Additional Discussion of ABF

We now discuss a number of practical issues to illustrate the strengths and weaknesses of ABF. 

Algorithm 1 Velocity Verlet loop with ABF is the assignment operator. 

Optimal sampling. As was pointed out earlier, the error in the derivative of A is proportional to ak j Jnk(N). The optimal sampling is therefore obtained when ak/ Jnk(N) is constant as a function of k. In regions where ak is large, additional sample points should be added to compensate. This is often a small effect but in some special cases is worth considering. In order to obtain the optimal sampling, the potential energy should be corrected as 

In this routine, the derivative of the free energy is calculated and the biasing force is added to 

Partition of forces. Going back to (4.33), we can derive a different equation 

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