Dear Inger,
No, it is only the mass. If you take a look at some of the recent publications on molecule interferometry (Gerlich2011, Nat. Comm. 2, 263), then you can find that the molecules are already very complex. However one finds always the maximum predicted quantum visibility in interferometry experiments. So why is that so? First, what we observe is single particle interferometry otherwise it would hardly be a quantum experiment. Roughly speaking this means every particle interferes only with itself and this is per definition identical - that is what we mean when we say we probe quantum superposition.
So then you could argue that other properties of the molecule play a role: internal states such as rotation, vibration or the conformation of the molecules, but again we don't see any indication in the experiments that those properties influence the centre of mass motion. These internal molecular properties are simply not coupled to the motion of the particles. This means in matter-wave experiments only the mass of the particle and they propagation speed is important. Both speed and mass define the de Broglie wavelength of the particle.
There is of course a dependency on particle mass distribution and that comes from the fact that you have to sum many single particle interferometry event to observe a nice interference pattern as for instance in Juffmann2012 [Nature Nanoscience, 2012]. As the interferometer is sensitive to a narrow band of particle de Broglie wavelengths one needs particles of almost the same mass to collect a nice interference pattern. This is taken care of by chemical purification of the molecules after synthesis and also by mass-selective detection with a mass spectrometer in the present experiment. But again this mass dispersion is not a fundamental limitation for molecule interference experiments; it is a technical issue. The question we ask with such experiments is if there is a fundamental reason for the quantum to classical transition - something we cannot overcome by technology.
Regards,
Authors