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

- Work independently: set priorities, manage your time

- Develop digital tools for chemistry

- use the Linux system

- Express various numerical methods as algorithms

- convert an algorithm into a programming language

- to understand which of these methods and tools are used in fields other than chemistry

- independently design and develop software tools, from the initial specifications through to the completion of the final product

Fundamentals of imperative and procedural programming; a programming language for scientific computing (such as Fortran 95).

Continuous, comprehensive assessment (3 projects).

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

and in 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 Differentiation of a Function
2. a) Simple methods
3. b) Quadrature method
4. c) Multidimensional integrals
5. (d) Numerical differentiation
6. Linear Systems, Roots, and Extremes
7. a) Solving linear systems (tridiagonal matrix, LU decomposition, method

(Gauss-Seidel iterative method)

1. b) Roots (bisection method, Newton-Raphson method)
2. c) Extremes (one-dimensional, Powell’s method, simulated annealing, genetic algorithms)
3. Diagonalization: Properties of Eigenvalue Equations
4. a) Householder's 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. Adjusting a Model
10. a) Principle of Least Squares
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 Fourier transform, FFT)
16. b) Pseudo-spectral methods

Administrative contact(s):

Master's in Chemistry Office

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