Perspective on Norman Ramsey’s theories of NMR chemical shifts and nuclear spin—spin coupling

Electron correlation and vibrational effects in predictions of paramagnetic NMR shifts

Electronic structure calculations are fundamentally important for the interpretation of nuclear magnetic resonance (NMR) spectra from paramagnetic systems that include organometallic and inorganic compounds, catalysts, or metal-binding sites in proteins. Prediction of induced paramagnetic NMR shifts requires knowledge of electron paramagnetic resonance (EPR) parameters: the electronic g tensor, zero-field splitting D tensor, and hyperfine A tensor. The isotropic part of A, called the hyperfine coupling constant (HFCC), is one of the most troublesome properties for quantum chemistry calculations. Yet, even relatively small errors in calculations of HFCC tend to propagate into large errors in the predicted NMR shifts. The poor quality of A tensors that are currently calculated using density functional theory (DFT) constitutes a bottleneck in improving the reliability of interpretation of the NMR spectra from paramagnetic systems. In this work, electron correlation effects in calculations of HFCCs with a hierarchy of ab initio methods were assessed, and the applicability of different levels of DFT approximations and the coupled cluster singles and doubles (CCSD) method was tested. These assessments were performed for the set of selected test systems comprising an organic radical, and complexes with transition metal and rare-earth ions, for which experimental data are available. Severe deficiencies of DFT were revealed but the CCSD method was able to deliver good agreement with experimental data for all systems considered, however, at substantial computational costs. We proposed a more computationally tractable alternative, where the A was computed with the coupled cluster theory exploiting locality of electron correlation. This alternative is based on the domain-based local pair natural orbital coupled cluster singles and doubles (DLPNO-CCSD) method. In this way the robustness and reliability of the coupled cluster theory were incorporated into the modern formalism for the prediction of induced paramagnetic NMR shifts, and became applicable to systems of chemical interest. This approach was verified for the bis(cyclopentadienyl)vanadium(II) complex (Cp₂V; vanadocene), and the metal-binding site of the Zn²⁺ → Co²⁺ substituted superoxide dismutase (SOD) metalloprotein. Excellent agreement with experimental NMR shifts was achieved, which represented a substantial improvement over previous theoretical attempts. The effects of vibrational corrections to orbital shielding and hyperfine tensor were evaluated and discussed within the second-order vibrational perturbation theory (VPT2) framework.

Calculating NMR Chemical Shifts for Paramagnetic Metal Complexes from First-Principles

Paramagnetic effects on NMR shifts (pNMR) for paramagnetic metal complexes are calculated from first-principles, without recourse to spin Hamiltonian parameters. A newly developed code based on complete active space (CAS) and restricted active space (RAS) techniques in conjunction with treating spin-orbit (SO) coupling via state interaction is applied to (13)C NMR shifts of actinyl tris-carbonate complexes, specifically [UO2(CO3)3](5-) and [NpO2(CO3)3](4-). The experimental pNMR shifts as well as the sizable difference of the (13)C NMR shift for these iso-electronic species are well reproduced by the calculations. Approximations to the pNMR shift equations using spin Hamiltonian parameters or the magnetic susceptibility are calculated for the same systems at the same level of theory, and it is shown how the approximations relate to the ab initio data.

Shielding and indirect spin-spin coupling tensors in the presence of a heavy atom: an experimental and theoretical study of bis(phenylethynyl)mercury

