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<p>We propose the use of the vibrational quantum defect (VQD) to select the best energy function that could better model the vibrational energy levels of diatomic molecules.We report an analysis of accurate experimental RKR energy data obtained from spectroscopy for the following molecular potentials: <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_20295_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="78" /> </InlineMediaObject> <EquationSource Format="TEX">\(^7\textrm{Li}_2(a^3\Sigma _u^+)\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_20295_Article_IEq2.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="78" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{Na}_2(5^1\Delta _g^+)\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_20295_Article_IEq3.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="69" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{K}_2(a^3\Sigma _u^+)\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_20295_Article_IEq4.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="74" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{Cs}_2(3^3\Sigma _g^+)\)</EquationSource> </InlineEquation>, and <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_20295_Article_IEq5.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="81" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{CO}(X^1\Sigma ^+)\)</EquationSource> </InlineEquation>. From these, we extract the vibrational quantum deviations (VQD) using various energy functions. Additionally, we demonstrate that a simple, clear and straightforward analysis of VQD graphs (VQD Versus vibrational energy) facilitates the establishment of the energy function that exhibits the smallest deviation. Moreover, we demonstrate that the VQD method is very sensitive for detecting inaccuracy of oscillator models, especially in the case of ground molecular potentials.</p>

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Accurate evaluation of molecular potential energy functions through vibrational quantum defect analysis

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  • 发表日期：

    2025年10月17日

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  • Haikel Jelassi,
  • Ridha Horchani,
  • Amira Zaouak

摘要

We propose the use of the vibrational quantum defect (VQD) to select the best energy function that could better model the vibrational energy levels of diatomic molecules.We report an analysis of accurate experimental RKR energy data obtained from spectroscopy for the following molecular potentials: \(^7\textrm{Li}_2(a^3\Sigma _u^+)\) , \(\textrm{Na}_2(5^1\Delta _g^+)\) , \(\textrm{K}_2(a^3\Sigma _u^+)\) , \(\textrm{Cs}_2(3^3\Sigma _g^+)\) , and \(\textrm{CO}(X^1\Sigma ^+)\) . From these, we extract the vibrational quantum deviations (VQD) using various energy functions. Additionally, we demonstrate that a simple, clear and straightforward analysis of VQD graphs (VQD Versus vibrational energy) facilitates the establishment of the energy function that exhibits the smallest deviation. Moreover, we demonstrate that the VQD method is very sensitive for detecting inaccuracy of oscillator models, especially in the case of ground molecular potentials.