Crystal Chemistry
A.Y. 2024/2025
Learning objectives
The course will provide the students with an overview of the modern methods for studying chemical bonding in solids with both experimental and theoretical approaches.
Expected learning outcomes
Competences in basic crystallography, included the ability of understanding and interpreting a single crystal X-ray diffraction pattern and judging the quality of a X-ray diffraction experiment; and in vector algebra in non-Cartesian systems.
Besides, students will acquire knowldge of modern methods for the real-space study of chemical bonding in solids, with focus on topological analysis of the charge density according to the Quantum Theory of Atoms in Molecules.
Besides, students will acquire knowldge of modern methods for the real-space study of chemical bonding in solids, with focus on topological analysis of the charge density according to the Quantum Theory of Atoms in Molecules.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
Course content
Point symmetries (summary). Translational symmetries. Elements of group theory, space groups. Crystal structures: crystal lattice, crystal system, Bravais lattice. Bragg Law. Reciprocal lattice (Ewald construction, limiting sphere, scattering vector). Crystallographic computing: reference systems, matric tensor, similitude transforms in direct and reciprocal spaces. Kinematic theory of the structure factor. Charge density, and its role in chemistry. Determination of the charge density from low-T X-ray diffraction data. Instruments: diffractometers, crystostats. Multipole models. Quantum Theory of Atoms in Molecules (QTAIM). Quantum subsystems. Eherenfest and Hesenberg theorems. Time evolution of a quantum observable: forces on quantum subsystems. Virial theorem. Topological atom. Properties of the charge density: Laplacian, ellipticity, electrostatic moments, integral properties. Charge density-based methods for studying non-covalent interactions: molecular recognition. Crystallization control, polymorphism, crystal engineering. Crystal Structure Prediction problem and possible computational approaches.
Point symmetries (summary). Translational symmetries. Elements of group theory, space groups. Crystal structures: crystal lattice, crystal system, Bravais lattice. Bragg Law. Reciprocal lattice (Ewald construction, limiting sphere, scattering vector). Crystallographic computing: reference systems, matric tensor, similitude transforms in direct and reciprocal spaces. Kinematic theory of the structure factor. Charge density, and its role in chemistry. Determination of the charge density from low-T X-ray diffraction data. Instruments: diffractometers, crystostats. Multipole models. Quantum Theory of Atoms in Molecules (QTAIM). Quantum subsystems. Eherenfest and Hesenberg theorems. Time evolution of a quantum observable: forces on quantum subsystems. Virial theorem. Topological atom. Properties of the charge density: Laplacian, ellipticity, electrostatic moments, integral properties. Charge density-based methods for studying non-covalent interactions: molecular recognition. Crystallization control, polymorphism, crystal engineering. Crystal Structure Prediction problem and possible computational approaches.
Prerequisites for admission
A minimum background in basic quantum mechanics and vector algebra is suggested. In detail: the student is expected to know the following concepts: quantum mechanical operators; hermiticity; basics of Scrhoedinger's wave mechanics; scalar and vector product; sum vector rules in Cartesian spaces. These contents are covered in the fundamental courses of mathematics, physics and physical chemistry of the Bachelor's Degree in Chemistry at the Università degli Studi di Milano.
Teaching methods
The course is delivered through lectures, which also include guided exercises. Lessons are held on the blackboard. Questions and interventions from students are encouraged. Lecture notes are made available to students through the e-learning platforms available at Unimi (for example, ARIEL).
Teaching Resources
- General crystallography: C. Giacovazzo et al, Fundamentals of Crystallography, Edited by C. Giacovazzo, International Union of Crystallography (IUCr), Oxford University Press, Oxford, UK, 1992 (or more recent)
- Applied crystallography: G. H. Stout & L. H. Jensen, X-ray Structure Determination: A practical guide, John Wiley and Sons, New York, USA, 1989
- Quantum Theory of Atoms in Molecules: R. F. W. Bader, Atoms in Molecules: A Quantum Theory, Clarendon Press - Oxford, UK, 1990
- Applied crystallography: G. H. Stout & L. H. Jensen, X-ray Structure Determination: A practical guide, John Wiley and Sons, New York, USA, 1989
- Quantum Theory of Atoms in Molecules: R. F. W. Bader, Atoms in Molecules: A Quantum Theory, Clarendon Press - Oxford, UK, 1990
Assessment methods and Criteria
An oral exam will be carried out at the end of the course and the student's performance evaluated by a grade on a 0-30 scale The exam is considered sufficient (passed) if the student achieves at least 18/30. Exceptional performances can merit a mention of honor (30/30 cum laude). The exam will consist in open questions. The teacher will verify whether the student (1) has a reasonable mastery of the basic notions; (2) has understood the general framework of the course and (3) is able to apply the acquired know-how to solve simple problems, also with reference to the pertinent scientific Literature.
CHIM/02 - PHYSICAL CHEMISTRY - University credits: 6
Lessons: 48 hours
Professor:
Lo Presti Leonardo
Shifts:
Turno
Professor:
Lo Presti LeonardoProfessor(s)
Reception:
To be arranged by e-mail
Prof. Lo Presti Office R21S, Dept. of Chemistry, Ground Floor, South Section