Magnetic shielding and indirect spin-spin coupling phenomena are tensorial properties and both their isotropic and anisotropic parts do affect NMR spectra. The involved interaction tensors, σ and J, can nowadays be theoretically calculated, although the reliability of such methods in the case of anisotropic parameters, Δσ and ΔJ, in systems involving heavy nuclei, yet demands testing. In this communication the results of the experimental and theoretical investigations of bis(phenylethynyl)mercury (I) labeled with (13)C isotope at positions neighboring Hg are reported. The theoretical calculations of molecular geometry and values of NMR parameters for I have been performed by the ZORA/DFT method, including the relativistic scalar and spin-orbit coupling contributions, using the PBE0 functional and TZP (or jcpl) basis set. These values have been confronted with the experimentally measured ones. The isotropic parameters have been measured by the standard (13)C and (199)Hg NMR spectra. The shielding anisotropies for the atoms in the central part of molecule I have been determined in a liquid sample using magnetic relaxation measurements. The relaxation data have been interpreted within the rotational diffusion theory, assuming the symmetrical top reorientation model. The anisotropies of one-bond (13)C-(199)Hg and two-bond (13)C-Hg-(13)C spin-spin couplings have been determined exploiting the temperature-dependent (13)C NMR spectra of I in the ZLI1167 liquid-crystal phase. We have found that our theoretical calculations reproduce experimental values of both isotropic and anisotropic NMR parameters very well.

Molecular orbital analysis of the inverse halogen dependence of nuclear magnetic shielding in LaX₃, X = F, Cl, Br, I

The NMR nuclear shielding tensors for the series LaX(3), with X = F, Cl, Br and I, have been computed using two-component relativistic density functional theory based on the zeroth-order regular approximation (ZORA). A detailed analysis of the inverse halogen dependence (IHD) of the La shielding was performed via decomposition of the shielding tensor elements into contributions from localized and delocalized molecular orbitals. Both spin-orbit and paramagnetic shielding terms are important, with the paramagnetic terms being dominant. Major contributions to the IHD can be attributed to the La-X bonding orbitals, as well as to trends associated with the La core and halogen lone pair orbitals, the latter being related to X-La π donation. An 'orbital rotation' model for the in-plane π acceptor f orbital of La helps to rationalize the significant magnitude of deshielding associated with the in-plane π donation. The IHD goes along with a large increase in the shielding tensor anisotropy as X becomes heavier, which can be associated with trends for the covalency of the La-X bonds, with a particularly effective transfer of spin-orbit coupling induced spin density from iodine to La in LaI(3).

A Combined Experimental and Quantum Chemistry Study of Selenium Chemical Shift Tensors

A comprehensive investigation of selenium chemical shift tensors is presented. Experimentally determined chemical shift tensors were obtained from solid-state 77Se NMR spectra for several organic, organometallic, or inorganic selenium-containing compounds. The first reported indirect spin-spin coupling between selenium and chlorine is observed for Ph(2)SeCl(2) where 1J(77Se,35Cl)iso is 110 Hz. Selenium magnetic shielding tensors were calculated for all of the molecules investigated using zeroth-order regular approximation density functional theory, ZORA DFT. The computations provide the orientations of the chemical shift tensors, as well as a test of the theory for calculating the magnetic shielding interaction for heavier elements. The ZORA DFT calculations were performed with nonrelativistic, scalar relativistic, and scalar with spin-orbit relativistic levels of theory. Relativistic contributions to the magnetic shielding tensor were found to be significant for (NH4)2WSe4 and of less importance for organoselenium, organophosphine selenide, and inorganic selenium compounds containing lighter elements.

195Pt NMR--theory and application

This critical review highlights the progress in (195)Pt NMR over the last 25 years. In particular, some of the recent applications of (195)Pt NMR in catalytic and mechanistic studies, intermetallics and drug binding studies are discussed. (195)Pt NMR chemical shifts obtained from both theoretical studies and experiments are presented for Pt(0), Pt(II), Pt(III) and Pt(IV) complexes. (195)Pt coupling with various nuclei (viz. coupling constants) have also been collected in addition to data on (195)Pt relaxation. The latest developments in the theoretical knowledge and experimental advances have made (195)Pt NMR into a rich source of information in many fields. (164 references.).

