# PHYSICAL CHEMISTRY 1

- Overview
- Assessment methods
- Learning objectives
- Contents
- Full programme
- Bibliography
- Delivery method
- Teaching methods
- Contacts/Info

General Chemistry course and basic knowledge of the first year Mathematics and Physics courses.

In particular

the understanding of the topics covered in the course requires the fundamentals of:

- Linear algebra

- Differential calculation in one and more variables

- Integral calculation in one and more variables

- Calculation with complex numbers

- Classical mechanics

Written exam, with attribution of a mark out of thirty.

The exam is divided into two parts. The first part consists of a questionnaire of multiple choice questions (4 possible choices) that cover all the topics of the course. The estimated time is 45 minutes. Overcoming the first part is the necessary condition to gain access to the second part, usually on the same day, which consists in the complete resolution of 4 exercises, similar to those already presented during lessons and exercises, in a time of 2 hours. The final grade proposed to the candidate is a weighted average of the marks of the two tests.

The exam can be taken from the end of the first semester and is considered passed if the candidate has obtained a grade equal to at least 18/30.

The objective of this course is to build a base of quantum mechanics and molecular spectroscopy, which are essential for chemical disciplines.

In particular, students will be able to:

- Know, at a basic level, the laws of quantum mechanics.

- Apply them numerically to the study of simple model systems but with important applications in chemistry and technology

-Know the basic elements of atomic and molecular spectroscopy and their applications in chemistry

- Find, starting from spectroscopic data, chemical-physical properties of atoms and molecules.

Learning these concepts is fundamental to understanding the structure and properties of atoms and molecules, including their reactivity. These knowledge bases are indispensable to be able to face, in a possible Master's Degree in Chemistry, the most thorough chemical area teachings provided by this degree course.

Elements of classical mechanics. Waves and electromagnetic radiation. Radiation-matter interaction and the electromagnetic spectrum. The basic ideas of spectroscopy. The limits of classical physics highlighted by the experiments: black body, Planck constant, photoelectric effect. Energy quantization. Central role of quantum mechanics in science, technology, and our everyday life.

The "wave-particle duality". The double slit experiment. De Broglie's report. The Heisenberg uncertainty principle. The position-moment indeterminacy and time-energy. Waves and wave packets. SchrÃ¶dinger's equation for the free particle.

The postulates of quantum mechanics. The concept of a quantum mechanical state. The wave function. Linear operators. Use of operators to obtain information on chemical systems (atoms, molecules, etc.) from the wave function. Eigenvalues â€‹â€‹and eigenfunctions. Definition of two operators switch. Physical consequences of the commutability / non-commutability of two operators, and relationship with the uncertainty between complementary quantities. Probability and amplitude. Born's interpretation. Probability distributions and mean values â€‹â€‹in classical mechanics and quantum mechanics. Overlap principle Overlapping states and collapse of the wave function. Outline of the temporal evolution of a quantum-mechanical system: the time-dependent SchrÃ¶dinger equation for stationary states.

Free particle vs. confined particle: origin of energy quantization. Acceptable and unacceptable functions, boundary conditions. The information obtainable from the wave function, meaning of the curvature. Particle confined in the one-dimensional, two-dimensional, three-dimensional box. Degeneration and symmetry. The zero point energy and its relationship with the uncertainty principle.

The Tunnel effect: some examples / applications.

The quantum-mechanical harmonic oscillator. The SchrÃ¶dinger equation for the harmonic oscillator. Eigenvalues, eigenfunctions, zero point energy. Symmetry of wave functions. Application of the harmonic oscillator model to molecular vibrations and limits of harmonic approximation. Vibrational spectroscopy. Transition dipole moment. Selection rules. Anharmonicity. Dissociation energy for a diatomic molecule. Vibrations of polyatomic molecules.

Angular momentum. Particle confined on a ring (two dimensions) and on a sphere (three dimensions). Permitted energies and wave functions. Spherical harmonics. The diatomic molecule as a rigid rotor. Introduction to rotational spectroscopy.

