Constraints in Molecular Dynamics: Theory and SHAKE Algorithm

This lecture covers the theory behind constraints in molecular dynamics simulations, focusing on the motivation to freeze fast vibrations, decoupling between fast and slow motions, and studying constrained motions. It explains formal theory with holonomic constraints and the method of Lagrange multipliers. The lecture also discusses enforcing constraints explicitly, applying constraints to simple cases, and the general method using Lagrange parameters. The SHAKE algorithm is detailed, including a schematic flow chart, partial updates, and considerations like no matrix inversion requirement and recalculating derivatives for better convergence.