Unit MOLECULAR QUANTUM MECHANICS AND PROGRAMMING IN COMPUTATIONAL CHEMISTRY
- Course
- Chemical sciences
- Study-unit Code
- A005347
- Curriculum
- Theoretical chemistry and computational modelling
- Teacher
- Andrea Lombardi
- Teachers
-
- Andrea Lombardi
- Hours
- 47 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
- Introduction to the principles of quantum mechanics. Dirac formalism. Quantum Models: particle in a box, harmonic oscillator, rigid rotor, Hhdrogen atom Approximation Methods: Born–Oppenheimer approximation, perturbation theory. Nonadiabatic effects. Quantum Dynamics: time-dependent Schrödinger equation, Fermi’s golden rule, Quantum tunneling and barrier penetration. Molecular scattering theory. Applications to Chemistry: potential energy surfaces, reaction dynamics, vibrational and rotational transitions. Programing in computational chemistry: solution of differential equations of quantum mechanics, use of computational chemistry software applied to molecular dynamics. Practical hands-on session.
- Reference texts
- -Modern Quantum Mechanics, J. J. Sakurai and Jim Napolitano. Cambridge University Press. -Molecular Quantum Mechanics, P.W. Atkins & R.S. Friedman .Supplementary material provided by the teacher
- Educational objectives
- Apply the Dirac and matrix formalism of quantum mechanics to chemical systems. Use the harmonic oscillator model to describe vibrational motion in molecules. Explain the Born–Oppenheimer approximation and its significance for potential energy surfaces. Analyze phenomena such as scattering, tunneling, and chemical reactions using time-dependent quantum mechanics.
- Prerequisites
- Knowledge of Quantum mechanics, physical chemistry, basic programming
- 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: October 2025. Course end: January 2026. The course will take place at the Department of Chemistry, Biology and Biotechnology
- Learning verification modality
- Final Exam (70%): Covers entire course. Lab Reports/Project (30%): One computational chemistry project or literature presentation Average duration of the oral exam: about 20 minutes, duration of the presentation about 15 minutes Evaluation: final grade out of thirtieths obtained from the weighted average of the grades obtained for the oral and the presentation 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. Introduction to Quantum Theory in Chemistry Historical context: failures of classical mechanics in explaining atomic phenomena Emergence of quantum theory: Planck’s hypothesis, Einstein and the photoelectric effect Wave-particle duality and the de Broglie hypothesis Schrödinger equation: time-dependent and time-independent forms Quantum states, probability amplitudes, and measurement postulates 2. Mathematical Formalism and Dirac Notation Hilbert space and basis sets Linear operators, Hermitian operators, eigenfunctions and eigenvalues Bra-ket notation and inner/outer products Commutators, uncertainty principle, and compatible observables Expectation values, operator algebra, and matrix representations 3. Quantum Mechanical Models of Simple Systems Particle in a Box: energy quantization, degeneracy, node structure Harmonic Oscillator: potential energy surface, zero-point energy, ladder operators Rigid Rotor: rotational energy levels, angular momentum quantization Hydrogen Atom: exact solutions, quantum numbers, radial and angular wavefunctions Spherical harmonics and orbital shapes 4. Approximation Methods in Molecular Quantum Mechanics Born–Oppenheimer Approximation: separation of nuclear and electronic motion, consequences for molecular structure and spectroscopy Nonadiabatic Coupling: breakdown of BO approximation, conical intersections, vibronic transitions 5. Quantum Dynamics Time-dependent Schrödinger Equation: formal solution, evolution operators Time-dependent Perturbation Theory: interaction picture, transition probabilities Fermi’s Golden Rule: derivation and use in spectroscopy and scattering Quantum Tunneling: one-dimensional barrier penetration, tunneling rate estimation, tunneling in proton and electron transfer reactions Wavepacket Dynamics: coherence, superposition, and time evolution Introduction to Molecular Scattering Theory: cross-sections, phase shifts, resonance 6. Molecular Applications of Quantum Mechanics Potential Energy Surfaces (PES): multidimensional surfaces, minima, transition states, reaction paths Reaction Dynamics: elementary reactions, transition state theory, reaction rate constants