formula = mhchem, greek = chemgreek, modules = thermodynamics, modules =
redox, modules = reactions

# Investigation of the luminescence of [UO2X4]^2- (X=Cl, Br) complexes in
organic phase using time-resolved laser-induced fluorescence spectroscopy and
quantum chemical simulations

Hanna Oher  DEN-Service d’Etudes Analytiques et de Réactivité des Surfaces
(SEARS), CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France  Univ.
Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules,
F-59000 Lille, France  Florent Réal  Univ. Lille, CNRS, UMR 8523 - PhLAM -
Physique des Lasers Atomes et Molécules, F-59000 Lille, France  Thomas
Vercouter  DEN-Service d’Etudes Analytiques et de Réactivité des Surfaces
(SEARS), CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
<EMAIL_ADDRESS>Valérie Vallet  Univ. Lille, CNRS, UMR 8523 - PhLAM -
Physique des Lasers Atomes et Molécules, F-59000 Lille, France
<EMAIL_ADDRESS>
###### Abstract

The luminescence properties of the [UO2Cl4]^2- complex in an organic phase,
especially the influence of large organic counter cations, have been studied
by time-resolved laser-induced fluorescence spectroscopy (TRLFS) and ab initio
modeling. The experimental spectrum was assigned by vibronic Franck-Condon
calculations on quantum chemical models based on relativistic density
functional approaches. The shape of the luminescence spectrum of the uranyl
tetrachloride complex is determined by symmetrical vibrations and geometrical
change upon emission. The possible change of the luminescence properties
depending on the first and second uranyl coordination sphere was predicted
theoretically for [UO2Br4]^2- and [R4N]2[UO2Cl4] ([R4N] = [Bu4N], [A336])
model systems. The computations reveal that for U(VI), the second coordination
sphere has little influence on the spectrum shape, making speciation of uranyl
complexes with identical first coordination-sphere ligands tedious to
discriminate. The computed structural changes agreed well with experimental
trends; theoretical spectra and peaks attribution are in a good accordance
with TRLFS and MCD data respectively.

##  I Introduction

The knowledge of the stoichiometries and stabilities of the chemical species
of uranium is of key importance for the understanding of the chemical
reactivity of uranium in environmental or industrial situations. The
speciation of uranium in solution has then been a major topic of
investigations by both experimental and theoretical methods. Among the
powerful spectroscopic techniques, time-resolved laser-induced luminescence
spectroscopy (TRLFS) has been widely used for the characterization of uranyl
species in solutions and in solid phases, because of its high sensitivity to
changes of the inner-sphere coordination of UO2^2+. The luminescence spectra
of uranyl complexes in solution show in general a narrow energetic range about
$6000\text{\,}{\mathrm{cm}}^{-1}$. In this region just a single electronic
transition between the initial and final states can be identified and it is
vibrationally resolved with bands to different vibrational quantum numbers
Visnak, Jakub and Sobek, Lukás (2016). In the case of mixtures of uranyl
species, the interpretation of TRLFS data can be difficult because of low
resolution and overlapping of the emission spectra in similar time frame. Then
spectroscopic considerations are often insufficient to unambiguously determine
the nature of the complexes. This is why a theoretical support based on
quantum chemical modeling appears as a way to better validate TRLFS data
interpretations by decomposing the different effects that might induce changes
in the emission spectra of uranyl complexes.

Several research teams have tried to simulate emission spectra of uranyl
complexes with quantum chemical methods Su  _et al._ (2011a, 2014, b), based
on either wave-function theory (WFT), or density functional theory (DFT).
While WFT methods are efficient for accurate calculations, the high computing
cost limits the simulation to small clusters of heavy elements like uranium.
DFT approaches are more appropriate for cost-effective calculations applied to
actinides, but can be challenged regarding the accuracy of the description of
the electronic ground state and excited states, and its ability to reproduce
low-lying electronic transitions and their vibronic resolution. Relativistic
effects, electron correlation, and spin-orbit coupling must be correctly taken
into account for those heavy elements. Tecmer et al. Tecmer  _et al._ (2011)
have evaluated the accuracy of pure and hybrid exchange-correlation
functionals for the bare uranyl cation isoelectronic uranium triatomics,
arguing that hybrid functionals can be used for quantitative prediction of the
low-lying excited states of uranyl. Uranyl tetrachloride complexes have been
thoroughly studied as a reference cluster because direct comparison with
luminescence data from crystals is possible Watkin  _et al._ (1991). Moreover,
this complex can also be stabilized in non-aqueous solvents Görller-Walrand
_et al._ (2004); Nockemann  _et al._ (2007); Sornein  _et al._ (2006), and is
of interest in some solvent extraction protocols Pascal E. Reiller (0000);
Hellé  _et al._ (2015). The structure of the uranyl tetrachloride is well-
established with four chloride ions in the equatorial plane of the UO2^2+
moiety, resulting in a $\mathrm{D_{4h}}$ symmetry. The effects of second-
sphere counter cations, solvent molecules or solvating agents have also to be
considered, as to quantify their influence on the structures, the electronic
states energies, and the vibronic progressions.

In this work we will compare the results of ab initio calculations to
experimental data obtained from a $n$-dodecane solution in which the uranyl
tetrachloride complex was extracted by a tetra-alkyl ammonium molecule
(Aliquate ® 336). The methodology is a step-by-step approach in order to
validate hypotheses and approximations that we made. The computations of the
ground and the excited state structural and vibrational parameters are
necessary for the understanding of theoretical and experimental spectra.
Because the main effect on the luminescence data is commonly accepted to
originate from the inner-sphere coordination, the first hydration sphere
chloride ligands were substituted by bromides to discuss the trends, validate
our method, and evaluate its applicability to other types of uranyl complexes.
We will also quantify the effects of outer-sphere counter ions and long-range
solvation on the computed spectra.

##  II Experimental details

###  II.1 Sample preparation

####  [A336]_2[UO_2Cl_4] in $n$-dodecane

The sample preparation method has been adapted from Hellé et al. Hellé  _et
al._ (2014, 2015). Aliquate ® 336 (98%) was purchased from Alfa Aesar. HCl
(32%), 1-decanol (99%) and n-dodecane were purchased from Sigma-Aldrich. HClO4
was purchased from Merck. All reagents were used as received without further
purification. A stock solution of uranium(VI) was prepared by dissolution of
U3O8 in a hot perchloric acid solution. The U(VI) concentration was checked by
inductively coupled plasma mass spectrometry (ICP-MS). The aqueous solution
was prepared by dilution of this stock solution into a
$5\text{\,}\mathrm{\textsc{m}}$ hydrochloric acid solution to get a uranium
(VI) concentration of ${10}^{-5}\text{\,}\mathrm{\textsc{m}}$. Deionized water
(Alpha-Q, Millipore, $18.2\text{\,}\mathrm{M}\Omega\mathrm{c}\mathrm{m}$) was
used for the preparation of all aqueous solutions.

