A polynomial version of the Generator Coordinate Dirac-Fock (p-GCDF) method is used to develop small and medium size relativistic prolapse-free Gaussian basis sets (SRPF and MRPF, respectively) for heavy and superheavy elements from <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3180_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$_{87}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>87</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>Fr to <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3180_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$_{118}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>118</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>Og. These basis sets are designed to work with uniform sphere and Gaussian nuclear models. The complete elimination of variational prolapse is achieved by exploring the characteristics of the p-GCDF method. The largest error obtained with respect to reference values of Dirac-Fock-Coulomb energies from the Gaussian nuclear model are 43.1 and 100.9 mHartree, respectively, for MRPF and SRPF sets, which occur for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="214_2025_3180_Article_IEq3.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$_{118}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>118</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>Og. The largest sizes of MRPF and SRPF sets are 31s27p17d12f and 28s24p15d10f, respectively. Thus, to our knowledge, these are the smallest sets free of variational prolapse ever developed for such elements.

Relativistic adapted Gaussian basis sets free of variational prolapse of small and medium size for francium through oganesson

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发表日期：

2025年3月29日

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Anne Kéllen de Nazaré dos Reis Dias,
Julielson dos Santos Sousa,
Eriosvaldo Florentino Gusmão,
Roberto Luiz Andrade Haiduke

摘要

A polynomial version of the Generator Coordinate Dirac-Fock (p-GCDF) method is used to develop small and medium size relativistic prolapse-free Gaussian basis sets (SRPF and MRPF, respectively) for heavy and superheavy elements from $_{87}$ $_{87}$ Fr to $_{118}$ $_{118}$ Og. These basis sets are designed to work with uniform sphere and Gaussian nuclear models. The complete elimination of variational prolapse is achieved by exploring the characteristics of the p-GCDF method. The largest error obtained with respect to reference values of Dirac-Fock-Coulomb energies from the Gaussian nuclear model are 43.1 and 100.9 mHartree, respectively, for MRPF and SRPF sets, which occur for $_{118}$ $_{118}$ Og. The largest sizes of MRPF and SRPF sets are 31s27p17d12f and 28s24p15d10f, respectively. Thus, to our knowledge, these are the smallest sets free of variational prolapse ever developed for such elements.