Charge-Transfer Excitations in Uranyl Tetrachloride ([UO2Cl4]2

Article pubs.acs.org/JPCA

Charge-Transfer Excitations in Uranyl Tetrachloride ([UO2Cl4]2−): How Reliable are Electronic Spectra from Relativistic Time-Dependent Density Functional Theory? Paweł Tecmer,† Radovan Bast,‡,§ Kenneth Ruud,‡ and Lucas Visscher*,† †

Amsterdam Center for Multiscale Modeling, Department of Chemistry and Pharmaceutical Sciences, VU University Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands ‡ Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø, N-9037 Tromsø, Norway § Laboratoire de Chimie et Physique Quantique, CNRS/Université de Toulouse 3 (Paul Sabatier), 118 route de Narbonne, 31062 Toulouse, France ABSTRACT: Four-component relativistic time-dependent density functional theory (TD-DFT) is used to study charge-transfer (CT) excitation energies of the uranyl molecule as well as the uranyl tetrachloride complex. Adiabatic excitation energies and vibrational frequencies of the excited states are calculated for the lower energy range of the spectrum. The results for TD-DFT with the CAM-B3LYP exchange−correlation functional for the [UO2Cl4]2− system are in good agreement with the experimentally observed spectrum of this species and agree also rather well with other theoretical data. Use of the global hybrid B3LYP gives qualitatively correct results, while use of the BLYP functional yields results that are qualitatively wrong due to the too low CT states calculated with this functional. The applicability of the overlap diagnostic of Peach et al. (J. Chem. Phys. 2008, 128, 044118) to identify such CT excitations is investigated for a wide range of vertical transitions using results obtained with three different approximate exchange−correlation functionals: BLYP, B3LYP, and CAM-B3LYP.

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a square, pentagonal, or hexagonal bipyramidal structure.23 In this process, the valence orbitals of the uranyl compound change their energetic ordering and mix to varying extent with the ligand orbitals. While some of this reordering can be explained by simple ligand-field arguments, it is of interest to apply higher level methods that include the ligands explicitly. One interesting application is to use rational design of complexing ligands to tune the properties of uraniumcontaining complexes for use in catalysis5,6,24 or to improve the process of nuclear waste separation and immobilization.4,25 Most important in this respect is the interaction of the uranyl molecule with its nearest ligands in the equatorial plane, perpendicular to the axial UO2 unit.7,22,23,26,27 Typically, these equatorial ligands are bonded to the uranium atom in a much weaker fashion than the axial oxygen atoms, and their influence on the uranyl unit can be considered as a perturbation that affects the uranium−oxo bonds but does not fundamentally change the bonds intrinsic properties.8,17,22,28,29 An indirect measure for the effects of the ligands on the two internal uranyl bonds is established by studying the changes in the U−O

INTRODUCTION Experimental and theoretical chemists show continued interest in uranium chemistry, which is not only due to its importance in nuclear energy production and nuclear waste separation1−4 but also because of the potential use of uranium in catalysis.5,6 The perhaps most studied uranium compound is the uranyl cation [UO2]2+, which is found as a stable unit in many crystal environments and also in solution.7 Because the bare cation is difficult to assess by experimental techniques, much attention has been devoted to calculations in order to determine its properties. Nowadays, high-level theoretical predictions for the bond length and electronic spectrum are available.8,9 In order to provide further insight and connect to experimental work, equally accurate theoretical investigations of ligated complexes are, however, desirable. This is more difficult because ligation increases the size of the system to be studied and involves electron donation into the unoccupied f-orbitals that are strongly split by spin−orbit coupling (SOC). Nevertheless, the chemical properties of uranyl are covered in a number of papers addressing its electronic structure, ionization potentials, bonding to various ligands, and electronic spectra.8−21 The uranyl molecule is found as a small building block in larger uranium-containing complexes,22 in which the uranium metal center is coordinated by ligands in the equatorial plane to © 2012 American Chemical Society

