# Ensemble Effects on Hydroxide Bond Dissociation Free Energies in Polyoxovanadate Clusters

## TL;DR

This paper shows how considering molecular ensembles improves predictions of hydroxide bond energies in vanadium clusters, aligning theory with experiments.

## Contribution

The study introduces a bilinear model and methodology that captures ensemble effects, reducing DFT calculations by 98% while maintaining high accuracy.

## Key findings

- Ensemble effects significantly influence hydroxide bond dissociation free energies in polyoxovanadate clusters.
- A bilinear model reconciles experimental and theoretical results with a root-mean squared error of 0.4 kcal/mol.
- A simplified methodology achieves 1 kcal/mol accuracy with 98% fewer DFT calculations.

## Abstract

Understanding structure-property relationships is foundational
to numerous modern chemistries, such as proton-coupled electron transfer
(PCET). However, an experimentally measured property is the result
of the behavior from an ensemble of molecules. Neglecting ensemble
effects, especially under complex chemical environments, may obfuscate
these relationships and lead to discrepancies between theory and experiment.
In this work, we demonstrate the impact of configurational entropy
and local chemical environments on hydroxide bond dissociation free
energies [BDFE­(O–H)] for a set of polyoxovanadate nanoclusters,
at ambient conditions. The O–H bond strengths are investigated
via density functional theory (DFT) coupled with statistical thermodynamic
analysis and bilinear modeling, and compared with previous experimental
results on the same systems, namely electrochemical solutions of:
[V6O13–x
(OH)
x
(TRIOLR)2]−2 (x = 2, 4, 6; R = NO2, Me) and [V6O11–x
(OMe)2(OH)
x
(TRIOLNO2
)2]−2 (x = 2, 4). Interestingly,
we find that ensemble effects, even at room temperature, can account
for a significant portion of the BDFE­(O–H) trend with the degree
of reduction via H atom binding, which cannot be fully captured by
single-structure, static DFT calculations. Moreover, we find that
the ensemble effects may be replicated statistically, requiring only
enumeration of energetically accessible H-binding sites. With the
ensemble effects resolved, we present a simple bilinear model to reconcile
remaining biases between experiment and ensemble-informed theory,
which corelate with cluster-specific electronic environment differences.
The bilinear model achieves outstanding accuracy vs experiments with
a root-mean squared error of 0.4 kcal/mol. Finally, based on the physicochemical
characteristics of hydrogen interaction with polyoxometalates, we
present a simple methodology that captures the BDFE­(O–H) trend
while dramatically reducing required DFT calculations by 98% and achieving
accuracy within 1 kcal/mol. Overall, this work elucidates the roles
and structural origins of configurational entropy and chemical effects
on polyoxometalate hydroxide bond energies, with potential applicability
to various atomically precise metal oxide systems. Importantly, it
introduces models for rapid and highly accurate property calculations
in connection with experiments.