First-Principles Calculation of 1H NMR Chemical Shifts of Complex Metal Polyhydrides: The Essential Inclusion of Relativity and Dynamics.

1H NMR spectroscopy has become an important technique for the characterization of transition-metal hydride complexes, whose metal-bound hydrides are often difficult to locate by X-ray diffraction. In this regard, the accurate prediction of 1H NMR chemical shifts provides a useful, but challenging, strategy to help in the interpretation of the experimental spectra. In this work, we establish a density-functional-theory protocol that includes relativistic, solvent, and dynamic effects at a high level of theory, allowing us to report an accurate and reliable interpretation of 1H NMR hydride chemical shifts of iridium polyhydride complexes. In particular, we have studied in detail the hydride chemical shifts of the [Ir6(IMe)8(CO)2H14]2+ complex in order to validate previous assignments. The computed 1H NMR chemical shifts are strongly dependent on the relativistic treatment, the choice of the DFT exchange-correlation functional, and the conformational dynamics. By combining a fully relativistic four-component electronic-structure treatment with ab initio molecular dynamics, we were able to reliably model both the terminal and bridging hydride chemical shifts and to show that two NMR hydride signals were inversely assigned in the experiment.

Introduction

Transition-metal hydride complexes play an important role in catalytic transformations, including transfer hydrogenation.[1−4] The study of their molecular and electronic structure is crucial for a better understanding of the reaction mechanisms and for the design of more efficient catalysts. Because metallic hydrides are difficult to locate by X-ray diffraction, their prime characterization is by NMR spectroscopy. Transition-metal hydride complexes with partially filled d shells often occupy extreme positions in the 1H NMR shift range, with low-frequency shifts as low as about −50 ppm.[5−7] These unusual 1H NMR shift values are primarily attributed to relativistic spin–orbit (SO) coupling, usually denominated by the SO-HALA (heavy atom on the light atom) effect,[8] which induces relativistic shielding at the hydrogen nuclei, leading to the characteristic negative 1H NMR chemical shifts.[6,8−13] A detailed discussion of the mechanisms that dictate the size and sign of the SO-HALA effect has recently been provided by Vícha et al.[7] In brief, partially occupied heavy-atom valence shells induce relativistic shielding at the light-atom nuclei, while empty heavy-atom valence shells induce relativistic deshielding. In particular, the light-atom nuclei are relativistically shielded by 5d2–5d8 and 6p4 metals. Interestingly, the maximum shielding in 5d transition-metal complexes is observed in 5d6(IrIII) complexes.[7]

Various novel iridium deactivation products formed in the catalytic conversion of glycerol into lactic acid[14] have been studied and characterized by combining experimental and computational approaches.[15−18] These iridium species have unique bow-tie structures generated by a central tetra- or hexairidium core bound to multiple N-heterocyclic carbene (NHC) and hydride ligands. For instance, a surprisingly high hydride content was found in the iridium hexamer [Ir6(IMe)8(CO)2H14]2+ complex (1; IMe = 1,3-dimethylimidazol-2-ylidene; Figure a).[15] The hydride ligands were not located by single-crystal X-ray diffraction studies, and a computational approach was instead adopted to estimate the hydrogen positions, converging into the complex structure shown in Figure , with 10 bridging and 4 terminal hydride ligands.[15]

Figure 1

(a) Optimized structure and (b) Ir6H14 core representation of the iridium polyhydride complex 1.

A complete assignment of all 1H and 13C NMR resonances, including the 1H NMR of hydride ligands, was achieved by combining the information gained from both density-functional-theory (DFT) geometry optimization and 1D/2D NMR experiments. Although this strategy was consistent with the experimental spectra and DFT data, the question then became whether the assignment of the hydride signals made as described above can be supported by more advanced methods. In this regard, the use of computational NMR spectroscopy based on relativistic electronic-structure theory provides an alternative route to reproducing the experimental spectra and support the characterization of these species. Therefore, we turned to the challenging task of computing the hydride 1H NMR chemical shifts of complex 1 by accurately taking into consideration relativistic, solvent, and dynamic effects. Although several individual effects can influence the quality of the calculated NMR parameters, various studies have demonstrated that the inclusion of both relativistic and solvent effects is essential for proper prediction of the NMR chemical shifts in transition-metal complexes.[19−22]

