Spatial Arrangement of Dynamic Surface Species from Solid-State NMR and Machine Learning-Accelerated MD Simulations

Aug 3, 2026

The study investigates how motional organic functional groups organize on solid surfaces by combining experimental dipolar-coupling measurements with machine-learning–accelerated molecular dynamics simulations. It addresses NMR distance-measurement biases caused by molecular motions, which can substantially reduce dipolar couplings and lead to overestimated internuclear distances. Using DeePMD-based force fields to reach long dynamical timescales, the work determines distances and interprets 1H–1H double-quantum/single-quantum correlation results for allyl-tethered mesoporous silica.

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CategoryResearch & Report

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Spatial Arrangement of Dynamic Surface Species

NMR distance constraints and motion-induced biases

MD simulation strategy with machine learning potentials

1H DQ/SQ correlation experiments and interpretation

Extracting dipolar couplings from sideband patterns

Received 00th January 20xx, Accepted 00th January 20xx Spatial Arrangement of Dynamic Surface Species from Solid-State NMR and Machine Learning-Accelerated MD Simulations Takeshi Kobayashi,a* Da-Jiang Liu,a* and Frédéric A. Perrasa DOI: 10. 1039/x0xx00000x The surface arrangement of motional organic functionalities is explored by experimental dipolar coupling measurements and the prediction of motionally-averaged coupling constant from molecular dynamics simulations. The use of machine learning potentials was key to reaching the timescale required. The distance between dynamic surface species are important in cooperative heterogeneous catalysis. NMR measurements of internuclear distances, which rely on the quantification of dipolar couplings, provide valuable constraints for determining the conformations of molecules and their arrangements. They are particularly valuable in materials that lack long-range order and thus cannot be studied using diffraction-based methods. 1-18 A well-known caveat, however, is that molecular motions have significant impacts on NMR-based distance measurements; for instance, SSNMR consistently overestimates bonded internuclear distances, when compared to single-crystal X-ray and neutron diffraction due to the librationsand vibrations of the molecule.19 Molecular motions that alter the internuclear vector direction, in particular, tend to dramatically reduce the magnitude of dipolar couplings, resulting in gross overestimations of internuclear distances. Common examples include methyl-rotation, which reduces 13C– 1H dipolar couplings to only 1/3 their original size,20, 21 and polymer chain dynamics which weaken 1H–1H dipolar couplings.22 The dynamics of organic and organometallic species tethered to silica materials have been studied using 2H NMR spectroscopy in addition to dipolar-based methods,23-31 often showing that surface species feature a high degrees of mobility. With general interest in developing methods to determine intersite distances on surfaces and gain insights into cooperativity a. U.S. DOE Ames National Laboratory, Ames, IA, 50011, USA. † Electronic Supplementary Information (ESI) available: See DOI: 10. 1039/x0xx00000x and isolation, it is necessary to find ways to recover accurate inter-site distances from NMR-based approaches. 15, 32-35 One potential approach for the accurate measurement of internuclear distances using NMR spectroscopy is the application of molecular dynamics (MD) simulations to analyze molecular motions and estimate their impacts on dipolar couplings, as originally introduced by Ishii et al. 19 In the context of surface species, Paterson et al. combined dipolar coupling measurement and applied direct density functional theory (DFT) MD simulations to gain insights into the dynamics of grafted metal complexes.36 While their approach was only partly successful in explaining the observed motions, this combination of accurate DFT MD methods for calculating dynamicallyaveraged dipolar coupling constants may well enable the use of NMR to analyze the structure and arrangement of mobile molecules on solid surfaces. Herein, we apply a combination of MD simulations and 1H– 1H distance measurements to explore the arrangement of allyl groups tethered to mesoporous silica nanoparticles (ALMSNs) .37 To counter the reorientational dynamics of the allyl groups,28 MD simulations need to cover timescales in excess of picoseconds to microseconds.38, 39 Targeting such longtimescales using DFT-based MD simulations is typically only achievable in very small systems. Recent advances in artificial intelligence have enabled the derivation of far less demanding force fields using DFT calculations and a machine learning (ML) approach. In this work, we used the DeePMD framework40 and related software.41 The proximity of functional groups was first probed using a 2D 1H double quantum / single-quantum (DQ/SQ) correlation experiment using the BABA recoupling sequence.42

FAQs

Why do molecular motions cause errors in NMR-derived inter-nuclear distances?

Motions alter the internuclear vector direction and change dipolar couplings, often reducing coupling magnitudes. This reduction leads to systematic overestimation of internuclear distances, including in solid-state NMR comparisons.

How does machine learning–accelerated MD enable the needed timescales?

Long reorientational dynamics require simulation windows beyond picoseconds to microseconds. ML potentials derived from DFT calculations reduce the computational cost, enabling DeePMD-based simulations at the required timescale.

What experiment was used to probe proximity among functional groups?

A 2D 1H double-quantum/single-quantum correlation experiment using the BABA recoupling sequence was used. It reveals correlations that distinguish intra- from intermolecular contacts.

Aug 3, 2026

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