Periodic trends in indirect nuclear spin-spin coupling tensors: relativistic density functional calculations for interhalogen diatomics

Experimental Evidence for Non-Fermi-Contact J Coupling Across Chalcogen Bonds in Ionic Salt Cocrystal Polymorphs

A pair of novel polymorphic ionic cocrystals of 3,4-dicyanotelluradiazole and tetraphenylphosphonium bromide are synthesized and are characterized by single-crystal XRD. Strong and directional non-covalent chalcogen bonds (ChB) between Te and Br are analyzed via solid-state NMR to reveal large and anisotropic J(125Te,79/81Br) coupling tensors, providing unequivocal evidence for non-Fermi contact contributions across ChBs. Along with large 79/81Br quadrupolar couplings for the Br- anions, these data provide new tools to characterize chalcogen bonds and to differentiate between ChB polymorphs.

Methylammonium Cation Dynamics in Methylammonium Lead Halide Perovskites: A Solid-State NMR Perspective

In light of the intense recent interest in the methylammonium lead halides, CH₃NH₃PbX₃ (X = Cl, Br, and I) as sensitizers for photovoltaic cells, the dynamics of the methylammonium (MA) cation in these perovskite salts has been reinvestigated as a function of temperature via ²H, ¹⁴N, and ²⁰⁷Pb NMR spectroscopy. In the cubic phase of all three salts, the MA cation undergoes pseudoisotropic tumbling (picosecond time scale). For example, the correlation time, τ₂, for the C-N axis of the iodide salt is 0.85 ± 0.30 ps at 330 K. The dynamics of the MA cation are essentially continuous across the cubic ↔ tetragonal phase transition; however, ²H and ¹⁴N NMR line shapes indicate that subtle ordering of the MA cation occurs in the tetragonal phase. The temperature dependence of the cation ordering is rationalized using a six-site model, with two equivalent sites along the c-axis and four equivalent sites either perpendicular or approximately perpendicular to this axis. As the cubic ↔ tetragonal phase transition temperature is approached, the six sites are nearly equally populated. Below the tetragonal ↔ orthorhombic phase transition, ²H NMR line shapes indicate that the C-N axis is essentially frozen.

On the calculation of second-order magnetic properties using subsystem approaches in a relativistic framework

The implementation of second-order magnetic properties in a frozen density embedding scheme in a four component relativistic framework is outlined and applied to model H₂X–H₂O systems (X = Se, Te, Po).

Relativistic Calculations of Nuclear Magnetic Resonance Parameters

Relativistic effects are important for the accurate evaluation of the observables of nuclear magnetic resonance (NMR) spectroscopy, the nuclear magnetic shielding and the indirect spin–spin coupling tensors. Some of the most notable relativistic effects, in particular for light elements in the vicinity of heavy nuclei, are due to spin–orbit effects, an effect difficult to evaluate when starting from a non-relativistic wavefunction. Two- and four-component relativistic methods include spin–orbit effects variationally, and the recent improvements in the computational efficiency of these methods open new opportunities for accurate calculations of NMR parameters also for molecules with heavy elements. We here present an overview of the different approximations that have been introduced for calculating relativistic effects with two- and four-component methods and how these methods can be used to calculate the NMR parameters. We will also give some examples of systems that have been studied computationally with two- and four-component relativistic methods and discuss the importance of relativistic effects on the shielding and indirect spin–spin coupling constants.

Quantitative structure parameters from the NMR spectroscopy of quadrupolar nuclei

Nuclear magnetic resonance (NMR) spectroscopy is one of the most important characterization tools in chemistry, however, 3/4 of the NMR active nuclei are underutilized due to their quadrupolar nature. This short review centers on the development of methods that use solid-state NMR of quadrupolar nuclei for obtaining quantitative structural information. Namely, techniques using dipolar recoupling as well as the resolution afforded by double-rotation are presented for the measurement of spin–spin coupling between quadrupoles, enabling the measurement of internuclear distances and connectivities. Two-dimensional J-resolved-type experiments are then presented for the measurement of dipolar and J coupling, between spin-1/2 and quadrupolar nuclei as well as in pairs of quadrupolar nuclei. Select examples utilizing these techniques for the extraction of structural information are given. Techniques are then described that enable the fine refinement of crystalline structures using solely the electric field gradient tensor, measured using NMR, as a constraint. These approaches enable the solution of crystal structures, from polycrystalline compounds, that are of comparable quality to those solved using single-crystal diffraction.

