Learning objectives
Knowledge and understanding: the students will acquire basic knowledge in quantum mechanics and specific knowledge on applications of quantum mechanics to chemically relevant problems.
Applying knowledge and understanding: the students will acquire the tools required to re-interpret and formally describe chemical knowledge acquired in basic chemical courses (wavefunction, orbitals, chemical bond, spin, etc...) to reinforce a coherent and robust frame of knowledge in chemical sciences..
Learning skills: the student will acquire methodological competences and the basic tools of chemical quantum mechanics as to be able to read and understand specialistic literature.
Communication skills: Mastering of the specialistic language as to allow the student to interact with experts in the chemical-physical field and to effectively transfer knowledge also to non-specialized audience.
Prerequisites
To fruitfully access the course, students must master basic mathematical tools, and have a good knowledge of basic concepts in physics.
Mandatorily: the exam can only be accessed if the student ha already obtained a positive evaluation on the following exams:
- Mathematics 1
- Physics 1
- Mathematics 2
Course unit content
The course consists in two different modules. A theoretical module introduces basic concepts of quantum mechanics and guides the students towards the understanding of atomic and molecular physics. The experimantal module is articulated in several experimental and computational sessions on related topics.
Full programme
Introduction to quantum mechanics (related laboratory experience: “quantum eraser”):
*the double-slit experiment, photon polarization and the superposition principle
*states & operators, vectors & matrices
*observables, eigenstates and measurements
*commutability & compatibility
*Schrödinger representation
*Schrödinger equation
Exact solutions of the Schrödinger equation (related laboratory experience: “vibro-rotational spectrum of HCl”):
*the free particle
*the particle in a box
*the harmonic oscillator
*the rigid rotor, angula momenta & spin
*one-electron atoms
Approximation methods:
*perturbation theory for stationary states
*variational method
Symmetry in quantum mechanics (related laboratory experience: “IR and Raman spectra of 3 salts with anions of different symmetry”):
*symmetry & group theory
*symmetry & quantum mechanics
*point groups, continuous groups
*exchange symmetry: fermions & bosons
Atoms & molecules: some basic concepts:
*the adiabatic approximation (Born-Oppenheimer)
*mean-field approximation, atomic/molecular orbitals
Atomic structure:
*configurations & aufbau
*coupling of angular momenta
*spin-orbit coupling
Molecular structure (related experience: “resolution of the π structure of a conjugated hydrocarbon”):
*chemical bond: the hydrogen molecule
*diatomic homonuclear molecules
*polyatomic molecules
*hybrid orbitals
*transition metal complexes
*electronic structure calculations (primer)
*the Huckel method
*vibrations of polyatomic molecules
Bibliography
The reference manual is:
P.W. Atkins and R.S. Friedman, Molecular Quantum Mechanics, Oxford University Press, 2011 - V edition
complemented with lecture notes available to the students.
Teaching methods
The integrated course develops in 80 hours of frontal teaching (56 for the theoretical module and 24 for the laboratory module), where basic concepts will be introduced; 36 hours of guided exercises (spread across the theoretical and the laboratory modules), to apply acquired knowledge to specific problems; 30 hours of laboratory experiences, where the introduced concepts will be applied.
Assessment methods and criteria
The exam is integrated: “Physical Chemistry II and Laboratory”. The exam verifies: (a) the mastering of basic concepts of quantum mechanics and their application to chemical problems; (b) the ability of the student to present relevant concepts in a clear and precise way, properly using technical-scientific language; (c) the capacity to face chemical problems using formal tools of quantum mechanics; (d) the capacity to extract information from the analysis of data.
The exam starts with a simple written test to evaluate if the student has the basic necessary skills (four basic questions to be asked in an hour). The students succeeding the written test are admitted to the oral proof, where they will be asked to describe one of the laboratory experiment, and two more questions will be asked on topics of the theoretical course. To pass the exam, the students must masters the topics in the programs of both modules, in terms of knowledge and of ability to reliably and properly communicate using the scientific technical language.
The exam dates reported in Esse3 are referred to the written test; the oral exam follows straight away.
Other information
Lecture notes are available online (Elly portal), separated for the two modules.
The teachers are available to the students upon request to discuss and clarify specific issues.
