Numerical methods for theoretical chemistry

During this course, students will learn about the main numerical methods used in scientific software, particularly in theoretical chemistry programs.

Hourly volumes:

CM: 21

TD: 9

- working independently: setting priorities, managing your time

- develop digital tools for chemistry

- use the Linux system

- express various numerical methods in the form of algorithms

- convert an algorithm into a programming language

- know which of these methods and tools are used in other fields outside chemistry

- Independently design and develop IT tools, from the initial specifications to the final product.

Fundamentals of imperative and procedural programming, programming language for scientific computing (Fortran 95, for example).

Continuous assessment (3 projects).

1. Interpolation, Extrapolation
2. a) Global interpolation (Lagrange polynomials, quotient polynomial, trigonometric)

and general by an analytic function)

1. b) Local interpolation (natural splines)
2. c) Multidimensional interpolation (bilinear and bicubic, splines) - Integration

(quadratures, analytical, multidimensional)

1. Integration and derivation of a function
2. a) Simple methods
3. b) Quadrature method
4. c) Multidimensional integrals
5. d) Digital derivation
6. Linear Systems, Roots, and Extremes
7. a) Solving linear systems (tridiagonal matrix, LU decomposition, method

Gauss-Seidel iterative)

1. b) Roots (bisection method, Newton-Raphson method)
2. c) Extrema (one-dimensional, Powell method, simulated annealing, genetic algorithms)
3. Diagonalization: Properties of Eigenvalue Equations
4. a) Householder reduction
5. b) Diagonalization of a tridiagonal matrix (QL algorithm, bisection)
6. c) Eigenvectors by inverse iteration
7. d) Lanczos method
8. e) Davidson method
9. Model Adjustment
10. a) Least squares principle
11. b) General linear method
12. c) Singular value decomposition
13. d) Nonlinear model (Levenberg-Marquardt)
14. Spectral and Pseudo-spectral Methods
15. a) Fourier transform (discrete transform, FFT)
16. b) Pseudo-spectral methods

Administrative contact(s):

Master's Program in Chemistry Secretariat

https://master-chimie.edu.umontpellier.fr/