Calculation of Dipole-Forbidden 5f Absorption Spectra of Uranium(V

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Letter

Calculation of Dipole-forbidden 5f Absorption Spectra of Uranium(V) Hexa-halide Complexes Yonaton N. Heit, Frédéric Gendron, and Jochen Autschbach J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b03441 • Publication Date (Web): 29 Jan 2018 Downloaded from http://pubs.acs.org on January 30, 2018

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Calculation of Dipole-forbidden 5f Absorption Spectra of Uranium(V) Hexa-halide Complexes

Journal: Manuscript ID Manuscript Type: Date Submitted by the Author: Complete List of Authors:

The Journal of Physical Chemistry Letters jz-2017-03441k.R1 Letter 24-Jan-2018 Heit, Yonaton; University at Buffalo - The State University of New York, Chemistry Gendron, Frédéric; University at Buffalo, Chemistry Autschbach, Jochen; State University of New York at Buffalo, Department of Chemistry

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Calculation of Dipole-Forbidden 5f Absorption Spectra of Uranium(V) Hexa-halide Complexes Yonaton N. Heit, Frédéric Gendron and Jochen Autschbach∗ Department of Chemistry University at Buffalo State University of New York Buffalo, NY 14260-3000, USA email: jochena@buffalo.edu January 24, 2018 Abstract: ‘Restricted’ active-space wave function calculations including spin-orbit coupling, in combination with Kohn-Sham density functional calculations of vibrational modes, were used to determine the vibronic and electronic absorption intensities of the near-infrared electric dipoleforbidden 5𝑓 –5𝑓 transitions of representative uranium(V) hexa-halide complex ions. The agreement with experimentally assigned vibronic and electronic transitions measured for powder or solution samples of salts of the complex ions is reasonable overall, and excellent for the experi′ mentally best-resolved 𝐸5∕2𝑢 → 𝐸5∕2𝑢 bands. The intensity of the vibronic transitions may be borrowed from ligand-to-metal charge-transfer excitations as well as 5𝑓 -to-6𝑑 metal-centered transi-tions. Magnetically allowed electronic transitions contribute to the two lower-frequency bands of the ligand-field spectrum.

Table of Contents Graphics

Keywords ab-initio theory, actinide complexes, relativistic effects, vibronic coupling, ligand-field transitions

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Within the highly active research of actinide compounds, the octahedral actinide (An) complexes AnX6𝑞–, X = halide, are among the most studied systems, experimentally and theoretically.1 The spectroscopic properties are governed by strong symmetry-based selection rules that may greatly simplify spectral assignments. Moreover, the ligand valence orbitals may interact with the 5𝑓 , 6𝑑, and 7𝑠 metal orbitals, such that the influence of orbital mixing and covalency1, 2 on the chemical and physical properties can be studied across the actinide series.3–7 Due to the ligandmetal bonding involving the 5𝑓 shell, crystal-field (CF) calculations may not be reliable. However, combined experimental / theoretical studies of actinide ligand-field (LF) absorption spectra have great potential to reveal the extent of such bonding, the 5𝑓 electron count / metal oxidation states, and other useful information complementary to other techniques. Particular attention has been paid to UX6–.7–14 Due to the 5𝑓 1 configuration, many of the associated properties can be understood based on a single-electron picture, and uranium is much more benign to work with than the neighboring actinides. The ground states (GS) and the LF excited states (ESs) were characterized by electron paramagnetic resonance (EPR), near infra-red (NIR) absorption spectroscopy, ligand X-ray absorption spectroscopy, CF and LF theory, as well as molecular orbital and correlated wavefunction theory. In a scalar relativistic (SR) and nonrelativistic framework, where spin-orbit (SO) coupling (SOC, also a relativistic effect) is ignored, the seven 5𝑓 orbitals are split by the 𝑂ℎ LF into 𝑎2𝑢 , 𝑡1𝑢 and 𝑡2𝑢 species, giving rise to molecular 𝐴2𝑢 , 𝑇1𝑢 and 𝑇2𝑢 LF states. The 𝑡1𝑢 and 𝑡2𝑢 metal orbitals may have covalent mixed 𝜎∕𝜋 and 𝜋 interactions, respectively, with the ligands (see Ref. 15 for plots) whereas the 𝑎2𝑢 orbital remains principally non-bonding and is the one with the single occupation in the 2 𝐴2𝑢 GS. SOC and other relativistic effects play an extremely important role for actinide complexes. Scalar Relativistic

