Electron-Spin Structure and Metal–Ligand Bonding in Open-Shell Systems from Relativistic EPR and NMR: A Case Study of Square-Planar Iridium Catalysts

Paramagnetic Effects in NMR Spectroscopy of Transition-Metal Complexes: Principles and Chemical Concepts

ConspectusMagnetic resonance techniques represent a fundamental class of spectroscopic methods used in physics, chemistry, biology, and medicine. Electron paramagnetic resonance (EPR) is an extremely powerful technique for characterizing systems with an open-shell electronic nature, whereas nuclear magnetic resonance (NMR) has traditionally been used to investigate diamagnetic (closed-shell) systems. However, these two techniques are tightly connected by the electron-nucleus hyperfine interaction operating in paramagnetic (open-shell) systems. Hyperfine interaction of the nuclear spin with unpaired electron(s) induces large temperature-dependent shifts of nuclear resonance frequencies that are designated as hyperfine NMR shifts (δHF).Three fundamental physical mechanisms shape the total hyperfine interaction: Fermi-contact, paramagnetic spin-orbit, and spin-dipolar. The corresponding hyperfine NMR contributions can be interpreted in terms of through-bond and through-space effects. In this Account, we provide an elemental theory behind the hyperfine interaction and NMR shifts and describe recent progress in understanding the structural and electronic principles underlying individual hyperfine terms.The Fermi-contact (FC) mechanism reflects the propagation of electron-spin density throughout the molecule and is proportional to the spin density at the nuclear position. As the imbalance in spin density can be thought of as originating at the paramagnetic metal center and being propagated to the observed nucleus via chemical bonds, FC is an excellent indicator of the bond character. The paramagnetic spin-orbit (PSO) mechanism originates in the orbital current density generated by the spin-orbit coupling interaction at the metal center. The PSO mechanism of the ligand NMR shift then reflects the transmission of the spin polarization through bonds, similar to the FC mechanism, but it also makes a substantial through-space contribution in long-range situations. In contrast, the spin-dipolar (SD) mechanism is relatively unimportant at short-range with significant spin polarization on the spectator atom. The PSO and SD mechanisms combine at long-range to form the so-called pseudocontact shift, traditionally used as a structural and dynamics probe in paramagnetic NMR (pNMR). Note that the PSO and SD terms both contribute to the isotropic NMR shift only at the relativistic spin-orbit level of theory.We demonstrate the advantages of calculating and analyzing the NMR shifts at relativistic two- and four-component levels of theory and present analytical tools and approaches based on perturbation theory. We show that paramagnetic NMR effects can be interpreted by spin-delocalization and spin-polarization mechanisms related to chemical bond concepts of electron conjugation in π-space and hyperconjugation in σ-space in the framework of the molecular orbital (MO) theory. Further, we discuss the effects of environment (supramolecular interactions, solvent, and crystal packing) and demonstrate applications of hyperfine shifts in determining the structure of paramagnetic Ru(III) compounds and their supramolecular host-guest complexes with macrocycles.In conclusion, we provide a short overview of possible pNMR applications in the analysis of spectra and electronic structure and perspectives in this field for a general chemical audience.

Mechanisms of Ligand Hyperfine Coupling in Transition-Metal Complexes: σ and π Transmission Pathways

Theoretical interpretation of hyperfine interactions was pioneered in the 1950s-1960s by the seminal works of McConnell, Karplus, and others for organic radicals and by Watson and Freeman for transition-metal (TM) complexes. In this work, we investigate a series of octahedral Ru(III) complexes with aromatic ligands to understand the mechanism of transmission of the spin density from the d-orbital of the metal to the s-orbitals of the ligand atoms. Spin densities and spin populations underlying ligand hyperfine couplings are analyzed in terms of π-conjugative or σ-hyperconjugative delocalization vs spin polarization based on symmetry considerations and restricted open-shell vs unrestricted wave function analysis. The transmission of spin density is shown to be most efficient in the case of symmetry-allowed π-conjugative delocalization, but when the π-conjugation is partially or fully symmetry-forbidden, it can be surpassed by σ-hyperconjugative delocalization. Despite a lower spin population of the ligand in σ-hyperconjugative transmission, the hyperfine couplings can be larger because of the direct involvement of the ligand s-orbitals in this delocalization pathway. We demonstrate a quantitative correlation between the hyperfine couplings of aromatic ligand atoms and the characteristics of the metal-ligand bond modulated by the trans substituent, a hyperfine trans effect.

