Is patenting based on theoretical findings possible? Imagine one, as part of their academic research, makes a theoretical finding of a new material with interesting properties based on a computer simulation. The method used in the simulation is sound and has been proven to provide reliable results.

Can the discoverer file a patent based on this theoretical work or does one need experimental confirmation that the new material indeed has the predicted properties before being able to file a patent?
The relevant concept here is "reduction to practice," which means that a concept has been sufficiently realized to make it believable.  Where, exactly, this bar lies depends on which field and which country you are dealing with.  

The United States, for example, used to have much stronger requirements for working models, but has recently introduced a notion of "preliminary filing" which lets one start the patent process before demonstrating a working model.  In some cases, particularly mechanical devices, the device (fortunately) might never actually have to be demonstrated in action.  In others, such as many types of biological invention, the science is considered so unpredictable that you cannot be considered to have reduced the idea to practice unless you have an actual working example.

For your particular question of computational material design, I do not know where the boundary of "reduction to practice" currently lies.  It is likely to be field-dependent (e.g., is this a mechanical macrostructure like a fabric, a simple atomic structure like a new alloy of steel, or a complex organic structure like a protein agglomerate), will depend on jurisdiction, and is likely to move again in the future as patent offices slowly come to accept the validity of more classes of models.  Thus, the overall answer is "it depends" and "talk to a patent lawyer."