Structure and bonding in rhodium coordination compounds: a 103Rh solid-state NMR and relativistic DFT study

This study demonstrates the application of 103Rh solid-state NMR (SSNMR) spectroscopy to inorganic and organometallic coordination compounds, in combination with relativistic density functional theory (DFT) calculations of 103Rh chemical shift tensors and their analysis with natural bond orbital (NBO) and natural localized molecular orbital (NLMO) protocols, to develop correlations between 103Rh chemical shift tensors, molecular structure, and Rh–ligand bonding. 103Rh is one of the least receptive NMR nuclides, and consequently, there are very few reports in the literature. We introduce robust 103Rh SSNMR protocols for stationary samples, which use the broadband adiabatic inversion-cross polarization (BRAIN-CP) pulse sequence and wideband uniform-rate smooth-truncation (WURST) pulses for excitation, refocusing, and polarization transfer, and demonstrate the acquisition of 103Rh SSNMR spectra of unprecedented signal-to-noise and uniformity. The 103Rh chemical shift tensors determined from these spectra are complemented by NBO/NLMO analyses of contributions of individual orbitals to the 103Rh magnetic shielding tensors to understand their relationship to structure and bonding. Finally, we discuss the potential for these experimental and theoretical protocols for investigating a wide range of materials containing the platinum group elements.

Rh magnetic shielding tensors were performed at the PBE0/SO level.b Balanced indicates that TZ2P was used for the entire molecule, whereas locally dense indicates that TZ2P was used for the rhodium atom and all directly bonded atoms, and DZ was used for all remaining atoms within the molecule.c The chemical shift distance between the 103 Rh magnetic shielding tensors (balanced vs. locally-dense basis sets).-1765 a Where indicated, the calculation produced one or more pairs of NLMOs with mixed in-plane vs. out-of-place local  symmetry.For the purpose of visualization, linear combinations of these NLMOs with clean symmetries were generated.The combined shielding contributions from these orbitals are the same for the original NLMOs and the symmetry-adapted linear combinations.In some cases, the contributions are grouped with other NLMOs of matching symmetry.b By construction, the scalar relativistic NLMOs have occupations of either 2 or 0. Contributions shown from unoccupied orbitals come about because of the SO electronic calculation modifying the ground-state density relative to that of the parent scalar relativistic calculation.c Rounded from sum of contributions at full numerical precision.d Numbers in parentheses indicate combined contributions from many equivalent NLMOs.
[Rh(NH3)5Cl] 2+ (1) Where indicated, the calculation produced one or more pairs of NLMOs with mixed in-plane vs. out-of-place local  symmetry.For the purpose of visualization, linear combinations of these NLMOs with clean symmetries were generated.The combined shielding contributions from these orbitals are the same for the original NLMOs and the symmetry-adapted linear combinations.In some cases, the contributions are grouped with other NLMOs of matching symmetry.b By construction, the scalar relativistic NLMOs have occupations of either 2 or 0. Contributions shown from unoccupied orbitals come about because of the SO electronic calculation modifying the ground-state density relative to that of the parent scalar relativistic calculation.c Rounded from sum of contributions at full numerical precision.d Numbers in parentheses indicate combined contributions from many equivalent NLMOs.(2) The chemical shift distance for atom v, dv, provides a comparison between a calculated and experimental chemical shift tensor with a single scalar value in ppm.Given two sets of principal components of chemical shift tensors, dv is defined by the following expression: . (3) A root-mean-square chemical shift distance for an ensemble of N chemical shift tensors (RMS) is determined by the following expression:

Scheme S2 .
Scheme S2.Illustration of the BRAIN-CP pulse sequence, with modifications highlighted: (i) the inclusion of a flip-back pulse (green box) can potentially reduce the recycle delay; (ii) a rampedamplitude 1 H spin-lock pulse (orange box) compensates for rf inhomogeneities at offsets far from the transmitter.

