  The synthesis and design of organic biradicals with tunable singlet-triplet
gaps has become the subject of significant research interest, owing to their
possible photochemical applications and use in the development of molecular
switches and conductors. Recently, tetrathiafulvalene tetrathiolate (TTFtt) has
been demonstrated to exhibit such organic biradical character in doubly ionized
bimetallic complexes. In this article we use high-level {\em ab initio}
calculations to interrogate the electronic structure of a series of
TTFtt-bridged metal complexes, resolving the factors governing their biradical
character and singlet-triplet gaps. We show that the degree of biradical
character correlates with a readily measured experimental predictor, the
central TTFtt C-C bond length, and that it may be described by a one-parameter
model, providing valuable insight for the future rational design of TTFtt based
biradical compounds and materials.
