Adaptive guided stochastic optimization: A novel approach for fitting the theoretical intensity parameters for lanthanide compounds

In this study, we introduce a state-of-the-art approach to enhance the fitting accuracy of theoretical intensity parameters in lanthanide spectroscopy. Lanthanide-based compounds play a pivotal role in a wide range of applications due to their distinctive photophysical characteristics. Theoretical understanding and computational descriptions are essential for advancing these applications. The Judd-Ofelt theory stands as a fundamental stone, offering insights into the luminescence exhibited by lanthanide compounds. Our methodology addresses the procedure of fitting charge factors ($g$ in the Simple Overlap Model) and ligand effective polarizabilities (${\alpha }^{\prime }$ in the Bond Overlap Model), quantities used for the determination of the intensity parameters (${\Omega }_{\lambda }$). We propose Adaptive Guided Stochastic Optimization (AGSO), a method that employs randomized initial points within predefined bounds for each variable. By iteratively updating variable bounds based on population statistics, AGSO systematically minimizes the error function with respect to experimental data. Extensive tests were conducted comparing AGSO with the well-established simulated annealing (SA) method. Remarkably, AGSO consistently outperformed SA, demonstrating its efficacy in fitting intensity parameters for various lanthanide compounds. Through AGSO, we offer a robust and efficient tool for the accurate study of lanthanide-based compounds, with broad implications for diverse applications.