1 Introduction

Mössbauer spectroscopy using the 73 keV transition from the I = 3/2 ground to the I = 1/2 first excited state of 193Ir has been considered as an optimal method to study hyperfine interactions in iridium containing materials because of its low natural line width of \(0.625 \ {\text{mm s}}^{-1}\) [1]. However, 193Ir Mössbauer spectroscopy requires 193Os as a radioactive source which has a half life time of 31d and needs to be prepared via neutron irradiation by a 192Os(n,γ)193Os reaction [2, 3]. This has hampered more widespread applications of 193Ir Mössbauer spectroscopy in the past although the 193Ir isotope has a high natural abundance of 62%.

The high brilliance at modern synchrotron sources and the recent development of monochromator systems for 73 keV with an energy resolution of 160 meV at the Dynamics Beamline P01 (PETRA III, DESY, Hamburg) now enables to excite the 73 keV level from the ground state to perform coherent nuclear forward scattering (NFS) experiments using the 193Ir nucleus. This set-up has been developed and used by Alexeev et al. [4] for the studies of magnetic and electronic properties of iridates which display both strong spin orbit coupling and strongly correlated electron systems.

Iridium containing materials play an important role in chemistry. For example, in photochemistry molecular iridium complexes are used in organic light-emitting diodes (OLEDs) [5, 6], organic solar cells [7], in photocatalysis [8], in car exhaust catalysts but also recently for initiating “water oxidation reactions " [9, 10]. In this process water is catalytically split into hydrogen and oxygen, a prerequisite to enable hydrogen as a sustainable storable energy source.

Here, we report the first 193Ir NFS experiments on a molecular material, namely a dinuclear iridium(I) complex, [IrCl(COD)]2 [11] with COD being cycloocta-1,5-diene (Fig. 1). This complex serves as a catalyst for hydrogenation and other chemical reactions [12,13,14,15,16,17,18,19,20,21,22]. It has been investigated by conventional 193Ir Mössbauer spectroscopy in the past [23, 24] which makes this system ideal for elucidating the potential of 193Ir NFS with respect to its chemical applications. In addition, we present density functional theory (DFT) calculations, which have been used to calculate the isomer shift and the quadrupole splitting of the dinuclear iridium(I) complex.

Fig. 1
figure 1

Structural view of the dinuclear iridium(I) complex [IrCl(COD)]2 investigated in this study. Ir atoms are displayed in dark blue, chloride atoms in green, carbon atoms in dark grey and hydrogens in grey [11]

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2 Materials and methods

Di-µ-chlorobis[(1,2,5,6-η)-1,5-cyclooctadiene]diiridium (C16H24Cl2Ir2; CAS No.: 12112-67-3) was synthesized as described in [25]. For 193Ir NFS experiments the sample was filled in a hole with a diameter of 2 mm and a length of 4 mm of a sample holder made of aluminium. The sample was tightly pressed into the sample volume and sealed with aluminium tape.

193Ir NFS experiments were performed at the Dynamics Beamline P01 (PETRA III, DESY, Hamburg) using the 40-bunch mode with a time separation of 192 ns between the electron bunches of the PETRA III storage ring.

The synchrotron radiation (SR) generated by the undulator source was monochromatized with a double-crystal monochromator (DCM) consisting of two Si(311) crystals (see Fig. 2) to about 10 eV. The medium resolution monochromator (MRM) reduced the energy bandwidth to about 160 meV. The MRM consisted of two asymmetric channel-cut silicon crystals, a Si(422) collimator crystal and a Si(800) energy selector crystal. Subsequently, the SR, monochromatized to 73.0 keV, was transmitted through the sample mounted in a He-closed cycle cryostat from Advanced Research Systems, Inc. The delayed resonantly scattered radiation was detected with an avalanche photo diode (APD) detector array. The APD detector allowed a time resolution of \(\sim\)0.6 ns and 193Ir-NFS time spectra could be obtained as early as 3 ns after the excitation by the SR pulses by using time gated electronics.

