THEORETICAL CHEMISTRY
Academic year and teacher
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- Versione italiana
- Academic year
- 2015/2016
- Teacher
- RENZO CIMIRAGLIA
- Credits
- 6
- Didactic period
- Secondo Semestre
- SSD
- CHIM/02
Training objectives
- Knowledge and understanding.
The aim of the course is to provide the students with an overview of nowadays' theoretical chemistry in its branches of quantum chemistry and computational chemistry. The course starts from the justification of the fundamental Born-Oppenheimer's approximation and analyzes the possible failures of it. Within the frame of electronic molecular structure the important concepts of one and two-electron density function (and density matrices) are provided with a view to a thorough understanding of the electronic correlation. Modern second-quantization techniques are then presented and illustrated in connection with the calculation of various approximations to the wave function; among these, particular stress is given to the Hartree-Fock equations, to the Moller-Plesset perturbation techniques, to multiconfiguration methods such as CASSCF, to the coupled-clusters techniques and to the techniques best suited to the calculation of excited states. Eventually the course presents the modern techniques based on the density functional theory (DFT) and looks through the most common exchange-correlation functionals.
Ability to apply knowledge and understanding.
At the conclusion of the course the student will be able: a) to judge when and in which cases the Born-Oppenheimer approximation turns out to be inadequate; b) to know how to discuss the properties and applications of the concept of density matrix; c) to know how to apply the concepts of second quantization to the modern techniques of calculation of molecular properties; d) to know how to apply the modern density functional techniques to concrete cases. Prerequisites
- Knowledge of basic physico-chemical disciplines.
Course programme
- Orders of magnitude of the electronic, vibrational and rotational energies in molecules. The Born-Oppenheimer approximation: the electronic hamiltonian, the separation of electronic and nuclear motion, electronic and nuclear wave functions, the operator of non-adiabatic coupling, its order-of-magnitude evaluation and possibility of neglect. Analytic evaluation of the non-adiabatic coupling, the non-crossing rule, weakly avoided crossing with an application to the ionic and covalent states of the NaCl molecule. Conical intersections.Electronic wavefunctions. Expansion in Slater determinants, configuration interaction (CI), Slater's rules.Electronic density and density matrix, the one- and two-particle matrices. Expansion of the density matrices in an orbital basis. The concept of "natural orbitals" and "occupation numbers". The density matrices and the electronic correlation. The two theorems of Hohenberg and Kohn; the Thomas-fermi-Dirac theory (hints).Second quantization techniques: creation and destruction operators for the electrons and their anticommutation properties. One- and two-electron operators in the language of second quantization; relationships with density matrices. Unitary transformations of the orbital basis. Determination of an optimal one-determinat function, Hartree-Fock's equations.Beyond Hartree-Fock: Moller-Plesset's perturbation techniques, multiconfiguration SCF methods, complete active spaces (CAS), the coupled-clusters method, the equations-of-motion method (EOM) for the calculation of excited states.DFT (Density Functional Theory) methods; Khon-Sham's equations, the exchange-correlation functional. Some of the most common functionals.
Didactic methods
- Theoretical/practical lessons.
Learning assessment procedures
- Oral examination.
The examination consists in three questions addressed to evaluating the abilities acquired by the student as to the discussion, in scientifically correct terms, of the topics exposed during the course. Reference texts
- A. Szabo, "Modern Quantum Chemistry", Dover editions.
R. Cimiraglia, "Methods of calculations of excited states", on line on the teacher's personal site accessible through www.unife.it
