Gallery

Gallery: fancy movies, explained

Metadynamics

This movie shows the way metadynamics works and the difference between the standard algorithm and the well-tempered one. In metadynamics one builds a time dependent bias designed so as to avoid re-exploring the already visited regions in the collective-variable space. The bias is grown at a constant rate by adding "computational sand" at the position where the system actually is. In the standard algorithm, the bias tends to compensate the underlying free energy, and thus can be used to estimate the free-energy landscape a posteriori. Notice that there is a fluctuating error. In the well-tempered algorithm, the speed at which the bias grows is opportunely decreased during the simulation. As a consequence, the bias does not exactly compensate the free-energy completely, and there is a residual thermodynamics force acting on the system. However, the free-energy can nevertheless estimated (the green line shows the difference between the estimate and the actual free-energy), and the error decreases as the simulation proceeds. For a more detailed discussion, refer to the original papers: Laio and Parrinello, Proc Natl. Acad. Sci. USA 99, 12562 (2002) and Barducci, Bussi and Parrinello, Phys. Rev. Lett. 100, 020603 (2008).

Car-Parrinello

Electrons: heavy vs light

In principles, in ab initio molecular dynamics one should minimize the electronic wavefunctions everytime the ions are moved. Car and Parrinello proposed a different strategy, which consists in assigning a mass to the electronic degrees of freedom, initializing them close to the minimum and moving the entire system (ions and electrons) with Newtonian dynamics. If the electrons are light enough, their oscillations will be adiabatically decoupled from the ionic vibrations, and the electrons will stay close to the minimum. If the electronic mass is choosen too large, however, their dynamics will be coupled with the ionic one and the electrons will equilibrate at a higher temperature, breaking the basis assumption of Car-Parrinello molecular dynamics. For more details, see Car and Parrinello, Phys. Rev. Lett. 55, 2471 (1985) and Sprik, J. Phys. Chem. 95, 2283 (1991).

Noise: white vs colored

However, when trying to apply stochastic dynamics to Car-Parrinello simulations one problem arises: the high frequency component in the noise are coupled with the electronic degrees of freedom, and the electrons get hotter and hotter. A possible solution is to filter the noise: using colored noise (instead of white noise) allows to perform stochastic molecular dynamics without affecting the temperature of the electronic degrees of freedom. For more details, see Ceriotti, Bussi and Parrinello, Phys. Rev. Lett. 102, 020601 (2009).