Charge Transfer Vibronic Transitions in Uranyl Tetrachloride

ARTICLE pubs.acs.org/JPCA

Charge Transfer Vibronic Transitions in Uranyl Tetrachloride Compounds Guokui Liu,*,† Nicholas P. Deifel,‡ Christopher L. Cahill,‡ Vladimir V. Zhurov,§ and A. Alan Pinkerton§ †

Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, United States Department of Chemistry, The George Washington University, Washington, D.C. 20052, United States § Department of Chemistry, University of Toledo, Toledo, Ohio 43606, United States ‡

bS Supporting Information ABSTRACT: The electronic and vibronic interactions of uranyl (UO2)2+ in three tetrachloride crystals have been investigated with spectroscopic experiments and theoretical modeling. Analysis and simulation of the absorption and photoluminescence spectra have resulted in a quantitative understanding of the charge transfer vibronic transitions of uranyl in the crystals. The spectra obtained at liquid helium temperature consist of extremely narrow zero-phonon lines (ZPL) and vibronic bands. The observed ZPLs are assigned to the first group of the excited states formed by electronic excitation from the 3σ ground state into the fδ,ϕ orbitals of uranyl. The Huang
Rhys theory of vibronic coupling is modified successfully for simulating both the absorption and luminescence spectra. It is shown that only vibronic coupling to the axially symmetric stretching mode is Franck
Condon allowed, whereas other modes are involved through coupling with the symmetric stretching mode. The energies of electronic transitions, vibration frequencies of various local modes, and changes in the OdUdO bond length of uranyl in different electronic states and in different coordination geometries are evaluated in empirical simulations of the optical spectra. Multiple uranyl sites derived from the resolution of a superlattice at low temperature are resolved by crystallographic characterization and time- and energy-resolved spectroscopic studies. The present empirical simulation provides insights into fundamental understanding of uranyl electronic interactions and is useful for quantitative characterization of uranyl coordination.

I. INTRODUCTION The electronic properties of uranyl (UO22+) in solution and solids have been an intriguing topic of chemistry and physics for several decades.1
9 Current research activities in both experimental and theoretical studies of uranyl complexes and solidstate compounds are increasingly active, primarily because of the need for advanced knowledge in actinide chemistry and materials sciences involved in the nuclear fuel cycle and environmental protection.10
12 Optical absorption and luminescence emission in uranyl compounds, which have an origin commonly known as a charge transfer transition, are important experimental probes of chemical structure and kinetics. A clear and fundamental understanding of the optical spectra of uranyl in compounds is essential to provide insights into its chemical properties. The chemistry of uranyl bearing compounds has seen tremendous growth recently, particularly in the synthesis and structural characterization of ‘hybrid’ materials. Notably, a wide variety of compounds have been prepared that exhibit interesting electronic properties,13 as well as U-molecular chemistry.14 Moreover, the family of known uranyl tetrachloride [UO2Cl4]2
compounds has expanded recently and such materials provide structures that may facilitate detailed studies of electronic interactions.15,16 r 2011 American Chemical Society

Experimental techniques such as lasers and synchrotron radiation have been applied to probing electronic states and transition dynamics of uranyl compounds in general in order to obtain more detailed information.10,11,17,18 Also important is the advance in computational capabilities, including ab initio calculations of electronic structure that provide theoretical interpretations to bonding properties of uranyl in compounds.19
22 Because the large number of electrons in an actinide ion imposes a great challenge to accurate ab initio calculations of electron correlation, the conventional empirical calculations using an effective operator Hamiltonian are still a better approach to analysis and modeling of the low-lying energy levels measured in optical spectroscopic experiments.23 The absorption occurring from the blue (shorter than 500 nm) to the ultraviolet (UV) region and the photoluminescence commonly observed from 500 nm down to 650 nm are widely utilized in characterization of uranyl coordination in complexes.11,12,24
27 These optical spectra have a common progressive profile weakly Received: October 19, 2011 Revised: December 1, 2011 Published: December 12, 2011 855

