# PHYSICAL CHEMISTRY 3

OVERVIEW

This course completes the preparation of Physical Chemistry, providing a description of the atomic and molecular structure, introducing the concepts of quantum mechanics and related electronic properties.

"Einstein said that if quantum mechanics is correct, the universe is crazy. Well, Einstein was right. The universe is crazy." - Daniel Greenberger

## AIMS AND CONTENT

LEARNING OUTCOMES

The teaching, on the acquisition of knowledge related to the field physical-chemical, it aims at providing the basic tools of quantum mechanics and its applications in the chemical (e.g. in molecular spectroscopy).

AIMS AND LEARNING OUTCOMES

The methodological tools and the basic language of quantum chemistry will be provided, which will allow the student to reinterpret in a formal way the basic chemical knowledge (chemical bond, wave function, radiation / matter interaction, etc ...) and to reinterpret these concepts in more depth.

In particular, the student's attendance and active participation in lectures, self-assessments / exercises proposed and individual study (supplemented by recommended textbooks) will allow him to:

- knowing in an analytical way some of the fundamental experiments that led to the crisis of classical physics;

- apply this knowledge to the critical description of the experiments analyzed with a view to an experimental design;

- identify the fundamental paradigms that led to the transition from classical to quantum physics;

- know general aspects of quantum mechanics both from a conceptual point of view (postulates of quantum mechanics, elements of the concept of measurement, elements of the concept of operator), both historical;

- to know in a circumstantial way the nature of the Hamiltonian operator and the Schrödinger equation, also through the analysis of some simple models (hole or potential barrier, two- and three-dimensional rotor, harmonic oscillator) assisted by exercises;

- apply this knowledge to construct the Hamiltonian operator for generic physical systems and solve simple problems related to the studied models;

- know in an adequate way (according to a three-year course, minimum level the associated concept map) the quantum mechanical problem of the solution exact hydrogen-like atom, the concept of atomic orbital, electron density, radial density;

- identify the fundamental physical-mathematical aspects related to the resolution of the hydrogen atom;

- apply this knowledge to solve simple problems related to the hydrogen atom;

- know some basic aspects of the approximate methods used in quantum mechanics (in particular the variational method and analysis of some aspects related to perturbative method);

- apply this knowledge to the variational problem of the interaction between two states;

- know the concept of spin (through the analysis of the Stern-Gerlach experiment, of the postulate of quantum mechanics correlated, hints of the effect of spin-orbit coupling with examples);

- identify the fundamental physical-mathematical aspects related to spin and describe their meaning, if necessary, apply this knowledge to simple exercises related;

- know in an adequate way (minimum level the associated conceptual map) the quantum mechanical problem related to the approximate solution of the atom multielectronic, the concept of potential and effective charge, polyelectronic wave function and its expression (concept of singlet, triplet, determinant state), the electron correlation problem, the definition of the Fock operator, the meaning of the spectroscopic notation and its derivation;

- identify the fundamental physical-mathematical aspects related to the resolution of the multielectronic atom in connection with the previous atom problem hydrogenic, approximate methods and the concept of spin;

- apply this knowledge to the solution of simple correlated exercises;

- know in an adequate way (minimum level the associated conceptual map) the quantum mechanical problem related to the approximate solution of a molecule, notes on the models used with particular attention to the LCAO method, evolution of the definition of the Fock operator, description of the concept of hybridization and notes on the fundamental aspects of the nature of the covalent bond;

- identify the fundamental physical-mathematical aspects related to the resolution of the quantum mechanical problem related to molecules in connection with evolution of the passage from the hydrogen-like atom to the multi-electronic one;

- apply this knowledge to the description of the properties of a molecule through the construction of the diagram of molecular orbitals and solve simple ones related exercises;

- know the basic chemical-physical aspects, also through semiclassical models, related to spectroscopy;

- knowing analytically some specific aspects of rotational, vibrational (IR and Raman) and electronic spectroscopy;

- apply this knowledge to the solution of simple correlated exercises;

- acquire the correct terminology for exposing the concepts of quantum mechanics with an adequate language.