Spin-Orbit

E1/2u F′3/2u 2

T1u

E′5/2u F3/2u 2

2

T2u

A2u

E5/2u

Figure 1: Mixing of UX6– LF states under the SOC. The dark dotted lines indicate the largest weights. The lighter dotted lines indicate smaller contributions. 2 ACS Paragon Plus Environment

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For UX6–, the SOC fundamentally alters the LF spectrum by mixing / splitting the 𝐴2𝑢 , 𝑇1𝑢 and ′ ′ 𝑇2𝑢 states to form double group symmetry species 𝐸5∕2𝑢 , 𝐹3∕2𝑢 , 𝐸5∕2𝑢 , 𝐹3∕2𝑢 , and 𝐸1∕2𝑢 (Γ7 , Γ8 , Γ7′ , Γ8′ , and Γ6 in Bethe notation), as sketched in Figure 1. (The prime is used here to distinguish between SO LF states of the same symmetry but different energy.). Furthermore, the strong SOC introduces a large orbital angular momentum in the GS10, 16–22 whose magnitude is determined by the LF splitting, the SOC, and the extent of metal-ligand covalency. The UV-Vis absorption spectra for actinide hexa-halides12 tend to be broad and feature-less. Gendron et al. recently examined the UV-Vis circular dichroism (MCD) spectrum of UCl6– by experiment and theory.15 It affords multiple bands with opposing signs assigned to dipole-allowed ligand-to-metal charge transfer (LMCT) and 5𝑓 -to-6𝑑 transitions of different symmetries. The energies of the 5𝑓 LF states were also investigated using ab-initio calculations,15, 22, 23 but ab-initio studies of the corresponding NIR intensities in the experimental spectra10–14 are lacking. The theoretical treatment of the NIR intensities is challenging, because in structures with an inversion center they are electronic-dipole forbidden. Weak intensity is brought about by vibronic coupling (VC), such that intensity is ‘borrowed’ from the dipole-allowed transitions. The experimental spectra also exhibit peaks that were assigned to purely electronic transitions. As spectulated by Ryan12 and supported by CF calculations,14 the electronic magnetic-dipole intensity can be comparable to the vibronic intensities. In this work, the NIR 5𝑓 LF transitions of UF6– and UCl6– are modeled theoretically with an allelectron relativistic ab-initio restricted active space (RAS) wavefunction approach including SOC. The Herzberg-Teller (H-T) VC approximation is used for the intensity borrowing from LMCT and 5𝑓 -to-6𝑑 transitions. The electronic magnetic-dipole intensities are calculated to be of comparable magnitude to the vibronic intensities in two of the LF bands. The 5𝑓 LF absorption spectra are well described by these calculations. Theoretical and computational details are provided in the Supporting Information (SI), Sections S1 and S2. Briefly, the H-T VC absorption intensity for an electric-dipole forbidden transition between two molecular quantum states, approximated as products of adiabatic electronic wavefunctions 𝜓𝑖 and nuclear vibrational wavefunctions 𝜙𝑖 , is determined in leading order24–28 by the absolute square of the transition dipole moment (TDM) 𝝁1,2 =

⟨𝜙1 | 𝝁𝑒1,2 (𝑄) |𝜙2 ⟩

=

∑ 𝑝

where

𝜕𝝁𝑒1,2 (𝑄) || ⟨𝜙1 |𝑄𝑝 |𝜙2 ⟩ | 𝜕𝑄𝑝 ||0

𝝁𝑒1,2 (𝑄) = ⟨𝜓1 (𝑞, 𝑄)| 𝝁𝑒 |𝜓2 (𝑞, 𝑄)⟩𝑞

(1)

(2)

and 𝝁𝑒 is the electronic electric dipole operator. 𝑄 and 𝑞 refer collectively to the nuclear and 3 ACS Paragon Plus Environment

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electronic coordinates, and 𝑄 = 0 defines the equilibrium structure. The derivatives are taken at 𝑄 = 0, which is not noted further. The 𝜙𝑖 are approximated by products of harmonic normal modes 𝑄𝑝 with angular frequencies 𝜔𝑝 . The 𝜓𝑖 depend parametrically on 𝑄. The ⟨𝜙1 |𝑄𝑝 |𝜙2 ⟩ integrals are determined using a recursive relation29 (see SI, Equation S4). We make the approximation that the normal modes and frequencies are the same for the different LF states and consider thermal populations of the lowest two harmonic oscillator levels. In this case, there can be vibronic transitions at the electronic transition energy 𝐸1,2 plus or minus one vibrational quantum ℏ𝜔𝑝 , with intensities scaled by the thermal Bolzmann weights. The electronic states are perturbed when the structure distorts along the normal modes. In lowest-order, the working equation for the dipole derivatives in Equation (1) is 𝜕𝝁𝑒1,2 (𝑄) 𝜕𝑄𝑝