Calculation of NMR parameters in transition-metal complexes requires both an accurate representation of the system (e.g., geometry) and environment (solution) and a high-level electronic-structure method for the NMR calculation itself.[21,23,24] Recent theoretical and implementational advances have made it possible to carry out all-electron quantum-chemical NMR calculations using a quasi-relativistic (two-component) or a fully relativistic (four-component) model with Hamiltonians including both scalar relativistic (SR) and SO interactions.[25,26] Likewise, ab initio molecular dynamics (AIMD) appears to be a particularly useful simulation technique to investigate the conformational flexibility of a system, including solvation effects and dynamical averaging of the calculated NMR chemical shifts.[27−30] Such first-principles calculations inherently account for anharmonicities, and the temperature can be set to study systems under more realistic conditions than static quantum-mechanical calculations at 0 K.[20]

Results and Discussion

Computational Relativistic Approach

The reported complex 1 is based on a polynuclear Ir6H14 core bound to eight NHC ligands. Each iridium center, NHC ligand, and metal hydride has a symmetrically equivalent partner due to the inversion center at the core of the complex. Thus, the spectroscopic data of 1 showed 7 inequivalent hydrogen signals (in a narrow range between −16 and −20 ppm) that were assigned to 14 classical hydride ligands.[15]Figure b displays the iridium atomic numbering, hydride labeling (Ha–Hg), and color code used in this study.

As a first approximation, the hydride 1H NMR chemical shifts δ(1H) of complex 1 were calculated based on a static (fully optimized) structure in the gas phase, reported by Campos et al.[15] at the ωB97xd/LANL2TZ*(Ir),6-311G**(N, C, H) level. The ωB97xd functional[31] produced the best results when benchmarked against other functionals in a similar iridium complex.[15,32] For the static δ(1H) shift calculations, the performance of the PBE[33,34] and KT2[35] functionals was assessed and the role of relativity was analyzed by comparing the nonrelativistic (NR) approach, the scalar relativistic zeroth-order regular approximation (SR-ZORA),[36−38] the two-component SO relativistic zeroth-order regular approximation (2c-ZORA),[36−40] and the four-component (4c) fully relativistic approach based on the Dirac–Coulomb Hamiltonian.[41,42] The 2c relativistic corrections with the ZORA Hamiltonian were performed using the ADF program.[43,44] To calculate the 4c relativistic corrections, we used the ReSpect program[45] with a four-component Dirac–Kohn–Sham method (4c-DKS); see the Computational Methods section for more details. For a direct comparison with the experiment, all calculated 1H shielding constants were converted to chemical shifts δ(1H) (in ppm) relative to the shielding of dichloromethane (CH2Cl2), computed at the same level of theory.

The resulting hydride 1H NMR chemical shifts, plotted as deviations from the experimental values (Δδ), are shown in Figure . The δ(1H) values of the hydrides calculated at the NR and SR-ZORA levels using the KT2 and PBE functionals deviate significantly from the experimental values with Δδ ≈ 3–8 ppm; see the blue and green columns in Figure . By contrast, inclusion of the SO contribution at the 2c-ZORA level improves the results significantly; the Δδ values at the 2c-ZORA level range between +1.4 and −1.1 ppm with the KT2 functional and between +1.8 and −0.3 ppm with the PBE functional; see Tables S1 and S2. The improved accuracy of the hydride shifts with inclusion of the SO interaction is to be expected, bearing in mind that the HALA effect is mostly due to SO coupling.[46−48] We conclude that the observed low-frequency signals of complex 1 hydrides are mostly due to strong SO effects. Surprisingly, the 4c-DKS method produced slightly larger deviations than the 2c-ZORA method (Figure ). The Δδ values at the 4c-DKS level range between −1.3 and −2.9 ppm for KT2 and between −0.3 and −2.0 ppm for PBE. According to these results obtained using a static optimized structure, the improvement in the relativistic treatment from 2c-ZORA to the fully relativistic 4c-DKS approach does not, in this particular case, lead to an improvement of the accuracy. However, this behavior may reflect an error cancellation at the 2c-ZORA level of theory, leading to a fortuitously good agreement with experiment. Certainly, this striking difference between the 2c-ZORA and 4c-DKS levels will be corrected after incorporating dynamical averaging in the 1H NMR shift calculations, as shown in section .

