Crystal Chemistry
(course in Italian)
Taching material, notes and more: see the Ariel2 website (you can log in with your student's email credentials).
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.
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.
Syllabus
Goals
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.
Acquired skills
(1) 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.
(2) Vector algebra in non-Cartesian systems.
(3) 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.
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.
The course might also incolve some practical computational exercises: quantum modelling of solid-state materials, multipole analysis and comparison between experimental and theoretical charge densities.
Suggested prerequisites
A minimum background in basic quantum mechanics and vector algebra is suggested.
Reference material
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
Assessment method
Oral: 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.
Language of instruction
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.
Acquired skills
(1) 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.
(2) Vector algebra in non-Cartesian systems.
(3) 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.
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.
The course might also incolve some practical computational exercises: quantum modelling of solid-state materials, multipole analysis and comparison between experimental and theoretical charge densities.
Suggested prerequisites
A minimum background in basic quantum mechanics and vector algebra is suggested.
Reference material
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
Assessment method
Oral: 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.
Language of instruction
Italian
Attendance Policy
Strongly recommended
Mode of teaching
Traditional
Attendance Policy
Strongly recommended
Mode of teaching
Traditional