Received: February 3, 2012 Revised: June 7, 2012 Published: June 11, 2012 7397

dx.doi.org/10.1021/jp3011266 | J. Phys. Chem. A 2012, 116, 7397−7404

The Journal of Physical Chemistry A

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stretching vibrations.30−32 More direct is the study of the effect of ligation on the electronic spectrum, considering the lowest excitations that comprise transitions internal to the uranyl unit, in particular excitations from the lowest bonding orbitals (σg, πg, πu, σu) to the nonbonding δu and ϕu orbitals.22 Theoretical modeling of ligation requires quantum-chemical methods that provide the necessary accuracy (better than about 2000 cm−1 or 0.25 eV) at an acceptable computational cost. Very accurate results can be obtained with highly correlated wave function methods (e.g., coupled cluster33−35 or complete active space second-order perturbation theory (CASPT2)36,37), but due to a steep computational scaling with the size of the active space, application of these methods is often limited to model complexes.9,12,20,38,39 Larger complexes with organic ligands are typically treated by density functional theory (DFT),40,41 which has a much lower computational cost.42 In the DFT approach, the electronic spectrum is usually obtained via its time-dependent generalization, time-dependent density functional theory (TD-DFT).43−45 While being a standard method for organic molecules, TD-DFT is not yet much tested for actinide complexes for which the correct ordering of energetically close-lying excitations to the different metal f-type orbitals is crucial. Due to the presence of ligand-to-metal charge-transfer (CT) states, the well-known problem of TDDFT in describing CT- and Rydberg (R)-type electronic transitions46,47 should be considered. Since this problem arises due to the near-sightedness of the local or generalized gradient exchange-correlation (xc) kernel, significant improvements can be achieved by including a fraction of exact exchange in the kernel. The family of range-separated hybrid xc functionals, of which CAM-B3LYP48 is one of the most widely used examples, looks particularly promising in this respect.49,50 In a recent study20 we found surprisingly accurate results when we benchmarked excitation energies obtained with this functional against coupled-cluster data. For a more detailed discussion of the performance of different xc functionals on small uranium species and the quality of calculated electronic transitions, we refer the reader to ref 20. In the current paper we will analyze in more detail why longrange-separated hybrid xc functionals perform so well for actinyl molecules. It is known that they dramatically improve upon description of Rydberg and charge-transfer transitions,51−55 but it is somewhat surprising that they are also able to give an improvement for excitations in small triatomic actinide cations. The benefit of including exact exchange for charge-transfer excitations is well understood: Dreuw et al.47 pointed out that conventional generalized-gradient approximation (GGA) functionals produce large errors when the occupied and virtual orbitals involved in the electronic transition are spatially well separated because the excitation energies then reduce to just the orbital energy differences whereas they should yield a difference between an ionization potential (for the region from which the electron leaves) and an electron affinity (for the region it is transferred to). Gritsenko and Baerends56 analyzed this problem further and proposed to interpolate between the correct asymptotic expressions for localized and the CT excitations using as a criterium the distance between the occupied and the virtual charge densities involved in the transition. In later work, Neugebauer, Gritsenko, and Baerends57 implemented this correction in a computationally simple protocol and studied the performance of the resulting functional in a number of model systems. A different approach was taken by Peach et al.:58 rather than

defining a corrected functional, they used the distance between occupied and virtual orbital densities to quantitatively correlate the character of the electronic excitation with the expected error in a GGA calculation. This yields a simple diagnostic test in which the spatial overlap in a given electronic excitation is measured by the Λ value