Figure 2

Deviations from the experimental hydride 1H NMR chemical shifts of complex 1 obtained by the NR, SR-ZORA, 2c-ZORA, and 4c-DKS methods with the KT2 and PBE functionals; see Tables S1 and S2 for numerical data and standard deviations. The labeling of the hydrides is the same as that in Figure .

For the purpose of validation, special attention was paid to the results obtained at the 2c-ZORA and 4c-DKS levels of relativistic treatment with the KT2 and PBE functionals; see the Computational Methods section. The overall performance of these approaches was evaluated on the basis of the total root-mean-square deviations (RMSDs) between the calculated and experimental values. The 2c-PBE and 2c-KT2 levels show the best performance, with nearly identical RMSD values of 0.8 and 0.9 ppm, respectively (Table ). However, the deviations vary significantly among the hydrides: the 2c-PBE method yields large deviations (Δδ > 1.0 ppm) for Hb and Hd, while the 2c-KT2 method yields large deviations for Hb, Hf, and Hg. At the four-component level, the 4c-PBE method can be considered to be an acceptable approximation with RMSD = 1.2 ppm, whereas the 4c-KT2 method shows the largest deviation from experimental values with RMSD = 2.4 ppm. In short, the δ(1H) values calculated at the 4c-DKS level depend strongly on the choice of the DFT functional.

Table 1

Comparison of the Static1H NMR Hydride Chemical Shifts of Complex 1 at the 2c-ZORA and 4c-DKS Relativistic Levels with the KT2 and PBE Exchange–Correlation Functionalsa

The 2c-ZORA(SO) results with TZ2P and ET-pVQZ basis sets; the 4c-DKS results with uncontracted dyall_vdz, IGLO-II basis sets. The reported values are deviations (Δδ) from the experimental 1H NMR chemical shifts.

Root-mean-square deviations between the calculated and experimental values.

In this study, we are particularly interested in a reasonable estimation of the 1H NMR chemical shifts to reproduce and confirm the assignment of experimental spectra. We have therefore analyzed the experimental and calculated relative δ(1H) values by using Hg as the reference; see Table . Note that the experimental Δδ values of Ha–Hf hydrides are in a very narrow range of only 3.1 ppm. This range is well reproduced by the calculations, with maximum Δδ values of ∼4.0 and ∼5.0 ppm at the 4c-DKS and 2c-ZORA levels, respectively. Likewise, the relative δ(1H) values calculated at the 4c-DKS level are close to the 2c-ZORA results, differing by 1.3 ppm or less (see Δδ in Table ). Compared with the relative experimental values, the 2c-ZORA method showed large deviations for the terminal Ha and Hb and bridging Hd hydrides, while the 4c-DKS method showed deviations for Hb and Hd (see ΔΔδ in Table ). According to the reported 2D nuclear Overhauser effect spectroscopy (NOESY) spectrum, which indicates the interactions between the hydrides and NHC ligands,[15] the Ha, Hb, and Hd hydrides exhibited the largest number of noncovalent interactions with the methyl groups of the ligand. Note that these interactions can also alter the NMR resonances of the hydrides and may thus be important for the calculated δ(1H) values.

Table 2

Summary of the Relative Static1H NMR Hydride Chemical Shifts of Complex 1 Calculated at the Two-Component ZORA (2c-KT2 and 2c-PBE) and Four-Component DKS (4c-KT2 and 4c-PBE) Levels and Comparison with Experimental Valuesa

2c-ZORA(SO) results with TZ2P and ET-pVQZ basis sets; 4c-DKS results with uncontracted dyall_vdz, IGLO-II basis sets.

Relative δ(1H) values by using Hg hydride as the reference.

Calculated as the difference between the relative Δδcalc and Δδexptl chemical shift values.

The suitability of the selected methods was also analyzed by comparing the absolute calculated and experimental δ(1H) trends from the Ha to Hf hydrides (Figure ). At the 2c-ZORA level, we find Hb > Hd with a large difference (Δδ > 1.0 ppm), while the 4c-DKS level leads to Hb ∼ Hd. Furthermore, these levels of theory do not fully reproduce the experimental trend; the observed Ha > Hb and Hc > Hd trends, for instance, are not reproduced by the calculations. Hence, although the calculated He–Hg shifts are in agreement with the experiment (decreasing in the order He > Hf > Hg), it is possible that the calculated 1H NMR chemical shifts are not sufficiently well described using a static optimized structure. In addition to the level of theory and relativistic effects, an important source of error in the NMR chemical shift calculations of transition-metal complexes arise from neglect of the solvation shell effects and/or conformational flexibility.[19−22] For this reason, we have additionally explored the solvent effects and dynamical behavior of complex 1.