=

∑ 𝑘≠1

⟨𝜓𝑘0 |𝝁𝑒 |𝜓20 ⟩

𝜕 ⟨𝜓10 |𝐻|𝜓𝑘0 ⟩ ∕𝜕𝑄𝑝 𝐸10 − 𝐸𝑘0

+

∑ 𝑘≠2

⟨𝜓10 |𝝁𝑒 |𝜓𝑘0 ⟩

𝜕 ⟨𝜓𝑘0 |𝐻|𝜓20 ⟩ ∕𝜕𝑄𝑝 𝐸20 − 𝐸𝑘0

(3)

where superscript ‘0’ indicates a state calculated at 𝑄 = 0. The terms 𝜕 ⟨𝜓𝑘0 |𝐻|𝜓𝑖0 ⟩ ∕𝜕𝑄𝑝 are found numerically by a finite-difference (FD) procedure utilizing a ‘floating’ atomic orbital (FAO) basis in which the wavefunction parameters are those for the equilibrium structure, but the AOs move with the distortions along 𝑄𝑝 . Orlandi30 argued that this approach allows an expansion of the perturbed wavefunctions in the basis of valence states instead of a huge number of terms including core-excited states. The FAO approach was realized by re-calculating all one- and two-electron AO integrals for the distorted structures and evaluating the Hamiltonian matrix elements with the 𝑄 = 0 wavefunction parameters. Thereby, the FAO technique avoids problems from rotations among degenerate state components or complex phase factors appearing in the FD steps. The SOC is treated in our calculations via RAS ‘state interaction’31 by diagonalizing a SO Hamiltonian in a basis of SR ‘spin free’ (SF) many-electron RAS wavefunctions, mixing different spin multiplicities if necessary, to determine the SO wavefunctions in the basis of 𝑀𝑆 components corresponding to the SF states. The SO matrix is determined efficiently with the help of effectiveone-electron Atomic Mean-Field Integrals (AMFI).32, 33 Extensive numerical tests confirmed that the AMFI code in the software utilizes a one-center approximation, i.e. there is no FAO vibronic contribution from the SO Hamiltonian. Accordingly, the SOC TDM is determined from 𝝁SO = 1,2

∑ 𝑘,𝑚

0∗ 0 𝑈𝑘1 𝑈𝑚2 ⟨𝜙𝑘 | 𝝁𝑒,SF (𝑄) |𝜙𝑚 ⟩ 𝑘,𝑚

(4)

where 𝑈𝑘𝑖0 is an element of the complex transformation of the SF to the SO states, determined for the equilibrium structure, and ⟨𝜙𝑘 | 𝝁𝑒,SF (𝑄) |𝜙𝑚 ⟩ is the vibronic TDM between a pair of SF 1,2 states. In keeping with our other approximations, the SOC is assumed to have no effect on the 4 ACS Paragon Plus Environment