Cleavage of an Aromatic C-C Bond in Ferrocene by Insertion of an Iridium Nitrido Nitrogen Atom

The intermolecular cleavage of C-C bonds is a rare event. Herein, we report on a late transition-metal terminal nitrido complex, which upon oxidation undergoes insertion of the nitrido nitrogen atom into the aromatic C-C bond of ferrocene. This reaction path was confirmed through ¹⁵N and deuterium isotope labeling experiments of the nitrido complex and ferrocenium, respectively. Cyclic voltammetry and UV/vis spectroscopy monitoring of the reaction revealed that oxidation is the initial step, yielding the tentative radical cationic nitrido complex, which is experimentally supported by extended X and Q-band electron paramagnetic resonance (EPR) and ENDOR, UV/vis, vT ¹H NMR, and vibrational spectroscopic data. Density functional theory (DFT) and multireference calculations of this highly reactive intermediate revealed an S = 1/2 ground state. The high reactivity can be traced to the increased electrophilicity in the oxidized complex. Based on high-level PNO-UCCSD(T) calculations and UV/vis kinetic measurements, it is proposed that the reaction proceeds by initial electrophilic exo attack of the nitrido nitrogen atom at the cyclopentadienyl ring and consecutive ring expansion to a pyridine ring.

Quadratic Spin-Orbit Mechanism of the Electronic g-Tensor

Understanding how the electronic g-tensor is linked to the electronic structure is desirable for the correct interpretation of electron paramagnetic resonance spectra. For heavy-element compounds with large spin-orbit (SO) effects, this is still not completely clear. We report our investigation of quadratic SO contributions to the g-shift in heavy transition metal complexes. We implemented third-order perturbation theory in order to analyze the contributions arising from frontier molecular spin orbitals (MSOs). We show that the dominant quadratic SO term─spin-Zeeman (SO²/SZ)─generally makes a negative contribution to the g-shift, irrespective of the particular electronic configuration or molecular symmetry. We further analyze how the SO²/SZ contribution adds to or subtracts from the linear orbital-Zeeman (SO/OZ) contribution to the individual principal components of the g-tensor. Our study suggests that the SO²/SZ mechanism decreases the anisotropy of the g-tensor in early transition metal complexes and increases it in late transition metal complexes. Finally, we apply MSO analysis to the investigation of g-tensor trends in a set of closely related Ir and Rh pincer complexes and evaluate the influence of different chemical factors (the nuclear charge of the central atom and the terminal ligand) on the magnitudes of the g-shifts. We expect our conclusions to aid the understanding of spectra in magnetic resonance investigations of heavy transition metal compounds.

Nature of NMR Shifts in Paramagnetic Octahedral Ru(III) Complexes with Axial Pyridine-Based Ligands