Figure 3

Summary of the absolute static1H NMR hydride chemical shifts of complex 1 calculated at the two-component ZORA (2c-KT2 and 2c-PBE) and four-component DKS (4c-KT2 and 4c-PBE) levels. The dashed green line indicates the experimental signals.

Solvent and Dynamics Effects on the 1H NMR Chemical Shifts

Our first approach to investigating the solvent effects was to compute the static1H NMR chemical shifts by including an implicit continuum model approach for describing the bulk solvation in CH2Cl2. Solvation corrections were calculated at the 2c-ZORA level using the implicit conductor-like screening solvent model (COSMO)[49,50] and at the 4c-DKS level using the polarizable continuum solver model (PCM).[51] However, inclusion of the COSMO and PCM models leads only to minor changes in the shifts, up to 0.08 and 0.26 ppm, respectively (see Δδsolv in Table S4). The solute–solvent interactions that affect the hydride δ(1H) chemical shifts of complex 1 therefore cannot be properly modeled with a continuum model, even though such models have been successfully used in several cases to describe the bulk solvent effects on NMR calculations.[52−54] Among the selected methods, the 2c-ZORA-COSMO method (estimated using the PBE exchange–correlation functional) shows the best performance with RMSD = 0.8 ppm (Table S3).

Additionally, to determine the importance of dynamics and the effect of solvation, we performed AIMD simulations using the CP2K program package[55] where complex 1 was surrounded by solvent molecules (CH2Cl2) and followed over time (see the Computational Methods section for details). From this trajectory, a total of 40 snapshots were used to yield dynamic (averaged) 1H NMR chemical shifts for the seven different hydrides (Ha–Hg) of complex 1. The molecular dynamics of complex 1 reveals drastic conformational changes on the Ir6H14 core region (Table S5 and Figures S1–S5). As a result, a large range of variation in the calculated 1H NMR shift values is observed along the full trajectory (40 ps), with changes of up to 9.2 ppm (estimated at the 4c-DKS level using the KT2 functional) for each of the hydrides (Figures S6–S9).

The dynamic1H NMR hydride chemical shifts were calculated at the 2c-ZORA and 4c-DKS levels with the KT2 and PBE functionals. Interestingly, inclusion of molecular dynamics caused significant changes in the δ(1H) chemical shift values and trends. In particular, the dynamical averaging significantly increased the δ(1H) values of hydrides Hb–Hg and slightly decreased the δ(1H) value of Ha (Figures S10 and S11). Analysis of the dynamic relative δ(1H) results by using Hg as the reference and a comparison with the experimental values are shown in Table . Notably, some deviations between the calculated and experimental results still persist in the dynamic approach; namely, the 2c-ZORA method shows large deviations in the relative δ(1H) values for Hb and Hd hydrides, while the 4c-DKS method shows deviations for Ha and Hd (see ΔΔδ in Table ).

Table 3

Summary of the Relative Dynamic1H NMR Hydride Chemical Shifts of Complex 1 Calculated at the Two-Component ZORA (2c-KT2 and 2c-PBE) and Four-Component DKS (4c-KT2 and 4c-PBE) Approaches and a Comparison with the Experimental Valuesa

The 2c-ZORA(SO) results with TZ2P and ET-pVQZ basis sets; the 4c-DKS results with uncontracted dyall_vdz, IGLO-II basis sets.

Relative δ(1H) values by using Hg hydride as the reference.

Calculated as the difference between the relative Δδcalc and Δδexptl chemical shift values.

