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.

中文翻译：

---

元素周期表中超重和反式二聚体的相对论状态枚举

我们采用了基于多项对称函数 (S-function) 技术的组合技术，用于穷举枚举和生成源自相对论 2 分量分子旋量的相对论 (ω-ω 状态) 状态，用于第七行超重二聚体 (Nh 2 -Ts 2 )、反式锕系二聚体 (Rf 2 -Rg 2 ) 和 Ac 2 。多项式发生器非常强大，以至于所有第七行超重二聚体或反式二聚体的相对论状态的完整集合被枚举并构建在单个生成函数中。我们已经计算并构建了 7p 嵌段和 6d 嵌段二聚体（Nh 2 -Ts 2 ，Rf 2 -Rg 2 ）的所有价 ω–ω 状态的枚举表。我们的结果表明，有 6455 个 S 函数项产生了 102,830 个价态 ω–ω 状态——所有这些都仅来自 Bh 2 的 6d 壳。