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dependent on the ligands bonded to the uranyl center, whereas fine structure in the spectra are sensitive to the ligand environment. In principle, the characteristic absorption and emission spectra reflect the nature of molecular geometry. Particularly, the vibrational fine structure carries information on the molecular bonding and symmetry in a uranyl complex. From the energy level structure point of view, optical excitation and luminescence emission directly involve electronic transitions between the ground and excited states and therefore, should be able to provide necessary information about the electronic structure of uranyl in complexes.2,8,10,20 However, no consensus has yet been achieved in theoretical calculations of the electronic states involved in these transitions. For instance, crystalline Cs2UO2Cl4 is one of the most studied uranyl systems by using spectroscopic experiments and theoretical calculations. DFT calculations by Denning et al.28 suggest that the ground state, or the highest occupied molecular orbital (HOMO), has a leading component of the Cl(3p) orbitals, whereas recent ab initio calculations by Pierloot and van Besien indicate that the ground state is dominated by U(5f) and O(2p) orbitals and the contribution from Cl orbitals is less than 1%.21 Controversially, the DFT calculations suggest that the ligand-to-metal charge transfer (LMCT) transition occurs primarily from Cl to U, but the ab initio calculations suggest LMCT from O to U. There is no doubt that vibronic coupling to electronic transitions is significant in the optical spectra of uranyl compounds.29 It gives rise to the most intense bands in both absorption and luminescence spectra. Apparently, the vibronic features in uranyl spectra are characteristically different from those usually observed in a spectrum of charge transfer transitions. For metal ions in inorganic crystals, a typical band of a charge transfer vibronic transition (CTVT) is usually broad and even shows no structure for identifying the zero-phonon lines (ZPLs) and vibration modes.30,31 This is mainly because of significant line broadening due to charge-transfer induced lattice displacements and charge-hole relaxation in the valence band. The large number of vibration modes coupled to a specific electronic transition also obscure fine structures in charge transfer vibronic spectra. In contrast, the spectra of uranyl in crystals have less vibronic side bands, and at low temperatures, have very narrow line widths comparable to the atomic-like f
f transitions. These two characteristics, determined primarily by the electronic properties of the tightly bonded uranyl ion, thus allow detailed spectroscopic analysis and theoretical modeling to obtain important information such as the origin and dynamics for each CTVT line in an observed spectrum. On the basis of current knowledge on electronic interactions in uranyl compounds, results obtained from spectroscopic experiments should provide more detailed information rather than just a “fingerprint” often used for characterizing uranyl coordination and structure variations.32
34 First, the ZPLs identified in an absorption or excitation spectrum provide an experimental basis for evaluation of the uranyl electronic interactions in terms of Coulomb interactions, spin
orbit coupling and crystal-field splitting.2,23 A theoretical analysis would thus allow a fundamental and quantitative understanding of uranyl bonding and coordination geometries. Because of intensive vibronic features, assigning ZPLs in a uranyl spectrum is not an easy task. It requires a clear understanding of the behavior of vibronic coupling. According to Franck
Condon principles, there are symmetryallowed and symmetry-forbidden vibronic couplings for an optically active ion (or color center) in dielectric crystals.29 As a result,

progressive and nonprogressive vibronic transitions are mixed and overlapped with the ZPLs. In such a case, a theoretical simulation of the observed spectrum would essentially ensure the accuracy of energy level assignment; and by doing so, various vibration modes and their coupling to electronic transitions would be determined as well. As it was previously demonstrated, a luminescence spectrum of uranyl in complexes or compounds can be interpreted satisfactorily by using the Huang
Rhys theory of ion
lattice vibronic interaction.34
36 Simulation of an absorption spectrum of uranyl is also possible with this theory. In this paper, we report the absorption (excitation) and luminescence spectra of [UO2Cl4](C10H10N2), [UO2Cl4](C12H14N2), and [UO2Cl4](C10H14N3) 3 2Cl 3 2H2O. Discussions of the spectroscopic properties and excited state dynamics is followed by theoretical simulations of both absorption and luminescence spectra using Huang
Rhys theory of vibronic interaction to extract information on physical interactions in the studied systems.

II. SYNTHESIS AND STRUCTURE CHARACTERIZATION A previously reported family of large size (>5 mm) single crystals containing the uranyl tetrachloride anion ([UO2Cl4]2
) were synthesized through room temperature reactions of uranium(VI) oxyacetate with several pyridinium cations in highly acidic chloride containing solutions.15,16 Three members of this family, [UO2Cl4](C10H10N2), [UO2Cl4](C12H14N2), and [UO2Cl4](C10H11N3)2 3 2Cl 3 2H2O are considered in this study (denoted herein as C1, C2, and C3 respectively). Single crystal fragments of these phases suitable for X-ray diffraction experiments were obtained by cutting the larger crystals yielded during synthesis. Room temperature crystal structures were previously reported by Deifel and Cahill.16 Readers are encouraged to refer to this study for structural descriptions and room temperature X-ray analyses. For the current investigation, low temperature X-ray data were collected at 20 K on a Rigaku R-axis Rapid diffractometer equipped with a previously described cooling device.37 Structures were solved using direct methods and refined using SHELXL.38 Refinement details may be found in the Supporting Information (Table S1). Crystallographic files in CIF format have also been deposited at the Cambridge Crystallographic Centre and may be obtained from http://www.ccdc. cam.ac.uk by citing reference codes 855229 to 8552312. The low temperature structures of C2 and C3 do not differ significantly from those observed at room temperature. As anticipated, a slight contraction of the unit cell parameters is noted, and no phase transitions were observed and the single crystallographically unique [UO2Cl4]2
site in each compound remain situated on centers of inversion. In the structure of C1 however, a superlattice emerges at low temperature to give a quadrupled unit cell containing three crystallographically unique [UO2Cl4]2
sites, two of which are on centers of inversion whereas the third is on a general position. Polyhedral representations of the extended structures observed at 20K are shown in Figures 1
3. Absorption spectra were obtained with a xenon lamp with light entered in the b
c plane of the crystals. Laser-induced excitation and luminescence spectra and decay data were obtained with a tunable pulsed dye laser. Samples were put in a cryostat and the temperature varied from room temperature down to liquid helium temperature below 4 K. 856

