Mathematics, Data & Molecular Modelling
Beschrijving
Course goals
After completing the course the student:
- has gained an understanding of molecular modelling and its specific applications in chemistry and life sciences (with a focus on classical methods)
- has gained insight into the choices one has to make to model a system properly (for instance: which degrees of freedom are relevant to solve a certain problem? How can I describe the interactions between particles? Which conformational search method is most suitable for my problem?)
- is able to apply a number of mathematical topics—such as partial differentiation, Taylor series, and various optimization and integration methods—within a general chemical context, and in particular in molecular modeling
- has gained some experience with modelling of (bio)chemical systems on computers and critical analysis of simulation results
Content
SK-B2WDMM replaces parts of the former courses ‘Wiskunde 2’ (SK-BWS2-13) and NMR-spectroscopy & molecular modelling (SK-B2NMRM)
This course teaches the principles of molecular modelling and the associated mathematical concepts. It has broad applications within the field of chemistry, life sciences and material sciences. Mathematics and molecular modeling lectures follow one another, where mathematical theory and methods are first covered and later reappear in specific aspects of molecular modeling.
The part on molecular modelling accentuates classical modelling methods (so no quantum description) for application to (biological) molecules and also provides an introduction to AI-based modelling methods. The student learns how molecules, their interactions and energetics can be described in a computer, and different methods to search the conformational space for energy minima.
The mathematics section builds on the mathematics course(s) from the first year of Chemistry and covers the necessary mathematical skills for second-year chemistry students following this course.
In this Math part the following topics will be discussed: partial derivatives, chain rule, Taylor approximation, Hessian matrix, minimization of energy surfaces, nonlinear systems, Fourier transform (discrete), numerical solution of differential equations (Verlet method), numerical integration of multiple integrals and basic linear algebra for AI calculations.
During exercise sessions, students, next solving problems, also get into contact with Python, both to visualize some of the modelling principles, and to analyze simulation data.
In the computer practical molecular modeling is used to predict on the basis of NMR data the structure of a biomolecular complex.
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