Relativistic effects are quite large for the actinide 5f and 6d open shells, and in the present study we present combinatorial enumeration of $$\upomega {{-}} \upomega $$ states of all 14 actinide (lanthanide) dimers using multinomial symmetric function (S-function) techniques. The techniques presented here enumerate all possible $$\upomega {{-}} \upomega $$ states that arise from relativistic 2-component molecular spinors composed of the 7s, 6d 5f, and possibly 7p shells of the actinide dimers Th2 through Lr2. The combinatorial enumerations techniques reveal that that for Americium dimer (Am2) there are 20,058,300 S-function terms of which only 616,227 terms satisfy the Pauli exclusion principle yielding 401,166,110 $$\upomega {{-}} \upomega $$ states (142.6 MB of output), all of which arise from primarily the 7s/6d/5f shells of Am. Explicit tables are constructed for the relativistic $$\upomega {{-}} \upomega $$ states for Th2 to Am2 with several restrictions imposed on the levels of excitations primarily to reduce the table sizes, and through the electron–hole equivalence $$\upomega {{-}} \upomega $$ states of the remaining dimers of the actinide row are enumerated. The computational and mathematical techniques also enumerate the $$\upomega {{-}} \upomega $$ states of Ce2 to Eu2 and by electron–hole equivalence Gd2 to Tm2, although spin–orbit splittings are smaller for lanthanides. A unique feature of the present combinatorial technique is that it facilitates any number of orbitals and any number of open shells including the possibility of 14 singly-occupied orbitals for actinide and lanthanide dimers, and thus providing for a technique to enumerate $$\upomega {{-}} \upomega $$ states arising from both very high spin open-shell states as well as low spin states exhaustively.