Predicting the Thermodynamic Stability of Ce/Ti Nanoclusters under Synthetic Conditions
Abstract
Predicting which molecular species will form under a given set of synthetic conditions requires determining their thermodynamic stability relative to precursors and competing products. For complex molecular systems in solution, this requires both accurate electronic-structure calculations and sufficient configurational sampling. Here, we investigate two hexanuclear Ce/Ti clusters that form under different synthetic conditions: a yellow Ce IV 4 Ti 2 cluster obtained under mild conditions and a red Ce III 2 Ti 4 cluster, presented here for the first time, that requires higher temperature, longer reaction times, and increased Ti precursor concentration. To determine whether the red cluster is thermodynamically less stable or instead kinetically hindered, we combine explicit-solvent configurational sampling using a fine-tuned foundation machine-learned interatomic potential with density functional theory calculations of the Gibbs free energies of formation. Simulated annealing identifies configurations approximately 1 eV lower in energy than those obtained by direct relaxation of the crystallographic structures. Despite requiring more forcing synthetic conditions, Ce III 2 Ti 4 is predicted to be 4.48 eV more stable than Ce IV 4 Ti 2 . Comparison with a hypothetical Ce IV 2 Ti 4 cluster separates this difference into a 2.86 eV stabilization associated with the Ce III oxidation state and a further 1.62 eV stabilization associated with the Ti-rich composition and corresponding cluster structure. The preference for CeIII is also found for the isolated solvated Ce ions, while the sampled Ce III 2 Ti 4 structures show reduced repulsion between capping ligands and a less distorted metal core. The calculations therefore identify Ce III 2 Ti 4 as the thermodynamic product, while its formation only under more forcing conditions is consistent with kinetic limitation. The results show that predicting the thermodynamic product in solution requires configurational sampling beyond direct optimization of experimentally determined structures.
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BibTeX
@misc{liu2026predicting,
title = {{Predicting the Thermodynamic Stability of Ce/Ti Nanoclusters under Synthetic Conditions}},
author = {Liping Liu and Haley Wellman and Zi-Ming Ye and Andrea Darù and Ria Zaman and Kent O. Kirlikovali and Omar K. Farha and Laura Gagliardi},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15009368/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009368/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Predicting the Thermodynamic Stability of Ce/Ti Nanoclusters under Synthetic Conditions
AU - Liping Liu
AU - Haley Wellman
AU - Zi-Ming Ye
AU - Andrea Darù
AU - Ria Zaman
AU - Kent O. Kirlikovali
AU - Omar K. Farha
AU - Laura Gagliardi
PY - 2026
DA - 2026/09/23
PB - ChemRxiv
DO - 10.26434/chemrxiv.15009368/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009368/v1
AB - Predicting which molecular species will form under a given set of synthetic conditions requires determining their thermodynamic stability relative to precursors and competing products. For complex molecular systems in solution, this requires both accurate electronic-structure calculations and sufficient configurational sampling. Here, we investigate two hexanuclear Ce/Ti clusters that form under different synthetic conditions: a yellow Ce IV 4 Ti 2 cluster obtained under mild conditions and a red Ce III 2 Ti 4 cluster, presented here for the first time, that requires higher temperature, longer reaction times, and increased Ti precursor concentration. To determine whether the red cluster is thermodynamically less stable or instead kinetically hindered, we combine explicit-solvent configurational sampling using a fine-tuned foundation machine-learned interatomic potential with density functional theory calculations of the Gibbs free energies of formation. Simulated annealing identifies configurations approximately 1 eV lower in energy than those obtained by direct relaxation of the crystallographic structures. Despite requiring more forcing synthetic conditions, Ce III 2 Ti 4 is predicted to be 4.48 eV more stable than Ce IV 4 Ti 2 . Comparison with a hypothetical Ce IV 2 Ti 4 cluster separates this difference into a 2.86 eV stabilization associated with the Ce III oxidation state and a further 1.62 eV stabilization associated with the Ti-rich composition and corresponding cluster structure. The preference for CeIII is also found for the isolated solvated Ce ions, while the sampled Ce III 2 Ti 4 structures show reduced repulsion between capping ligands and a less distorted metal core. The calculations therefore identify Ce III 2 Ti 4 as the thermodynamic product, while its formation only under more forcing conditions is consistent with kinetic limitation. The results show that predicting the thermodynamic product in solution requires configurational sampling beyond direct optimization of experimentally determined structures.
ER -