The organic solution was prepared by dissolving weighed amounts of Aliquate ®
336 and 1-decanol in sufficient amount of n-dodecane to get a concentration of
${10}^{-2}\text{\,}\mathrm{\textsc{m}}$ of Aliquate ® 336 with 1% of
1-decanol. It was then pre-equilibrated by contact with a uranium-free
$5\text{\,}\mathrm{\textsc{m}}$ hydrochloric acid solution during
$2\text{\,}\mathrm{h}$ of shaking and separated.

For uranium extraction, $2\text{\,}\mathrm{mL}$ of the aqueous solution was
contacted with an equal volume of the pre-equilibrated organic solution. The
mixture was shaken in a thermomixer at
$20\text{\,}\mathrm{\SIUnitSymbolCelsius}$ during $1\text{\,}\mathrm{h}$, and
about $2\text{\,}\mathrm{mL}$ of the organic phase was sampled after
$2\text{\,}\mathrm{h}$ of decantation for the spectroscopic measurements.

###  II.2 Time-Resolved Laser-Induced Fluorescence Spectroscopy

The sample was put in a $1\text{\,}\mathrm{cm}$-long quartz cuvette that was
placed in a TRLFS set-up as described afterwards. The excitation wavelength
was provided by a tunable OPO system (PantherEx OPO, Excel Technology) pumped
by a Nd/YAG laser at $355\text{\,}\mathrm{nm}$ (Surelite-I, Excel Technology).
The excitation was tuned to $\lambda_{ex}$ = $427\text{\,}\mathrm{nm}$ which
corresponds to a maximum of absorption by uranium(VI) in our samples. The
$5\text{\,}\mathrm{ns}$ laser pulses were generated at
$10\text{\,}\mathrm{Hz}$ for an energy of about $3.15\text{\,}\mathrm{mJ}$.
The detection set-up has already been described elsewhere Vercouter  _et al._
(2008). The luminescence signal was collected during a gate width of
$200\text{\,}\mathrm{\SIUnitSymbolMicro s}$, at a gate delay of
$100\text{\,}\mathrm{ns}$ after the excitation by the laser pulse. The
luminescence spectrum of the sample was recorded at room temperature ($22\pm
1\text{\,}\mathrm{\SIUnitSymbolCelsius}$). The luminescence spectrum presented
in this work was obtained after 1000 accumulations. The background noise was
subtracted from recorded spectrum.

###  II.3 Computational details

Since our aim is to use quantum chemical methods to elucidate the luminescence
band shapes of the complexes, several data are required. The ground-state and
first excited state geometries, their associated harmonic frequency spectra
and Hessian matrices have to be computed in order to obtain the overlap
integrals between the vibrational wave-functions associated to the ground and
excited states - Frank-Condon factors (FCFs). The FCFs were computed using
ezSpectrum 3.0 Mozhayskiy and Krylov  program by taking all necessary data
generated by the ab initio packages described below. The Duschinsky rotations
were used as implemented in the program. The numbers of vibrational quanta in
excited and ground state were selected to be one and five, respectively. All
the spectra were computed at $300\text{\,}\mathrm{K}$.

#### Model systems

The interactions of uranyl with the first and second coordination spheres
affect the electronic structure of uranium. As the influence of the chloride
ligands in UO2Cl4^2- complex was excellently reviewed by variety of
experimental Denning (2007); Denning  _et al._ (1981); Nockemann  _et al._
(2007); Hopkins  _et al._ (2001); Görller-Walrand  _et al._ (2004) and
theoretical methods Ruipérez and Wahlgren (2010); Pierloot  _et al._ (2007);
Pierloot and van Besien (2005); Matsika and Pitzer (2001); Gomes  _et al._
(2013), this system was selected as a benchmark to quantify the effect of
ligands in the first coordination sphere by substituting chlorides by
bromides, and the effect of the counter-ions in the second coordination
sphere, i.e. the quaternary ammonium cations. Furthermore, to discuss the
importance of long-range solvent effects, the model systems were computed in
gas phase and with inclusion of solvent effect (n-dodecane and acetone). The
structures are represented in Fig. 4

Figure 1: [UO2X4]^2-

Figure 2: [Bu4N]2[UO2X4]

Figure 3: [A336]2[UO2X4]

Figure 4: The complexes structures of [R4N]2[UO2X4] ([R4N] = [Bu4N], [A336]
and X=Cl, Br) in gas phase optimized at the DFT/PBE0 level of theory.

#### Structures of the ground and excited states, and harmonic frequencies

In the sake of keeping the computational costs within week scale and of
simplifying the data analysis, the structures of the uranyl tetrahalides
complexes were enforced to $D_{4h}$ symmetry, whereas no symmetry constrains
were applied to the complexes with a second coordination sphere. All the
ground-state molecular geometries were optimized including the relativistic
effects at the spin-free level in the gas phase and with solvent effect using
Density functional Theory (DFT). The Kohn-Sham equation was solved using the
hybrid PBE0 functional Ernzerhof and Scuseria (1999). The structure of the
first low-lying excited state was optimized using the time-dependent
(TD)-DFT/PBE0 method as implemented in Turbomole V7.3 2018 TUR (2007) and
Gaussian 16 Frisch  _et al._ (2016) codes. The vibrational harmonic
frequencies were computed using either an analytic Hessian matrix or numerical
finite differences of the gradient. All geometries considered for the vibronic
spectra calculations represent true minima as they have no imaginary
frequencies. The optimized structures are available in ESI.

In these calculations, def2-TZVP (second generation of triple-$\zeta$
polarization quality) Karlsruhe basis sets Weigend  _et al._ (1998); Weigend
and Ahlrichs (2005) have been used for all light elements (H, C, N, O, Cl).
For the heaviest atoms, small-core Relativistic Effective Core
Pseudopotentials (RECP) were used, namely the 60-core electron one for uranium
Küchle  _et al._ (1994); Cao  _et al._ (2003) along with the def-TZVP (first
generation of triple-$\zeta$ polarization quality) basis set Eichkorn  _et
al._ (1997), and the 28-core electrons ECP for bromine with the associated
aug-cc-pVTZ-PP basis set Peterson  _et al._ (2003). To speed up the
calculations, the resolution of the identity approximation to compute the
Coulomb Integrals (RI-J) Deglmann  _et al._ (2004); Bauernschmitt  _et al._
(1997) with appropriate auxiliary basis sets Weigend (2006); Eichkorn  _et
al._ (1997) was employed.

