  Time-Resolved Laser-Induced Fluorescence Spectroscopy (TRLFS) and cryo-TRLFS
are sensitive tools for \textit{in situ} speciation of low-level uranium in
aqueous samples, including natural waters. To tailor, often ill-conditioned
(i.e., leading to ambiguous interpretations), multi-linear analysis,
first-principles based theoretical computation (Molecular Dynamics and Quantum
Chemistry) of luminescence spectra would be beneficial. We present a
methodology to simulate TRLFS and cryo-TRLFS spectra and present vibrationally
resolved luminescence spectra for aquo complex [UO$_2$(H$_2$O)$_5$]$^{2+}$(aq).
Comparison to experimental data, interpretation of spectra in the terms of a
minimal non-redundant set of spectroscopic parameters (peak spacing \omega, the
0' $\rightarrow$ 0 peak position T$_{00}$, envelope shape parameter \Delta R,
average peak width \sigma and luminescence life-times) and shifts due to ligand
coordination are discussed. The minimum theory-experiment deviation in T$_{00}$
(exp. $\sim$ 20 485 cm$^{-1}$) has been reported for SORECP/TD-DFT with
LB$\alpha$ functional - 20 cm$^{-1}$, 90 cm$^{-1}$ and 100 cm$^{-1}$ for
different models, a similar level of agreement has been met for \omega$_{gs}$.
The RMS along configuration space sampling CMD trajectory for T$_{00}$
corresponds well to \sigma. Preliminary predictivity study for a small set of
uranyl complex species and comparison of pseudo-potential (SORECP) and
all-electron results for [UO$_2$(H$_2$O)$_5$]$^{2+}$(g) are appended.