In recent decades, transition-metal coordination compounds have been extensively studied for their antitumor and antimetastatic activities. In this work, we synthesized a set of symmetric and asymmetric Ru(III) and Rh(III) coordination compounds of the general structure (Na⁺/K⁺/PPh₄⁺/LH⁺) [trans-M^IIIL(eq)_nL(ax)₂]^- (M = Ru^III or Rh^III; L(eq) = Cl, n = 4; L(eq) = ox, n = 2; L(ax) = 4-R-pyridine, R = CH₃, H, C₆H₅, COOH, CF₃, CN; L(ax) = DMSO-S) and systematically investigated their structure, stability, and NMR properties. ¹H and ¹³C NMR spectra measured at various temperatures were used to break down the total NMR shifts into the orbital (temperature-independent) and hyperfine (temperature-dependent) contributions. The hyperfine NMR shifts for paramagnetic Ru(III) compounds were analyzed in detail using relativistic density functional theory (DFT). The effects of (i) the 4-R substituent of pyridine, (ii) the axial trans ligand L(ax), and (iii) the equatorial ligands L(eq) on the distribution of spin density reflected in the "through-bond" (contact) and the "through-space" (pseudocontact) contributions to the hyperfine NMR shifts of the individual atoms of the pyridine ligands are rationalized. Further, we demonstrate the large effects of the solvent on the hyperfine NMR shifts and discuss our observations in the general context of the paramagnetic NMR spectroscopy of transition-metal complexes.

Theoretical Studies on the Photophysical Properties of the Ag(I) Complex for Thermally Activated Delayed Fluorescence Based on TD-DFT and Path Integral Dynamic Approaches

Theoretical calculation not only is a powerful tool to deeply explore photophysical processes of the emitters but also provides a theoretical basis for material renewal and design strategy in the future. In this work, the interconversion and decay rates of the thermally activated delayed fluorescence (TADF) process of the rigid Ag(dbp)(P₂-nCB) complex are quantitatively calculated by employing the optimally tuned range-separated hybrid functional (ω*B97X-D3) method combined with the path integral approach to dynamics considering the Herzberg-Teller and the Duschinsky rotation effects within a multimode harmonic oscillator model. The calculated results show that the small energy splitting ΔE(S₁-T₁) = 742 cm^-1 (experimental value of 650 cm^-1) of the lowest singlet S₁ and triplet T₁ state and proper vibrational spin-orbit coupling interactions facilitate the reverse intersystem crossing (RISC) processes from the T₁ to S₁ states. The k _RISC rate is estimated to be 1.72 × 10⁸ s^-1 that is far more than the intersystem crossing rate k _ISC of 7.28 × 10⁷ s^-1, which will greatly accelerate the RISC process. In addition, the multiple coupling routes of zero-field splitting (ZFS) interaction can provide energetically nearby lying states, to speed up the RISC pathway, and restrict the phosphorescence decay rate. A smaller ZFS D-tensor of 0.143 cm^-1, E/D ≈ 0.094 ≪ 1/3, and Δg > 0 are obtained, indicating that the excited singlet states are hardly mixed into the T₁ state; thus, a lower phosphorescence decay rate (k _p = 9.29 × 10¹ s^-1) is expected to occur, and the T₁ state has a long lifetime, which is helpful for the occurrence of the RISC process. These works are in excellent agreement with the experimental observation and are useful for improving and designing efficient TADF materials.

Crystal and Substituent Effects on Paramagnetic NMR Shifts in Transition-Metal Complexes

Nuclear magnetic resonance (NMR) spectroscopy of paramagnetic molecules provides detailed information about their molecular and electron-spin structure. The paramagnetic NMR spectrum is a very rich source of information about the hyperfine interaction between the atomic nuclei and the unpaired electron density. The Fermi-contact contribution to ligand hyperfine NMR shifts is particularly informative about the nature of the metal–ligand bonding and the structural arrangements of the ligands coordinated to the metal center. In this account, we provide a detailed experimental and theoretical NMR study of compounds of Cr(III) and Cu(II) coordinated with substituted acetylacetonate (acac) ligands in the solid state. For the first time, we report the experimental observation of extremely paramagnetically deshielded ¹³C NMR resonances for these compounds in the range of 900–1200 ppm. We demonstrate an excellent agreement between the experimental NMR shifts and those calculated using relativistic density-functional theory. Crystal packing is shown to significantly influence the NMR shifts in the solid state, as demonstrated by theoretical calculations of various supramolecular clusters. The resonances are assigned to individual atoms in octahedral Cr(acac)₃ and square-planar Cu(acac)₂ compounds and interpreted by different electron configurations and magnetizations at the central metal atoms resulting in different spin delocalizations and polarizations of the ligand atoms. Further, effects of substituents on the ¹³C NMR resonance of the ipso carbon atom reaching almost 700 ppm for Cr(acac)₃ compounds are interpreted based on the analysis of Fermi-contact hyperfine contributions.