#### Vertical absorption and emission energies

Based on the benchmark calculations carried out by Tecmer et al. Tecmer  _et
al._ (2011, 2012, 2013) on a series of uranium(VI)-based compounds, the
CAM-B3LYP Yanai  _et al._ (2004) exchange-correlation functional was found to
be more accurate than PBE0 for uranyl valence transition energies. Thus, to
accurately position the “hot bands”, the vertical excitation and emission
energies with and without accounting for solvent effect were obtained from the
ground and excited-state structures, respectively, with TD-DFT single-point
calculations with the latter functional and the Amsterdam Density Functional
package (ADF2018.01) Baerends  _et al._ . All atoms were described by TZ2P
Slater-type basis sets van Lenthe and Baerends (2003) (triple-$\zeta$ with two
polarization functions quality). The scalar relativistic (SR) and spin-orbit
coupling (SOC) effects were accounted for by the ZORA Hamiltonian van Lenthe
_et al._ (1993).

#### Continuum solvent models

Long-range solvent effects were modeled by polarized continuum medium models,
with two similar flavors, the Continuum Polarizable Conductor Model (CPCM)
Barone and Cossi (1998); Cossi  _et al._ (2003) one implemented in Gaussian 16
program, and the conductor-like screening model (COSMO) model Klamt and
Schüürmann (1993); Klamt (1995); Klamt and Jonas (1996) implemented in the ADF
package.

##  III Results and discussions

###  III.1 Experimental luminescence spectra

The time-resolved luminescence spectrum of the uranyl sample in the presence
of chloride ions and Aliquate ® 336 in n-dodecane with 1% of 1-decanol is
shown on Figure 5 (black line). It is superimposed with the spectrum (red
line) acquired by Görller-Walrand et al. in similar conditions and in acetone
Görller-Walrand  _et al._ (2004). The spectrum also compares well to those
obtained earlier in chloroaluminate Hopkins  _et al._ (2001),
tetraalkylammonium Sornein  _et al._ (2006) and pyrrolidinium Nockemann  _et
al._ (2007) ionic liquids. The spectrum of [A336]2[UO2Cl4] in n-dodecane in
Figure 5 show an electronic transition maximum ("hot band”) at low energy
about $21\,000\text{\,}{\mathrm{cm}}^{-1}$ followed by a series of vibronic
peaks in the
$20\,300\text{\,}{\mathrm{cm}}^{-1}16\,000\text{\,}{\mathrm{cm}}^{-1}$ range,
which is typical of the [UO2Cl4]^2- species with a $D_{4h}$ coordination
symmetry Denning  _et al._ (1976). A mono-exponential decay with a
fluorescence lifetime of $0.3\text{\,}\mathrm{\SIUnitSymbolMicro s}$ was
measured for the uranium(VI) sample in a presence of chloride ions, Aliquate ®
336 and n-dodecane. It confirms the formation of a unique complex, which was
assumed to be [A336]2[UO2Cl4] with four chloride ions coordinated to uranyl in
its equatorial plane, consistently with the extracted complex stoichiometry
Pascal E. Reiller (0000).

Figure 5: Recorded luminescence spectra of [Bu4N]2[UO2Cl4] in acetone (the
maxima taken from Ref.[7], the Lorentzian shape computed) and [A336]2[UO2Cl4]
in n-dodecane. Vertical dashed red line shows the “hot band” position and
$R_{n},(n=1-5)$ corresponds to vibronic progression region. Details on the
spectral data are available in Table S1 of the ESI.

The decomposition of the [A336]2[UO2Cl4] luminescence spectra has been
performed by Reiller et al. Pascal E. Reiller (0000). The poor resolution of
the presently used apparatus did not allow to resolve well some of the
transitions, and revealed only the wide components. Moreover, a difference of
the relative intensities is observed around
$20\,295\text{\,}{\mathrm{cm}}^{-1}$ in $n$-dodecane due to the long gate
width selected for our measurements and small deviations, as the spectrum was
predicted by a Lorentzian fit (Table S1 in ESI). The spectrum in $n$-dodecane
is shifted to the blue side by $30\text{\,}{\mathrm{cm}}^{-1}$, compared to
the one in acetone, and only by $5\text{\,}{\mathrm{cm}}^{-1}$ with respect to
the one in [Bu3MeN][Tf2N] ionic liquid Sornein  _et al._ (2006). Thus, from
the measurements, one can conclude that neither the counter-ion nor the type
of solvent have any significant influence on the position of maxima of the
luminescence bands. The change in the relative intensities of the transitions
along the vibronic progression has been attributed by Sornein et al. Sornein
_et al._ (2006) to the formation of C-H…Cl hydrogen bonding between the
chloride of the [UO2Cl4]^2- moiety and a hydrogen atom of a cation present in
the ionic liquid. As we are using an aprotic solvent (n-dodecane), this effect
may also be present in our uranyl tetrachloride sample.

The spacing between the vibronic progressions of the luminescence spectrum
corresponds to the ground state uranyl stretching frequency value $\nu_{s}$.
The bands are not equally spaced, as the oscillator strength of the electronic
transition from the excited state to the highest vibrational level of the
ground state is very small. As a result large uncertainty exist on the
determination of the “hot band” maximum. One can extract $\nu_{s}$ value by
only taking into account the spacing between the vibrational maxima of the
same nature for [A336]2[UO2Cl4] in $n$-dodecane. The resulting $\nu_{s}$ value
amounts to $836\pm 18\text{\,}{\mathrm{cm}}^{-1}$. It is in good agreement
with the values, $823\pm 14\text{\,}{\mathrm{cm}}^{-1}$,
$825\text{\,}{\mathrm{cm}}^{-1}$, and $850\pm 25\text{\,}{\mathrm{cm}}^{-1}$
observed in acetone Görller-Walrand  _et al._ (2004), [C_4mim][Tf_2N]
Nockemann  _et al._ (2007), and in [Bu3MeN][Tf2N] Sornein  _et al._ (2006),
respectively. This vibration corresponds to a Raman active vibration of the
uranyl unit and can be correlated to the yl-U-O bond length. Using the empiric
relation of Bartlett and Cooney Bartlett and Cooney (1989):

$R_{\ce{U-O}}/(\mathbf{\AA})=106.5\times\nu_{s}^{-2/3}+0.575$ (1)

we calculated the U-O bond length to be equal to $1.77\pm
0.01\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ (using $\nu_{s}$ = $836\pm
18\text{\,}{\mathrm{cm}}^{-1}$) for our uranyl sample. This value is in a good
agreement with all experimental data listed in Table 1, and can therefore
serve as reference data to assess the accuracy of the ab initio calculations
we will now discuss.

###  III.2 Ground and excited state structures of the uranyl tetrahalide
complexes

#### Uranyl tetrahalide dianions

The structure of uranyl tetrachloride dianion has been well-studied by the
variety of theoretical and experimental techniques Dau  _et al._ (2012);
Tecmer  _et al._ (2012); Pierloot and van Besien (2005); Watkin  _et al._
(1991); Servaes  _et al._ (2005); Wilson  _et al._ (2011); Denning (2007);
Deifel and Cahill (2010). Insofar as the inclusion of all effects like in
experimental conditions is challenging for ab initio calculations because of
the difficulties in building chemically relevant models and the fast growing
of the computational costs as the model expands, the present quantum chemical
study was performed on models with increasing chemical complexity, to approach
the solution sample.