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III. RESULTS Absorption, excitation and luminescence spectra of the studied compounds were obtained from samples with the temperature varied from 4 to 300 K. The absorption spectrum and laserinduced fluorescence spectrum of C3 at 4 K are shown in Figures 4 and 5, respectively. Similar spectra for C2 and C1 are shown in Figures 6
9. Temperature-dependent line broadening in the spectra is induced by thermal population of various vibronic states including coupling to the lattice phonon modes. Analysis and simulation were performed on the low temperature

spectra in which line broadening induced by thermal phonons is mostly eliminated. The luminescence emission arises from the electronic transition from the lowest excited state, and from the thermally populated upper state to the ground state, and also from the vibronic transitions coupled to the ZPLs. All vibronic transitions progress up to six harmonics in a frequency of approximately 800 cm
1. The absorption spectra recorded from 20 000 up to 26 000 cm
1 arise from the excitation of an electron into a number of excited states (marked by the vertical arrows) and from the coupled vibration modes. The progressing of vibronic transitions in the absorption spectra is similar to that in the emission spectra, but with a lower frequency about 700 cm
1. The overall profile of both luminescence and absorption spectra exhibits well-recognized characteristics of uranyl in crystals. First, the lines are extremely sharp. In particular, measured at liquid helium temperature, the line width of the ZPLs is narrower than 1 cm
1, comparable to that of the parity forbidden f
f transitions in a lanthanide or actinide ion in a single crystal.39,40 Second, as it is shown with high resolution in Figure 10, the ZPL of the emission spectrum overlaps very well with the first ZPL of the absorption spectrum, indicating that the Stark shift between excitation and emission is negligible in the uranyl compounds. The sharp ZPLs and negligible Stark shift suzggest that the electronic states involved in the optical absorption and emission are very localized and the ZPLs are similar to intraionic electronic transitions rather than LMCT transitions. This result excludes the possible Cl-to-U charge transfer suggested by previous DFT calculations.28 On the other hand, the harmonic progressing of the vibronic transitions up to fifth order is observed in the luminescence and absorption spectra. The progression occurs apparently only on one frequency (energy) at approximately 830 cm
1 in the luminescence spezctra and 710 cm
1 in the absorption spectra. This frequency corresponds to the vibration of the symmetric stretching mode of the uranyl ion.2 The frequency

Figure 1. Portion of a single unit cell of C1, [UO2Cl4](C10H10N2), shown approximately along [001]. In this and subsequent figures, yellow polyhedra are [UO2Cl4]2
species (with green Cl atoms), blue spheres are N atoms and black lines are C atoms. U1 and U2 are on centers of inversion whereas U3 is on a general position. The distance between the uranyl centers are DU2
U3 = 5.464 Å, DU1
U2 = 10.050 Å, and DU1
U3 = 5.469 Å.

Figure 2. Polyhedral representation of the extended structure of C2, [UO2Cl4](C12H14N2), along [001]. Hydrogen atoms are omitted for clarity. 857

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Figure 3. Polyhedral representation of the extended structure of C3, [UO2Cl4](C10H11N3)2 3 2Cl 3 2H2O, along [100]. The red spheres represent solvent H2O and hydrogen atoms have been omitted for clarity.

Figure 4. Absorption spectrum of C3 at 4 K in comparison with a theoretical simulation. The electronic energy levels (ZPLs) are marked by the vertical arrows.

Figure 5. Luminescence spectrum of C3 at 4 K in comparison with a theoretical simulation. The insert is an expansion of the spectra showing emission from the two lowest excited states 3Δ1(E1, E2).

reduction suggests an expansion of the axial bond of OdUdO in the excited states of predominantly 5f character. Another common characteristic of the spectra shown in Figures 5
10 is a relatively small number of vibronic lines associated

with the ZPLs. The density of phonon states is typically high in crystals. Even if only the local vibrational modes are taken into 858

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Figure 6. Absorption spectrum of C2 at 4 K in comparison with a theoretical simulation. The electronic energy levels (ZPLs) are marked by the vertical arrows. The strong peaks between 22 500 and 24 200 cm
1 are saturated because of stronger absorption and the thickness of the sample.

Figure 9. Energy- and time-resolved excitation spectra of C1 at 4 K. All spectra were recorded using a pulsed laser of 5 ns pulse width. Spectrum a was recorded by monitoring the luminescence at 19128 cm
1 and delay of the detecting time by 1 μs. Spectrum b was recorded at 19220 cm
1 and 0.1 μs, and spectrum c at 19249 cm
1 and 0.6 ms.

Figure 7. Luminescence spectrum of C2 at 4 K in comparison with a theoretical simulation.