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vibrational wavefunctions in the 5𝑓 manifold. The SF VC matrix elements involving two different multiplicities are zero, such that only spin-doublets contribute to the VC in our calculations. The 𝑈𝑘𝑖0 essentially only mix the SF LF doublet states among each other. UX6– ions in solids may have distorted octahedral GS structures (but usually keeping the inversion center), and the 𝐹3∕2𝑢 excited LF quartet states may split into doublets due to the GS distortions or ES Jahn-Teller (J-T) effects. Recent slightly distorted X-ray diffraction (XRD) structures for UF6– and UCl6–15, 34 were used for most calculations. Additional spectra were created for UCl6– to test the impact of using J-T distorted ES structures for the H-T expansion. Harmonic vibrational modes and frequencies were obtained from SR density functional theory (DFT) calculations using Gaussian 09,35 the B3YLP hybrid functional,36 a 60-electron core potential37 and ECP60MWBSEG38 valence basis for U, and the 6-311G(d) for the ligands. J-T distorted ES structures were optimized with time-dependent DFT for the SR 2 𝑇2𝑢 and 2 𝑇1𝑢 states that provide the dominant contributions to the SO LF states according to Figure 1. Normal modes for 𝑂ℎ optimized structures were mapped onto the XRD or ES structures to generate the VC, using the FD procedure and software from Reference 39. RAS40 self-consistent field (SCF) wavefunctions were calculated with a developer’s version of Molcas version 841 using the second-order Douglas-Kroll-Hess (DKH2) all-electron relativistic Hamiltonian42 and ANO-RCC basis sets contracted to TZP quality.43, 44 The dynamic correlation was treated by second-order perturbation theory (PT2)45 with a real shift of 0.2 for UCl6– and 0.3 for UF6–. The following active spaces were used: RAS(6,3|1,7|0,5) UCl6–, meaning single excitations out of a ‘ras1’ space of 6 electrons in three 𝑡1𝑔 ligand orbitals, a principal ‘ras2’ space of 1 electron in the seven 5𝑓 orbitals, and single excitations into a ‘ras3’ space of the five 6𝑑 orbitals. The computational setup is similar to the recent UCl6– MCD study of Reference 15, where plots of the relevant metal and ligand orbitals are shown. Here, inversion symmetry for the states was not explicitly used to avoid problems in the FD steps. The the 5𝑓 -to-6𝑑 energies were improved by PT2(0,0|1,7|0,5). For UF6–, 𝑡1𝑢 and 𝑡1𝑔 ligand orbitals were required to in the ras1 space to achieve SCF convergence. LF and LMCT transitions were obtained with RAS/PT2(12,6|1,7|0,0), and 5𝑓 to-6𝑑 transitions with RAS/PT2(0,0|1,7|0,5). All SF doublet (and quartet) states that were possible for a given active space were determined. The RAS State Interaction (RASSI) program and AMFI integrals were used for the SOC.31 RAS/PT2-SO magnetic dipole and quadrupole intensities were computed according to Ref. 46 (see SI, Sec. S1). The computed UV-Vis absorption spectra are shown in Figure 2. Only 5𝑓 -to-6𝑑 transitions into 𝐹3∕2𝑔 states, which also split due to distortions, have non-negligible intensity. The allowed LMCT transitions are into 𝐹3∕2𝑔 and 𝐸5∕2𝑔 states. The UCl6– spectrum shows a large red shift from PT2 for the 5𝑓 -to-6𝑑 energies. The absorption spectrum calculated with PT2 energies for these states agrees well with the spectrum from Reference 15. We did not use PT2 for the UCl6– LMCT 5 ACS Paragon Plus Environment

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Oscillator strength

−

f→d LMCT

−

f→d LMCT

a) UF6 RAS−SO

0.06

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−

f→d LMCT

−

f→d LMCT

b) UCl6 RAS−SO

0.05 0.04 0.03 0.02 0.01

c) UF6 PT2−SO

0.06 Oscillator strength

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


d) UCl6 f → d PT2−SO

0.05 0.04 0.03 0.02 0.01

40

45

50

55

60

65

70

75

80

85

90

95

20

25

Wavenumber ( 103 cm−1)

30

35

40

45

50

55

Wavenumber ( 103 cm−1)

Figure 2: Calculated UV-Vis spectra for UF6– and UCl6–. The spectra were Gaussian broadened with a 𝜎 of 0.100 eV. states, because with the present active space the energies became too red-shifted. The PT2 correlation effects on the 5𝑓 -to-6𝑑 energies can be attributed to ligand – metal bonding involving the 6𝑑 shell, which would ideally require pairs of bonding and antibonding orbitals in the principal active space to be described at the RAS level. For UF6–, the covalency is less pronounced and accordingly PT2 has much less of an effect on these transitions. The LMCT part of the spectrum drops significantly in energy with PT2, however. The computed 5f LF NIR absorption spectra for UF6– and UCl6– are shown in Figures 3 and 4 alongside selected experimental spectra. In the latter, absorption peaks that were previously assigned to purely electronic transitions are colored in green. For comparison with the experimental spectra, the calculated intensities were Gaussian broadened with root mean square (rms) widths chosen to reproduce the experimental band widths qualitatively. Table S3 in the SI shows that the electronic energies for the 5𝑓 states obtained with different active spaces are in reasonable agreement with available experimental data and previous active-space wavefunction calculations. The 15 vibrational degrees of freedom of UX6– can be grouped in 𝑂ℎ symmetry (see SI, Sec. S4) into 𝜈1 (𝐴1𝑔 ), 𝜈2 (𝐸𝑔 ), 𝜈3 (𝑇1𝑢 ), 𝜈4 (𝑇1𝑢 ), 𝜈5 (𝑇2𝑔 ), and 𝜈6 (𝑇2𝑢 ). The three ungerade modes, 𝜈3 , 𝜈4 , and 𝜈6 , generate the vibronic intensities of the 𝑂ℎ 5𝑓 LF transitions. In Table 1, the calculated vibrational frequencies are compared to experimental data; the agreement with the experimental frequencies obtained in condensed phase is satisfactory. Overall, the calculations reproduce the experimental spectra quite well in terms of the visibility