Fig. 2
figure 2

Set-up for 193Ir NFS at beamline P01, PETRA III: DCM - double crystal monochromator consisting of Si (311) single crystals (grey); MRM - medium resolution monochromator consisting of Si(422) (blue) and Si(800) (dark grey) single crystals

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For the determination of the quadrupole splitting (\(\varDelta {E}_{Q}\)) and the isomer shift (\(\delta\)) the 193Ir-NFS data were analyzed with the CONUSS software [26] as described in Alexeev et al. [4].

DFT calculations were used to calculate the hyperfine parameters \(\delta\) and \(\varDelta {E}_{Q}\) on the basis of the crystal structure of [IrCl(COD)]2 [11]. Structure optimization and Natural bond orbital (NBO) analysis [27] was performed with Gaussian 16 [28] using Grimme’s dispersion with the original D3 damping function [29] for the functional TPSSTPSS and the basis set QZVP [30, 31]. Kohn-Sham Molecular orbitals (MOs) and their energies were calculated and graphically represented by the Gauss View mode.

With the optimized structures, calculations of the hyperfine parameters were performed using the Orca 5.0 programme [32]. For this purpose, all-electron calculations of the SARC (segmented all-electron relativistically contracted) basis sets were used, which have been specially developed for scalar relativistic calculations and have been adapted to the Douglas-Kroll-Hess Hamiltonian of the second order (DKH2) [31]. The DKH-def2-TZVP basis set [30] was used for C, H, F, Br and Cl and the SARC-DKH-TZVP basis set [33] was used for the two Ir atoms. Calculations were performed with both TPSS and B3LYP functionals. The convergence criteria and grid points for the self-consistent field (SCF) calculations were set to Tight SCF (energy change \(1\cdot {10}^{-8} au\)). All SCF calculations were performed with the resolution of the Identity Approximation (RI) [34]. The programme Orca_eprnmr implemented in Orca was used to calculate the electron density \({\rho }_{0}\) and the electric field gradient (EFG) tensor at the iridium core [34].

3 Results and discussion

Figure 3 shows a 193Ir NFS spectrum of [IrCl(COD)]2 obtained at T = 10 K. The spectrum shows a beating pattern with a time period of about 5 ns which originates from the non-zero EFG of the two equivalent Ir sites in [IrCl(COD)]2. The beating pattern could be successfully reproduced by a simulation with CONUSS which gave \(\varDelta {E}_{Q}=3.82\left(4\right) {\text{ mm s}}^{-1}\). There are small deviations between experimental and simulated data occurring at > 25 ns which may be due by some spurious bunches of the synchrotron. Nevertheless, the so obtained value of the quadrupole splitting is in excellent agreement with those obtained by conventional 193Ir Mössbauer spectroscopy for this complex at liquid He temperatures (\(3.81\left(2\right) {\text{ mm s}}^{-1}\) [23] and \(3.85\left(2\right) {\text{ mm s}}^{-1}\), respectively [24]).

Fig. 3
figure 3

193Ir NFS spectrum of [IrCl(COD)]2 obtained at 10 K (black circles) (left) with the APD detector mounted behind the sample inside a closed cycle cryostat (right). The red line is a simulation performed with CONUSS [20] yielding \(\varDelta {E}_{Q}=3.82\left(4\right) \text{ mm s}^{-1}\)  

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For the determination of the isomer shift a data set with a metallic iridium foil as a single-line reference was collected. The corresponding 193Ir NFS spectrum is shown in Fig. 4. The interference of the 73 keV resonantly scattered quanta originating from the iridium foil and the [IrCl(COD)]2 sample leads to the disappearance of the regular beating structure visible in Fig. 3. A simulation with CONUSS using two Ir sites with \(\varDelta {E}_{Q}=3.82 \ {\text{mm s}}^{-1}\) representing [IrCl(COD)]2 and \(\varDelta {E}_{Q}=0 \ {\text{mm s}}^{-1}\) for the metallic Ir foil yields \(\delta =\pm 0.87(4) \ {\text{mm s}}^{-1}\) for the complex. It is important to note that the sign of \(\delta\) cannot be obtained using the set-up displayed in Fig. 4. Indeed, conventional 193Ir Mössbauer spectroscopy showed that the sign of the isomer shift of [IrCl(COD)]2 is negative. Nevertheless, the absolute \(\delta\)-value obtained in this study is in excellent agreement with the reported values of \(-0.88\left(1\right) {\text{ mm s}}^{-1}\) [23] and \(-0.87\left(1\right) {\text{ mm s}}^{-1}\) [24].

