The results of electronic
and vibrational structure simulations
are an invaluable support for interpreting experimental absorption/emission
spectra, which stimulates the development of reliable and cost-effective
computational protocols. In this work, we contribute to these efforts
and propose an efficient first-principle protocol for simulating vibrationally-resolved
absorption spectra, including nonempirical estimations of the inhomogeneous
broadening. To this end, we analyze three key aspects: (i) a metric-based selection of density functional approximation (DFA)
so to benefit from the computational efficiency of time-dependent
density function theory (TD-DFT) while safeguarding the accuracy of
the vibrationally-resolved spectra, (ii) an assessment
of two vibrational structure schemes (vertical gradient and adiabatic
Hessian) to compute the Franck–Condon factors, and (iii) the use of machine learning to speed up nonempirical
estimations of the inhomogeneous broadening. In more detail, we predict
the absorption band shapes for a set of 20 medium-sized fluorescent
dyes, focusing on the bright ππ
★ S0 → S1 transition and using experimental
results as references. We demonstrate that, for the studied 20-dye
set which includes structures with large structural variability, the
preselection of DFAs based on an easily accessible metric ensures
accurate band shapes with respect to the reference approach and that
range-separated functionals show the best performance when combined
with the vertical gradient model. As far as band widths are concerned,
we propose a new machine-learning-based approach for determining the
inhomogeneous broadening induced by the solvent microenvironment.
This approach is shown to be very robust offering inhomogeneous broadenings
with errors as small as 2 cm–1 with respect to genuine
electronic-structure calculations, with a total CPU time reduced by
98%.