A straight-forward measurement for any superconductor is how the transition temperature varies with pressure (and thus volume). Calculating this variation is not easy. For example, in a simple BCS superconductor one would have to calculate how the phonon spectrum, electron phonon-coupling constant, and density of states vary with pressure. Presumably this can be done with some electronic structure method such as based on density functional theory (DFT).
But, how about in a strongly correlated electron system? One would have to first find how the parameters in some Hubbard type model varied with pressure. Then one has the extremely tricky issue of calculating Tc as a function of the Hubbard model parameters.
It turns out that the volume dependence of Tc in organics is dramatically larger than in cuprates and elemental superconductors.
I was recently drawn to the paragraph below from this paper by a football team (11 authors!)
Comparative thermal-expansion study of β″-(ET)2SF5CH2CF2SO3 and
κ-(ET)2Cu(NCS)2: Uniaxial pressure coefficients of Tc and upper critical fields
Note that simple models (e.g., Sommerfeld, Debye) predict that energy scales such as the Fermi energy and Debye temperature scale with the volume according to some exponent of order one. Hence, this exponent of 40 for the organics Tc is amazing!
I disagree somewhat with the conclusion of the last sentence of the paragraph: that this extreme sensitivity "underlies the role of the lattice degrees of freedom for the superconducting instability for this class of materials." I don't think this shows that electron-phonon coupling is involved directly in superconductivity. It could be just that Tc is quite sensitive to the Hubbard model parameters. Small variations in the latter do drive the system closer or further from the Mott transition.
Yet, the challenge remains to calculate this volume sensitivity from theory!
A very modest but useful first step would be to first see if a DFT-based calculation can reproduce the measured bulk compressibility.