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(a) Reiseld and Crosby spectrum for CsUF6 at 75 K

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(b) Ryan spectrum of (C6H5)4AsUF6 at room temperature

E5/2u → E´5/2u

E5/2u → E´5/2u

E5/2u → F3/2u

E5/2u → F´3/2u E5/2u → F´3/2u

electronic υ3 υ4 υ6

Oscillator strength X 106

(c) RASSCF computed spectrum for UF6− at 75 K

E5/2u → E1/2u


(d) RASSCF computed spectrum for UF6− at 298 K

6.0 E5/2u → E´5/2u

E5/2u → E´5/2u

5.0 4.0 3.0

E5/2u → E1/2u E5/2u → F´3/2u

E5/2u → F3/2u

E5/2u → F´3/2u

E5/2u → F3/2u

E5/2u → E1/2u

2.0 1.0 electronic υ3 υ4 υ6

(e) CASPT2 computed spectrum at 75 K for UF6− at 298 K


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


E5/2u → E´5/2u

6.0

E5/2u → E´5/2u

5.0 E5/2u → F´3/2u

4.0 3.0


(f) CASPT2 computed spectrum at 298 K for UF6− at 298 K

E5/2u → F´3/2u

E5/2u → E1/2u

E5/2u → F3/2u

E5/2u → E1/2u

E5/2u → F3/2u

2.0 1.0 6

8

10

12

14

16

6

8

10

12

14

16

Wavenumber (103 cm−1)


Figure 3: 5𝑓 LF spectrum of of UF6–. The experimental peaks are from Refs. 11 and 12. The purely ′ electronic 𝐸5∕2𝑢 → 𝐸5∕2𝑢 transition assigned is colored green. Calculated spectra were Gaussian ′ broadened with a 𝜎 of 0.010 eV for 𝐸5∕2𝑢 → 𝐹3∕2𝑢 , 0.003 eV for vibronic 𝐸5∕2𝑢 → 𝐸5∕2𝑢 , 0.002 eV ′ for the electronic 𝐸5∕2𝑢 → 𝐸5∕2𝑢 and 0.020 eV elsewhere. Dashed lines indicate transitions out of the first excited vibrational mode. of individual peaks, the shapes of the bands, and the intensities of the bands relative to each other. There are noticeable variations among the experimental spectra, indicating effects from solid state packing or solvent. In the literature, some weak NIR vibronic peaks were assigned to dual coupling involving the ungerade modes and 𝜈1 ,10, 11, 47 or modes that do not belong to the internal UX6– vibrations.14 The UF6– spectra from Hecht et al.14 also exhibited weak NIR peaks which could potentially be due to vibrational structure from gerade modes for LF transitions with magnetic dipole intensity. These effects are not covered by our model. The previously assigned purely electronic peaks in the experimental spectra correspond to ′ 𝐸5∕2𝑢 → 𝐸5∕2𝑢 . The ab-initio calculations indeed produce electronic peaks with intensities comparable to the vibronic transitions. These peaks are seen in solution- and solid-state experimental


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(a) Selbin et al. spectrum of (n−C3H7)4NUCl6 in SOCl2 at room temperature

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(b) Ryan spectrum of (C6H5)4AsUCl6 at room temperature

E5/2u → E´5/2u

E5/2u → E´5/2u

E5/2u → E1/2u

E5/2u → E1/2u E5/2u → F´3/2u

E5/2u → F´3/2u

E5/2u → F3/2u


(c) RASSCF level spectrum from EXPT structure at 298 K


E5/2u → F´3/2u

6.0 E5/2u → F3/2u

5.0

E5/2u → E´5/2u


(d) RASSCF spectrum from ES structures at 298 K

E5/2u → E´5/2u

E5/2u → E1/2u

E5/2u → F´3/2u

4.0 E5/2u → E1/2u

3.0 E 5/2u → F3/2u 2.0 1.0 electronic (e) RASSCF with f → d CASPT2 spectrum from EXPT structure at 298 K υ3


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(f) RASSCF with f → d CASPT2 spectrum from ES structures at 298 K