Because the dynamic δ(1H) chemical shift calculations are not in full agreement with the experimental trend, we systematically examined all of the results obtained for each of the hydrides. Note first that the largest difference between the 2c-ZORA and 4c-DKS relativistic levels is mostly due to the changes in the two terminal Ha and Hb hydrides (Figure a). Raising the level from the quasi-relativistic 2c-ZORA to the fully relativistic 4c-DKS approximation causes a large shielding on these two hydrides, decreasing the chemical shifts by approximately −2.0 ppm (using PBE). Certainly, the different coordination modes of the hydrides (bridging vs terminal) can affect directly the chemical shift values and help to distinguish between them. Compared with the bridging hydrides, the terminal Ha and Hb exhibit the largest SO effects (Table S7). The SO-ZORA approach is often sufficiently accurate but can lead to a poor performance when a large shielding contribution from the SO term is present.[40,56] Hence, the increasing magnitude of the SO effects appears to deteriorate the 2c-ZORA results. In contrast, the results obtained for the bridging Hc–Hf hydrides are consistent upon comparison of the 2c-ZORA and 4c-DKS levels. The calculated δ(1H) chemical shifts for Hc, He, and Hf hydrides are in good agreement with the experimental data, while a large deviation was found for Hd (Figure a). Among the selected methods, the dynamic 4c-DKS results using the PBE functional must be considered to be the most reliable because they represent the highest level of theory employed and feature the smallest deviation (RMSD = 0.6 ppm).

Figure 4

Summary of the absolute dynamic1H NMR hydride chemical shifts of complex 1 calculated at the two-component ZORA (2c-KT2 and 2c-PBE) and four-component DKS (4c-KT2 and 4c-PBE) approaches: (a) comparison with the experimental values; (b) comparison swapping the experimental Ha by Hd values. The dashed green line indicates the experimental signals.

On the basis of the above analysis, our results indicate that two signals, the terminal Ha and bridging Hd hydrides, were assigned inversely in the experimental study. To support this proposal, we analyzed the dynamic δ(1H) chemical shifts by swapping the experimental Ha by Hd values (Figure b). The reassignment of Ha to Hd significantly improved the correlation with the experimental data. For instance, the dynamic δ(1H) chemical shift values calculated at the 4c-DKS level showed an excellent agreement between theory and experiment for all hydrides (RMSD = 0.2 ppm); see Figure S12. At the 2c-ZORA level, all of the bridging hydrides (Hc–Hf) were obtained in good agreement with the experiment, but substantial deviations (>1.0 ppm) were observed for the terminal Ha and Hb hydrides. Although some minor differences between the 4c-DKS and 2c-ZORA approaches can be expected, for example, from the different types of basis sets (Gaussian vs Slater basis sets in ReSpect and ADF, respectively), our results demonstrate the need to include the relativistic effects at a four-component level.

Compatibility of Reassignment with the Experimental Data

To check if the proposed reassignment is compatible with the original experimental spectra, we have investigated the reported information from both DFT calculations and 1D/2D NMR experiments. In the experimental study, NOE cross-peaks were traced for the seven hydride resonances. The interactions between the hydrides and N–Me groups gave 18 intense and 7 weaker NOE signals.[15] The DFT-optimized structure was used to rationalize the NOESY spectrum on the basis of the calculated H···H distances between the hydrides and N–Me groups, with only one of the possible assignments being consistent with all of the 2D NMR and DFT data.

Important for the assignment, only three of the resonances due to the N–Me groups present a single strong NOE peak with a metal hydride. In agreement with the NOESY spectrum, the optimized structure showed only three methyl groups whose protons exhibited a single H···H distance below 3.0 Å, namely, C(1), C(2), and C(3). Nevertheless, it should be noted that the NHC ligands are very flexible and present conformational changes that are not considered in the static optimized structure. Thus, we have analyzed the H···H distances (Å) between the metal hydrides and the N–CH3 wingtips. The interactions of the C(1), C(2), and C(3) methyl groups with Ha, Hb, and Hd are shown in Figure . Both static and dynamic H···H bond distances show that C(1), C(2), and C(3) exhibit a strong interaction with hydrides Ha, Hb, and Hd, respectively. Nevertheless, analysis of the dynamic Ha–C(3) distances along the trajectory reveals also considerable strong interactions (below 3.0 Å) between C(3) and Ha (Figure ). Thus, while the static optimized structure shows that the C(3) methyl group interacts with a single metal hydride (Hd), the dynamic structure indicates that C(3) can interact with two metal hydrides (Ha and Hd).

Figure 5

H···H distances (Å) between Ha, Hb, and Hd metal hydrides and N–CH3 wingtips of complex 1. The evolution of the H···H distances (Å) between the Ha and Hd metal hydrides and the N–CH3(3) wingtip is shown at the top right. The results of the equivalent Ha′ and Hd′ hydrides are shown as light-colored lines.

