# PTML models of self assembled ligand free nanoparticle catalysts for cross coupling reactions

## TL;DR

This paper uses computational models to predict the efficiency of nanoparticle catalysts in chemical reactions, aiming to reduce costs and improve sustainability.

## Contribution

The novel contribution is the development of PTML models for predicting catalyst performance in ligand-free cross-coupling reactions.

## Key findings

- MLR model achieved 7.4% MAE and 12.2% RMSE in predicting reaction yields.
- ANN models showed better performance with MAE as low as 5.8% and high precision in classification.
- PTML models can guide catalyst selection and optimize reaction conditions effectively.

## Abstract

Cross-coupling reactions have transformed the synthesis of complex and valuable compounds used in pharmaceuticals, materials science, and chemical synthesis. Transition metal nanoparticle (NP) catalysts represent a promising strategy within this field, but their behavior and efficiency continue under investigation. The use of computational models enables rapid design, optimization, and understanding of the behavior of these molecules, thereby reducing the costs and time. In this study, the perturbation theory and machine learning (PTML) approach was used to construct a predictive model for estimating yield after multiple reuses (up to 10) of self-assembled Au- or glass-supported transition metal NP catalysts under ligand-free conditions and diverse cross-coupling reactions. The studied reactions include Suzuki–Miyaura, Kumada, Negishi, Buchwald-Hartwig, C(sp2)- and C(sp3)-H functionalization, and double carbonylation. A comprehensive dataset was built, and multiple linear regression (MLR) and artificial neural network (ANN) models were built and compared. The best MLR model achieved MAE = 7.4% and RMSE = 12.2% on the test set, demonstrating robust performance for yield prediction. Among the ANN models, MLP (9:9-20-9-1:1) and RBF (9:9-70-1:1) regression models showed similar results, with test MAE of 5.9% and 5.8% respectively, and both showed test RMSE of 9.8%. MLP (9:9-20-18-1:1) classification model showed high precision (97.0%) and recall (93.8%), effectively distinguishing high- and low-yielding reactions. These results highlight the potential of PTML-based models to guide catalyst and reaction condition selection, optimize catalytic systems, and minimize synthesis costs and environmental impact.

The online version contains supplementary material available at 10.1038/s41598-025-14080-2.