Enumeration of relativistic states for superheavy and transactinide dimers in the periodic table

We have employed combinatorial techniques based on multinomial symmetric function (S-function) techniques for exhaustive enumeration and generation of relativistic (ω–ω states) states originating from relativistic 2-component molecular spinors for the seventh row superheavy dimers (Nh 2 -Ts 2 ), transactinide dimers (Rf 2 -Rg 2 ) and Ac 2 . The multinomial generators are so powerful that the complete set of relativistic states of all seventh row superheavy dimers or transactinide dimers are enumerated and constructed in a single generating function. We have computed and constructed the enumeration tables for all valence ω–ω states for the 7p-block and 6d-block dimers (Nh 2 -Ts 2 , Rf 2 -Rg 2 ). Our results show that there are 6455 S-function terms giving rise to 102,830 valence ω–ω states- all arising only from the 6d shells of Bh 2 . Extension of the developed techniques to relativistic 4-component and 4-spinors arising from fermionic spin-3/2 particles are also suggested with potential applications NMR spectroscopy.