Λ=

∑i , a κia2Oia ∑i , a κia2

(1)

where Oia are moduli of the two orbitals (occupied and virtual), Oia = ⟨|Ψa|||Ψi|⟩, and κia = Xia + Yia are elements of the solution vectors of the TD-DFT generalized eigenvalue problem.44 On the basis of the Λ value, three different categories of electronic excitations were defined: Rydberg (roughly 0.08 ≤ Λ ≤ 0.27), charge-transfer (0.06 ≤ Λ ≤ 0.72), and local (0.45 ≤ Λ ≤ 0.89) excitations.58 The relatively wide range of Λ for the CT excitations is associated with the fact that these types of transitions can possess both short- or long-range character with the short-range excitations sometimes being difficult to distinguish from local (L) excitations.59,60 In the present work, we study the applicability of this diagnostic test to identify possible problems in the TD-DFT description of actinide complexes. As a model compound for this study we chose the uranyl tetrachloride [UO2Cl4]2− ion, which is convenient for the following reasons: (a) it exhibits a well-defined closed-shell ground state, (b) its D4h point group symmetry simplifies the study of the equatorial ligand effects, (c) an experimental electronic spectrum of the Cs2UO2Cl4 crystal is available as a reference, and (d) it is large enough to enable charge-transfer excitations yet small enough to allow for detailed analysis. We will first briefly revisit the uranyl molecule before presenting our theoretical investigation of the electronic spectrum of the uranyl tetrachloride molecule. Due to the importance of SOC we apply a relativistic SOC TD-DFT approach. Our aim is to assign the character of each transition with respect to its origin (i.e., local, charge-transfer, or Rydberg types), compare this to the calculated value of the Λ parameter, and study the excitation energy using xc functionals that are based on the same functional (BLYP) but differ in the inclusion of exact exchange (BLYP,61,62 none; B3LYP,63,64 global hybrid with 19% exact exchange; CAM-B3LYP,48 local hybrid with 19% of exact exchange at short range and 65% at long range).

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COMPUTATIONAL DETAILS Geometry and Basis Sets. The structure of uranyl tetrachloride as it is found in the cesium chloride host65 shows a distortion from D4h symmetry. For our purpose it is better to consider an idealized structure because the differences to the true structure are not so important8,17 and use of a higher symmetry allows for both a drastic reduction of computational expense and simplification of analysis of the data. Assignments are therefore given according to the full D∞h symmetry of uranyl and for the idealized D4h structure of uranyl tetrachloride, respectively. All calculations were performed in the D2h point group symmetry, which is the highest possible symmetry for TD-DFT calculations in the DIRAC10 program.66 The ground-state energy minimum was taken from a calculation with the CAM-B3LYP xc functional and the triple-ζ basis set of Dyall67 for the uranium atom and the aug-cc-pVTZ basis sets of Dunning68 for the oxygen and 7398



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chlorine atoms. At this geometry (i.e., Re (U−O) = 1.764 Å and Re (U−Cl) = 2.712 Å), vertical excitation energies were calculated. Geometries of the excited states were obtained by varying both U−O bond lengths simultaneously (symmetric stretch) in steps of 0.01 Å in a range of 1.70−1.90 Å, while the U−Cl bond lengths were kept frozen at the ground-state equilibrium distance of 2.712 Å.65,69 The points on the resulting potential energy curve were used for a subsequent second-order polynomial fit to obtain minima and adiabatic excitation energies. Five points closest to the minima were used to numerically evaluate vibrational frequencies using the five-point stencil formula. Relativity. The all-electron TD-DFT calculations were performed with a development version of the DIRAC10 program.66 The four-component Dirac−Coulomb Hamiltonian was used, which means that the relativistic corrections from the two-electron Darwin as well as Breit terms were neglected. Moreover, the (SS|SS) integrals that originate from the small component of the four-component Dirac spinor were replaced by a simple point-charge model.70 Note that we used nonrelativistic xc approximations, as it has been shown that such an approximation works well in combination with the four-component relativistic densities.18 TD-DFT. Excitation energies were obtained with a noncollinear approach of TD-DFT, as implemented in the DIRAC10 program.18 The adiabatic approximation with a full derivative of the functional was used in the xc kernel. Tight convergence criteria of 10−8 au were used for the TD-DFT solver to obtain converged excitation energies. For every irreducible representation in the D2h point group, the 15 lowest roots were taken into account in the TD-DFT solver, Table 1. The overlap diagnostic

