Toward a realistic theoretical electronic spectra of metal aqua ions in solution: The case of Ce(H2O)n3+ using statistical methods and quantum chemistry calculations.

Accurately predicting spectra for heavy elements, often open-shell systems, is a significant challenge typically addressed using a single cluster approach with a fixed coordination number. Developing a realistic model that accounts for temperature effects, variable coordination numbers, and interprets experimental data is even more demanding due to the strong solute-solvent interactions present in solutions of heavy metal cations. This study addresses these challenges by combining multiple methodologies to accurately predict realistic spectra for highly charged metal cations in aqueous media, with a focus on the electronic absorption spectrum of Ce3+ in water. Utilizing highly correlated relativistic quantum mechanical (QM) wavefunctions and structures from molecular dynamics (MD) simulations, we show that the convolution of individual vertical transitions yields excellent agreement with experimental results without the introduction of empirical broadening. Good results are obtained for both the normalized spectrum and that of absolute intensity. The study incorporates a statistical machine learning algorithm, Gaussian Mixture Models-Nuclear Ensemble Approach (GMM-NEA), to convolute individual spectra. The microscopic distribution provided by MD simulations allows us to examine the contributions of the octa- and ennea-hydrate of Ce3+ in water to the final spectrum. In addition, the temperature dependence of the spectrum is theoretically captured by observing the changing population of these hydrate forms with temperature. We also explore an alternative method for obtaining statistically representative structures in a less demanding manner than MD simulations, derived from QM Wigner distributions. The combination of Wigner-sampling and GMM-NEA broadening shows promise for wide application in spectroscopic analysis and predictions, offering a computationally efficient alternative to traditional methods.