<p>A deep understanding of thermophysical properties is crucial for accurately predicting the behavior of molecules under extreme conditions. In this work, we present a comprehensive methodology grounded in statistical mechanics, which integrates quantum, semiclassical, and classical formulations of the partition function for diatomic species. As a case study, this methodology was applied to homonuclear alkali-metal dimers through the fitting of high-level ab initio calculations to the Extended Hartree–Fock Approximate Correlation Energy. A total of 154 potential energy curves were considered, with explicit consideration of low-lying electronic states. This approach enables accurate modeling of both low and high-temperature regimes for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">${\textrm{Li}}_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>Li</mtext> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\textrm{Na}_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>Na</mtext> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\textrm{K}_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>K</mtext> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\textrm{Rb}_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>Rb</mtext> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\textrm{Cs}_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>Cs</mtext> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> , and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\textrm{Fr}_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>Fr</mtext> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>. Our results reveal that neglecting excited electronic states leads to significant deviations in key properties, particularly heat capacity and enthalpy at elevated temperatures. Systematic trends along the alkali-metal series are observed. The methodology demonstrates agreement with experimental data and underscores the limitations of classical approaches, where the quantized nature of molecular eigenvalue becomes non-negligible. This framework provides a robust and generalizable tool for reliable prediction of thermodynamic properties in molecular systems, the results emphasize the fundamental role of electronic structure in determining thermodynamic properties, and they can be directly extended to improve high-temperature models in chemical kinetics, plasma physics, and materials science.</p>

Thermophysical Properties of Alkali Metals: A Partition Function Theory Approach Including Low-Lying Electronic States

期刊论文
发表日期：

2025年8月19日

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Carlos D. da Silva,
Marcos D. S. Alves,
Ramon S. da Silva,
Maikel Y. Ballester

摘要

A deep understanding of thermophysical properties is crucial for accurately predicting the behavior of molecules under extreme conditions. In this work, we present a comprehensive methodology grounded in statistical mechanics, which integrates quantum, semiclassical, and classical formulations of the partition function for diatomic species. As a case study, this methodology was applied to homonuclear alkali-metal dimers through the fitting of high-level ab initio calculations to the Extended Hartree–Fock Approximate Correlation Energy. A total of 154 potential energy curves were considered, with explicit consideration of low-lying electronic states. This approach enables accurate modeling of both low and high-temperature regimes for ${\textrm{Li}}_{2}$ ${Li}_{2}$ , $\textrm{Na}_{2}$ ${Na}_{2}$ , $\textrm{K}_{2}$ $K_{2}$ , $\textrm{Rb}_{2}$ ${Rb}_{2}$ , $\textrm{Cs}_{2}$ ${Cs}_{2}$ , and $\textrm{Fr}_{2}$ ${Fr}_{2}$ . Our results reveal that neglecting excited electronic states leads to significant deviations in key properties, particularly heat capacity and enthalpy at elevated temperatures. Systematic trends along the alkali-metal series are observed. The methodology demonstrates agreement with experimental data and underscores the limitations of classical approaches, where the quantized nature of molecular eigenvalue becomes non-negligible. This framework provides a robust and generalizable tool for reliable prediction of thermodynamic properties in molecular systems, the results emphasize the fundamental role of electronic structure in determining thermodynamic properties, and they can be directly extended to improve high-temperature models in chemical kinetics, plasma physics, and materials science.