Momentum-Enhanced HMC

This section is used to introduce the momentum-enhanced hybrid Monte Carlo (MEHMC) method that in principle converges to the canonical distribution. This ad hoc method uses averaged momenta to bias the initial choice of momenta at each step in a hybrid Monte Carlo (HMC) procedure. Because these average momenta are associated with essential degrees of freedom, conformation space is sampled effectively. The relationship of the method to other enhanced sampling algorithms is discussed. 

One general approach to enhancing sampling, which is the focus of this section, is based on the fact that both fast and slow dynamical modes contribute to the time evolution of biomolecular systems, but in most cases the motions of primary interest are the slow ones, which typically correspond to the largest structural changes [72, 73], 

The direction of slow motion can be found from normal-mode diagonalization. However, such a procedure would require, for a system of N particles, cal- 

As we shall see below, a useful strategy to identify the slow manifold is to calculate an average of the momentum, p, over r time units during a molecular dynamics propagation 

In order for the averaged momentum p to point along the slow manifold (i.e., for the components of momentum in the fast manifold to average to zero), one has to choose the averaging time r so as to be several times longer than the period of the fast modes but shorter than those of the slow modes. 

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