Unit QUANTUM METHODS IN COMPUTATIONAL CHEMISTRY
- Course
- Chemical sciences
- Study-unit Code
- A005341
- Curriculum
- Theoretical chemistry and computational modelling
- Teacher
- Andrea Lombardi
- Teachers
-
- Andrea Lombardi
- Hours
- 42 ore - Andrea Lombardi
- CFU
- 6
- Course Regulation
- Coorte 2025
- Offered
- 2025/26
- Learning activities
- Caratterizzante
- Area
- Inorganico-chimico fisico
- Academic discipline
- CHIM/03
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- English
- Contents
- The course covers several exact, approximate, and numerical methods to solve the time-dependent molecular Schrödinger equation, and applications including calculations of molecular electronic spectra. More advanced topics include introduction to the semiclassical methods.
- Reference texts
- J. Zhang, Theory and Application of Quantum Molecular Dynamics, World Scientific.
Lecture notes - Educational objectives
- By the end of the course, the student must be able to:
Solve the time-dependent Schrödinger equation with a basis method.
Derive and apply the sudden and adiabatic approximations.
Derive the time-dependent perturbation theory and Fermi's Golden Rule.
Illustrate the connections between the Newtonian, Lagrangian, and Hamiltonian approaches to classical mechanics.
Expound how electronic spectra can be computed via the autocorrelation functions.
Apply the Fourier and split-operator methods to solve the time-dependent Schrödinger equation numerically. - Prerequisites
- Basic quantum mechanics
- Teaching methods
- Lectures with slides and blackboard derivations, problem-solving sessions Computational labs. Group discussions on recent literature or review articles
- Other information
- Course start: March 2026. Course end: May 2026. The course will take place at the Department of Chemistry, Biology and Biotechnology
- Learning verification modality
- Final Exam (80%): Covers entire course. Practical sessions (20%). Final grade out of thirtieths obtained from the weighted average of the grades obtained for the oral and the practical sessions evaluation. For information on support services for students with disabilities and/or DSA visit the page http://www.unipg.it/disabilita-e-dsa
- Extended program
- 1. Review of classical molecular dynamics.
Langrangian and Hamiltonian formalisms, phase space.
Classical molecular dynamics and thermodynamics in phase space.
2. Exact real-time quantum dynamics.
Time-dependent Schrödinger's equation. Born-Oppenheimer approximation and potential energy surfaces.
Time-correlation functions.
Methods of quantum propagation of wave functions. Split operator method and the fast Fourier transform.
3. Approximate methods for quantum dynamics. Sudden approximation. Adiabatic approximation.
Time-dependant perturbation theory.
Fermi's Golden Rule.
4. Semiclassical dynamics.
Old quantum theory and the WKB approximation.
Wigner function.
Van Vleck propagator.
Semiclassical initial value representation. - Obiettivi Agenda 2030 per lo sviluppo sostenibile