υ4 υ6

6.0

E5/2u → E1/2u

5.0

E5/2u → E´5/2u

E5/2u → E1/2u

E5/2u → E´5/2u

E5/2u → F3/2u


E5/2u → F´3/2u

E5/2u → F´3/2u

4.0 3.0 E 5/2u → F3/2u 2.0 1.0 4

6

8

10

12

4

6


8

10

12


Figure 4: 5𝑓 LF spectrum of UCl6– The experimental peaks are from Refs. 10 and 12 The purely electronic 𝐸5∕2𝑢 → 𝐸5∕2𝑢 transition assigned in the is colored in green. Calculated spectra were ′ Gaussian broadened with a 𝜎 of 0.002 eV for vibronic 𝐸5∕2𝑢 → 𝐸5∕2𝑢 , 0.001 eV for the electronic ′ 𝐸5∕2𝑢 → 𝐸5∕2𝑢 and 0.010 eV elsewhere. Dashed lines indicate transitions out of the first excited vibrational mode. spectra, without strong perturbations of the surrounding vibronic peak patterns expected for 𝑂ℎ . We conclude that the previous assignments as purely electronic transitions were correct. The magnetic-dipole intensity is roughly of the same order of magnitude as the VC intensity, and 4 orders of magnitude weaker than an electric-dipole allowed transition due to a 𝑐 −2 prefactor46 (see Eqs. (S12) in the SI). The electric quadrupole contributions were negligible for this and the other transitions due to an additional Δ𝐸 3 prefactor which is very small in atomic units for the LF transitions. The calculations show that the lowest energy 𝐸5∕2𝑢 → 𝐹3∕2𝑢 bands also have some ′ electronic magnetic-dipole intensity, while the 𝐸5∕2𝑢 → 𝐹3∕2𝑢 and 𝐸5∕2𝑢 → 𝐸1∕2𝑢 band do not, – 14 consistent with prior CF calculations for UF6 . The electronic magnetic-dipole intensity for the 𝐸5∕2𝑢 → 𝐹3∕2𝑢 is overshadowed by the intensity of the VC transitions. We proceed with a discus8 ACS Paragon Plus Environment

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sion of the individual LF bands, in order of increasing wavenumber, and a brief analysis of the vibronic coupling. 𝐸5∕2𝑢 → 𝐹3∕2𝑢 : The spectrum of Reiseld and Crosby (RC) UF6– shows two major sub-bands, each with fine structure.11 These bands where also noted by Ryan,12 but due to overlap with a signal from the (C6H5)4As– counter ion, no analysis was offered. The calculations suggest that the lower-frequency sub-band is mainly due to the vibronic peaks from 𝜈6 and 𝜈4 , with additional magnetic-dipole intensity. The other sub-band is caused by VC with 𝜈3 . There is a minor third sub-band above 6×103 cm−1 in the RC spectrum that was assigned to dual VC with 𝜈3 and 𝜈1 and is therefore not present in our calculations. The RC spectrum has a clearly visible doublet in the first sub-band, which our model suggests is due to the 𝐹3∕2𝑢 splitting. The energy difference between the doublet peaks in the RC spectrum is about 103 cm−1 and reasonably close to the splitting of 100 / 109 cm−1 calculated with RAS-SO / PT2-SO. (Note, however, that Hecht et al.14 only saw a splitting of 19 and 27 cm−1 for LiUF6 and 𝛼-NaUF6, respectively). The qualitative appearance of this and the other Gaussian-broadened UF6– bands from RAS vs. PT2 is very similar. Therefore, we do not further discuss the differences between the two sets of calculations in detail. For UCl6–, this transition is outside the range of the spectrum reported by Ryan,12 and the solution spectrum of Selbin et al. lacks resolution.10 Nevertheless, the calculations provide meaningful insight. UCl6– has a similar splitting of 𝐹3∕2𝑢 due to distortions from the octahedral GS structure. Using an optimized ES structure produces a notably smaller splitting. In principle, one should expect two sub-bands, one at lower-frequency dominated by the VC with 𝜈6 and other with 𝜈3 , similar to UF6–. Due to the smaller wavenumber differences for UCl6–, an experimental spectrum would require better resolution than the one for UF6– in order to display two distinct subbands. Using the PT2 energies for the 5𝑓 -to-6𝑑 transitions causes some changes in the vibronic intensities because the PT2 energies are much lower. However, this hardly alters the qualitative appearance of the Gaussian-broadened spectrum for this or the other LF bands. ′ 𝐸5∕2𝑢 → 𝐸5∕2𝑢 : This band is very well resolved in the experimental spectra of both complexes. A striking feature is the magnetically allowed electronic peak already mentioned above. The Table 1: Vibrational frequencies in cm−1 for the modes relevant for the VC.†