Figure 10. High resolution excitation and emission spectra of C3. The emission spectrum was recorded at 40 K and the excitation at 10 K. Two ZPLs correspond to the electronic transitions between the singlet ground state and the two lowest excited states 3Δ1(E1, E2) are separated by 6 cm
1. The difference between the energies measured in the emission and excitation spectra is less than 1 cm
1.

account, numerous vibronic side lines are expected in the spectrum of an optical center in such a crystal. The absence of vibronic bands arising from lattice modes indicates that the uranyl ion is electronically isolated from one another within the crystalline lattice. The spectra obtained in the present work are similar to that of uranyl in other tetrachloride crystals such as Cs2UO2Cl4.2 In comparing the spectra for C3 and C2, the profiles are very similar. A group of lines progress with the same

Figure 8. Absorption spectrum of C1 at 4 K in comparison with a theoretical simulation that assumes uranyl ions occupy three sites with energies listed in Table 2. 859

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slightly from 6 cm
1 for site a and site b, and 8 cm
1 for site c, the doublets are attributed to the two ZPLs rising from the crystal field splitting of the lowest doublet 3Δ1.

IV. DISCUSSION 1. Electronic States and Zero Phonon Lines. On the basis of molecular orbital theory, the HOMO in a uranyl complexe is a 3σu orbital, which is a highly hybridized configuration of the O(2s, 2p) and U(5p, 5f, 6d, 7s) atomic orbitals. The electrons of the Cl(3p) orbitals may contribute to some extent. Determination of contributions from the participating orbitals to the HOMO is a challenge. Different theoretical calculations give quite different results.19,21,28 Because the electronic transitions taking place in optical excitation or luminescence emission directly involve the HOMO, they thus provide information on its characteristics. In comparison with the less understood ground state, the low-lying excited states of uranyl in complexes consist predominantly of the 5f orbitals. Under a strong axial field of D∞h symmetry induced by the tightly bonded OdUdO linear molecule, the 5f orbitals split8,19 into the nonbonding orbitals 5fδu and 5fju and bonding orbitals 5fπu and 5fσu. The nonbonding orbitals have lower energies. When spin
orbit coupling and Coulomb exchange interaction are considered, the nonbonding orbitals further split into 8 excited states defined in L-S notation as 3ΔΩg with Ω = 1, 2, 3, 1Δ2 g, 3ΦΩg with Ω = 2, 3, 4, and 1Φ3 g. With energy levels spreading from 20 000 cm
1 to over 30 000 cm
1, these splittings primarily determine the profile of the absorption spectrum in the visible and near UV region. For uranyl in crystals, each of these Λ
S states can be further split by crystal field interaction into two crystal field levels. Because the four Cl
are always bonded in the equatorial plane as shown in Figure 1 through Figure 3, a uranyl tetrachloride anion typically has site symmetry of D4h which can be further reduced to C2h. In D4h symmetry, only the Ω = 2 states have the first order crystal field coupling that induces significant energy splittings, whereas other states may split through mixing of the Ω = 2 states, and thus have much smaller crystal field splittings. The states with Ω = 1, and 3 are degenerate in D4h symmetry. As previously determined from experimental analysis and theoretical calculations,2,19 the lowest excited doublet in Cs2UO2Cl4 is a 3Δ1 doublet and the crystal field splitting of this doublet is only on the order of 1 cm
1, whereas the crystal field splitting of 3Δ2 and 3Φ2 increases up to 1000 cm
1. However, in the crystals we studied the symmetry is lower than D4h. As shown in Figures 1
3 and Table S1, the distances between the uranium center and the four chlorides are never equal. The difference is induced by the nonequivalent CHN matrix in the equatorial plane. A [UO2Cl4] octahedron is linked unequally through the Cl
ions to the CHN matrix with approximately C2h symmetry. Therefore, the degeneracy is removed and the splitting of 3Δ1 should be much larger than that in Cs2UO2Cl4. If we consider the uranyl center in the framework of crystal field theory, Coulomb exchange interaction, spin
orbital coupling and crystal field interaction together determine the energy levels of the excited states. The axial field and equatorial field are two components of the crystal field potential. For uranyl in different tetrachloride compounds, the energy levels of the lowlying excited states are expected to have modest variations, but changes in the ordering of the multiplets are unlikely to occur. That is why the spectra for the three uranyl tetrachloride compounds we studied in the present work have the same scale and

Figure 11. Dynamics of the luminescence emission from site c (a) and site b (b) of uranyl centers in C1, with luminescence energy at 19220 and 19249 cm
1, respectively. The decay curves were recorded at 4 K when uranyl at site a was excited at 20458 cm
1. The solid curves are fittings to a single exponential decay for site b and growth and decay for site c.