D4h

σ+g σ+u

a1g a1u eg eu b1g⊕b2g b1u⊕b2u eg eu a1g⊕a2g a1u⊕a2u

πg πu δg δu ϕg ϕu γg γu

RESULTS AND DISCUSSION

Vertical Excitation Energies. For a comprehensive analysis of the spectrum of uranyl and uranyl tetrachloride we refer to the review papers by Denning.22,71,72 At low energy, the spectrum is characterized by transitions from the σu highest occupied molecular orbital (HOMO) to the ϕu and δu uranium orbitals. These transitions are split by the crystal field and spin−orbit interactions and could be considered to have some CT character due to the fact that the HOMO is a bonding combination of uranium 5f and 6p and oxygen 2p orbitals, while the ϕu and δu orbitals are nonbonding uranium 5f orbitals. In the CASSCF calculations by Pierloot and van Besien,8 this orbital contains only 30−40% oxygen character, making the transition very local to the uranium. Mulliken analysis of this orbital with the different LYP-based functionals points to an even stronger localization with the oxygen character amounting to only 26% and again a negligibly small contribution from the chlorides in the uranyl chloride calculation. It is therefore convenient to first discuss the transitions in the bare uranyl before turning to the calculations that include the chloride ligands. From Table 2, we immediately note the qualitative differences between the three functionals that we employ. As expected, the B3LYP functional yields too low excitation energies when compared to CAM-B3LYP and underestimates transition energies by up to 2000 cm−1. Even larger deviations up to 5000 cm−1 from the reference CAMB3LYP excitation energies are observed for the BLYP xc functional. Those errors can be correlated with the overlap diagnostic values that are also given in Table 2: for the transitions to the ϕ(5/2)u orbital, errors are 5000 and 2000 cm−1 with the diagnostics Λ = 0.5 and 0.49 for the BLYP and B3LYP, respectively. The errors in transitions to the other spin−orbit component, the ϕ(7/2)u orbital, are around 4000 and 1500 cm−1 for BLYP and B3LYP, respectively, at the same value of the diagnostic of Λ = 0.5. Smaller errors of about 3000 cm−1 are found in the excitation energies that correspond to transitions from the σu to the δu orbitals, 1Σ+g → 3Δg and 1Σ+g → 1Δg, and again correlate reasonably well with the Λ values. An exception is the fourth Eg state in Table 2, which exhibits a difference of about 4500 cm−1. For all transitions the values are above the 0.45, which was defined as the lower threshold for local excitations by Peach et al.58 The still rather large errors that are found and are partly repaired by the global hybrid and to a larger extent by the more refined long-range separated hybrid are probably best interpreted as arising from the very different nature of the exchange interactions in the partly bonding σ(1/2)u orbital and the pure f orbitals to which the electron is excited. Because all these transitions can still be considered local and due to the high symmetry (cf. Table 1), their characterization is rather straightforward. This situation changes when we look at uranyl tetrachloride. It is now much more difficult to match the transitions that are computed with the different functionals because of the admixture of artificially low-lying states corresponding to CT from the chloride ligands. This is also evident from the Λ values that drop to 0.33−0.51 and now show much more scatter upon changing the functional. In order to rationalize these differences, we will also compare our results to the other theoretical results that are available in the literature. In Table 3, we compare the results obtained with the CAM-B3LYP xc functional to a semiempirical crystal field model (CFT),73

Table 1. Subduction of the Relevant Irreducible Representations of the D∞h Point Group Toward Those of the D4h Subgroup77 D∞h

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method of Peach et al.58 was implemented into a development version of the DIRAC10 code and used in TD-DFT calculations with three different approximate xc functionals: BLYP,61,62 B3LYP,63,64 and CAM-B3LYP.48 Since the detailed discussion by Denning in his 1992 review paper,71 in which he concluded that all observed lower energy states (below 29 000 cm−1) are of gerade symmetry, most studies have been limited to gerade states. This is also sufficient for our purpose, but we note that a number of low-energy ungerade states show up in this part of the spectrum when the BLYP functional is used. We have not analyzed these states in detail because the too low energy is an artifact of this functional. 7399



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Table 2. SOC Vertical Excitation Energies (in cm−1)a UO22+

