The ligand-ligand coupling in excited states of homoleptic metal-organic and related compounds of the platinum metal group depends strongly on the metal d or MLCT character in these states. In particular, in triplet slates, which mostly represent the lowest excited states, the metal participation is displayed in the amount of zero-field splitting (zfs) Detailed investigations in recent years have demonstrated that complexes with very small metal participation and thus small zfs, like [Rh(bpy)(3)](3+) and [Pt(bpy)(3)](3+), exhibit spatially localized or ligand-centered triplets. Compounds with large metal character as in (MLCT)-M-3 states have large zfs, and the states are delocalized over the metal and the different ligands, as found for [RU(bpy)(3)](2+) and [Os(bpy)(3)](2+). By chemical variation, it is possible to obtain a compound characterized by an intermediate position between the two extreme situations. Such a compound is Pt(2-tbpy)(2) with 2-thpy(-) = 2-(2-thienylpyridinate). It is one of the main subjects of this investigation to study whether in Pt(2-thpy)(2) the lowest excited triplet is spatially extended over both ligands. This is done by comparing highly resolved emission (and excitation) spectra of perprotonated Pt(2-thpy-h(6))(2), partially deuterated Pt(2-thpy-h(6))(2-thpy-d(6)), and perdeuterated Pt(2-thpy-d(6))(2). These spectra display clear fingearprints with respect to spatial extensions of the excited states. The required high resolution is obtained when the compounds are dissolved in an n-octane matrix (Shpol'skii matrix) and are measured at low temperature (T = 1.3 and 4.2 K). The deuterated compounds are studied for the first time. Interestingly, it is found that all three triplet sublevels of Pt(2-thpy)(2) are spatially extended over both ligands. This result is of high importance, since it tells us that already a moderate metal d or MLCT character in the lowest triplet stare of homoleptic compounds of the platinum metal group leads, at least in a rigid matrix, to spatially delocalized excited states.