Validation of the Optimized Protocol

Additionally, we studied in detail the case of the [Ir4(IMe)8H10]2+ complex 2, for which the exact positions of the hydrides were known from neutron diffraction experiments.[18] This species is based on a polynuclear Ir4H10 core similar to complex 1, with four terminal hydrides, four equivalent hydrides bridging the shorter Ir···Ir edges, and two equivalent hydrides bridging the longer Ir···Ir edges (Figure a). In agreement with the neutron diffraction structure, the 1H NMR spectrum showed three inequivalent H signals integrating to 10 classical hydride ligands in a 4:4:2 ratio.[18]

Figure 6

(a) Ir4H10 core representation of the iridium polyhydride complex 2. (b) Summary of the absolute dynamic1H NMR hydride chemical shifts of complex 2 calculated at the four-component DKS (4c-KT2 and 4c-PBE) approach.

The hydride chemical shifts of complex 2 were first examined with a static protocol, based on a fully optimized structure at the ωB97xd/LANL2TZ*(Ir),6-311G**(N, C, H) level and subsequent 1H NMR calculations at the 2c-ZORA and 4c-DKS levels. The static approach performs well, reproducing the experimental trend Ha > Hb > Hc (Figure S15). The calculated shifts yield small RMSD values that range between 0.61 ppm (2c-KT2) and 1.05 ppm (4c-PBE), although the deviations seen for each hydride differ appreciably among the selected methods (Tables S8 and S9). The dynamic protocol was then tested at the 4c-DKS level using the KT2 and PBE exchange–correlation functionals (Tables S10 and S11). As shown in Figure b, the hydride 1H NMR chemical shifts δ(1H) calculated at the 4c-PBE method yielded the trends closest to experiment and showed the smallest deviation (RMSD = 0.41 ppm). Notably, the optimized dynamic protocol at the 4c-PBE approach was proven to be the most accurate in the prediction of the 1H NMR hydride chemical shifts of complex 2, which is consistent with the results obtained for complex 1. Hence, this is a reliable protocol to calculate the NMR chemical shifts of the terminal and bridging hydrides and has potential utility for the assignment of hydride signals in other challenging metal polyhydrides.[57−59]

Conclusions

In this study, we calculated the 1H NMR hydride chemical shifts of the iridium polyhydride complex 1 by accurately taking into consideration relativistic, solvent, and dynamic effects. The reliability of the computed 1H NMR hydride values was assessed by comparing them with the experimental signals reported by Campos et al., providing a new strategy to predict and support the characterization of these species. The calculated 1H NMR hydride chemical shifts are strongly dependent on the relativistic treatment; the SO contribution is the most important for the accurate reproduction of the NMR shift ranges, in particular, for the terminal Ha and Hb hydrides. The static1H NMR chemical shifts calculated using both the 2c-ZORA and 4c-DKS approaches do not fully follow the experimental trend, showing large deviations for the Ha, Hb, and Hd hydrides. Furthermore, the 4c-DKS level was shown to be highly dependent on the choice of the DFT exchange–correlation functional, where the PBE functional performs better than KT2.

The role of an implicit solvent model was found to be negligible for the hydride chemical shifts, with minor changes of up to 0.2 ppm (estimated at the 4c-DKS level using the PBE functional). By contrast, the effect of dynamical averaging using AIMD simulations resulted in significant changes in the 1H NMR chemical shift values and trends. The dynamic1H NMR chemical shifts at the 4c-DKS level showed large deviations for the Ha and Hd hydrides, which were inversely assigned in the experiment. The reassignment of Ha and Hd gave significantly improved correlations with the experimental data. The 4c-DKS level showed an excellent agreement between theory and experiment for all hydrides (RMSD = 0.2 ppm). In contrast, the 2c-ZORA level gave good results for the bridging Hc–Hg hydrides but failed for the terminal Ha and Hb hydrides, showing the importance of including a four-component relativistic methodology.

Among the selected methods, the 4c-DKS level using the PBE functional and including dynamical averaging when calculating the 1H chemical shifts showed the best performance, providing a means to accurately predict both the terminal and bridging hydride shift ranges. Moreover, the same computational protocol was successfully validated with complex 2. The relativistic and dynamic effects are of crucial importance and the main factors that influence the quality of the NMR δ(1H) predictions, showing that simpler standard protocols should be used with care. Hence, this study reports an important and useful protocol for the NMR characterization of complex metal polyhydride complexes.