frequency, and the structures of the spectra vary accordingly in both intensities and positions. This similarity indicates the isolated nature of [UO2Cl4]2
in the compounds studied and thus provides a guide for theoretical analysis and simulation. In C2 and C3, there is only one uranyl site confirmed by the observed absorption and luminescence spectra, whereas multiple uranyl sites in C1 were identified in the spectra recorded at liquid helium temperatures. As shown in Figure 9, the excitation spectrum of C1 consists of three groups of lines belonging to three different uranyl sites identified in the crystal structure shown in Figure 1 and Table S1 (Supporting Information). The lines belonging to different sites can be selectively probed using energy-selected and time-resolved excitation and luminescence measurements. With luminescence emission monitored at different wavelengths, three spectra of different origins were identified with the lowest energy excited state (first ZPL) located at 20125, 20080, and 20049 cm
1, and attributed to three uranyl sites named a, b, and c, respectively. Energy-selected and timeresolved fluorescence decay measurements shown in Figure 11 further confirm that uranyl occupies different sites in C1. At 4 K, after site a is excited, sites b and c with lower energies get equally populated and emit with quite different decay times of 0.12 and 1.96 ms, respectively. The emission from site c, which has the lowest energy, exhibits a rising component corresponding to the luminescence decay of site b. The rising time of site c luminescence is approximately equal to the decay time of site b luminescence. Site a absorbs more strongly but relaxes nonradiatively via energy transfer to the uranyl sites with lower energies. These results clearly indicate cascade energy transfer from site a to site b and site c, and from site b to site c. The rate of energy transfer from site a to site b and site c is much shorter than that from site b to site c. As shown in Figure 1, the distance between U1 and U2 is approximately two times of the distances between U1 and U3, and U2 and U3. Because the rate of energy transfer depends on the distance between donor and acceptor, the crystallographic structure and site-resolved luminescence decay dynamics together suggest an assignment of U3 to site a, and U1, U2 to site b, site c. It is noticed that each of the uranyl sites has a doublet structure in the lowest energy band. With energies varying 860

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V. SIMULATION OF ABSORPTION AND LUMINESCENCE SPECTRA

similar structures which are similar also to the previously studied tetrachloride crystal of Cs2UO2Cl4.2,19 In comparing the absorption and emission spectra shown in Figures 5
8, there is no evidence of a Stark shift of the electronic transitions between the ground state and the low-lying excited states. A section of high resolution absorption and luminescence spectra for C3 is plotted in Figure 10. The well-overlapped ZPLs at 19 991 and 19 996 cm
1 suggest that the resonant electronic transition is more like a 5f
5f transition rather than LMCT because there is no observable Stark shift arising from holerelaxation as expected in LMCT. Our results thus support the result obtained from ab initio calculations made by Pierloot and van Besien that the low-lying excited states are dominated by the 5f orbitals, and the ground state 3σ has negligible contribution from the ligand electrons Cl(3s,3p) in the equatorial plane.21 As predicated by Matsika and Pitzer,19 the LMCT from the Cl(3s,3p) orbitals to the uranyl center in uranyl tetrachloride may occur at a much higher energy level at approximately 33 000 cm
1. 2. Vibronic Coupling. As far as an isolated uranyl ion is concerned, the structure of vibration modes is simple. It includes only three modes, namely the symmetric and asymmetric stretching modes (ν1 and ν2) and the bending mode (ν3) of the OdUdO axial structure. In the ground state, the typical values of vibration frequency determined from luminescence or Raman spectra are typically about 830 cm
1 for the symmetric stretching mode, 920 cm
1 for the asymmetric stretching mode, and 250 cm
1 for the bending mode. Because of the nonbonding 5f characteristics, the U
O bond length is expected to increase in the excited state observed in absorption (excitation) spectra. As a result, the frequencies of the stretching modes should become lower than that in the ground state. According to Franck
Condon (FC) selection rules in vibronic transitions,29 only the symmetric stretching mode is allowed in coupling to electric dipole transitions in the uranyl ion.34,36 Therefore, as a notable characteristic of uranyl spectra, including absorption and emission, vibronic bands progress harmonically up to six orders in the symmetric stretching modes. Known as false origins, the non-FC modes ν2 and ν3 are coupled along with the FC mode and progress in the same frequency as ν1. Coupling to ligand vibration modes adds complexity to the vibronic features in uranyl spectra. In tetrachloro-uranyl compounds, an isolated cluster of uranyl tetrachloride [UO2Cl4]2‑ is relatively simple. With four Cl
ions in the equatorial plane, [UO 2 Cl4 ]2‑ forms an octahedron with D 4h symmetry. The vibration modes in such a structure has been studied.2 Including the three intrinsic OdUdO modes of the uranyl ion, there are 11 orthogonal vibration modes in a uranyl tetrachloride of octahedral structure. The ligand modes have frequencies separated into two groups, five U
Cl bending modes with frequencies centered around 120 cm
1, and three U
Cl stretching modes with frequencies close to 250 cm
1 coincident with the U
O bending mode. Our experimental results indicate that not all these modes are coupled to the ZPLs in the tetrachloro-uranyl compounds. It is also shown that vibronic transitions associated with these ligand modes appear only through coupling to the progressive OdUdO symmetric stretching mode. In addition, lattice modes with energies less than 100 cm
1 are also observed in the spectra. These lattice modes are sensitive to ligand structure. The organic motifs for linking the tetrachlorouranyl anions influence the vibration modes and the electronic states in the studied systems through variation in the symmetry and strength of the crystal field.