UO2Cl42−

b

symmetry D4h (internal UO22+)

typec

BLYP

B3LYP

CAM-B3LYP

BLYP

B3LYP

CAM-B3LYP

Eg, σ(1/2)u → δ(3/2)u B1g, σ(1/2)u → ϕ(5/2)u B2g, σ(1/2)u → ϕ(5/2)u Eg, σ(1/2)u → ϕ(5/2)u B2g, σ(1/2)u → δ(3/2)u B1g, σ(1/2)u → δ(3/2)u Eg, σ(1/2)u → ϕ(7/2)u A2g, σ(1/2)u → ϕ(7/2)u A1g, σ(1/2)u → ϕ(7/2)u Eg, σ(1/2)u → δ(5/2)u B2g, σ(1/2)u → δ(5/2)u Eg, π(Cl)(3/2)u → ϕ(5/2)u B1g, σ(1/2)u → δ(5/2)u B2g, π(Cl)(3/2)u → ϕ(5/2)u B1g, π(Cl)(3/2)u → ϕ(5/2)u

L L L L L L L L L L L CT L CT CT

12 955(0.62) 7492(0.50) 7492(0.50) 8990(0.50) 14 711(0.61) 14 711(0.61) 17 053(0.50) 14 867(0.49) 14 867(0.49) 18 413(0.50) 23 068(0.52)

14 423(0.61) 10 699(0.49) 10 699(0.49) 12 132(0.49) 16 341(0.61) 16 341(0.61) 19 555(0.56) 17 774(0.49) 17 774(0.49) 21 149(0.52) 24 805(0.49)

15 709(0.61) 12 502(0.49) 12 502(0.49) 13 913(0.49) 17 673(0.60) 17 673(0.60) 21 044(0.56) 19 587(0.48) 19 587(0.48) 22 912(0.56) 26 803(0.55)

23 068(0.52)

24 805(0.49)

26 803(0.55)

17 236(0.50) 16 026(0.50) 16 471(0.50) 16 053(0.50) 17 911(0.51) 17 936(0.51) 22 056(0.49) 23 161(0.44) 23 187(0.45) 24 413(0.44) 23 964(0.50) 21 121(0.44) 24 271(0.45) 22 336(0.41) 22 311(0.43)

18 010(0.47) 18 179(0.44) 18 721(0.44) 19 672(0.44) 20 397(0.45) 20 440(0.45) 24 325(0.38) 25 701(0.35) 25 758(0.35) 27 754(0.35) 28 247(0.39) 29 101(0.37) 28 680(0.39) 28 992(0.38) 27 792(0.33)

19 235(0.44) 19 473(0.44) 20 037(0.44) 21 093(0.48) 21 800(0.46) 21 897(0.47) 25 700(0.47) 27 223(0.43) 27 271(0.43) 29 778(0.42) 30 588(0.46) 30 803(0.42) 30 956(0.42) 31 144(0.40) 32 628(0.33)

D4h characterization and assignment in terms of internal uranyl excitations; Λ parameter is given in parentheses (all transition energies are aligned with the CAM-B3LYP values for the uranyl tetrachloride molecule). bSymmetry correspondences are given in Table 1. cL and CT denote local and charge-transfer excitation energies, respectively. a

Table 3. SOC Vertical Excitation Energies (in cm−1)a TD-DFT symmetry D4h CF modelc a Eg a B2g a B1g b Eg b B1g b B2g c Eg a A2g a A1g c B1g d Eg c B2g

20 126 20 643 21 045 22 603 22 022 21 997 26 146 27 809 27 813 27 412 29 417 27 785

SAOPd

CAMB3LYP

20 954 20 884 21 335 22 108 22 420 22 570 26 882 27 678 27 682 27 666 28 364 28 561

19 235 20 037 19 473 21 093 21 897 21 800 25 700 27 223 27 271 30 956 29 778 30 588