Fig. 4
figure 4

193Ir NFS spectrum of [IrCl(COD)]2 obtained at 10 K (black circles) (left) with an iridium foil mounted in the beam path (right). Temperature of the iridium foil was 300 K. The red line is a simulation performed with CONUSS [20] using \(\varDelta {E}_{Q}=3.82(4) \text { mm s}^{-1}\) for the Ir sites of [IrCl(COD)]2 yielding \(\delta =0.87(4) \text { mm s}^{-1}\) for the complex

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It has been shown by [35] that experimentally observed isomer shifts are related to the theoretically calculated electron density at the iridium nucleus \({\rho }_{0}^{calc}\) via the following relation:

$$\delta =a\left({\rho }_{0}^{calc}-b\right)+c$$

The parameters \(a\), \(b\) and \(c\) are fit parameters which need to be obtained from a series of complexes with known experimental values of \(\delta\) and calculated \({\rho }_{0}^{calc}\) which can be obtained by DFT methods based on known molecular structures. For 57Fe containing complexes this approach has been shown by various authors to be very successful [36, 37] The same strategy has been used recently within the frame of a DFT study to calculate 193Ir Mössbauer spectroscopic parameters [34].

For the determination of \({\rho }_{0}^{calc}\) of the complex [IrCl(COD)]2 investigated in this study DFT calculations of the various iridium(I), iridium(III) and iridium (IV) complexes listed in ref. [34] were repeated with the Orca 5.0 programme [32] as described in the Materials and Methods section. Table 1 provides a list of the iridium complexes and experimental \(\delta\) values and lists the charge and multiplicity of the complexes used for the calculations. The Cartesian coordinates of the complexes were taken from [34]. Our DFT calculations performed with both, the functional TPSS and B3LYP gave slightly different\({\rho }_{0}^{calc}\) values than reported in ref. [34] (Table 1) and were used to perform a linear regression analysis between \({\rho }_{0}^{calc}\) and measured \(\delta\) values as shown for both functionals in Fig. 5. For [IrCl(COD)]2 we obtain electron densities at the iridium core of 2657326.5773 \({\text{a}\text{u}}^{-3}\) when using TPSS and 2658125.7642 \({\text{a}\text{u}}^{-3}\) when using B3LYP. With the parameters \(a\), \(b\) and \(c\) given in Table 2 the calculated isomer shifts for the complex are \({\delta }_{TPSS}=-0.58 \text{ mm s}^{-1}\) and \({\delta }_{B3LYP}=-0.65 \text{ mm s}^{-1}\). Although the absolute values of the calculated isomer shifts are below the experimental value of \(\delta =-0.87 \text{ mm s}^{-1}\) the DFT calculations also give a negative sign of the isomer shift as has been observed by conventional 193Ir Mössbauer spectroscopy.

Table 1 Experimental isomer shifts \(\delta\) of iridium complexes listed in ref. [2, 23, 24, 34, 38] and calculated electron densities at the iridium nucleus \({\rho }_{0}^{calc}\) obtained by DFT calculations performed in this study with the functionals TPSS and B3LYP
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Fig. 5
figure 5

Experimental \(\delta\) -values as a function of calculated \({\rho }_{0}\)-values for the TPSS (a) and B3LYP (b) functionals. The black points represent the experimental data (Table 1) and the red line the result of a linear regression analysis with parameters \(a\), \(b\) and \(c\) listed in Table 2