𝜈3 𝜈4 𝜈6 †

T1𝑢 T1𝑢 T2𝑢

Calc. 533 172 132

UF6– Expt.12 (s) 525𝑎 170𝑎 129 𝑏

Expt.11 (s) 503𝑎 150𝑏 100𝑏

Calc. 300 114 83

UCl6– Expt.12 (s) 309𝑎 122𝑎 95𝑏

Expt.10 (l) 315𝑎 121𝑏 92𝑏

(s) and (l) indicate measurements for a solid or liquid solution, respectively. 𝑎 From infrared absorption spectra. 𝑏 From vibronic bands in the NIR spectra.


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magnetic-dipole oscillator strength in the computational model is weaker than the surrounding VC. The electronic peak in the Gaussian-broadened spectra were less broadened than the VC peaks in order to reproduce the appearance of the experimental spectra better. The peaks directly on either side of the electronic transition are due to VC with 𝜈4 and 𝜈6 , with varying degrees of resolution of the two modes in the experimental spectra. The intensity differences between the vibronic peaks at higher vs. lower frequency reflects the Boltzmann populations of the zeropoint vs. first excited vibrational modes in the GS, which is well reproduced by the calculations. For UF6– the intensity is clearly more evenly balanced for 𝜈4 & 𝜈6 at room temperature when compared to the 75 K RC spectrum. The group of electronic and 𝜈4 , 𝜈6 vibronic transitions is surrounded by a Boltzmann-weighted pair of 𝜈3 vibronic peaks. Due to the larger vibrational frequency, the de-excitation 𝜈3 vibronic peak is very weak in the 75 K UF6– spectrum but more pronounced in the room temperature solid state spectra. The calculations reproduce the features ′ of the 𝐸5∕2𝑢 → 𝐸5∕2𝑢 band’s fine structure very well. For the experimental UF6– spectrum and the solution-phase spectrum of UCl6–, the peak heights are decreasing toward higher frequency in the order electronic, 𝜈4 & 𝜈6 , and 𝜈3 . This order is also found in the calculations, except with RASSO for UF6–. The relative intensities appear to be sensitive to perturbations in the experiments, not only to approximations in the calculations. For example, the UCl6– experimental spectra for solution and solid show a different ordering of the peak heights. ′ 𝐸5∕2𝑢 → 𝐹3∕2𝑢 : The experimental spectra show two sub-bands, with shoulders indicating an underlying fine structure.10–12 One possible reason for the appearance of two sub-bands is the ′ splitting of 𝐹3∕2𝑢 . In the calculations, the splitting from distortions of the GS structure is too small to account for the appearance of the two sub-bands. For UCl6–, we explored the possibility that the band splitting is due to stronger distortions in the ES than in the GS. The calculations (spectra (d) and (f) in Figure 4) indicate that this is definitely a possibility. These calculations produce Gaussian broadened bands with 3 main peaks and several shoulders, however. The UCl6– calculations ′ would reproduce the experimentally observed band shape better either if the predicted 𝐹3∕2𝑢 splitting were stronger, or if the 𝜈6 ∕𝜈3 vibronic intensity ratio were smaller than currently predicted. ′ For UF6–, the 𝐹3∕2𝑢 splitting due to distortions in the ES would have to be over 103 cm−1 . TDDFT optimizations were successful in producing such a splitting, but the resulting structure produced a poor vibronic spectrum due to contributions from gerade normal modes, indicating that this part of the UF6– LF spectrum likely requires a more refined theoretical treatment than adopted for this study. 𝐸5∕2𝑢 → 𝐸1∕2𝑢 : For UF6–, the RC spectrum does not seem to show a distinct band, and the band in Ryan’s spectrum is not well resolved. The computations for UF6– produce a shoulder-peak band shape, with the shoulder being due to VC with 𝜈6 and the peak due to 𝜈3 . For UCl6–, the spectrum of Selbin et al. features a broad peak, with a shoulder at higher frequency. Ryan’s solid 10 ACS Paragon Plus Environment