Furthermore, the course aims to develop the student's skills and competences, enabling him to elaborate links between the concepts acquired with the basic chemical knowledge, and the different concepts developed in the course of teaching. For each conceptual block they are provided, voluntarily by

part of the student concerned, of the supplementary notes.

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 and General and Inorganic Chemistry.

Teaching methods

The teaching corresponds to 48 hours of lectures, held in Italian (please note that there is also an individual and effective study commitment of 102 hours).

The lecture notes, as a rule, are available on the aulaweb page (dedicated to teaching) at the same time as the relative contents are held in the classroom.

In this context, at the discretion of the teacher, self-tests (open-ended, multiple-choice questions or numerical exercises) and/or iterative and non-interactive auxiliary materials are uploaded on the aulaweb page, in order to facilitate individual study of the students.

SYLLABUS/CONTENT

- Introduction to quantum mechanics.

- 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 experiment of the two slits, black body and specific heats).

- The Schrödinger equation and the postulates of quantum mechanics (Introduced the concept of state, wave function, operator and in axiomatic form discussed the postulates of quantum mechanics, introduction to the concept of measurement and uncertainty principle. Introduction to the Schrödinger equation and its implications).

- Quantum mechanics applied to simple systems.

- Particle in a potential barrier/well (hints of tunnel effect)
- Particle with rotational motion
- Harmonic oscillator

- Approximate methods for solving Schrödinger's equation.

- Variational method (general discussion of the concept, simple applications)
- Perturbative methods (outline)

- The atomic structure (case of hydrogen atom, spin, polyelectronic atoms, Slater determinants, vector model, spectroscopic notation).

- Hydrogen-like model and its extension to multielectronic atoms.
- Atomic orbitals.

- The molecular structure. (case of diatomic and polyatomic molecules, basic concepts on the nature of the bond, construction of Walsh diagrams, general considerations)

- MO-LCAO method to build the polyelectronic wave function.
- The covalent bond.

- Applications of quantum mechanics in molecular spectroscopy.

- Interaction of radiation / matter.
- Rotational spectroscopy
- Vibrational spectroscopy
- Electronic 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

**Ricevimento:** All working days, by appointment.

## LESSONS

Teaching methods

The teaching corresponds to 48 hours of lectures, held in Italian (please note that there is also an individual and effective study commitment of 102 hours).

The lecture notes, as a rule, are available on the aulaweb page (dedicated to teaching) at the same time as the relative contents are held in the classroom.

In this context, at the discretion of the teacher, self-tests (open-ended, multiple-choice questions or numerical exercises) and/or iterative and non-interactive auxiliary materials are uploaded on the aulaweb page, in order to facilitate individual study of the students.

LESSONS START

From 27 September 2021, according to the timetable shown on http://www.chimica.unige.it/didattica/orari_CTC or https://corsi.unige.it/8757/p/studenti-orario

ORARI

## EXAMS

Exam description

The exam is oral, has a duration of at least 45 minutes and is conducted by two tenured professors.

Mind out there! In variation to the normal practice adopted in the CCS, for this course (for the purpose of better organizational management of the exam), enrollment must be made 5 working days before the exam date.

The oral test, normally, includes four questions to verify the acquisition of the concepts inherent to the topics covered in the course, synoptically:

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

b) Hydrogenoic and/or polyelectronic atom (corresponding to the fifth point of the program).

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

d) Spectroscopy (corresponding to the seventh point of the program).

Assessment methods

At the beginning of the course and on the corresponding site on aulaweb, students are provided with a docimology table (expressed out of thirty) with an indication of the criteria evaluative in relation to the acquisition of knowledge, competences and skills / abilities related to teaching and the corresponding achievable score.

The oral exam is aimed at verifying the achievement of an adequate level of knowledge of the topics developed / discussed during the lessons and the ability to use the correct terminology combined with the coherence of exposition of the concepts.

In particular, the following will be assessed, through the discussion of topics developed in the program and / or the resolution of exercises: the depth and coherence of the acquired knowledge on quantum chemical methodologies; the ability to use this knowledge in the description of atomic and / or molecular systems; the skills in using the knowledge and skills acquired in critically describing specific cases of chemical-physical systems.

The initial question of the proof is related to the choice of a postulate of quantum mechanics to be critically discussed (also in connection with the passage from classical to quantum physics).