QUANTUM CHEMISTRY

This course is one of the core educational activities in the Master's degree in Sustainable Chemistry and Technology, that describes some of the common approaches of quantum mechanics to the fundamental understanding of chemical systems. The microscopic (or molecular) perspective builds on atomic and molecular models to predict macroscopically observable properties will be studied. In particular, we will discuss two main themes during this course including quantum mechanics and spectroscopy. Learning objectives involve developing an understanding of quantum mechanical principles, and applying these principles to master the underlying concepts of electronic structure for atoms, molecules and nanostructures.

The student active participation and attendance at classes (theoretical lessons and practical activities) together with independent study, will allow to reach the following abilities of learning and comprehension:
1. to learn the main mathematical methods used in quantum mechanics;
2. to learn the standard methods to study molecular and nano-structured systems;
Linking material learned in class to modern physical chemistry techniques and research will be highlighted to give you opportunities to see how Physical Chemists are solving current, real-world problems.

This is a math-intensive course, and it is expected that students have previous experience with calculus. In addition, students should be familiar with the concepts learned in calculus-based physics. We will review some mathematical principles along the way so that students can focus on learning the physical chemistry material.

1. Mathematical background
- Complex numbers
- Hilbert spaces
- Linear operators

2. Foundation of quantum mechanics (QM)
- Operators in QM
- Postulates of QM
- Simultaneous observables

3. Analytical solutions in one dimension
- Free particle
- Particle in a box
- The Harmonic oscillator
- Generalization to three dimensions

4. Rotational motion
Angular momentum
Spin
Combination of angular momenta

5. Atoms
- The hydrogen atom
- Hydrogen-like and Rydberg atoms
- The many-electron problem

6. Molecules
- Born-Oppenheimer approximation
- Potential energy surfaces and spectroscopy
- Molecular orbital theory
- H2 molecule: molecular orbital vs. valence bond
- Heteronuclear and polyatomic molecules

7. Advanced topics
- Electronic structure calculations
- Electronic structure of solids

P. Atkins, R. S. Friedman, "Molecular Quantum Mechanics", Oxford University Press, 4th Edition, 2005

The exam will consist of an oral test (expected duration 30 minutes), in which it will be verified that the student has acquired the main contents of the course, the approach and language of quantum mechanics, and the ability to relate what has been learned to basic processes and phenomena in atomic and molecular physics. These elements will be equally taken into account in determining the grade.
The student will have the opportunity to present a topic of his/her choice, either taken from the course contents or on some complementary topic to be agreed with the teacher.
This will be followed by open questions spanning over the course program.

oral

The grading scale following the oral exam reflects, as an indicative reference, the following evaluation scheme:

18-21: Basic knowledge of the subject, with essential presentation and possible conceptual gaps. Limited ability to apply the acquired content and establish connections between concepts.
22-24: Fair knowledge of the topics covered, with generally clear but not always in-depth exposition. Partial ability to apply the acquired content and establish connections between concepts.
25-27: Good mastery of the subject, with generally clear and accurate exposition. Ability to connect concepts and apply them to concrete cases with a certain degree of autonomy.
28-30: Excellent knowledge of the topics, with clear and accurate exposition. Ability for critical analysis and advanced application of knowledge.
30 cum laude: Outstanding mastery of the subject, with the ability for original and in-depth elaboration.

Lectures with the support of a blackboard and slides

Accessibility, Disability and Inclusion

Accommodation and support services for students with disabilities and students with specific learning impairments:
Ca’ Foscari abides by Italian Law (Law 17/1999; Law 170/2010) regarding supportservices and accommodation available to students with disabilities. This includes students with mobility, visual, hearing and other disabilities (Law 17/1999), and specific learning impairments (Law 170/2010). In the case of disability or impairment that requires accommodations (i.e., alternate testing, readers, note takers or interpreters) please contact the Disability and Accessibility Offices in Student Services: disabilita@unive.it.