The ABF Algorithm

When biasing the system, an external force AV is applied to improve the sampling along . Since this force is added, the calculation of the derivative of — to must be modified. Consider (4.35). The first term does not require any correction since x and x are sampled according to the correct distribution. However x includes the ABF force whose contribution needs to be removed to compute the free energy derivative. The correction is equal to 

The full ABF algorithm consists of two parts, which are summarized below (Algorithms 1 and 2). Any molecular dynamics code can easily be updated to include these modifications. 

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