1. A Modified Model of Huang and Rhys Theory for Vibronic Transitions. The theory developed originally by Huang

and Rhys for vibronic transitions of F-centers in solids is restricted to one vibration mode and an invariant electric dipole moment that induces vibronic transitions in a crystalline lattice.35,41 In many cases, this theory can be applied also to interpretation of vibronic transitions in crystals with multiple vibration modes if the vibronic coupling is not too strong so that the harmonic approximation is still valid.32 For uranyl in dielectric crystals, such conditions are met because the local vibration modes are orthogonal and the Franck
Condon selection rule allows only the OdUdO symmetric stretching mode to couple to the electronic transitions. In an optical spectrum, lines include both electronic transitions between two electronic states (ZPL) and vibronic transitions. If these transitions involve only one vibration mode with energy pv, the overall spectral profile is determined primarily by the ZPL energy Ezp, vibration energy pv and the Huang
Rhys parameter S, and can be expressed as32,33
 ∞ n þ 1 N=2 IðEÞ ¼ I0 exp½
ð2n þ 1ÞS n N ¼0
 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi EZP ( Npv 5=2 - 3=2  IN ð2S nðn þ 1ÞÞgðEÞ EZP

∑

ð1Þ where n¼

1 expðpv=kTÞ
1

is the phonon occupation number at temperature T, and " # 1 ðEZP ( Npv
EÞ2 gðEÞ ¼ pffiffiffiffiffiffiffiffiffiffi exp
2σ 2 2πσ2

ð2Þ

ð3Þ

is a Gaussian line shape function. I0 is the intensity of the ZPL which should depend on the cross section of the ZPL transition with energy EZP. σ is the line width including a temperature independent inhomogeneous contribution due to defects and structure disordering, and phonon-induced homogeneous broadening that depends on temperature. IN(2S(n(n + 1))1/2) is the Nth order modified Bessel function of the first kind.41 Taking into account the frequency correction to the intensity of the absorption or emission spectrum, “+” and “
”in eq 1 are for absorption (or excitation) and emission, respectively. At low temperature or for high energy modes when pv . kT, n , 1. Equation 1 thus can be approximately modified to
 SN EZP ( Npv 5=2 - 3=2 gðEÞ IðEÞ ¼ I0 exp½
S EZP N N!

∑

ð4Þ For uranyl in crystals, the progressing energy pv is about 850 cm
1 in emission spectra and 720 cm
1 in absorption spectra. Therefore, the approximation of eq 4 is valid even at room temperature for describing the harmonic progression in the energies of the symmetric and asymmetric stretching modes. Consistent with Franck
Condon selection rules, the observed luminescence and absorption spectra all progress with the same frequency of the OdUdO symmetric stretching mode ν1 . 861

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Table 1. Energies of the Electronic States, Two Uranyl Stretching Modes and Huang
Rhys Parameters for Uranyl in the Tetrachloride Crystals C2 and C3 C3 state

leading Λ
S terms


1

energy (cm )

Σ

G

C2
1

ν1/ν2 (cm )

S


1

energy (cm )

ν1/ν2 (cm
1)

S

0

831/908

0.9

0

846/932

0.8

Δ1

19 991

709/723

1.2

19 962

725/733.5

1.2

E2 E3

Δ1 3 Δ2, 3Φ2

19 997 20 327

709/723 700/714

1.2 1.2

19 965 20 285

725/733.5 716/724.5

1.2 1.4

E4

3

Δ2, 3Φ2

21 466

692/706

1.2

21 166

708/716.5

1.4

Δ3

21 900

705/719

1.2

21 916

721/729.5

1.4

Δ3

22 095

705/719

1.2

22 297

725/733.5

1.4

Φ2, 3Δ2,

22 311

705/719

1.2

22 465

721/729.5

1.4

Φ2, 3Δ2,

22 665

701/715

1.2

22 635

717/725.5

1.4

3

E1

3

E5

3

E6

3

E7

3

E8

3

Other modes including the asymmetric stretching mode ν2 and uranyl bending mode ν3 appear in the spectra, and progress in ν1. This characteristic behavior of uranyl indicates that the non Franck
Condon vibronic transitions progress through coupling to ν1. These modes are usually called the false origins of the progressing vibronic transitions arising from the symmetric stretching mode.6,34,42 Therefore, the multimode vibronic spectrum can be constructed as a superposition of the lines due to the symmetric stretching mode and progression lines arising from the true origin at EZPk, and false origins at EZPk ( pvjk: 2 !
ðEZPk ( Npv1k
EÞ2 6 6exp 2σ21k SNk 6 pffiffiffiffiffiffiffiffiffiffiffi ffi Ik ðEÞ ¼ I0k expð
Sk Þ ∑ 6 6 2πσ21k N N!4
ðEZPk ( ðNpv1k þ pvjk Þ
EÞ2 exp 2σ 2jk qffiffiffiffiffiffiffiffiffiffiffi cj þ j6¼ 1 2πσ 2jk