The ligand NMR shifts in paramagnetic acetylacetonato Cr(III) and Cu(II) complexes have been predicted and measured in the solid state and interpreted by relativistic DFT calculations. The effects of the metal atom, ligand, and crystal packing on the spin delocalization and polarization reflected in the Fermi-contact contribution to the hyperfine interaction are rationalized.

Zwitterionic Ru(III) Complexes: Stability of Metal-Ligand Bond and Host-Guest Binding with Cucurbit[7]uril

A wide range of ruthenium-based coordination compounds have been reported to possess potential as metallodrugs with anticancer or antimetastatic activity. In this work, we synthesized a set of new zwitterionic Ru(III) compounds bearing ligands derived from N-alkyl (R) systems based on pyridine, 4,4'-bipyridine, or 1,4-diazabicyclo[2.2.2]octane (DABCO). The effects of the ligand(s) and their environment on the coordination stability have been investigated. Whereas the [DABCO-R]⁺ ligand is shown to be easily split out of a negative [RuCl₄]^- core, positively charged R-pyridine and R-bipyridine ligands form somewhat more stable Ru(III) complexes and can be used as supramolecular anchors for binding with macrocycles. Therefore, supramolecular host-guest assemblies between the stable zwitterionic Ru(III) guests and the cucurbit[7]uril host were investigated and characterized in detail by using NMR spectroscopy and single-crystal X-ray diffraction. Paramagnetic ¹H NMR experiments supplemented by relativistic DFT calculations of the structure and hyperfine NMR shifts were performed to determine the host-guest binding modes in solution. In contrast to the intramolecular hyperfine shifts, dominated by the through-bond Fermi-contact mechanism, supramolecular hyperfine shifts were shown to depend on the "through-space" spin-dipole contributions with structural trends being satisfactorily reproduced by a simple point-dipole approximation.

Remarkable reversal of 13C-NMR assignment in d1, d2 compared to d8, d9 acetylacetonate complexes: analysis and explanation based on solid-state MAS NMR and computations

13C solid-state MAS NMR spectra of a series of paramagnetic metal acetylacetonate complexes; [VO(acac)2] (d1, S = ½), [V(acac)3] (d2, S = 1), [Ni(acac)2(H2O)2] (d8, S = 1), and [Cu(acac)2] (d9, S = ½), were assigned using modern NMR shielding calculations. This provided a reliable assignment of the chemical shifts and a qualitative insight into the hyperfine couplings. Our results show a reversal of the isotropic 13C shifts, δiso(13C), for CH3 and CO between the d1 and d2versus the d8 and d9 acetylacetonate complexes. The CH3 shifts change from about -150 ppm (d1,2) to roughly 1000 ppm (d8,9), whereas the CO shifts decrease from 800 ppm to about 150 ppm for d1,2 and d8,9, respectively. This was rationalized by comparison of total spin-density plots and computed contact couplings to those corresponding to singly occupied molecular orbitals (SOMOs). This revealed the interplay between spin delocalization of the SOMOs and spin polarization of the lower-energy MOs, influenced by both the molecular symmetry and the d-electron configuration. A large positive chemical shift results from spin delocalization and spin polarization acting in the same direction, whereas their cancellation corresponds to a small shift. The SOMO(s) for the d8 and d9 complexes are σ-like, implying spin-delocalization on the CH3 and CO groups of the acac ligand, cancelled only for CO by spin polarization. In contrast, the SOMOs of the d1 and d2 systems are π-like and a large CO-shift results from spin polarization, which accounts for the reversed assignment of δiso(13C) for CH3 and CO.