When comparing our CAM-B3LYP results to these SOCCASPT28,28 values, we see that almost all low-energy CAMB3LYP excitations are about 2000−3000 cm−1 (exceptional is a B2g state with a smaller deviation of 1000 cm−1) lower in energy than the SOC-CASPT28 results. For the higher energy excitations, the agreement with the results of Ruipérez and Wahlgren28 is quite good. In comparison with the SAOP TDDFT data of Pierloot et al.,17 we see absolute differences in excitation energies of around 1000 cm−1 for most excitation energies except the a B1g, c B2g, and d Eg states, where the difference increases up to 2000 cm−1, and c B1g where difference increased up to 3000 cm−1. With CAM-B3LYP, the first true CT state appears well above 30 000 cm−1, in agreement with the calculation of Ruipérez and Wahlgren.28 If we now return to Table 2, we note that the pure GGA functional BLYP puts the chloride-to-uranyl CT states in between two groups of local (L) excitations in the region from 21 000 to 22 000 cm−1. The σ(1/2)u → ϕ(5/2)u transitions remain relatively pure and are significantly shifted up by the Pauli repulsion from the equatorial chloride ligands. This repulsion is smaller for the δu orbitals, which makes the lowest excitation a σ(1/2)u → δ(3/2)u transition. For these transitions we see more mixing with CT states, which for some of them leads to large shifts relative to the CAM-B3LYP and other reference values. It is interesting that the third B2g transition at 23 964 cm−1 shows significant mixing with a CT state at 22 336 cm−1 while still having the relatively large Λ value of 0.50. For the other states in this group, the Λ value is lower than in uranyl, correctly signaling the increased admixture of CT character. Adding exact exchange via the global hybrid functional B3LYP shifts the CT states up to the region of the ϕ7/2u excitations and leads to an increased mixing between L and CT states. This is evident from the Λ value, which drops below 0.4 for a whole range of states with this functional. These values are the lowest ones observed in this study, although the differences with respect to reference values are not much larger than in uranyl. For this functional the Λ diagnostic therefore indicates a larger error than is actually found. Going to CAM-B3LYP, the higher amount of exact exchange in the limit pushes the CT

CASPT2 Ruipéreze Pierlootf 22 870 23 090 23 745 24 450 24 636 25 222 26 143 28 580 28 746 30 158 30 326 31 052

21 024 21 273 22 125 22 859 24 056 24 339 27 494 29 842 29 849 31 991 31 961 32 523

a

Comparison of different methods. In references, where the distortion from the idealized D4h point group symmetry was taken into account, we have averaged the excitation energies in the Eg symmetry. bAll c electronic transitions are local (L) to the UO2+ 2 ion. Reference 73. d e f Reference 17. Reference 28. Reference 8.

TD-DFT results obtained by Pierloot et al.17 with the SAOP74,75 model potential, and two sets of complete active space second-order perturbation theory (CASPT236,37) data8,28 with SOC included a posteriori. All of these methods deal with the [UO2Cl4]2− model system, which includes only the first shell of anions. Due to the different choices of active space, the two SOC-CASPT2 studies yield somewhat different spectra. While Pierloot and van Besien defined the active space for the uranyl tetrachloride molecules to be similar to the one that is optimal for a bare uranyl molecule, Ruipérez and Wahlgren28 decreased the number of nonbonding orbitals in the [UO2]2+ unit and added an extra 3p orbital from the chlorides to the active orbital space to allow for charge transfer from the ligands to the uranyl. In their studies, the first CT excitation from the chloride ligand to the uranium metal center was indeed calculated at 33 226 cm−1, followed by a manifold of other CT transitions at higher energy. 7400



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Figure 1. Error in the excitation energies made by BLYP and B3LYP xc functionals in comparison with the reference data (CAM-B3LYP).

