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PreprintCC BY-NC-NDChemRxiv

Exact orientational thermodynamics of multipole rank pairs: a two-valued low-temperature heat-capacity law, with new data for 28 rank pairs (L = 2-24) and 29 real molecule pairs

  • Fuxing Lin1
  1. 1Hunan Institute of Engineering
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Abstract

New results and new data reported in this work. This paper reports a primary data set and the law it yields, not a survey of the literature. (i) Orientational partition functions 𝑍(𝑦) and low-temperature interaction heat capacities 𝛾 = 𝐢𝑣/π‘˜π΅ are computed for 28 multipole rank pairs spanning 𝐿 = 𝑛 +π‘š = 2 to 𝐿 = 24, each entry obtained by up to three mutually independent numerical routes β€” the large-𝑦 tail of the thermal coupling function, the exact fluctuation formula, and the sublevel-volume exponent β€” and each with the coupling-minimum structure measured independently of the exponent. (ii) The exact second-moment identity is verified by direct quadrature for nine rank pairs to a maximum relative deviation of 6.8 Γ— 10βˆ’14. (iii) Zero-parameter predictions β€” dominant channel, coupling scale and freezing temperature π‘‡βˆ— β€” are given for 29 real molecule pairs (H2O, NH3, CO2, C2H4, CH4, BF3, CH3I, SF6, among others), and split them into the two low-temperature classes. (iv) A negative result is reported rather than omitted: the widely used singleparameter universality of the thermal coupling function Ξ¦π‘›π‘š(𝑦) is falsified, with relative deviations up to 47%. (v) The orientation average is reduced exactly to a three-dimensional integral and the kernel is obtained from a three-term recurrence valid at any rank, which removes the monomial-expansion ceiling of the earlier 𝐿 ≀ 16 version. Every number quoted is tabulated in the main text (Tables 1, 2, 2a-2c, 3, 4) and in the Supporting Information (S1-S12), and the complete machine-readable data and code are openly archived (Zenodo DOI 10.5281/zenodo.23086356).

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Cite

BibTeXRIS
BibTeX
@misc{lin2026exact,
  title = {{Exact orientational thermodynamics of multipole rank pairs: a two-valued low-temperature heat-capacity law, with new data for 28 rank pairs (L = 2-24) and 29 real molecule pairs}},
  author = {Fuxing Lin},
  howpublished = {ChemRxiv},
  year = {2026},
  month = oct,
  doi = {10.26434/chemrxiv.15010099/v1},
  url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010099/v1},
  note = {CC BY-NC-ND},
}
RIS
TY  - UNPB
TI  - Exact orientational thermodynamics of multipole rank pairs: a two-valued low-temperature heat-capacity law, with new data for 28 rank pairs (L = 2-24) and 29 real molecule pairs
AU  - Fuxing Lin
PY  - 2026
DA  - 2026/10/08
PB  - ChemRxiv
DO  - 10.26434/chemrxiv.15010099/v1
UR  - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010099/v1
AB  - New results and new data reported in this work. This paper reports a primary data set and the law it yields, not a survey of the literature. (i) Orientational partition functions 𝑍(𝑦) and low-temperature interaction heat capacities 𝛾 = 𝐢𝑣/π‘˜π΅ are computed for 28 multipole rank pairs spanning 𝐿 = 𝑛 +π‘š = 2 to 𝐿 = 24, each entry obtained by up to three mutually independent numerical routes β€” the large-𝑦 tail of the thermal coupling function, the exact fluctuation formula, and the sublevel-volume exponent β€” and each with the coupling-minimum structure measured independently of the exponent. (ii) The exact second-moment identity is verified by direct quadrature for nine rank pairs to a maximum relative deviation of 6.8 Γ— 10βˆ’14. (iii) Zero-parameter predictions β€” dominant channel, coupling scale and freezing temperature π‘‡βˆ— β€” are given for 29 real molecule pairs (H2O, NH3, CO2, C2H4, CH4, BF3, CH3I, SF6, among others), and split them into the two low-temperature classes. (iv) A negative result is reported rather than omitted: the widely used singleparameter universality of the thermal coupling function Ξ¦π‘›π‘š(𝑦) is falsified, with relative deviations up to 47%. (v) The orientation average is reduced exactly to a three-dimensional integral and the kernel is obtained from a three-term recurrence valid at any rank, which removes the monomial-expansion ceiling of the earlier 𝐿 ≀ 16 version. Every number quoted is tabulated in the main text (Tables 1, 2, 2a-2c, 3, 4) and in the Supporting Information (S1-S12), and the complete machine-readable data and code are openly archived (Zenodo DOI 10.5281/zenodo.23086356).
ER  -