Crystal Chemistry
A.Y. 2018/2019
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
(1) Basi 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.
(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.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course 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) Basi 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
English
Attendance Policy:
Strongly recommended
Mode of teaching:
Traditional
Website: [optional]
/https://lloprestic.ariel.ctu.unimi.it/v5/Home/ (Ariel2 website)
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) Basi 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
English
Attendance Policy:
Strongly recommended
Mode of teaching:
Traditional
Website: [optional]
/https://lloprestic.ariel.ctu.unimi.it/v5/Home/ (Ariel2 website)
CHIM/02 - PHYSICAL CHEMISTRY - University credits: 6
Lessons: 48 hours
Professor:
Lo Presti Leonardo
Professor(s)
Reception:
To be arranged by e-mail
Prof. Lo Presti Office R21S, Dept. of Chemistry, Ground Floor, South Section