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f−d LMCT


(a) Contribution of the PT2 UF6− spectrum for at 298 K

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(b) Contribution terms of the RASSCF with f → d PT2 UCl6− spectrum at 298 K

f−d LMCT

E5/2u → F´3/2u

6.0 5.0

E5/2u → E1/2u

4.0 E5/2u → F´3/2u

3.0

E5/2u → E1/2u

2.0 1.0

E5/2u → F3/2u

E5/2u → E´5/2u E5/2u → F3/2u

− 2.0 (c) Cross terms for PT2 UF6 spectrum at 298 K


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.0

E5/2u → E´5/2u

(d) Cross terms for RASSCF with f → d PT2 UCl6− spectrum at 298 K E5/2u → F´3/2u

E5/2u → F3/2u

E5/2u → E1/2u

E5/2u → F3/2u

E5/2u → F´3/2u

E5/2u → E´5/2u

0.0 E5/2u → E´5/2u

−1.0 −2.0

E5/2u → E1/2u

−3.0 −4.0 6.0

8.0

10.0

12.0

14.0

16.0

4.0

6.0


8.8

10.0

12.0


Figure 5: Vibronic 5𝑓 LF intensity contributions from LMCT and 5𝑓 -to-6𝑑 states, and from cross terms. Calculations for XRD structures with PT2 corrections. state spectrum is better resolved and reveals a doublet surrounded by shoulders, with the shoulder at lower frequency being very weak. The calculations using the ES distorted structure reproduce the qualitative features seen in the experiments better than the GS structure. The doublet peak may correspond to the Boltzmann-weighted pair of vibronic 𝜈6 transitions; the shoulders surrounding the doublet are then assigned to the 𝜈3 vibronic peaks. Alternatively, the UCl6– doublet peak could be caused by 𝜈6 and 𝜈3 because the wavenumber difference for these modes as reported by Ryan is 216 cm−1 and the peak separation is 190 cm−1 . The shoulder at higher frequency would then require a mechanism that is not included in our computational model. Vibronic Analysis: Per Equation (3), the vibronic TDM can be partitioned into additive contributions from the LMCT and 5𝑓 -to-6𝑑 states. The oscillator strength then has positive LMCT and 5𝑓 -to-6𝑑 contributions, along with positive or negative LMCT – 5𝑓 -to-6𝑑 cross terms. The resulting partitioning of the vibronic oscillator strengths is shown in Figure 5 for the spectra with PT2 corrections and in Figure S1 of the SI for the RAS calculations. The prominence of the 5𝑓 -to-6𝑑 band in the UV-Vis spectrum of UF6– (Figure 3) goes along with a dominance of these transitions in the vibronic 5𝑓 LF intensities. The intensity borrowing from LMCT states is not negligible, but remains weak. For UCl6–, both sets of states are important. LMCT transitions dominate in the RAS 5𝑓 vibronic spectrum, because the 5𝑓 -to-6𝑑 states are at too high energy. With PT2 corrections, however, the 5𝑓 -to-6𝑑 and cross term contributions to the intensities increase and in some cases even overpower the contributions from the LMCT states.


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In summary, the agreement of the electric dipole-forbidden LF absorption spectra of two representative U(V) hexa-halide complexes, obtained from active-space wavefunction calculations, ′ with experimental spectra is excellent for the 𝐸5∕2𝑢 → 𝐸5∕2𝑢 band, which has the best-resolved bands in the experiments. For the lowest-frequency LF band (𝐸5∕2𝑢 → 𝐹3∕2𝑢 ), the agreement is ′ also quite good, and reasonable agreement is obtained for the higher-frequency 𝐸5∕2𝑢 → 𝐹3∕2𝑢 and 𝐸5∕2𝑢 → 𝐸1∕2𝑢 bands. The intensity of the vibronic transitions may be borrowed from LMCT excitations as well as uranium-centered 5𝑓 -to-6𝑑 transitions, with the latter being dominant for UF6– and the former generally more important for UCl6–. Magnetically allowed 5𝑓 -to-5𝑓 elec′ tronic transitions are prominent in the 𝐸5∕2𝑢 → 𝐹3∕2𝑢 and 𝐸5∕2𝑢 → 𝐸5∕2𝑢 bands but overshadowed by VC transitions in the 𝐸5∕2𝑢 → 𝐹3∕2𝑢 band.

Acknowledgments The authors acknowledge support from the U.S. Department of Energy, Office of Basic Energy Sciences, Heavy Element Chemistry program, grant DE-SC0001136, and thank the Center for Computational Research (CCR) at the University at Buffalo for providing computational resources.

Supporting Information Additional computational details, additional computational results, XYZ structures used for the calculations, normal mode data. This material is available free of charge via the Internet at http://pubs.acs.org.

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Calculation of Dipole-Forbidden 5f Absorption Spectra of Uranium(V

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