Hydrogen atom and hydrogenoid systems.

The solutions of the radial equation for hydrogenoid atoms, energies, and atomic orbital.

Wave functions and probability density, radial and angular functions. The quantization of the angular momentum and the relative quantum numbers.

The emission spectra of the hydrogenoid atoms and the series of spectral lines.

Electronic spin, spin operators. Helium atom. Atoms with many electrons. The Pauli exclusion principle. Electronic configurations, Hund rules. Atomic spectra and selection rules.

Elements of classical mechanics. Waves and electromagnetic radiation. Radiation-matter interaction and the electromagnetic spectrum. The basic ideas of spectroscopy. The limits of classical physics highlighted by the experiments: black body, Planck constant, photoelectric effect. Energy quantization. Central role of quantum mechanics in science, technology, and our everyday life.

The "wave-particle duality". The double slit experiment. De Broglie's report. The Heisenberg uncertainty principle. The position-moment indeterminacy and time-energy. Waves and wave packets. SchrÃ¶dinger's equation for the free particle.

The postulates of quantum mechanics. The concept of a quantum mechanical state. The wave function. Linear operators. Use of operators to obtain information on chemical systems (atoms, molecules, etc.) from the wave function. Eigenvalues â€‹â€‹and eigenfunctions. Definition of two operators switch. Physical consequences of the commutability / non-commutability of two operators, and relationship with the uncertainty between complementary quantities. Probability and amplitude. Born's interpretation. Probability distributions and mean values â€‹â€‹in classical mechanics and quantum mechanics. Overlap principle Overlapping states and collapse of the wave function. Outline of the temporal evolution of a quantum-mechanical system: the time-dependent SchrÃ¶dinger equation for stationary states.

Free particle vs. confined particle: origin of energy quantization. Acceptable and unacceptable functions, boundary conditions. The information obtainable from the wave function, meaning of the curvature. Particle confined in the one-dimensional, two-dimensional, three-dimensional box. Degeneration and symmetry. The zero point energy and its relationship with the uncertainty principle.

The Tunnel effect: some examples / applications.

The quantum-mechanical harmonic oscillator. The SchrÃ¶dinger equation for the harmonic oscillator. Eigenvalues, eigenfunctions, zero point energy. Symmetry of wave functions. Application of the harmonic oscillator model to molecular vibrations and limits of harmonic approximation. Vibrational spectroscopy. Transition dipole moment. Selection rules. Anharmonicity. Dissociation energy for a diatomic molecule. Vibrations of polyatomic molecules.

Angular momentum. Particle confined on a ring (two dimensions) and on a sphere (three dimensions). Permitted energies and wave functions. Spherical harmonics. The diatomic molecule as a rigid rotor. Introduction to rotational spectroscopy.

Hydrogen atom and hydrogenoid systems.

The solutions of the radial equation for hydrogenoid atoms, energies, and atomic orbital.

Wave functions and probability density, radial and angular functions. The quantization of the angular momentum and the relative quantum numbers.

The emission spectra of the hydrogenoid atoms and the series of spectral lines.

Electronic spin, spin operators. Helium atom. Atoms with many electrons. The Pauli exclusion principle. Electronic configurations, Hund rules. Atomic spectra and selection rules.

The course PHYSICAL CHEMISTRY 1 does not provide for the adoption of a single reference text. The teacher recommends a set of university-level texts, in Italian or English, among which students can choose the one that suits them best.

The 9 CFU course corresponds to 72 hours of lectures. All lessons are supported by slides prepared by the teacher and downloadable from the e-learning site of the course.

Exercises are also planned (36 hours) so that students can optimally acquire the concepts explained in lectures by applying them in numerical exercises

The teacher receives, by appointment, every working day at her studio, located on the 1st floor of the Via Valleggio 9 headquarters, Como.