The spin-free optimized ground and the first excited state distances between
uranium and the coordinated atoms of the [UO2Cl4]^2- and [UO2Br4]^2- together
with experimental data are shown in Table 1.

In the [UO2Cl4]^2- gas-phase PBE0 calculations, the ground state
$\mathrm{R_{U-O}}$=$1.758\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ value is in
a good agreement with $1.766\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ obtained
with the CCSD(T) wave-function method, while
$\mathrm{R_{U-Cl}}$=$2.714\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ comes out
shorter than $2.735\text{\,}\mathrm{\SIUnitSymbolAngstrom}$. Moreover, the
PBE0 geometries are in good accordance with the all-electron CAM-B3LYP results
reported by Tecmer et al. Tecmer  _et al._ (2012). This gives us confidence in
the ability of PBE0 to provide fairly accurate geometries of the uranium
containing complexes. The inclusion of solvent effects on [UO2Cl4]^2- does not
significantly change the $\mathrm{R_{U-O}}$ distance as compared to the gas-
phase calculations, but it shortens $\mathrm{R_{U-Cl}}$ as the solvent
polarity increases. Keeping in mind that we do not have strictly the same
conditions as in the experiment, it is worth examining trends in both
theoretical and experimental data. The comparison of the experimental crystal
structure of Cs_2UO_2Cl_4 Watkin  _et al._ (1991) with the structure of uranyl
tetrachloride dianion in acetonitrile Servaes  _et al._ (2005) shows that the
$\mathrm{R_{U-O}}$ bond length is almost the same in both conditions, while
$\mathrm{R_{U-Cl}}$ values are found to be longer in solution by about
$0.01\text{\,}\mathrm{\SIUnitSymbolAngstrom}$.

To quantify the influence of the ligand nature in the first equatorial
coordination sphere, the chloride ligands were replaced by bromide ligands
which have the same type of bonding with uranium, but larger ionic radii. The
uranyl ion coordinated by four bromide ligands has been prepared in crystal
form Wilson  _et al._ (2011), while it is hardly stabilized in solution. The
experimental structure of Cs2UO2Br4 crystal shows that $\mathrm{R_{U-O}}$
distance ($1.777\text{\,}\mathrm{\SIUnitSymbolAngstrom}$) is almost equal to
the one found in the chloride homologue, Cs2UO2Cl4
($\mathrm{R_{U-O}=1.774\r{A}}$), whereas the $\mathrm{R_{U-Br}}$ distance is
longer by $0.149\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ than
$\mathrm{R_{U-Cl}}$. The gas-phase geometries of [UO2Cl4]^2- and [UO2Br4]^2-
follow this trend; the substitution of chloride by bromide ligands leads to
the insignificant stabilization of $\mathrm{R_{U-O}}$, and the U-Br distance
is longer by $0.169\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ than the U-Cl one
because of a weaker uranium-bromide ionic interaction. The latter lengthening
is larger by $0.063\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ than in the
crystals, simply because our quantum model does not account for crystal
packing effects.

Table 1: Ground and excited state geometries of the [UO2X4]^2-, X = Cl, Br compared to selected previous results. |  $\mathrm{R_{U-O}}$, Å |  $\mathrm{R_{U-X}}$, Å | Compound/media | Method | Ref.
---|---|---|---|---|---
Ground state
[UO2Cl4]^2- | 1.758 | 2.714 | gas-phase | R-ECP/PBE0 | this work
| 1.766 | 2.735 | gas-phase | CCSD(T) | [48]
| 1.764 | 2.712 | gas-phase | all-electron/CAM-B3LYP | [35]
| 1.774 | 2.671 |  Cs2UO2Cl4 | X-ray | [6]
| 1.759 | 2.699 | CPCM n-dodecane | R-ECP/PBE0 | this work
| 1.761 | 2.683 | CPCM acetone | R-ECP/PBE0 | this work
| 1.770 | 2.680 | acetonitrile | EXAFS | [49]
[UO2Br4]^2- | 1.750 | 2.883 | gas-phase | R-ECP/PBE0 | this work
| 1.749 | 2.905 | gas-phase | R-ECP/CAM-B3LYP | this work
| 1.777 | 2.820 |  Cs2UO2Br4 | X-ray | [50]
Excited state
[UO2Cl4]^2- | 1.789 | 2.721 | gas-phase | R-ECP/PBE0 | this work
| 1.844 | 2.685 |  Cs2UO2Cl4 | Two-photon absorption | [15]
| 1.790 | 2.706 | CPCM n-dodecane | R-ECP/PBE0 | this work
| 1.791 | 2.692 | CPCM acetone | R-ECP/PBE0 | this work
[UO2Br4]^2- | 1.778 | 2.895 | gas-phase | R-ECP/PBE0 | this work
| 1.780 | 2.918 | gas-phase | R-ECP/CAM-B3LYP | this work

The lowest triplet excited state in [UO2X4]^2- complexes arises from the
excitation of an electron out of the bonding $\sigma_{u}$ orbital that
involves the uranyl unit and the halide valence orbitals to the nonbonding
orbitals $\delta_{u},\phi_{u}$ localized on uranium. When such transition
occurs the U-O bond weakens and the excited state potential curve shifts along
the U-O symmetric stretching mode to larger distances and becomes flatter
Pierloot  _et al._ (2007). Looking at the excited state geometries of the
uranyl tetrahalide dianions one can note a lengthening of the
$\mathrm{R_{U-O}}$ bond by $0.031\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ and
$0.028\text{\,}\mathrm{\SIUnitSymbolAngstrom}$, in [UO2Cl4]^2- and
[UO2Br4]^2-, respectively, since the excitation depopulates the U-O bonding
$\sigma_{u}$ orbital. The differences of the $\mathrm{R_{U-X}}$ bonds are
small, about $0.010\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ in average,
because the $\sigma_{u}$ orbital has small contributions from the halide
valence p orbitals. From highly resolved low-temperature two-photon absorption
spectra of Cs2UO2Cl4, Denning et al. Denning  _et al._ (1976); Denning (2007)
determined that the U-O and U-Cl bonds elongate by
$0.070\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ and
$0.014\text{\,}\mathrm{\SIUnitSymbolAngstrom}$, respectively. Unfortunately,
there is no technique available to get the excited state geometry of the
complex in a liquid to precisely quantify the geometrical change upon
excitation. However, it can be estimated from the geometries obtained with a
continuum solvent model. Long-range solvent effects affect the excited state
structure in the same way as for the ground state. Thus, from solvent-
optimized ground and excited-states geometries, we report elongations of the
U-O and U-Cl bonds of $0.03\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ and
$0.008\pm 0.001\text{\,}\mathrm{\SIUnitSymbolAngstrom}$, in line with what was
measured by Denning et al. in the Cs2UO2Cl4 crystal.

