Quantum Chemistry:
Hartree-Fock theory. Correlation energy and configuration interaction. Molecular complexes energies and basis set superposition error. Molecular properties.
Statistical Mechanics:
Statistical ensembles and thermodynamic potentials. Virial theorem and equipartition of the energy. Fluctuations. Monte Carlo methods. Distribution functions in complex fludis.
Part one: Frank Jensen, Introduction to computational Chemistry, Oxford UP, 1999. Errol Lewars, Introduction and Applications of Molecular and Quantum mechanics, Kluwer 2003.
• Part two: David Chandler, Introduction to Modern Statistical Mechanics, Oxfors UP 1987. Daan Frenkel and Berend Smit, Understanding Molecular Simulations, Academic Press 2002.
Learning Objectives
The course is divided in two distinct parts: The first part includes the theoretical basis for modern quantum chemistry. The second part is an elementary introduction to modern statistical mechanics.
Prerequisites
Courses required: none
Courses recommended: none
Teaching Methods
Total number of hours for Lectures (hours): 54
Type of Assessment
Oral exam. Eight annual session.
Course program
Part 1: QUANTUM CHEMISTRY (3 CFU)
• Elements of linear Algebra.
• Hartree Fock theory for atoms and molecules. Closed shell and Open-Shell systems.
• HF calculation of the hydrogen molecule. The dissociation problem and the unrestricted solution.
• Spin states for many electron systems. Ladder operators and Slater determinants. Spin contamination and spin adapted orbitals.
• Electron correlation energy. Configuration interaction.
• Density functional theory: Hoenberg-Khon theorem and Kohn and Sham equations. Local density and Local Spin density approximation.
• Calculation of intermolecular energies and basis set superposition error.
Part 2: STATISTICAL MECHANICS (3 CFU)
• Statistical ensembles , phase space and equilibrium
• Ergodic theorem. Liouville theorem
• Microcanical, Canonical, and grancanonical ensembles.
• Partition functions and thermodynamical potentials
• Virial theorem and equipartition of the energy. Fluctuations
• Monte Carlo methods for complex systems. Metropolis algorithm.
• Structural properties of complex systems: pair correlation functions. Measure of the g(r) through Neutron scattering experiments.
• Systems out of equilibrium:Fluctuation dissipation theorem.