∑




EZPk ( ðNpv1k Þ  EZPk

5=2 - 3=2

Table 2. Electronic Energies and Huang
Rhys Parameters for Uranyl in Tetrachloride Crystal C1 at Different Sites energy (cm
1) state

leading Λ
S terms

S

site c

site b

site a

Σ Δ1

0.9 1.1

0 20 049

0 20 080

0 20 125

G E1

3

Δ1

1.1

20 057

20 084

20 131

Δ2, 3Φ2

1.1

20 362

20 380

20 451

Δ2, 3Φ2

1.2

20 974

21 015

21 118

3

E2 E3

3

E4

3

E5

3

Δ3

1.2

21 912

21 996

22 085

E6

3

Δ3

1.2

22 467

22 615

22 805

Because the progression energy Npv1 span is much larger than the gaps between the low lying excited states with energy levels at EZPk, spectral overlap is significant and must be considered in analysis of an absorption spectrum. At room temperature, emission originates from the lowest two excited states, which are quasi-degenerate with energies separated on the order or less than 10 cm
1. Instead of eq 5, a summation over k for multiple excited states with zero-phonon energies of EZPk is required in order to properly simulate a uranyl absorption spectrum. 2. Comparison with Experiments. Equation 5 has been used for simulating the luminescence and absorption spectra of C2 and C3, respectively. As shown in Figures 4
7, the calculated spectra agree quite well with the experimental spectra, thus confirming that the theoretical model we developed is effective for modeling spectra of uranyl compounds. The agreement was achieved through adjusting of the parameters expressed in eq 5, which include the frequencies of various vibration modes, Huang
Rhys parameter, line width and intensity. The values of the parameters resulting from the simulation are listed in Tables 1
3. The spectroscopic properties of C2 and C3 are very similar. Relatively small changes in both electronic energy levels and vibration frequencies are resolved from the simulation. Such a similarity indicates that the [UO2Cl4]2‑ cluster is quite isolated in the crystal lattice. Different matrices for linking the clusters impose only modest changes in electronic and vibronic interactions. Whereas the frequencies of the symmetric and asymmetric stretching modes for the uranyl center are more significantly dependent on the electronic states, the frequencies of other modes and the Huang
Rhys parameter are less sensitive to the excited states.

!3

7 7 7 7 5 ð5Þ

where k is an index for the kth excited state and I0k is an intensity constant proportional to the electronic cross section between the ground state and excited state. In eq 5, we assume that the vibration frequency of a specific mode depends on the electronic state. Although this assumption is inconsistent with the conditions in which eq 1 was obtained, a small change in frequency should be tolerated within this theoretical framework.41 For each ZPL originating from state k, there are associated vibronic lines arising from various local vibration modes. In eq 5, these include the OdUdO symmetric stretch mode ν1k, the asymmetric mode ν2k, the bending mode ν3k and other local modes involving the equatorial ligands. Notably, in previous assignments of absorption spectra for uranyl in similar tetrachloride compounds,2 frequency mixing of multiple modes was considered. Such type of multimode mixing is not considered here because, as we will show in the following, other than coupling with ν1 no other types of mode mixing are apparent in the spectra we observed in the present work. 862

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For uranyl in the ground state (ν1 = 830 cm
1), RU
O = 178.1 pm in comparison with the values of 175.0 to 177.4 pm obtained from the XRD listed in Table S6 (Supporting Information). Assuming this relation also applies to the excited state in which ν1 reduces to 709 cm
1, the bond length of uranyl in the first excited state increases to RU
O = 191.4 pm, an expansion of 13.3 pm. On the other hand, based on the Huang
Rhys model, the variation of equilibrium position of the uranyl center is expected to change according to29,44 rffiffiffiffiffiffiffiffi 2pS ð7Þ ΔR ¼ mν

Table 3. Comparison of the Vibration Energies (cm
1) of Uranyl in the Tetrachloride Crystals for the Ground State (G) and the First Excited State (E1) C3 mode

structure

G

C2 E1

G

C1 E1

G

E1

ν1

O
U
O sym str

831

709

846

725

840

714

ν2

O
U
O asym str

908

723

932

734

927

725

ν3

O
U
O bend

258

247

252

238

250

237

ν4

U
Cl sym str

269

278

269

275

278

255

ν5 ν6/ν11

U
Cl str U
Cl str/rock

239

211 173

125

210 131

105

215 190

ν7

U
Cl bend

130

113

ν8

U
Cl bend

119

90

ν9

U
Cl bend

88

78

νL

lattice

43

52

110 96 35

93

where m is the effective mass, approximately the mass of two oxygens. When ν = 832 cm
1 from the fluorescence spectrum is substituted in eq 7, a change of ΔR = 13.8 pm is obtained, agreeing very well with the empirical estimation. At liquid helium temperature, line broadening induced by thermal phonons is eliminated. The sharp ZPLs with a line width of approximately 1.0 cm
1 indicate that the crystals have a highly crystallized structure with little disordering and defects. As we pointed out above, the sharp ZPLs also suggest that the electronic states involved in the transitions are highly localized—like 5f
5f intraconfiguration excitation rather than ligand-to-metal charge transfer transitions.21,23 In simulation of the absorption spectra, changes of line width from 1 cm
1 (partially due to instrument resolution) for the first two ZPLs to up 10 cm
1 for the ZPLs and vibronic lines at higher energies (above 26 000 cm
1) were made. In the higher energy region, increased overlapping of the progressive vibronic lines leads to apparent line broadening. In addition, as indicated by a larger value of the S parameter, stronger vibronic coupling is the primary factor in line broadening. Stronger vibronic coupling could lead to nonharmonic behavior. As a result, the vibronic transitions do not progress at the same frequency.

