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<p>We present a comparative study of noninteger-n Slater-type functions (NISTFs) and conventional Slater-type functions (CSTFs) for modeling electron density properties of neutral atoms from He to Xe using minimal basis sets. Radial moments <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\langle {r}^{k}\rangle\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">⟨</mo> <msup> <mrow> <mi>r</mi> </mrow> <mi>k</mi> </msup> <mo stretchy="false">⟩</mo> </mrow> </math></EquationSource> </InlineEquation> (k = –2 to + 4), the Quantum Similarity Index (QSI), and information-theoretical measures—Kullback–Leibler (KL) divergence and Relative Fisher Information (RFI)—were used to assess accuracy against near Hartree–Fock quality reference densities. NISTFs consistently outperformed CSTFs across 291 of 318 moments. They also showed smoother QSI trends and lower divergence values in KL and RFI analyses. These results demonstrate the effectiveness of NISTFs in representing electron density within the Hartree–Fock-Roothaan method. Additionally, we observed a notable relationship between QSI deviations and total energy errors for both NISTF and CSTF basis sets.</p>

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A Comparative Study of Slater-Type Functions with Integer and Noninteger Principal Quantum Numbers for Evaluating Atomic Electron Density Accuracy

  • 期刊论文

  • 发表日期：

    2026年2月6日

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  • Ercan Sahin

摘要

We present a comparative study of noninteger-n Slater-type functions (NISTFs) and conventional Slater-type functions (CSTFs) for modeling electron density properties of neutral atoms from He to Xe using minimal basis sets. Radial moments \(\langle {r}^{k}\rangle\) ⟨ r k ⟩ (k = –2 to + 4), the Quantum Similarity Index (QSI), and information-theoretical measures—Kullback–Leibler (KL) divergence and Relative Fisher Information (RFI)—were used to assess accuracy against near Hartree–Fock quality reference densities. NISTFs consistently outperformed CSTFs across 291 of 318 moments. They also showed smoother QSI trends and lower divergence values in KL and RFI analyses. These results demonstrate the effectiveness of NISTFs in representing electron density within the Hartree–Fock-Roothaan method. Additionally, we observed a notable relationship between QSI deviations and total energy errors for both NISTF and CSTF basis sets.