The analysis of vibrational frequencies is very important for the
characterization of the theoretical luminescence spectra, as specific
vibrations appear in the vibronic progression. Some of the ground-state
vibrational frequencies are responsible for the band spacing in the
experimental luminescence spectrum, while the atomic displacement between the
ground and excited-state geometries is responsible for the intensities ratio.
The uranium - halide ($\nu_{\mathrm{U-X}}$), uranium -
oxygen($\nu_{\mathrm{s}}$) symmetrical stretching modes and uranium - oxygen
bending mode ($\nu_{\mathrm{b}}$) contribute to the luminescence spectra shape
to a large extent, and their values for the [UO2Cl4]^2- and [UO2Br4]^2-
complexes are listed in Table 2. The uranium - oxygen asymmetrical stretching
mode ($\nu_{\mathrm{a}}$), which is vibronically silent, is also shown to
discuss trends. Using the vibrational perturbation theory Barone (2004, 2005)
as implemented in Gaussian 16 Frisch  _et al._ (2016), we have computed the
anharmonic corrections, which turned out to be small, of the order of $5$ and
$3\text{\,}{\mathrm{cm}}^{-1}$ for the ground and excited states respectively
(See Table S2 in the ESI).

For the gas-phase [UO2Cl4]^2- model, the computed $\nu_{\mathrm{U-Cl}}$,
$\nu_{\mathrm{b}}$, $\nu_{\mathrm{s}}$ and $\nu_{\mathrm{a}}$ frequencies are
smaller in the excited state than in the ground state by 4, 4, 80 and
$115\text{\,}{\mathrm{cm}}^{-1}$, respectively. The PBE0 calculations
reproduce with an impressive accuracy the measured red shift of the stretching
mode, $\nu_{\mathrm{s}}$, $82\text{\,}{\mathrm{cm}}^{-1}$, in Cs2UO2Cl4, and
underestimates that for the bending mode, $20\text{\,}{\mathrm{cm}}^{-1}$. The
latter discrepancy has negligible impact as the symmetric stretching
$\nu_{\mathrm{s}}$ dominates the vibronic progressions in the luminescence
spectra.

Table 2: Ground and excited state vibrational frequencies (in $\mathrm{cm^{-1}}$) of the [R4N]_2[UO_2X_4], ([R4N] = [Bu4N], [A336])compounds. System | $\nu_{\mathrm{U-X}}$ | $\nu_{\mathrm{b}}$ | $\nu_{\mathrm{s}}$ | $\nu_{\mathrm{a}}$ | Method | Ref.
---|---|---|---|---|---|---
Ground state
[UO_2Cl_4]^2- | 237 | 275 | 894 | 974 | R-ECP/PBE0 gas-phase | this work
| 235 | 269 | 889 | 960 | R-ECP/PBE0 n-dodecane | this work
| 241 | 265 | 889 | 949 | R-ECP/PBE0 acetone | this work
Cs2UO2Cl4 | 264 [15] | 250 | 832 | 915 | Raman and IR in solid | [46]
[Me4N]2[UO2Cl4] |  |  | 831 | 909 | Raman and IR in solid | [54]
[Et4N]2[UO2Cl4] | 240 | 263 | 869 |  | Raman in solid | [55]
[Bu4N]2[UO2Cl4] | 270 | 286 | 869 | 945 | R-ECP/PBE0 gas-phase | this work
| 258 | 262 | 833 | 919 | Raman and IR in CH2Cl2 solution | [56]
[A336]2[UO2Cl4] | 266 | 288 | 876 | 957 | R-ECP/PBE0 gas-phase | this work
[UO2Br4]^2- | 144 | 262 | 907 | 988 | R-ECP/PBE0 gas-phase | this work
[C7H16NO2][UO2Br4] | 173 | 252 | 826 | 904 | Raman and IR in solid | [57]
Excited state
[UO2Cl4]^2- | 233 | 271 | 814 | 859 | R-ECP/PBE0 gas-phase | this work
| 236 | 268 | 811 | 854 | R-ECP/PBE0 n-dodecane | this work
| 240 | 263 | 808 | 848 | R-ECP/PBE0 acetone | this work
Cs2UO2Cl4 |  | 230 | 750 | 830 | N.A. | [7]
[Bu4N]2[UO2Cl4] | 266 | 281 | 799 | 845 | R-ECP/PBE0 gas-phase | this work
[A336]2[UO2Cl4] | 261 | 284 | 802 | 854 | R-ECP/PBE0 gas-phase | this work
[UO2Br4]^2- | 151 | 264 | 876 | 935 | R-ECP/PBE0 gas-phase | this work

Turning now to the vibrational frequencies obtained with solvent effects, we
observed opposite behavior of the U-Cl and U-O frequencies. With increasing of
polarity the $\nu_{\mathrm{U-Cl}}$ stretching frequencies insignificantly
increase (4 and $7\text{\,}{\mathrm{cm}}^{-1}$) for the ground and excited
states, respectively, while the uranyl $\nu_{\mathrm{b}}$, $\nu_{\mathrm{s}}$
and $\nu_{\mathrm{a}}$ decrease by 5 up to $25\text{\,}{\mathrm{cm}}^{-1}$ in
both states. This shift of the ground-state frequencies should be observable
in the computed luminescence spectra, namely in the spacing between the
vibrationally resolved peaks, while the minor change of the excited state
frequencies should only affect the vibronic intensities.

The substitution of chlorides by bromides in the uranyl equatorial plane lead
to the following changes in the vibrational spectra. Compared to uranyl
tetrachloride, the $\nu_{\mathrm{b}}$ value decreased by less than
$10\text{\,}{\mathrm{cm}}^{-1}$ in both ground and excited states. The
$\nu_{\mathrm{s}}$ increased by 13 and $62\text{\,}{\mathrm{cm}}^{-1}$ in the
ground and excited states, respectively. Similarly, the $\nu_{\mathrm{a}}$
increased by $14\text{\,}{\mathrm{cm}}^{-1}$ for the ground and
$76\text{\,}{\mathrm{cm}}^{-1}$ for the first excited state. The U-Br
stretching mode is $83\text{\,}{\mathrm{cm}}^{-1}$ lower in both ground and
excited states than the U-Cl symmetric stretching vibration. This is in line
with the ground-state experimental trends measured for Cs2UO2Cl4 with
[C7H16NO2][UO2Br4] (91, 2, 6 and 9 $\mathrm{cm^{-1}}$ for
$\nu_{\mathrm{U-Br}}$, $\nu_{\mathrm{b}}$, $\nu_{\mathrm{s}}$ and
$\nu_{\mathrm{a}}$, respectively). These changes indicate that the bromide
ligand has a smaller effect on the electronic structure of uranium than
chloride, since the U-Br bond strength is essentially ionic and has less
impact on the U-O bonding. Consistently, the uranium - oxygen symmetrical
stretching frequency is higher than in the chloride complex and close to the
bare uranyl value. For [UO2Br4]^2- we estimate a shift of frequencies between
the ground and excited state equal to 6, 2, 31 and 53 $\mathrm{cm^{-1}}$ for
$\nu_{\mathrm{U-Br}}$, $\nu_{\mathrm{b}}$, $\nu_{\mathrm{s}}$ and
$\nu_{\mathrm{a}}$, respectively.