142 94

105

81

78

38

52

There is a common trend in the variation of the Huang
Rhys parameter. The value of the Huang
Rhys parameter is less than 1 for fitting the luminescence spectra and increases to 1.2 for the absorption spectra. They are consistent with the relative intensities of the vibronic harmonics. In the absorption spectra, the ZPLs are always weaker than the first harmonic band. Because of the overlapped vibronic transitions to multiple electronic states, the absorption spectrum is much more complicated than the emission spectrum. Except for the line of the lowest energy, unambiguous identification of the ZPLs is difficult. Simulation is a key for identification of the electronic energy levels as marked by the vertical arrows in Figure 4 and Figure 6. Along with the three intrinsic modes of the uranyl center, the stretching and bending modes for U
Cl structures are identified. In addition, a low-frequency band from 40 to 50 cm
1 also appears in the spectra. We attribute this low-frequency band to a lattice mode that is active to optical transitions. The model of Huang
Rhys theory we used is based on the assumption that, under optical excitation, the equilibrium position changes, but the vibration frequency is invariant. This is not true in uranyl compounds. From our experimental results, changes in the frequencies of vibration modes are observed and listed in Table 1 and Table 3. The largest changes are for the U
O symmetric and asymmetric stretching modes. Because of the U
O bond expansion in the excited states, the frequencies of the stretching modes are reduced. In both crystals, the value of ν1 is reduced from about 830 cm
1 to 710 cm
1, whereas the changes of frequencies of the vibration modes involving U
Cl coupling are much less significant. These changes are clearly understood as a result of the bond length expansion that depends on the electronic states. Because the frequency changes are not significant, application of the Huang
Rhys model expressed in eq 1 and eq 5 is still valid here for the uranyl compounds. A further modification of the theoretical model to allow changes in both equilibrium position and vibration frequency would provide a more accurate explanation. In conventional approaches, lattice expansion and frequency changes are correlated in vibronic transitions. The relationship between the OdUdO bond length and the frequency of its symmetric stretching mode was previously established empirically and expressed as4,43 RU
O ðpmÞ ¼ 10650½ν1 ðcm
1 Þ
2=3 þ 57:5

VI. CONCLUSIONS Development of an analytical model of uranyl vibronic interaction is much needed for establishing a correlation between spectroscopic properties and chemical coordination of uranyl in complexes and compounds. We have demonstrated that a modified model of the Huang
Rhys theory of ion-phonon interactions in solids can be applied to analysis and simulation of electronic and vibronic transitions of uranyl in crystals. In such a model simulation, important information such as the excited state energy levels, the frequencies of local vibration modes and the dynamics of ion-lattice coupling in terms of the Huang
Rhys parameter and the line width can be obtained. To our knowledge, this is the first time that low temperature absorption spectra of a uranyl compound have been simulated with a theoretical model. It is shown that for uranyl tetrachloride in an organic matrix, the electronic transitions between the ground state and the low lying excited states behave very much like intra 5f-configuration transitions rather than ligand-to-metal charge transfer transitions. The vibronic coupling is primarily limited within the uranyl
tetrachloride cluster. We have found that for uranyl in the tetrachloride crystals, the progression of vibronic transitions occurs only on the OdUdO symmetric stretching mode ν1. Other local modes couple to ν1 individually, but no mixing of more than two modes was identified. These observations indicate that the electronic interaction of uranyl is quite localized and the influence of the ligand (lattice) environment is relatively weak.

ð6Þ 863

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The Journal of Physical Chemistry A

ARTICLE

This explains why the spectroscopic properties of the three uranyl compounds are similar. The organic components in these materials are essential for arranging the crystalline structure, but have only minor influence on the spectroscopic behavior of the uranyl ion. While the present work provides insight into a fundamental understanding of the intriguing nature of uranyl electronic properties, it is also demonstrated that empirical simulation of the absorption spectra allows accurate identification of the electronic transitions along with the overlap features of vibronic transitions. In particular, such a simulation is able to resolve the coupled vibronic transitions with high resolution and accuracy, and therefore, to provide more detailed information on electronic interactions and local structure rather than just a “fingerprint” of uranyl speciation and structure characterization as previously reported in the field of uranyl chemistry.

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’ ASSOCIATED CONTENT

bS Supporting Information. Low temperature crystallographic data, atomic coordinates and equivalent isotropic displacement parameters, and selected bond lengths and angles. This material is available free of charge via the Internet at http://pubs.acs.org. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT Work performed at Argonne National Laboratory was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, under Contract DE-AC02-06CH11357. C.L.C. and N.P.D. are grateful to the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, Heavy Elements Program, U.S. Department of Energy, under Grant DE-FG02-05ER15736 at GWU. Additional support from the Materials Science of Actinides, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award Number DE-SC0001089 is noted. ’ REFERENCES (1) Jørgensen, C. K.; Reisfeld, R. In Uranyl Photophyics, Clarke, M. J. e. a., Ed.; Springer-Verlag: Berlin, 1982; Vol. 50, pp 121
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