Teaching

Quantum Chemistry (1^st level Degree in Chemistry)

Prof. Gian Franco Tantardini

ECTS credits: 6, Code: F45025

The Dawn of Quantum Theory:

Blackbody Radiation, Photoelectric Effect, Vibration of Atoms in Crystals, Hydrogen Atomic Spectrum, De Broglie Waves, Uncertainty Principle.

The Classical Wave Equation:

One-Dimensional W. E., Separation of Variables, Superposition of Normal Modes, Vibrating Membrane.

The Schroedinger Equation:

Linear Operators, Eigenvalue Problems, Interpretation of the Wave Function, Average Quantities, Particle in a Box.

The Postulates of Quantum Mechanics:

State Functions, Observable Quantities and Eigenvalues, Commutators, Hermitian Operators, Commutating Operators, Time Dependent Schroedinger Equation.

The Harmonic Oscillator:

Energy Levels and Wave Functions, Hermite Polynomials, H.O. as a Model of a Diatomic Molecule.

The Rigid Rotator:

Energy Levels and Spherical Harmonics.

The Hydrogen Atom:

Energy Levels and Orbitals.

Approximation Methods:

Variational Method, First Order Perturbation Theory.

Many Electron Atoms:

Hartree Fock Equations, Self Consistent Field, Antisymmetry of the Wave Function, Slater Determinant, Atomic Term Symbols.

Molecules:

Born-Oppenheimer Approximation, Molecular Orbital Theory, SCF-LCAO.MO Wave Function, Hartree-Fock-Roothaan Equations.

Reference books:

D.A. McQuarrie, Quantum chemistry, 2^nd ed., University Science Books, USA, 2008
I. N. Levine, Quantum chemistry , 5^th ed., Prentice Hall Inc., USA, 2000

Physical Chemistry B (2^nd level Degree in Chemistry)

Prof. Gian Franco Tantardini

ECTS credits: 6 (5 for Lessons + 1 for Exercises), Code: F83004

Periodic structures and crystal lattices:

symmetry operations, Miller indices, Bravais lattices, simple crystal structures. Reciprocal lattice. Diffraction, Laue’s equations, Bragg’s law, Brillouin zones, structure factors and diffraction methods.

Internal energy of crystals:

Atomic dynamics in crystals: potential, equations of motion, lattice vibrations, normal modes, dispersion relationships, acoustic and optic phonons, phonon thermal capacity. Planck distribution, Einstein and Debye models. Free electron model. Fermi-Dirac distribution, thermal capacity of the electron gas. Nearly free electron model, Tight Binding approximation, Bloch functions, energy bands, density of states, Fermi surfaces.

Structure of solid surfaces:

surface reconstruction, structures of adsorbates, experimental methods for surface investigations. Processes at solid surfaces: physisorption, molecular and dissociative chemisorption, adsorption dynamics. Molecular approach to catalysis.

Exercises:

Examples and problem solution.

Reference books:

H. Ibach, H. Luth, Solid State Physics. An Introduction to Principles of Material Science, Springer-Verlag, 3^a ed., 2003
K. W. Kolasinski, Surface Science. Foudations of Catalysis and Nanoscience, John Wiley & Sons LTD, 2002

Further readings:

N. W. Ashcroft, N. D. Mermin, Solid state physics, Harcourt Brace College Publishers, 1976
G. A. Somorjai, Introduction to surface chemistry and catalysis, John Wiley & Sons, 1994
A. Gross, Theoretical surface science, Springer-Verlag, New York, 2003

Theoretical Chemistry (2^nd level Degree in Chemistry)

Dr.Rocco Martinazzo, Dr.Michele Ceotto

ECTS Credits: 6, Code: F83018

Introduction:

Linear algebra. Dirac notation. Time-dependent Schrodinger equation (TDSE). Variational principles and perturbation theory.

Separation of electronic and nuclear motions:

Born-Oppenheimer approximation. Adiabatic and diabatic states.

Wavefunction methods for electrons:

The N-electron problem. Orbitals and Slater determinants. Basis functions. Hartree-Fock approximation. Electron correlation: configuration interaction and perturbative approaches.

Density Functional Theory for electrons:

Hohenberg-Kohn theorems. Kohn-Sham equations. Density functionals. Pseudopotentials. Applications.

Chemical reaction theory:

Collision theory in classical and quantum mechanics. Scattering operators. Numerical solution of the TDSE. Feynman's path integrals. Semiclassical theory. Transition state theory. Brownian motion and Langevin equation. Kramers theory.

Reference Books:

A. Szabo and N.S. Ostlund, Modern Theoretical Chemistry, Mc Graw-Hill Inc., New York, 1989
R. G. Parr and Yang, Density-Functional Theory of Atoms and Molecules, Oxford University Press, New York, 1989
D. Tannor, Introduction to Quantum Mechanics: A Time-Dependent Perspective, University Science Books, Sausalito, CA, 2007

Further readings:

A. Messiah, Quantum mechanics, Dover Publications, New York, 2000
R.D. Levine, Molecular Reaction Dynamics, Cambridge University Press, Cambridge, 2005