#### Organic cation - uranyl tetrachloride: [A336]2[UO2Cl4]

The [UO2Cl4]^2- dianion in interaction with the organic ligand has been
prepared in the conditions described in the experimental section. The sample
was prepared based on the general ion-exchange mechanism Sato (1972); Barbano
and Rigali (1978), where in our scheme the extracting substance was Aliquate ®
336\. Then the final compound is predicted to be the uranyl tetrachloride
associated with two extractant cations of methyltrioctylammonium
[A336]2[UO2Cl4] as a result of an ion-exchange mechanism Pascal E. Reiller
(0000) Interestingly, Görller-Warland et al. Görller-Walrand  _et al._ (2004)
stabilized the [UO2Cl4]^2- dianion in solution with tetrabutylammonium
chloride (Bu4NCl), a ligand belonging to the group of tetraalkylammonium salts
as the Aliquate ® 336\. For our purpose, the geometries of ground and
luminescent states of complexes were optimized with the two tetraalkylammonium
cations placed in the second sphere in a $trans$ position. The bond distances
are shown in Table 3, while the vibrational frequencies are shown in Table 2.

If one compares the computed geometrical parameters to that of the models
without an explicit second-coordination sphere (Table 1), the counter-cations
induce a weakening of uranyl bond and the loss of the $\mathrm{D_{4h}}$
symmetry. These changes are due to the presence of a weak hydrogen bond
between the hydrogen atoms of the alkyl chains of cation with the oxygen and
chloride atoms of uranyl tetrachloride unit Sornein  _et al._ (2006) (see ESI
Figure S1, Table S3). The ground-state geometries of uranyl tetrachloride in
[Bu4N]2[UO2Cl4] and [A336]2[UO2Cl4] have been found to be nearly the same; the
$\mathrm{R_{U-O}}$ bond lengths are longer by about
$0.010\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ than in the bare [UO2Cl4]^2-
complex. Moreover, because of the symmetry distortion and interaction of
chloride ligands with the counter ion, the $\mathrm{R_{U-Cl}}$ distances
differ by 0.026 up to $0.118\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ as
compared to the bare [UO2Cl4]^2-. Despite our theoretical model does not
account for the crystal-field influence, these gas-phase structures are in a
good accordance with the experimental crystal structures measured for parent
compounds with a shorter alkyl chain, such as [Me4N]2[UO2Cl4] and
[Et4N]2[UO2Cl4]) Schnaars and Wilson (2013). This observation makes us
conclude that the chain length of a tetraalkilammonium cation has merely no
influence on the $\mathrm{R_{U-O}}$ and $\mathrm{R_{U-Cl}}$ values and that
both organic counter-cations (R4N) interact with the uranyl tetrachloride
dianion in a similar way. Since the influence of long-range solvent effects on
the [UO2Cl4]^2- bare complexes is negligible, we rely in the following on the
gas-phase structures for the [R4N]2[UO2Cl4] complexes.

The addition of two counter-cations in our chemical model does not change the
nature of the first excited state, which still is the excitation out of the
$\sigma_{u}$ orbital to a $\delta_{u}$ non-bonding orbital. As a result, the
luminescent-state geometry is impacted by the counter-cations as the ground-
state one: as compared to the bare [UO2Cl4]^2- complexes, the
$\mathrm{R_{U-O}}$ stretches by $0.028\text{\,}\mathrm{\SIUnitSymbolAngstrom}$
for [R4N]2[UO2Cl4] and the $\mathrm{R_{U-Cl}}$ distances are increased by
$0.003$ up to $0.027\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ for both types of
complexes. From these computed differences of the $\mathrm{R_{U-Cl}}$, we may
expect different ratios of relative intensities in the vibronic progressions
of the uranyl chloride and uranyl bromide complexes.

Table 3: Ground and excited state geometries of the [R4N]2[UO2Cl4] compounds compared to selected experimental results. |  $\mathrm{R_{U-O}}$, Å |  $\mathrm{R_{U-Cl}}$, Å | Compound | Method | Ref.
---|---|---|---|---|---
Ground state |  |  |  |  |
| 1.766(6) | 2.648(1)-2.677(1) |  [Me4N]2[UO2Cl4] | X-ray | [54]
| 1.76(2)-1.77(3) | 2.65(1)-2.68(1) |  [Et4N]2[UO2Cl4] | X-ray | [54]
| 1.769 | 2.596-2.753 |  [Bu4N]2[UO2Cl4] | R-ECP/PBE0 | this work
| 1.767 | 2.609-2.740 |  [A336]2[UO2Cl4] | R-ECP/PBE0 | this work
Excited state
| 1.796 | 2.599-2.780 |  [Bu4N]2[UO2Cl4] | R-ECP/PBE0 | this work
| 1.795 | 2.614-2.761 |  [A336]2[UO2Cl4] | R-ECP/PBE0 | this work

The calculated frequencies have been compared with data from experimental
Raman and IR measurements of different crystals or liquid samples of
[R4N]2[UO2Cl4] Schnaars and Wilson (2013); Newbery (1969); Gal  _et al._
(1984). The computed symmetrical stretching frequency $\nu_{\mathrm{s}}$
([Bu4N]2[UO2Cl4]) matches the value measured for the [Et4N]2[UO2Cl4] crystal
Newbery (1969). For [Bu4N]2[UO2Cl4], the gas-phase computed frequencies
$\nu_{\mathrm{U-Cl}}$, $\nu_{\mathrm{b}}$, $\nu_{\mathrm{s}}$ and
$\nu_{\mathrm{a}}$ are overestimated by 12, 24, 36 and
$26\text{\,}{\mathrm{cm}}^{-1}$, respectively, with respect to the values
measured in dichloromethane solution Gal  _et al._ (1984). From emission
spectroscopy measurements, symmetric-stretching vibrational frequency
($\nu_{\mathrm{s}}$) for [Bu4N]2[UO2Cl4] in acetone and for [A336]2[UO2Cl4] in
$n$-dodecane, were estimated at $823$ Görller-Walrand  _et al._ (2004) and
$836\text{\,}{\mathrm{cm}}^{-1}$, respectively. Our gas-phase calculations for
these exact complexes yield slightly blue-shifted values, $869$ and
$876\text{\,}{\mathrm{cm}}^{-1}$. We conclude that, our theoretical models and
methods are appropriate to capture structural and spectroscopic trends.