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Table 2 Parameters of the linear regression analysis shown in Fig. 5 for the TPSS and B3LYP functionals
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The DFT calculations performed in this study also deliver the main components of the EFG tensor \({V}_{xx}\), \({V}_{yy}\) and \({V}_{zz}\) in its principal axis system (\(\mid {V}_{xx} \mid \le \mid {V}_{yy} \mid \le \mid {V}_{zz} \mid\)). With the asymmetry parameter \(\eta =({V}_{xx}-{V}_{yy})/{V}_{zz}\) and the quadrupole moment Q the quadrupole splitting is given as:

$$\varDelta {E}_{{Q}_{exp}}=\frac{eQ{V}_{zz}}{2}\sqrt{1+\frac{{\eta }^{2}}{3}}$$

Taking Q = 0.751 b for the first excited nuclear state of 193Ir and the expression \(eQ{V}_{zz}\left[{mm \ s}^{-1}\right]=(eQ{V}_{zz}\left[J\right]\times c\left[{mm \ s}^{-1}\right])/{E}_{\gamma }\left[J\right]\) with the speed of light c in units of \({mm \ s}^{-1}\) allows to obtain \(\varDelta {E}_{Q}\) in its usual units since the DFT package ORCA delivers the EFG tensor components in units of au.

In this way we obtained for both functionals TPSS and B3LYP a positive sign of the quadrupole splitting and slightly different absolute values of \(\varDelta {E}_{Q}^{B3LYP}=+4.70 \ { \text{mm s}}^{-1}\text{; }\eta^{B3LYP}=0.29\) and \(\varDelta {E}_{Q}^{TPSS}=+4.25 \ { \text{mm s}}^{-1}\text{; }\eta^{TPSS}=0.43\). Giving the fact that for quadrupole splittings of 57Fe containing compounds deviations between experimental and DFT calculated \(\varDelta {E}_{Q}\) values in the order of \({ \sim1 \ \text{mm s}}^{-1}\) are not uncommon [39] we consider the agreement with the experimental value of \(\varDelta {E}_{Q}=3.82 \ {\text{mm s}}^{-1}\) at least for the complex [IrCl(COD)]2 investigated here as reasonable.

Gal et al. [24] argued that \(\delta =-0.87 \ \text{mm s}^{-1}\) of [IrCl(COD)]2 is unusually high compared to other Ir(I) complexes which show typically \(\delta \sim-4 \ \text{mm s}^{-1}\). They attributed this to a σ donation into the 6s orbitals as well as hybridization of the 6s with the 5\({d}_{{z}^{2}}\) orbitals. According to our NBO analysis, the electron configuration of the iridium is 6s(0.48)5d( 8.02)6p( 0.32)7p( 0.19). The eight occupied MOs with 5d character according to the reference frame given in Fig. 6 are shown in Fig. 7. Our calculations indicate that the 5p and 5s-orbitals prevail their character as expected (Fig. 8).

Fig. 6
figure 6

Coordinate axes system of the electronic orbitals of the right iridium atom of the complex chosen from the symmetry axis of the \({d}_{{z}^{2}}\) orbital. Note that inversion of the z-axis would interchange the x and y axes. The latter were chosen from the symmetry axes of the p orbitals

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Fig. 7
figure 7

DFT calculated Kohn-Sham molecular orbitals with 5d character obtained from the optimized structure of [IrCl(COD)]2. Numbers in brackets represent the number of the molecular orbitals as given in the output-file of Gaussian16

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Fig. 8
figure 8

DFT calculated Kohn-Sham molecular orbitals with 5p and 5s character obtained from the optimized structure of [IrCl(COD)]2. Numbers in brackets represent the number of the molecular orbitals as given in the output-file of Gaussian16

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The DFT calculations presented here show a positive \({V}_{zz}\) which is in contradiction with the reported presumably negative \({V}_{zz}\) assumed by Gal et al. [24]. Future experimental investigations with NFS experiments in high external fields can serve to determine the sign of the quadrupole splitting and may shine more light on the binding properties of catalytically active iridium complexes.

4 Conclusions

In this work it has been shown that the 193Ir NFS is an excellent alternative to conventional 193Ir Mössbauer spectroscopy. Moreover, we have shown that it is possible to calculate Mössbauer parameters like the isomer shift and the quadrupole splitting using state of the art DFT methods with satisfying accuracy. The combination of experimental 193Ir NFS and quantum chemical DFT methods may represent an important technique for future characterisation of the magnetic and electronic properties of iridium containing molecular systems.