Markov Chain Monte Carlo Sampling for Target Analysis of Transient Absorption Spectra

Global and target analysis techniques
are ubiquitous tools for
interpreting transient absorption (TA) spectra. However, characterizing
uncertainty in the kinetic parameters and component spectra derived
from these fitting procedures can be challenging. Furthermore, fitting
TA spectra of inorganic nanomaterials where the component spectra
of different excited states are nearly or completely overlapped is
particularly problematic. Here, we present a target analysis model
for extracting excited-state spectra and dynamics from TA data using
a Markov chain Monte Carlo (MCMC) sampler to visualize and understand
uncertainty in the model fits. We demonstrate the utility of this
approach by extracting the overlapping component spectra and dynamics
of single- and biexciton states in CsPbBr3 nanocrystals.
Significantly, refinement of the component spectra is accomplished
by fitting the entire fluence-dependent series of ensemble TA data
using the Poisson statistics of photon absorption, providing multiple
checks for internal consistency. The MCMC method itself is highly
general and can be applied to any data set or model framework to accurately
characterize uncertainty in the fit and aid model selection when choosing
between different models.