Thermodynamic integration with harmonic reference

The Helmholtz free energy ($A$) of a fully interacting system (1) can be expressed in terms of that of harmonic system (0) as follows

:$A_{1} = A_{0} + \Delta A_{0\rightarrow 1}$ 

where $\Delta A_{0\rightarrow 1}$ is anharmonic free energy. The latter term