Table 4. SOC Adiabatic Excitation Energies and Vibrational Frequenciesa CASPT2c

SOC-CId

symmetry D4h

Re (U−O) [Å]

Te [cm−1]

ωe [cm−1]

Re (U−O) [Å]

Te [cm−1]

x A1g a Eg a B2g a B1g b Eg b B1g b B2g c Eg a A2g a A1g c B1g c B2g

1.783 1.836 1.844 1.826 1.846 1.846 1.847 1.842 1.854 1.854

20 028 20 330 21 139 21 809 22 984 23 228 26 534 28 527 28 530

819 712 703 698 711 721 714 722 703 703

1.728 1.790 1.792 1.790 1.794 1.806 1.806 1.805 1.808 1.807 1.816 1.817

20 363 21 013 21 838 22 819 24 618 24 780 26 763 29 169 29 145 33 510 34 159

experimente

CAM-B3LYP ωe [cm−1]

Re (U−O) [Å]

Te [cm−1]

ωe [cm−1]

ωe [cm−1]

Te [cm−1]

968 885 879 878 874 902 900 904 896 890

1.764 1.802 1.807 1.806 1.808 1.806 1.806 1.802 1.810 1.809 1.814 1.813

18 792 19 451 18 890 20 480 21 231 21 333 25 234 26 533 26 585 28 952 30 192

819 728 733 736 738 736 739 738 741 742 724 709

20 096 20 406 21 316 22 051 22 406 22 750 26 222 27 720 27 757 29 277 29 546

832 715 710 696 711 717 711 725 705 705 680 734

a Comparison of different methods with experimental results. In references, where the distortion from the ideal D4h point group symmetry was taken into account, we averaged excitation energies in the Eg symmetry. bAll of the electronic transitions have local (L) UO22+ character. cReference 8. d Reference 16. eReferences 69 and 71.

states out of this area and restores the clear identification in terms of L and CT states. With this functional, all 12 (including the 4 2-fold degenerate Eg) states that may be formed out of the uranyl σu to ϕu and δu transitions remain relatively pure. We note that this observation could only be made by analyzing the excitations in detail (using the composition of the orbitals and the coefficient obtained in the TD-DFT calculations) and studying the trend when changing the xc functional. The Λ diagnostic is useful but condenses information into a single number that may be hard to interpret in the case of severe mixing between states, as occurs in the B3LYP calculation. The general performance of the overlap diagnostic test is also illustrated in Figure 1, where the differences in excitation energies between CAM-B3LYP and BLYP as well as CAMB3LYP and B3LYP as a function of the BLYP and B3LYP Λ values are plotted. The better performance of B3LYP over BLYP is indeed visible, and for BLYP a clear trend is easy to observe for the uranyl ion: smaller Λ values correspond to large discrepancy between BLYP and CAM-B3LYP. For the uranyl

tetrachloride we do observe a correlation but also outliers, as already noted above. Adiabatic Excitation Energies. The vertical excitation energies were sufficient for a qualitative comparison with the experimental values. A more precise comparison is possible as well, however, because the high resolution of the experimental spectrum allowed for identification of the band origins and determination of adiabatic excitation energies. To make such a comparison, we calculated the adiabatic excitation spectrum of uranyl tetrachloride with the CAM-B3LYP xc functional. These results are summarized in Table 4 and compared to the experimental data as well as to SOC-CASPT2 and SOC configuration interaction (SOC-CI)76 values. We note that our CAM-B3LYP and the reference SOC-CASPT28 calculations correspond to the idealized D4h structure, while the SOC-CI16 calculations allowed for a small distortion consistent with the Xray structure of UO2Cl4Cs265 and used an extended crystalline environment, i.e., including more than the first shell of anions. 7401



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Figure 2. Excited-state curves of UO2Cl42− along the symmetric U−O stretching mode.

SOC-CASPT2 and significantly outperform that of SOC-CI. The CAM-B3LYP vibrational spectra differs from experimental values by only 20 cm−1 in the lowest part of the spectrum, and this discrepancy increases up to 40 cm−1 in the higher lying states.

