Unit ELEMENTARY QUANTUM CHEMISTRY
- Course
- Chemistry
- Study-unit Code
- 55155106
- Curriculum
- In all curricula
- Teacher
- Paola Belanzoni
- Teachers
-
- Paola Belanzoni
- Hours
- 42 ore - Paola Belanzoni
- CFU
- 6
- Course Regulation
- Coorte 2018
- Offered
- 2019/20
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Academic discipline
- CHIM/03
- Type of study-unit
- Opzionale (Optional)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
1. Elementary quantum mechanics. The wavefunction. Operators and mean values. The eigenvalue equation and the spectrum. Measurement in quantum mechanics. Time evolution and the Schrödinger equation.
2. The electronic structure of chemical systems in the fixed-nuclei framework. The Hamiltonian operator (non relativistic). The orbital model. Coulomb and exchange interactions. Hartree-Fock equation. The LCAO-SCF method. Potential energy surfaces and chemical reaction profiles.
3. Beyond the orbital model. Electron correlation. Configuration interaction.
4. Introduction to Density Functional Theory. One-electron density function. Exchange-correlation energy. Kohn-Sham equation.- Reference texts
Lecture notes written by the teacher.- Educational objectives
The student is exposed to the principal ideas and methods of modern quantum chemistry. He/she will understand and be able to assess the applicability and limitations of the main theoretical models used for the calculation of the electronic structure of chemical systems. The knowledge acquired will enable the student to profitably study more detailed aspects of the discipline.- Prerequisites
Elementary calculus. Derivative and integral. Basic linear algebra: vector, matrices and their manipulation. Fundamental physics concepts: force, energy, electric charge. Newton equation, Coulomb equation.- Teaching methods
Frontal lectures. The lecture slides are written and projected in class; after each lesson, they are collected in a pdf file and made available to the students.- Other information
The teacher may be contacted at any time (email for appointment) for questions and assistance in the study.- Learning verification modality
The oral examination will assess the general understanding of the fundamental aspects and results discussed in class, and of their conceptual relationships. It is usually necessary, and anyway useful, that the student illustrate his/her arguments by writing schemes and/or equations at the blackboard or on paper. The exam usually consists of a couple of questions covering both the general aspects of quantum theory and the more specific aspects and methods of quantum chemistry. The overall duration of the exam does not usually exceeds 15 minutes.- Extended program
- Introduction to quantum mechanica. Probability distributions for observable properties. Discrete and continuous distributions. The delta function.
The wavefunction and its meaning. Momentum space. Complete sets of basis functions and the Fourier transform. Uncertainty principle.
The superposition principle and interference phenomena.
Expectation values and distribution momenta. Quantum operators. Hermitian operators. Non commuting operators. Functions and vectors. Operators and matrices. Dirac notation.
Variance. Eigenvalue equation and property spectra. Eigenvalues and eigenfunctions. Discrete and continuous spectra. Degeneracy. Measurement in quantum mechanics.
Variational principle and algebraic eigenvalue equation. Commuting and non-commuting operators. Eigenvalue equation factorization.
Time evolution. Schrödinger equation. Stationary states. TIme evolution of expectation values.
Non-relativistic hamiltonian operator. The Born-Oppenheimer approximation and the electronic hamiltonian. One-electron and two-electron operators. Separability. The orbital model. One-electron approximation. Coulomb energy and coulomb operator. Hartree equation.
Antisymmetry principle. Slater determinant and exchange energy. Exchange operator. Hartree-Fock equation. Recursivity and the SCF model. Atomic basis sets and 4-index coulomb integrals. The LCAO-SCF procedure.
Atomic basis functions. Slater orbitals and gaussian functions. Basis set types and naming conventions.
Mulliken population analysis. Use of symmetry.
Potential energy surfaces and chemical reaction profiles. Geometry optimization and transition state optimization. Mathematical characterization and search methods. Newton method.
Virtual and occupied orbitals. Configurations and Configuration Interaction. Electron correlation. The hamiltonian matrix. Full-CI and truncated CI. SDCI.
Density functions. Introduction to Density Functional Theory. Hohenberg and Kohn theorems. Exchange-correlation energy. Kohn-Sham equation. Exchange-correlation potentials.