A DFT/ZORA Study of Cadmium Magnetic Shielding Tensors: Analysis of Relativistic Effects and Electronic-State Approximations

Uniform chi-squared model probabilities in NMR crystallography

A nearly universal component of NMR crystallography is the ranking of candidate structures based on how well their first-principles-predicted NMR parameters align with the results of solid-state NMR experiments. Here, a novel approach for assigning probabilities to candidate models is proposed that quantifies the likelihood that each model is the correct experimental structure. This method employs hierarchical Bayesian inference and leverages explicit prior probabilities derived from a uniform distribution of potential candidate structures with respect to chi-squared values. The resulting uniform chi-squared (UC) model provides a more cautious estimate of candidate probabilities compared to previous approaches, assigning decreased likelihood to the best-fit structure and increased likelihood to alternate candidates. Although developed here within the context of NMR crystallography, the UC model represents a general method for assigning likelihoods based on chi-squared goodness-of-fit assessments.

Understanding Cu(i) local environments in MOFs via63/65Cu NMR spectroscopy

The field of metal-organic frameworks (MOFs) includes a vast number of hybrid organic and inorganic porous materials with wide-ranging applications. In particular, the Cu(i) ion exhibits rich coordination chemistry in MOFs and can exist in two-, three-, and four-coordinate environments, which gives rise to many structural motifs and potential applications. Direct characterization of the structurally and chemically important Cu(i) local environments is essential for understanding the sources of specific MOF properties. For the first time, 63/65Cu solid-state NMR has been used to investigate a variety of Cu(i) sites and local coordination geometries in Cu MOFs. This approach is a sensitive probe of the local Cu environment, particularly when combined with density functional theory calculations. A wide range of structurally-dependent 63/65Cu NMR parameters have been observed, including 65Cu quadrupolar coupling constants ranging from 18.8 to 74.8 MHz. Using the data from this and prior studies, a correlation between Cu quadrupolar coupling constants, Cu coordination number, and local Cu coordination geometry has been established. Links between DFT-calculated and experimental Cu NMR parameters are also presented. Several case studies illustrate the feasibility of 63/65Cu NMR for investigating and resolving inequivalent Cu sites, monitoring MOF phase changes, interrogating the Cu oxidation number, and characterizing the product of a MOF chemical reaction involving Cu(ii) reduction to Cu(i). A convenient avenue to acquire accurate 65Cu NMR spectra and NMR parameters from Cu(i) MOFs at a widely accessible magnetic field of 9.4 T is described, with a demonstrated practical application for tracking Cu(i) coordination evolution during MOF anion exchange. This work showcases the power of 63/65Cu solid-state NMR spectroscopy and DFT calculations for molecular-level characterization of Cu(i) centers in MOFs, along with the potential of this protocol for investigating a wide variety of MOF structural changes and processes important for practical applications. This approach has broad applications for examining Cu(i) centers in other weight-dilute systems.

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.

Relativistic DFT Calculations of Cadmium and Selenium Solid-State NMR Spectra of CdSe Nanocrystal Surfaces

Solid-state NMR spectra have been used to probe the structure of CdSe nanocrystals and propose detailed models of their surface structures. Density functional theory (DFT)-optimized cluster models that represent probable molecular structures of carboxylate-coordinated surface sites have been proposed. However, to the best of our knowledge, 113Cd and 77Se chemical shifts have not been calculated for these surface models. We performed relativistic DFT calculations of cadmium and selenium magnetic shielding tensors on model compounds with previously measured solid-state NMR spectra with (i) the four-component Dirac-Kohn-Sham (DKS) Hamiltonian and (ii) the scalar and (iii) spin-orbit levels within the ZORA Hamiltonian. Molecular clusters with Cd and Se sites in varying bonding environments were used to model CdSe (100) and CdSe(111) surfaces capped with carboxylic acid ligands. Our calculations identify the observed 113Cd isotropic chemical shifts δ(iso) of -465, -318, and -146 ppm arising from CdSeO3, CdSe2O2, and CdSe3O surface groups, respectively, with very good agreement with experimental measurements. The 113Cd chemical shifts linearly decrease with the number of O-neighbors. The calculated spans (δ11 - δ33) encompass the experimental values for CdSe3O and CdSe2O2 clusters but are slightly larger than the measured value for CdSeO3 clusters. Relativistic DFT calculations predicted a one-bond 113Cd-77Se scalar coupling of 258 Hz, which is in good agreement with the experimental values of 250 Hz. With a dense coverage of carboxylic acid ligands, the CdSe (100) surface shows a distribution of Cd-Se bond lengths and J-couplings. Relativistic DFT simulations thus aid in interpretation of NMR spectra of CdSe nanocrystals and related nanomaterials.