Numerical methods for theoretical chemistry

In 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 time

- developing digital tools for chemistry

- use the Linux system

- express various numerical methods in algorithmic form

- convert an algorithm into a programming language

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

- design and develop IT tools independently, from specifications to final tool production

Basics of imperative and procedural programming, programming language for scientific computing (e.g. Fortran 95).

Continuous assessment (3 projects).

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

and general by an analytical function)

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

(quadrature, 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 Extrema
7. a) Solving linear systems (tridiagonal matrix, LU decomposition, method

iterative Gauss-Seidel)

1. b) Roots (bisection method, Newton-Raphson)
2. c) Extrema (one-dimensional, Powell's 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's method
9. Model adjustment
10. a) Least squares principle
11. b) General linear method
12. c) Singular value decomposition
13. d) Non-linear model (Levenberg-Marquardt)
14. Spectral and Pseudo-Spectral Methods
15. a) Fourier transform (discrete transform, FFT)
16. b) Pseudo-spectral methods

Administrative contact(s) :

Secretariat Master Chemistry

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