Machine learning-based correction for spin-orbit coupling effects in NMR chemical shift calculations.

Area of Science:

• Computational Chemistry
• Spectroscopy
• Machine Learning

Background:

• NMR spectroscopy is crucial for molecular structure elucidation.
• Relativistic effects, particularly spin-orbit coupling, are vital for accurate NMR calculations involving heavy atoms.
• Existing methods struggle to efficiently incorporate these relativistic effects.

Purpose of the Study:

• To develop a machine learning (ML) model to approximate spin-orbit (SO) coupling contributions to NMR chemical shifts.
• To enable accurate relativistic NMR calculations with minimal computational cost.
• To investigate the transferability and performance of the ML model for various heavy p-block elements.

Main Methods:

• A Δ-machine learning (Δ-ML) method was developed using computed reference data.
• The model was trained on spin-orbit zeroth-order regular approximation (ZORA) DFT calculations for 6388 structures.
• The ML model approximates SO contributions for 13C and 1H NMR chemical shifts.

Main Results:

• The ML method recovers ~85% of SO contribution for 13C and ~70% for 1H NMR shifts.
• The approach is computationally inexpensive, adding virtually no extra cost to scalar-relativistic calculations.
• The model demonstrates transferability to other DFT methods and performs well on organotin and organolead compounds.

Conclusions:

• The developed Δ-ML method significantly enhances the accuracy of NMR chemical shift predictions in the presence of heavy atoms.
• Combining this SO-contribution model with previous ML methods for correlation effects can halve the deviation from experimental values.
• This work provides a powerful tool for computational chemists studying relativistic effects in NMR.