The difference in computed harmonic frequencies of [UO2Cl4]^2- in the two
[R4N]2[UO2Cl4] complexes is found to be small, the maximum variation from one
counter ion to another is $12\text{\,}{\mathrm{cm}}^{-1}$, for the asymmetric
uranyl stretching mode. The counter-ions in the second-coordination sphere
only sligthly affect the calculated frequencies with respect to the
[UO2Cl4]^2- bare ion; the uranium-chloride stretching mode is
$29\text{\,}{\mathrm{cm}}^{-1}$ higher, the uranyl bending mode has increased
by $13\text{\,}{\mathrm{cm}}^{-1}$, while the uranyl symmetrical and
asymmetrical stretching modes were found to be lower by $18$ and
$14\text{\,}{\mathrm{cm}}^{-1}$, respectively. This is a result of the loss of
symmetry together with the interplay of some motions of hydrogen and carbon
atoms in alkyl chain in the vibrational motions. Based on the Franck-Condon
principle, one can note that it should improve the band spacing between the
vibronic progressions of theoretical luminescence spectrum that will be
discussed further.

The shifts of theoretical frequencies between the ground and excited state of
[A336]2[UO2Cl4] are found to be similar to what was experimentally obtained
for Cs2UO2Cl4. The computed uranyl symmetrical stretching mode shifted by
$74\text{\,}{\mathrm{cm}}^{-1}$, very close to the experimental value of
$82\text{\,}{\mathrm{cm}}^{-1}$. However, the $\nu_{\mathrm{U-Cl}}$ and
$\nu_{\mathrm{b}}$ do not vary during the excitation. We will later discuss
the impact of this on the computed vibronic spectra.

###  III.3 Theoretical absorption and emission energies

As the luminescence spectrum of uranium (VI) complexes arises from the
electronic transition from the lowest excited state to the ground state,
coupled to progression of vibronic bands, the examination of the whole
electronic spectrum is useless. In this step, we aim at foreseeing the
sensitivity of the quantum chemical method on the first triplet excited state
absorption and emission energies of the uranyl tetrachloride complex, and on
the spectral features of uranium (VI) complexes.

The [UO2Cl4]^2- dianion electronic spectrum have been computed previously at
the different levels of theory and detailed discussions of the electronic
structure can be found in the literature Pierloot  _et al._ (2007); Pierloot
and van Besien (2005); Matsika and Pitzer (2001); Tecmer  _et al._ (2012).
From the previous studies it is known that for uranyl dication coordinated by
ligands the lowest excited state arises from the $\sigma_{u}$ highest
molecular orbital (HOMO) to the $\delta_{u}$ lowest unoccupied orbital (LUMO).
The HOMO corresponds to the bonding combination of uranium 5f and 6p and
oxygen 2p atomic orbitals, and 3p orbital of first-shell ligands, while the
LUMO is a nonbonding uranium 5f orbital (Figure 8). The detailed analysis of
the atomic orbitals contributions performed with multi-reference CASSCF
(complete active space self-consistent field) calculations by Pierloot and van
Beisen Pierloot and van Besien (2005) suggests that the lowest-lying
excitation corresponds to a metal-centered transition from the bonding to
nonbonding orbital of uranium, with a marginal ligand-to-metal charge transfer
character. Hence, we can use in our discussion the UO2^2+ spin-free notations
($D_{\infty h}$), thus labelling the ground state as ${}^{1}\Sigma_{g}^{+}$
and the luminescent state as ${}^{3}\Delta_{g}$.

The vertical absorption $\mathrm{E_{VA}}$ and emission $\mathrm{E_{VE}}$
energies, were obtained at all-electron SOC CAM-B3LYP level of theory and are
reported here together with experimental values (Table 4). They were computed
with the summation of the fully relativistic electronic vertical energies
associated with the spin-free zero-point energies correction. It should be
noted that the experimental data correspond to the band-origin values obtained
from polarized absorption or luminescence spectra and emission energies taken
from UV-Visible spectroscopic measurements. Thus the direct comparison with
theoretical results is not relevant, but we rather discuss whether the
theoretical data reproduce the experimental trends.

Table 4: Experimental and computed electronic transition energies of uranyl tetrahalide complexes (in $\text{\,}{\mathrm{cm}}^{-1}$). All-electron SOC CAM-B3LYP level of theory, the fully relativistic electronic vertical energies associated with the spin-free ZPE correction. | Theor. | Exp.
---|---|---
| $\mathrm{E_{VA}}$ | $\mathrm{E_{VE}}$ | Band-origin | Emission
[UO2Cl4]^2- gas-phase | 20737 | 19924 | 20096 a |
[UO2Cl4]^2- acetone | 20822 | 20116 |  |
[UO2Br4]^2- gas-phase | 20746 | 20041 | 19968 b |
[Bu4N]2[UO2Cl4] acetone |  | 20009 | 20097 c | 21000 c
[A336]2[UO2Cl4] $n$-dodecane |  | 20041 |  | 21025
a Ref. [46], b Ref. [60], c Ref. [7]

As seen in Table 4, the vertical absorption energy of [UO2Cl4]^2- increases by
$85\text{\,}{\mathrm{cm}}^{-1}$ with the addition of acetone due to its small
polarity. A blue shift of $117\text{\,}{\mathrm{cm}}^{-1}$ is observed when
chlorides are replaced by bromides ligands. On the contrary, the band origins
seem red shifted by $128\text{\,}{\mathrm{cm}}^{-1}$, from chloride to bromide
complexes according to experimental data Denning  _et al._ (1976); Flint and
Tanner (1982) The presence of multiple non-equivalent uranyl sites in
[UO2Br4]^2- crystal studied by Flint et al. Flint and Tanner (1982) may cause
a reverse shift of the whole spectrum and hampers a direct comparison between
theoretical and experimental results.

The luminescent state is known to be more sensitive to the solvent polarity
Lakowicz (2006). We indeed observed a larger shift of about
$192\text{\,}{\mathrm{cm}}^{-1}$ with the inclusion of acetone solvent than
for absorption energies. With addition of Bu4N in the second coordination
sphere, the $\mathrm{E_{VE}}$ increased by $85\text{\,}{\mathrm{cm}}^{-1}$, as
expected since the displacements between the ground and excited state
[UO2Cl4]^2- geometries are larger with than without counter cations. Both
theoretical $\mathrm{E_{VE}}$ and experimental emission energies of
[UO2Cl4]^2- are blue shifted by $32$ or $25\text{\,}{\mathrm{cm}}^{-1}$ when
immersed in $n$-dodecane or acetone, respectively.