Computational Methods

The static1H NMR hydride chemical shifts of the iridium polyhydride [Ir6(IMe)8(CO)2H14]2+ (1) and [Ir4(IMe)8H10]2+ (2) complexes were calculated using the optimized structure reported at the ωB97xd/LANL2TZ*(Ir),6-311G**(N, C, H) level, which proved best in simulating the X-ray structure.[15] Additionally, dynamic δ(1H) chemical shifts were obtained from quantum-chemical calculations based on an ensemble of structures from AIMD simulations. AIMD simulations of complex 1 were run in an explicit dichloromethane (CH2Cl2) solvent according to the Born–Oppenheimer approximation using the CP2K program package.[55] The initial model system, created using the PACKMOL package,[60] consists of complex 1 (optimized at the ωB97xd/LANL2TZ*(Ir),6-311G**(N, C, H) level) surrounded by 233 CH2Cl2 molecules in a cubic box of 30.0 Å3 edge to reproduce the appropriate density of 1.325 g/mL. The simulation cell was treated under periodic boundary conditions for all AIMD calculations performed using the Kohn–Sham DFT with the PBE exchange–correlation functional,[33,34] in a mixed DZVP Gaussian[61] and auxiliary plane-wave (200 Ry cutoff) basis set. Core electrons were described using pseudopotentials of the Goedecker–Teter–Hutter type.[62] Dispersion forces were taken into account using Grimme’s D3 model.[63] AIMD simulations of complex 2 were performed in similar conditions, using a smaller cubic box of 25.0 Å3 edge containing 136 CH2Cl2 solvent molecules.

The initial configuration was relaxed by AIMD simulation using a microcanonical (NVE) ensemble, until an average temperature of 298 K was reached. After equilibration, the simulation was then run by using a canonical (NVT) ensemble with a temperature of 298 K maintained with the CSVR algorithm.[64] The trajectory was extended up to 40 ps (complex 1) and 30 ps (complex 2), with a time step of 0.25 fs. From the long 40 ps simulation, a total of 40 snapshots taken at regular 1 ps intervals were used for obtaining the dynamic average of the 1H NMR shielding constants. Because we are interested in the chemical shifts of the thermodynamic ensemble of structures, the molecular coordinates were taken as provided by AIMD simulation without further geometry optimizations.

Relativistic 1H NMR Chemical Shift Calculations

The calculations of the hydride 1H NMR chemical shifts were performed using the 4c-DKS method in combination with the Dirac–Coulomb Hamiltonian,[41,42] as implemented in the ReSpect program.[45] The PBE[33,34] and KT2[35] functionals were tested because both functionals have been proven to give reliable data for NMR chemical shifts; the KT2 functional is specifically optimized to provide high-quality shielding constants for light main-group nuclei. Hybrid exchange–correlation functionals require computationally more demanding calculations and were not considered in this study. Mixed uncontracted basis sets were employed to preserve high accuracy at lower computational cost, combining Dyall’s VDZ[65−68] basis set for iridium and the IGLO-II[69] basis set for the rest of the light atoms; Dyall’s basis sets are designed for relativistic calculations and perform well for calculation of the NMR parameters,[70] while IGLO basis sets are designed for computation of the magnetic properties. For acceleration of the calculations, the relativistic electron repulsion integrals and related two-electron Fock contributions were calculated using the resolution-of-identity for the two-electron Coulomb term,[71] which has demonstrated good accuracy for large systems while reducing the computational cost. All of the hydride δ(1H) chemical shifts were performed in the gas phase, and the solvent effects were assessed in the static δ(1H) calculations using the PCM[51] for CH2Cl2.

The four-component results were compared with those obtained by a quasi-relativistic 2c-ZORA(SO) method,[36−40] as implemented in the Amsterdam Density Functional (ADF) program,[44] using either the PBE or KT2 functional in conjunction with all-electron Slater-type orbital basis sets designed for relativistic ZORA calculations, combining the triple-ζ quality plus two sets of polarization functions (TZ2P)[73] basis set for iridium and the even-tempered polarized valence quadruple-ζ (ET-pVQZ)[72] basis set for the rest of the light atoms. Solvation effects were taken into account through the implicit COSMO[49,50] model for simulating bulk solvation in CH2Cl2. The gauge-origin dependence was handled using gauge-including atomic orbitals (GIAO) approach.[42,74]

A dataset collection of the computational results is available in the ioChem-BD repository[75] and can be accessed via 10.19061/iochem-bd-6-69.