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A Δ-learning strategy for interpretation of spectroscopic observables

Lookup NU author(s): Luke Watson, Dr Thomas PopeORCiD, Professor Thomas Penfold



This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


Accurate computations of experimental observables are essential for interpreting the high information content held within x-ray spectra. However, for complicated systems this can be difficult, a challenge compounded when dynamics becomes important owing to the large number of calculations required to capture the time-evolving observable. While machine learning architectures have been shown to represent a promising approach for rapidly predicting spectral lineshapes, achieving simultaneously accurate and sufficiently comprehensive training data is challenging. Herein, we introduce Δ-learning for x-ray spectroscopy. Instead of directly learning the structure-spectrum relationship, the Δ-model learns the structure dependent difference between a higher and lower level of theory. Consequently, once developed these models can be used to translate spectral shapes obtained from lower levels of theory to mimic those corresponding to higher levels of theory. Ultimately, this achieves accurate simulations with a much reduced computational burden as only the lower level of theory is computed, while the model can instantaneously transform this to a spectrum equivalent to a higher level of theory. Our present model, demonstrated herein, learns the difference between TDDFT(BLYP) and TDDFT(B3LYP) spectra. Its effectiveness is illustrated using simulations of Rh L3-edge spectra tracking the C–H activation of octane by a cyclopentadienyl rhodium carbonyl complex.

Publication metadata

Author(s): Watson L, Pope T, Jay RM, Banerjee A, Wernet P, Penfold TJ

Publication type: Article

Publication status: Published

Journal: Structural Dynamics

Year: 2023

Volume: 10

Online publication date: 06/11/2023

Acceptance date: 17/10/2023

Date deposited: 06/11/2023

ISSN (electronic): 2329-7778

Publisher: AIP Publishing LLC


DOI: 10.1063/4.0000215


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Funder referenceFunder name
EP/W008009/1 Open Fellowship
Leverhulme Trust (Project No. RPG-2020-268)