It is worth noting that in the experimental spectra, the band-origin value of
[UO2Cl4]^2- is the same within $1\text{\,}{\mathrm{cm}}^{-1}$ in the Cs2UO2Cl4
crystal and in [Bu4N]2[UO2Cl4] in acetone. This is fully consistent with the
fact that the excitation molecular orbitals (See Figure 8) of the luminescent
state do not show any contribution from the second-sphere counter-ions.

Figure 6: HOMO

Figure 7: LUMO

Figure 8: The highest occupied and lowest unoccupied molecular orbitals of
[Bu4N]2[UO2Cl4] in gas phase obtained at RECP DFT/PBE0 level of theory.

###  III.4 Theoretical luminescence spectra

To simplify the comparison within all spectra, let them be obtained from our
quantum chemical calculations or from experiment, they are all normalized so
that the first peak matches the experimental amplitude. Neither homogeneous
and heterogeneous line broadening effects are included because of their
complicated prediction Su  _et al._ (2011a). We will thus only discuss the
stick spectra.

The most relevant parameters influencing the spectral intensity distribution
are the vibrational wavefunctions of both initial and excited states. The
spectral shape is significantly linked to the bond-length changes between the
two electronic states, as identified by Su et al. Su  _et al._ (2011b) thanks
to a semi-classical vibronic approach. Especially, they concluded that the
computed bond-length of the excited state is estimated without a sufficient
accuracy to properly simulate the intensities. In our study, the theoretical
luminescence spectra of [UO2Cl4]^2- and [UO2Br4]^2- in gas phase are displayed
on Figure 9. In all uranium-based compounds at room temperature
($300\text{\,}\mathrm{K}$), luminescence arises from a low oscillator strength
electron transition followed by the vibrational progression in the
$\nu_{\mathrm{s}}$ mode of the electronic ground state, as the
$\nu_{\mathrm{s}}$ is totally symmetric and preserves the symmetry of the
vibronic (electronic+vibrational) wave function. The first observed band
corresponds to the 0-0 vibrational transition. In the [UO_2Cl_4]^2-, the
totally symmetric $\nu_{\mathrm{U-Cl}}$ mode is also excited vibronically,
contributing to a line in the vibronic progression which is distant from the
0-0 line by $235\text{\,}{\mathrm{cm}}^{-1}$. However, as we already commented
upon the fact that the U-X lengthening from the ground and excited states is
underestimated by our quantum approach, we cannot expect the computed relative
intensities to match the experimental ones. Still, our predicted spectra place
the peaks distribution and band spacing in great agreement with the
experimental results. The complete assignment of the observed peaks is
provided in ESI.

Figure 9: Theoretical luminescence spectra of [UO2Cl4]^2- and [UO2Br4]^2- in
gas phase computed at $300\text{\,}\mathrm{K}$.

Setting the [UO2Cl4]^2- spectra computed in gas phase with those computed in
$n$-dodecane and acetone solvents (See Fig. S2 of the ESI) reveals that long-
range solvent interactions have no influence on the spectral profile. However,
[UO2Br4]^2- luminescence spectrum displays some more intense contributions and
longer vibronic progressions than [UO2Cl4]^2- (see the bottom panel on Fig.
9). This results from a larger geometrical displacements between the ground
and excited state structures (see Table S10 in ESI), which leads to the
appearance of several U-Br vibrational modes in a spectrum. The computed
luminescence spectrum of [A336]2[UO2Cl4] in gas phase is overlaid with the
experimental one on Figure 10. This figure highlights the fact that both the
energy positions and the band spacing of the computed vibronic transitions
match nicely the experimental envelope, though with the reserve that the band
spacing is somewhat red shifted as the ground state symmetrical stretching is
slightly overestimated by the R-ECP DFT/PBE0 level of theory. The added value
of the theoretical simulation lies in the assignment of the vibronic levels,
as detailed in Table S9 of the ESI. In agreement with Görller-Walrand et al.
Görller-Walrand  _et al._ (2004) results, our theoretical approach reproduced
a contribution from symmetrical stretching and rocking vibrational modes. On
the contrary, the doubled U-Cl symmetrical vibrational mode contribution was
observed rather than out-of-plane bending of equatorial ligands contribution.

Figure 10: Experimental and theoretical luminescence spectra of
[A336]2[UO2Cl4] in $n$-dodecane and a gas-phase respectively at
$300\text{\,}\mathrm{K}$.

##  IV Conclusions

Probing and quantifying the long-range effects of large organic counter-
cations on [UO2Cl4]^2- complex luminescence spectra was realized by two
approaches, one experimental using TRLFS, and the second using _ab initio_
-based approaches. For the latter, relativistic DFT quantum chemical methods
were found to be quantitative and effective tools to rationalize and predict
uranium-based complex luminescence properties. Thanks to a benchmark with
respect to previous studies on [UO2Cl4]^2-in crystal and solvent phases, we
have been able to assess the degree of reliability of such an approach by
comparison of ground and luminescence states structures and frequencies.
However, this theoretical protocol reaches some limitations, since we were not
able to compute the exact geometrical displacements of the complexes upon
excitation from the ground to first excited state. As a result, the computed
intensities of the vibronic bands do not coincide with the experimental ones.
Conversely, the peak positions of the luminescence spectra are correctly
reproduced, and the band spacings and theoretical assignments are in a good
accordance with our experimental data.

In this work, we have used step-wise growing chemical models to quantify the
influence of i) the first coordination sphere by substituting chloride anions
by bromides; ii) the influence of second-sphere counter cations; iii) and
long-range solvent effects with a polarizable continuum model, with the aim of
approaching the experimental conditions. We have found that both long-range
solvent effect and outer-sphere counter ion have a little influence on
vibronic intensities, while their effect is more significant for the
prediction of other spectroscopic parameters, such as emission energies and
vibronic band spacings of the [UO2Cl4]^2- complex. This also confirms that the
TRLFS spectroscopy may not be sensitive enough to discriminate long-range
interactions induced by the counter-cations present in the vicinity of the
luminescent center.

## Acknowledgements

We acknowledge support by the French government through the Program
"Investissement d’avenir" (LABEX CaPPA / ANR-11-LABX-0005-01 and I-SITE ULNE /
ANR-16-IDEX-0004 ULNE), as well as by the Ministry of Higher Education and
Research, Hauts de France council and European Regional Development Fund
(ERDF) through the Contrat de Projets État-Région (CPER CLIMIBIO).
Furthermore, this work was granted access to the HPC resources of
[CINES/IDRIS/TGCC] under the allocation 2018-2019 [A0050801859] made by GENCI.
We also acknowledge the CEA for the PhD grant attributed to H.O.

## Associated content

The following file supplemental-uo2x4-Oher.pdf is available free of charge. It
contains:

  * •

Figures of theoretical spectra of the [UO2Cl4]^2- obtained with the long-range
counter-ion and solvent effects.

  * •

Tables of assignments for theoretical and experimental spectra.

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