Computational Techniques for Molecular Modeling

Projects of the numerical part of the course Computational Techniques for Molecular Modeling @ PoliMi - First Edition, Spring 2021

Team

• Luca Caivano (Mathematical Engineering)
• Andrea Della Libera (Chemical Engineering)
• Manfred Nesti (Mathematical Engineering)
• Valeria Pajola (Chemical Engineering)
• Alessandro Pegurri (Chemical Engineering)
• Bruno Ursino (Mathematical Engineering)
• Chiara Vitale (Chemical Engineering)

Assignments

Assignment 1

• Implement a simulator of the conservative double pendulum using the Velocity-Verlet method as symplecting integrator and study the accuracy of trajectories and total energy with respect to time step.
• Reformulate the model so that the contraints are accounted for, simulating in cartesian coordinates using the SHAKE method.
• Apply the Velocity-Verlet method to the Frozen Argon Crystal example as in Hairer, Lubich, Wanner - Geometric Numerical Integration - Section I.4.

Assignment 2

Reproduce the example in Gabriel, Knapek, Zumbusch - Numerical Simulation in Molecular Dynamics - Section 3.6.1 using periodic boundary conditions.

Assignment 3

Reproduce the example of Rayleigh-Taylor instability with Coulomb potential in Gabriel, Knapek, Zumbusch - Numerical Simulation in Molecular Dynamics - Section 7.4.1.

Assignment 4

For the C2H6 molecule

• Compute the equilibrium using GAUSSIAN
• Compute forces by invoking GAUSSIAN and parse output via Octave / Bash script
• Implement a descent method in Octave to perform the optimization using for example Gradient, BFG and Nonlinear Conjugate Gradien as descent directions
• Apply box constraints via orthogonal projection with feasible Projected Gradient or Projected quasi-Newton
• Apply Reduced Rank Extrapolation

Assignment 4.5 (only for 5CFU course version)

Implement also the Quadratic Line Search (video reference)