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<p>The electronic states arising from the 5g-row of the periodic table are far less explored compared to other lighter elements in the periodic table. Relativistic effects are extremely large for the 5g-row elements (E-121 to E-138) due to a large nuclear charge approaching the inverse of the fine structure constant. The large relativistic effects result in a molecular spinor nature of the electronic states leading to a substantial mixing of electronic states with different spin multiplicities and differing spatial symmetries. Hence we present the combinatorial enumeration of ω–ω states arising for the 5g-row dimers by employing multinomially-driven symmetric function methods. The combinatorial techniques enumerate all possible ω–ω states originating from the relativistic 2-component molecular spinors for all the 5g-row dimers. There is a combinatorial explosion of electronic states, for example, a 5g-mid-row dimer with 18 electrons exhibits <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10910_2025_1715_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="96" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{4,537,567,650}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>4,537,567,650</mtext> </math></EquationSource> </InlineEquation> terms in the S-functions. The S-functions for the 5g-row dimers are constructed, and from the S-function terms, those that comply with the Pauli exclusion principle result in a large number of relativistic ω–ω states for the 5g-row dimers. We have constructed the combinatorial tables for the relativistic ω–ω states of several 5g-row dimers subsequent to stipulating several conditions imposed on the level of electron excitations so that the combinatorics is manageable. Furthermore we invoke the electron–hole equivalence to mirror the ω–ω states for the remaining dimers of the 5g-row to enumerate them. Consequently, the developed technique enumerates the ω–ω states arising from up to 18 open-shell states without any restrictions making it applicable to numerous ω–ω states with varied quantum numbers.</p>

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Combinatorial S-function method for relativistic spinor states of 5g-row dimers: (E-121)2 to (E-137)2

  • 期刊论文

  • 发表日期：

    2025年4月15日

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  • Krishnan Balasubramanian

摘要

The electronic states arising from the 5g-row of the periodic table are far less explored compared to other lighter elements in the periodic table. Relativistic effects are extremely large for the 5g-row elements (E-121 to E-138) due to a large nuclear charge approaching the inverse of the fine structure constant. The large relativistic effects result in a molecular spinor nature of the electronic states leading to a substantial mixing of electronic states with different spin multiplicities and differing spatial symmetries. Hence we present the combinatorial enumeration of ω–ω states arising for the 5g-row dimers by employing multinomially-driven symmetric function methods. The combinatorial techniques enumerate all possible ω–ω states originating from the relativistic 2-component molecular spinors for all the 5g-row dimers. There is a combinatorial explosion of electronic states, for example, a 5g-mid-row dimer with 18 electrons exhibits \(\text{4,537,567,650}\) 4,537,567,650 terms in the S-functions. The S-functions for the 5g-row dimers are constructed, and from the S-function terms, those that comply with the Pauli exclusion principle result in a large number of relativistic ω–ω states for the 5g-row dimers. We have constructed the combinatorial tables for the relativistic ω–ω states of several 5g-row dimers subsequent to stipulating several conditions imposed on the level of electron excitations so that the combinatorics is manageable. Furthermore we invoke the electron–hole equivalence to mirror the ω–ω states for the remaining dimers of the 5g-row to enumerate them. Consequently, the developed technique enumerates the ω–ω states arising from up to 18 open-shell states without any restrictions making it applicable to numerous ω–ω states with varied quantum numbers.