A dimension staircase for orientational heat capacity: nature skips the 3/2 rung
Abstract
The low-temperature orientational heat capacity of an interacting multipole pair is conventionally taken to be two-valued: 3/2 k B for axially symmetric moments and 2 k B otherwise. Here I evaluate it for all 101,666,280 molecular geometries of the OMol25 dataset and show that this is the bottom rung of a staircase: the exponent is a count, not a case split, γ = C v / k B = Σ i 1/ p i , which for two rigid nonlinear molecules is exactly γ = D / 2 and leaves only the rungs 3/2, 2 and 5/2. Of 11,325,000 pairs drawn uniformly from the whole dataset none occupies the 3/2 rung ( P < 3.26 x 10 -7 ; structural bound 4.187 x 10 -7 ), and the rest split 12.05% and 87.95% between γ = 2 and 5/2, so nearly the whole molecular world shares one coefficient: 5/2 k B = 20.79 J mol -1 K -1 per mole of pairs. The 3/2 rung is deleted rather than thermally suppressed (a 0.129 Å C-H bending amplitude exceeds the 0.1 Å scale at which a C 3v rotor saturates its axiality defect), so no temperature recovers it.
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BibTeX
@misc{lin2026dimension,
title = {{A dimension staircase for orientational heat capacity: nature skips the 3/2 rung}},
author = {Fuxing Lin},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15010225/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010225/v1},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - A dimension staircase for orientational heat capacity: nature skips the 3/2 rung
AU - Fuxing Lin
PY - 2026
DA - 2026/10/11
PB - ChemRxiv
DO - 10.26434/chemrxiv.15010225/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010225/v1
AB - The low-temperature orientational heat capacity of an interacting multipole pair is conventionally taken to be two-valued: 3/2 k B for axially symmetric moments and 2 k B otherwise. Here I evaluate it for all 101,666,280 molecular geometries of the OMol25 dataset and show that this is the bottom rung of a staircase: the exponent is a count, not a case split, γ = C v / k B = Σ i 1/ p i , which for two rigid nonlinear molecules is exactly γ = D / 2 and leaves only the rungs 3/2, 2 and 5/2. Of 11,325,000 pairs drawn uniformly from the whole dataset none occupies the 3/2 rung ( P < 3.26 x 10 -7 ; structural bound 4.187 x 10 -7 ), and the rest split 12.05% and 87.95% between γ = 2 and 5/2, so nearly the whole molecular world shares one coefficient: 5/2 k B = 20.79 J mol -1 K -1 per mole of pairs. The 3/2 rung is deleted rather than thermally suppressed (a 0.129 Å C-H bending amplitude exceeds the 0.1 Å scale at which a C 3v rotor saturates its axiality defect), so no temperature recovers it.
ER -