A More Concise Expression

The first term can be computed in a straightforward way using the Lagrange multiplier A. A derivation similar to the one given in Sect. 4.5.3 [see (4.27)] leads to 

The Fixman potential is not needed here since we are sampling with Hamiltonian Jtf. The second term is (4.31) can be expressed in terms of 

If we are interested (as is almost always the case) in computing free energy differences, the factor y/nj2/3 can be ignored. The factor Ze r represents a contribution to the free energy, in addition to the mechanical forces given by A, due to entropic effects. 

This expression involves only the computation of the gradient of . A comparison with (4.28) which requires the same constrained simulation but a different equation for dA/d underscores the simplicity of this new expression. A similar expression was derived by Schlitter et al. 141 -44]. 

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