thermodynamic integration in NPT ensemble

[ronbenin]

Dear friends,
I have a question regarding thermodynamic integration in the NPT ensemble.

Suppose I vary the parameter a from 0 to 1, where 0 is the reference state whose free energy I know and 1 corresponds to the state whose free energy I want to find out. then is the formula to calculate the free energy of 1
1 1
/ /
G(1)-G(0)=| <dU/da> da + P(V(1)-V(0)) OR G(1)-G(0)=| <dU/da> da + P(V(0)-V(1))
/ /
0 0

OR


1
/
G(1)-G(0)=| [d(U+PV)/da] da
/
0
where V is the volume, U is the potential energy and P is the [ressure, G is the Gibb's free energy.

Thanks.