion of the commission, the exam may be administered in written form.

For students with DSA and/or disabilities, please refer to the University regulations, in particular to point g of the following document link and in general to the following link1.

For any further information not included in the teaching sheet, please contact the teacher.

OFFICE HOURS FOR STUDENTS: All working days, by appointment.