The CAM-B3LYP excited-state curves are plotted in Figure 2. This figure clearly shows the different nature of the states. The six lowest lying excitations up to b B2g that arise from the uranyl 3Φ and 1Φ states remain close in energy, indicating only a modest perturbation by the chlorides. The calculated bond lengths are 0.04 Å shorter than the SOC-CASPT2 values but agree well with the SOC-CI values of Matisika and Pitzer.16 The first excited-state curve (a Eg) crosses the second excited curve (a B1g) at ca. 1.84 Å. This crossing was also seen in a SOC-CASPT2 study (Figure 2 in ref8) at about 0.02 Å to the right of the minimum with the only difference being that the second excited state has a B2g character there. The CAMB3LYP incorrectly predicts the first B1g excited state below the first B2g state with respect to SOC-CASPT2, SOC-CI, and experimental data. All of the bands in this region of the spectrum represent pure internal uranyl transitions and are characteristic for uranyl compounds (excitations from the lowest occupied σ orbitals to the nonbonding fϕ and fδ orbitals of the uranium VI ion).8,9,17,20−22 The second part of the spectrum is separated from the first one by ca. 4000 cm−1, which agrees very well with experimental data.69 Apart from the c Eg state, these Δ states have a slightly longer U−O bond length of up to 1.814 Å (c B1g). The same trend is observed in the SOC-CASPT2 and SOC-CI studies (see Table 4), although the first one predicts somewhat longer and the latter one shorter bond lengths in general. The overall agreement between CAM-B3LYP and SOC-CI is very good in terms of U−O bond distances, but these values are 0.03−0.04 Å lower than the SOC-CASPT2 data that should have a more complete description of dynamical correlation. Both of the correlated methods give local excitation energies that are about 1500 cm−1 higher than the CAM-B3LYP values and give an excellent match with the experimental data. This indicates that CAM-B3LYP systematically underestimates the local transitions but is capable of predicting the correct ordering of the high-lying states. The good quality of the CAM-B3LYP functional is also confirmed by the vibrational frequencies listed in Table 4. The calculated numerical vibrational frequencies agrees well with

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CONCLUSIONS We investigated the local and charge-transfer states of the uranyl tetrachloride complex with three different xc functionals (BLYP, B3LYP, and CAM-B3LYP). In order to characterize the states, we implemented and applied the overlap diagnostic test of Peach et al.58 in a four-component relativistic framework to verify whether this tool can provide an adequate identification of the character of the states. Our studies indicate that GGA BLYP is not able to reproduce the electronic spectra of this complex. Already for excitations local to uranyl we observe qualitative differences with reference data and errors amount to more than 10 000 cm−1 when considering CT excitations from the ligands. These errors are alleviated by use of the global hybrid, B3LYP, but the ligand to metal CT states are still predicted quantitatively incorrect. B3LYP can be used for a qualitative estimate of the lower electronic transitions, but the more refined CAM-B3LYP functional is certainly preferable for a quantitative investigation of the electronic spectrum. The accuracy of four-component TD-DFT using the CAM-B3LYP functional approaches that of SOC-CASPT2 and SOC-CI. In our current implementation of the four-component TD-DFT method we can treat rather large systems (up to about 40 atoms or 300 electrons), and still larger systems are easily accessible using a two-component approach to treat relativity. More importantly, the TD-DFT approach using CAM-B3LYP also gives access to the region of the spectrum that is dominated by CT states, which are hard to treat with an active space method as the active space that is necessary would become prohibitively large. We found the overlap diagnostic method to be a useful tool in identifying CT states. More experience with its applications to actinides is necessary, however, because the presence of electronically rather different internal (inside the actinyl ion) 7402



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states restricts the range of values that is calculated to lower values than is common for lighter elements. Part of the error for these kinds of transitions is due to the rather different orbitals that are chemically active in the actinide, leading to large differences in exchange interactions, already for atomic transitions.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS P.T. and L.V. acknowledge financial support from The Netherlands Organization for Scientific Research (NWO) via the Vici program and support for computational resources from the Dutch National Computing Facilities (NCF). R.B. and K.R. kindly acknowledge support from the Norwegian Research Council through a Center of Excellence Grant (Grant No. 179568/V30).

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Charge-Transfer Excitations in Uranyl Tetrachloride ([UO2Cl4]2

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