66913 - Physical Chemistry 1

Learning outcomes

The students learn: to master their mathematical knowledge in order to apply it to problems in Physical Chemistry; the fundamentals of molecular symmetry and of quantum mechanics for following studies in atomic and molecular structure;to apply the methods of quantum mechanicsfor studying the electronic properties, especially the energy levels,of atoms and simple molecules.

Course contents

• Module 1

1. Molecular symmetry and group theory: Symmetry concept; Types of symmetry; Point symmetry operations; The algebraic structure of a group: definition, multiplication table, properties and definitions; Classification of point symmetry groups.

2. Vector spaces and linear transformations: Vector spaces, Matrix algebra, Matrices and linear transformations, Determinants, Invertible matrices, Orthogonal matrices, Complex matrices, The eigenvalue problem, Similarity transformations and diagonalization, Hermitian matrices. Function spaces. 

3. Matrix representations and character theory: Symmetry operations as linear transformations in ordinary 3D space; Matrix representations of symmetry groups; Functions as bases for representations; Equivalent representations; Reducible and irreducible representations; Great orthogonality theorem of representations and characters; Character tables.

4. Symmetry and quantum mechanics: The postulates of quantum mechanics: states, operators and observables; The Schrödinger equation; Interpretation of the wavefunction; Time evolution; Matrix formulation; Symmetry of the Hamiltonian; Symmetry and degeneracy; Integrals and selection rules.

5. Ordinary and partial differential equations: First-order separable differential equations; Linear first-order equations; Second-order homogeneous linear equations with constant coefficients. Applications: classical harmonic oscillator, particle in a one-dimensional box and on a ring. Second-order inhomogeneous linear equations; Separation of variables. Applications: particle in a rectangular box and in a circular box.

• Module 2 and 3

1.  Heisenberg Uncertainty Principle
2. Postulates of Quantum Mechanics
3. Free Particle
4. Particle in a Box
5. Confined Particle
6.  Particle on a Ring
7. Harmonic Oscillator
8. Particle in a Central Field
9. Particle on a Sphere
10. Two-Body Systems
11. Hydrogen-like Atom
12. Spin
13. Principle of Indistinguishability
14. Laboratory work: Numerical solutions of quantum mechanical problems 

Readings/Bibliography

Module 1

• Main reference textbook:

1. L. Dore, Simmetria e Chimica: Introduzione all'applicazione della teoria dei gruppi,, Editografica, 2025.

• Suggested supplementary readings:

1. E. Steiner, The Chemistry Maths Book, 2nd ed., Oxford University Press, 2008.
2. D.M. Bishop, Group Theory and Chemistry, Dover Publications, 1993.

Module 2

• Suggested complimentary readings:

1. W. Atkins and R.S. Friedman, Molecular Quantum Mechanics, Oxford University Press, 2010.
2. L. Susskind and A. Friedman, Quantum Mechanics. The Theoretical Minimum, Penguin Books, 2015.
3. G. Auletta, M. Fortunato and G. Parisi, Quantum Mechanics, Cambridge University Press, 2009.

Supplementary teaching material - e.g. lecture notes (reference for Module 2), exercises, summary sheets, presentations - will be made available on the University’s Virtuale platform.

Teaching methods

The course is organized in three learning modules: Mathematical Methods for Chemistry (5 credits, 48 hours)  and Atomic and Molecular Structure (4 credits) with its additional module of laboratory work (1 credit). Classes of the first module are given in the first semester; classes of the second and third  modules are given in the second semester.

The first module consists of in-person lectures, which include the presentation of theoretical concepts and the guided solution of exercises to support learning.
The second module is delivered through frontal lectures.
The third module involves numerical laboratory activities focused on the simulation of quantum phenomena and computational analysis using Matlab.

All students must attend Module 1, 2 on Health and Safety, online.

Assessment methods

Learning assessment is evaluated only by means of the final examination. This aims at verifying the student's knowledge and skills by means of one test for each semester.

For the first module, the assessment consists of a written exam (3 hours) followed by an oral exam.
The written exam involves solving problems without access to teaching materials. It serves as a qualifying step: students must obtain a minimum score of 16/30 in the written exam to be admitted to the oral exam. The written exam score contributes to the final assessment of the module but is not averaged with the oral exam score: the final grade is determined based on the oral exam.
The oral exam, approximately one hour in length, includes a discussion of the written paper and responses to two main questions on topics covered during the course.

The examination covering the contents of the second and third modules consists of a written test involving the solution of a numerical problem, which serves as a qualifying step for admission to the subsequent oral exam. The oral exam focuses on theoretical topics and includes a discussion of the laboratory activity report.

The final grade is the arithmetic mean of the grades obtained for each learning module.

For both oral exams, evaluation is based on content mastery, clarity of presentation, the ability to link theory and practice, and autonomy in discussion. The grading criteria are as follows:

• Sufficient (18–20): basic knowledge; mostly correct expression, but uncertain and not well structured.

• Good (21–24): solid understanding; overall adequate explanation, though mostly rote and with limited ability to connect topics.

• Very good (25–27): strong command of content; well-structured presentation with analytical ability.

• Excellent (28–30L): complete and in-depth knowledge; rigorous, independent and critical discussion. Honors are awarded in cases of outstanding performance.

Students with learning disorders and\or temporary or permanent disabilities: please, contact the office responsible (https://site.unibo.it/studenti-con-disabilita-e-dsa/en/for-students ) as soon as possible so that they can propose acceptable adjustments. The request for adaptation must be submitted in advance (15 days before the exam date) to the lecturer, who will assess the appropriateness of the adjustments, taking into account the teaching objectives.

Teaching tools

Classroom lectures are supported by a projector and a whiteboard; the computer lab is used for Module 3.

For the first module, the Virtuale platform provides a compendium divided into 10 sections, aligned with the weekly course topics. Each section serves as a guide to follow the course, offering organizational outlines, bibliographic references, and selected exercises. The compendium is intended to support weekly study and classroom participation, while in-depth theoretical work is to be carried out using the main reference textbook. Presentations used during lectures and Matlab Live Script files are also available to guide students through the numerical activities.

Office hours

See the website of Luca Dore

See the website of Assimo Maris

See the website of Luca Bizzocchi