(6.27) |

where stands for the statistical average of the quantity enclosed in angular parentheses computed for a constrained ensemble and is a mass metric tensor defined as:

It can be shown [66,68,67,70] that the free energy gradient can be computed using the equation:

where is the Lagrange multiplier associated with the parameter used in the SHAKE algorithm [81]. The free-energy difference between states (1) and (2) can be computed by integrating the free-energy gradients over a connecting path:

Note that as free-energy is a state quantity, the choice of path connecting (1) with (2) is irrelevant.