69807:  Solid state in Chemistry

The course is intended for graduate students and 3^rd-year undergraduates. The course starts with the basic property of crystalline solids – spatial periodicity – and shows how various properties that are characteristic of solids and phenomena that can be measured in solid materials follow from their spatial periodic structure. In addition, we also introduce certain theoretical concepts that are unique to periodic solids and then use them in our discussions.

The topics of the course include:

• Crystal structure, periodicity, Bravais lattices, unit cells.
• X-Ray diffraction from crystals, Bragg's law, reciprocal lattice, Brillouin zones.
• Crystal vibrations, dispersion relations, phonons, specific heat, melting criterion.
• Bonding types in solids. Ionic, covalent, metallic, hydrogen and van der Waals bonding.
• Electronic structure. Bloch theorem, nearly free and tightly bound electrons, bands, the bandgap, density of states, Fermi energy. Metals, insulators and semiconductors.
• Modern methods in electronic structure.

Methodologically the course naturally connects to the undergraduate courses: Introduction to the Chemical Bond, Inorganic Chemistry and Physical Chemistry, as well as to the advanced courses on materials, quantum chemistry and density functional theory.

The written assignment prepared by the students allows them to study in depth a specific topic from the rich world of solid state phenomena, and summarize their findings in writing, according to accepted scientific standards.

Offered since 2019, usually in the Fall semester.

80112: Mathematical Introduction for Chemistry and Earth Sciences Students (2)

This is a compulsory course aimed at Chemistry and Earth Sciences students at the second semester of their first bachelor year. The course intends to provide the students with the mathematical tools they need in studying courses in chemistry and physics. Upon successful completion of the course, the students should be familiar with the main mathematical concepts and methods in many-variable calculus, vector analysis and ordinary differential equations, and be able to apply them to problems in chemistry.

The topics of the course include:

1. Overview: vectors – addition, subtraction, scalar and vector products.
2. Many-variable functions: partial derivatives, directional derivative. Examples in chemistry.
3. Vector and scalar fields. Derivatives of vectors. Gradient. Examples in physics and chemistry.
4. The operator nabla. Divergence, curl and laplacian. Examples.
5. Analysis of a many-variable function: minima, maxima, saddle points. Constraints and Lagrange multipliers.
6. Integral of a many-variable function. Change of variables, Jacobian. Examples and applications.
7. Line integrals, conserving fields. Surface integrals. Flux.
8. Green, Gauss and Stokes theorems.
9. Spherical and cylindrical coordinates. Gradient, divergence and Laplacian in these coordiantes.
10. Ordinary differential equations (ODEs). Types and common examples in chemistry and physics.
11. First order ODEs. Selected solution methods. Initial conditions.
12. Second order ODEs. Solution independence. Homogeneous and inhomogeneous ODEs.

Offered since 2020, in the Spring semester.