A theoretical investigation of the remarkable nuclear spin-spin coupling pattern in [(NC)(5)Pt-Tl(CN)](-)

We address the problem of the interpretation of heavy nucleus spin-spin couplings for systems being studied in solution. Solvation can create counterintuitive features concerning the spin-spin couplings, which are enhanced by relativistic effects due to the presence of heavy nuclei. This should therefore be taken into consideration for the discussion of spectra obtained from solution. Evidence for such solvent effects is provided by a relativistic density functional study of [(NC)(5)Pt-Tl(CN)](-) (I). It is demonstrated that the remarkable experimentally observed spin-spin coupling pattern, e.g., (2)J(Tl-C) >> (1)J(Tl-C) and J(Pt-Tl) approximately 57 kHz, is semiquantitatively reproduced by our calculations if both relativistic effects and solvation are taken into account. Solvent effects are very substantial and shift the Pt-Tl coupling by more than 100%, e.g. Relativistic increase of s-orbital density at the heavy nuclei, charge donation by the solvent, and the specific features of the multicenter C-Pt-Tl-C bond are responsible for the observed coupling pattern.

Hyperfine Parameters for Aluminum Hydride: An ab Initio Molecular Orbital Study

An extensive ab initio molecular orbital study of the (27)Al nuclear spin-rotation and nuclear quadrupolar coupling constants in aluminum hydride, AlH, has been performed. The (27)Al nuclear spin-rotation constant (C( perpendicular)), calculated to be approximately 300 kHz, was neglected in a previous analysis of the hyperfine structure in the microwave spectrum (M. Goto and S. Saito, Astrophys. J. 452, L147-148 (1995)). Unfortunately, the ab initio calculations do not provide a definitive value for the aluminum nuclear quadrupolar coupling constant, but suggest a value of -49+/-4 MHz. It is apparent that the microwave study of AlH should be repeated. Copyright 2001 Academic Press.

Solvent effects on heavy atom nuclear spin-spin coupling constants: a theoretical study of Hg-C and Pt-P couplings

The computation of indirect nuclear spin-spin coupling constants, based on the relativistic two-component zeroth order regular approximate Hamiltonian, has been recently implemented by us into the Amsterdam Density Functional program. Applications of the code for the calculation of one-bond metal-ligand couplings of coordinatively unsaturated compounds containing (195)Pt and (199)Hg, including spin-orbit coupling or coordination effects by solvent molecules, show that relativistic density functional calculations are able to reproduce the experimental findings with good accuracy for the systems under investigation. Spin-orbit effects are rather small for these cases, while coordination of the heavy atoms by solvent molecules has a great impact on the calculated couplings. Experimental trends for different solvents are reproduced. An orbital-based analysis of the solvent effect is presented. The scalar relativistic increase of the coupling constants is of the same order of magnitude as the nonrelativistically obtained values, making a relativistic treatment essential for obtaining quantitatively correct results. Solvent effects can be of similar importance.

Hyperfine Structure in the Rotational Spectrum of GaF: A Comparison of Experimental and Calculated Spin-Rotation and Electric Field Gradient Tensors

The high-resolution pure rotational spectrum of GaF has been measured using a Balle-Flygare-type Fourier transform spectrometer. Improved nuclear quadrupolar coupling constants and rotational constants have been obtained along with the first reported fluorine spin-rotation constant for gallium fluoride, C(I) ((69)Ga(19)F, v = 0) = +32.0(21) kHz. Accurate spin-rotation tensors from microwave or molecular beam spectroscopy are particularly important to NMR spectroscopists and theoreticians because these data provide information about anisotropic nuclear magnetic shielding in the absence of intermolecular effects. For quadrupolar nuclei such as gallium, the quadrupolar interaction is sufficiently large that it is very difficult to characterize shielding tensors directly via NMR spectroscopy. The experimentally determined nuclear quadrupolar coupling constants and spin-rotation constants for GaF are compared with the results of a series of high-level ab initio calculations carried out at various levels of theory with a range of basis sets. Further calculations on BF and AlF, supplemented with available experimental data for InF and TlF, allow for the investigation of trends in nuclear magnetic shielding, spin-rotation, and electric field gradient tensors in the group-13 fluorides. Calculations at the MP2/6-311++G** and MP2/6-311G(2df, 2pd) levels provide the most consistently satisfactory results in comparison with the experimental data. Copyright 2000 Academic Press.