Figure S1 .
Figure S1.Experimental PXRD pattern of [Rh(NH3)5Cl]Cl2 in orange, and corresponding simulation based on the known crystal structure (both at 298 K) in black.

Figure S2 .
Figure S2.Experimental PXRD patterns (colored lines), and corresponding simulations based on the known crystal structures (black lines).An impurity is marked by as asterisk.

Figure S3 .
Figure S3.Clusters models used to model the lattice effects on computed 103 Rh magnetic shielding tensors.

Figure S4 .
Figure S4.Orientations of the principal values of the 103 Rh magnetic shielding tensors, as calculated at the PBE0/SO level.The yellow vectors show the orientations of two principal values, with the third oriented perpendicular to the page.

Figure S5 .
Figure S5.The combination of long contact pulses of 30 ms, ramped-amplitude 1 H spin-lock pulses, and flip-back pulses greatly reduces experimental times, relative to experiments acquired using shorter contact pulses (15 -16 ms), constant-amplitude 1 H spin-lock pulses, and no flipback pulse.All data were acquired at 21.1 T using the BRAIN-CP sequence.

Figure S7 .
Figure S7.Calculations of 103 Rh magnetic shielding tensors using complete first coordination shell clusters of molecules (yellow) or isolated molecules (purple) as structural models.All calculations were performed at the PBE0/SO level.Black lines represent the best fits, with the equations provided.

Figure S15 .
Figure S15.Isosurfaces for primary NLMOs contributing to the Rh isotropic shielding in the cluster model for the [Rh(NH3)5Cl]Cl2 complex in the crystal.

Figure S16 .
Figure S16.Isosurfaces for primary NLMOs contributing to the Rh isotropic shielding in the cluster model of the Rh(CO)2(acac) crystal.

Supplement 1 :
Chemical Shift Distance.The relationship between calculated principal components of the 103 Rh magnetic shielding tensors (  ,calc ) and experimental principal components of 103 Rh chemical shift tensors (  ,exp ) is described by the following expression: v denotes the rhodium site (v = 1, 2, …, N), the index i denotes the principal component of the shielding tensor (i = 1, 2, 3), A represents the slope of the correlation line, and B represents the interpolated shielding of the reference state.Calculated chemical shifts (  ,calc ) are derived from the following expression:   ,calc = ( −   ,calc )/.

Table S1 .
Some experimental parameters for the 1 H-103 Rh BRAIN-CP spectra shown in Figures1 -2.

Table S2 .
More experimental parameters for the 1 H-103 Rh BRAIN-CP spectra shown in Figure2.

Table S3 .
Experimental parameters for the 1 H-103 Rh BRAIN-CP spectra shown in Figures 3 and S4.
aThe spectrum in Figure

Table S4 .
Experimental parameters for the 1 H-103 Rh BRAIN-CP spectra shown in Figures 4 and S5.

Table S5 .
Crystallographic information and CSD/ICSD codes for all materials.

Table S6 .
Convergence of GIPAW calculations of 103 Rh magnetic shielding tensors with respect to plane-wave cutoff energy and k-point spacing in Rh(CO)2(acac). a a In these calculations, atomic coordinates were first optimized, followed by calculation of the 103 Rh magnetic shielding tensor at the same level.

Table S7 .
Calculated 103 Rh magnetic shielding tensors for isolated molecules using balanced and locally dense basis sets.a,b

Table S8 .
Summary of calculated 103 Rh magnetic shielding tensors.

Table S9 .
Summary of NLMO contributions to 103 Rh isotropic shielding for isolated rhodium complexes (absent crystal embedding).

Table S11 .
Summary of NLMO contributions to103Rh isotropic shielding for rhodium complexes in a cluster-model crystal embedding.By construction, the scalar relativistic NLMOs have occupations of either 2 or 0. Contributions shown from unoccupied orbitals come about because of the SO electronic calculation modifying the ground-state density relative to that of the parent scalar relativistic calculation.
b Rounded from sum of contributions at full numerical precision.c Numbers in parentheses indicate combined contributions from that many equivalent NLMOs.