Learning objectives
Knowledge and understanding: the students will acquire specific knowledge on applications of quantum mechanics to problems of interest for material science.
Applying knowledge and understanding: the students will acquire the tools required to re-interpret and formally describe chemical knowledge acquired in previous courses (wavefunction, orbitals, chemical bond, spin, etc...) to reinforce a coherent and robust frame of knowledge.
Learning skills: the student will acquire methodological competences and the basic tools of quantum mechanics as to be able to read and understand specialist 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.
Course unit content
Methods of approximation
Symmetry in Quantum Mechanics
Atoms and molecules: some basic concepts
Atomic structure
Molecular structure
Introduction to quantum chemical calculations
Molecular spectroscopy: a primer
Computational Lab (1 CFU, 12 hours):
- Intro to Hartree-Fock method, Roothan-Hall equations, Density Functional Theory (DFT);
- Intro to Linux environment;
- Computational experience 1: geometry optimization and energy calculation at the Hartree-Fock level for the water molecule;
- Computational experience 2: Calculation at DFT level of benzene optimized geometry; calculation and visualization of the benzene electrostatic potential map, calculation and visualization of benzene normal modes;
- Computational experience 3: Calculation of the electrostatic potential map of pyridine and protonated pyridine. Calculation of the protonation energy of pyridine. Calculation and comparison of the vibrational spectrum of pyridine and protonated pyridine;
- Computational experience 4: Computational study of an n-alkane: construction of the input molecular geometry, geometry optimization, frequency calculation, electrostatic potential map calculation, visualization of the Hartree-Fock molecular orbitals;
- Architecture of a supercomputer and guided tour of the University cluster.
Lab Activities:
-quantum eraser
-quantum confinement in ZnO nanocrystals
-IR and Raman spectra of inorganic salts
-preparation and characterization of luminescent polymeric films
Full programme
Approximation methods
*perturbation theory for stationary states
*variational method
Symmetry in quantum mechanics
*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
Molecolar structure
*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
Quantum chemical calculations: an introduction to DFT
Molecular spectrosocpy: (a) optical spectrosocpy, selection rules; (b) the basic NMR experiment
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 course, integrated with a laboratory course, develops in 40 hours of frontal teaching where basic concepts will be introduced. An additional credit will be devoted to practical exercise for quantum chemical calculation..
Assessment methods and criteria
The exam, integrated with the corresponding Laboratory, verifies (a) the mastering of basic concepts of quantum mechanics and their application to problems of interest to material science; (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 problems using formal tools of quantum mechanics;(d) the capacity to extract information from the analysis of data.
Other information
lecture notes are available to the students.
The teacher is available to the student upon request to discuss and clarify specific issues.