Spying on the boron-boron triple bond using spin-spin coupling measured from 11B solid-state NMR spectroscopy

Boron–boron J coupling constants provide new insight into the nature of the boron–boron triple bond.

There is currently tremendous interest in the previously documented example of a stable species exhibiting a boron–boron triple bond (Science, 2012, 336, 1420). Notably, it has recently been stated using arguments based on force constants that this diboryne may not, in reality, feature a boron–boron triple bond. Here, we use advanced solid-state NMR and computational methodology in order to directly probe the orbitals involved in multiple boron–boron bonds experimentally via analysis of ¹¹B–¹¹B spin–spin (J) coupling constants. Computationally, the mechanism responsible for the boron–boron spin–spin coupling in these species is found to be analogous to that for the case of multiply-bonded carbon atoms. The trend in reduced J coupling constants for diborenes and a diboryne, measured experimentally, is in agreement with that known for alkenes and alkynes. This experimental probe of the electronic structure of the boron–boron multiple bond provides strong evidence supporting the originally proposed nature of the bonds in the diboryne and diborenes, and demonstrates that the orbitals involved in boron–boron bonding are equivalent to those well known to construct the multiple bonds between other second-row elements such as carbon and nitrogen.

Direct Characterization of Metal-Metal Bonds between Nuclei with Strong Quadrupolar Interactions via NMR Spectroscopy

Metal-metal bonds can be difficult to characterize directly. We demonstrate that J couplings between metal nuclei experiencing strong quadrupolar interactions can be easily measured from well-defined splittings in NMR spectra of powdered samples. Using (69/71)Ga NMR, it is shown that homonuclear J coupling, which is four orders of magnitude smaller than the quadrupolar coupling in a series of compounds featuring gallium-gallium bonds, can be extracted with a 2-D NMR experiment. The dependence of the multiplets on crystal symmetry reveals information on the structures of two Ga-Ga-bonded compounds for which diffraction data are unavailable. Interpretation of the data in a molecular orbital framework provides insight into the nature of the metal-metal bond.

Symmetry-amplified J splittings for quadrupolar spin pairs: a solid-state NMR probe of homoatomic covalent bonds

Chemically informative J couplings between pairs of quadrupolar nuclei in dimetallic and dimetalloid coordination motifs are measured using J-resolved solid-state NMR experiments. It is shown that the application of a double-quantum filter is necessary to observe the J splittings and that, under these conditions, only a simple doublet is expected. Interestingly, the splitting is amplified if the spins are magnetically equivalent, making it possible to measure highly precise J couplings and unambiguously probe the symmetry of the molecule. This is demonstrated experimentally by chemically breaking the symmetry about a pair of boron spins by reaction with an N-heterocyclic carbene to form a β-borylation reagent. The results show that the J coupling is a sensitive probe of bonding in diboron compounds and that the J values quantify the weakening of the B-B bond which occurs when forming an sp(2)-sp(3) diboron compound, which is relevant to their reactivity. Due to the prevalence of quadrupolar nuclei among transition metals, this work also provides a new approach to probe metal-metal bonding; results for Mn2(CO)10 are provided as an example.

A ZORA-DFT and NLMO study of the one-bond fluorine–X indirect nuclear spin-spin coupling tensors for various VSEPR geometries

Zeroth-order regular approximation (ZORA) density functional theory (DFT) calculations of one-bond X–19F indirect nuclear spin-spin coupling (J) tensors were performed on a series of fluorine-containing compounds covering several valence shell electron pair repulsion (VSEPR) theory geometries for which J, by symmetry, is not required to be axially symmetric. The calculations show that the antisymmetric components of J are only of the same order of magnitude as the principal components of the symmetric J-coupling tensor for a few geometries, and that in cases of approximate axial symmetry along the bond, J remains nearly axially symmetric with its unique component along the bond. In general, different species having the same nominal geometry tend to have similar tensor orientations, magnitudes of anisotropy of J relative to the isotropic coupling constant, as well as the same dominant contributions from the different coupling mechanisms. Structures are also systematically modified to determine how the tensor components depend on geometrical parameters. The isotropic coupling constants are subsequently interpreted using a natural localized molecular orbital (NLMO) approach. Our results could prove to be useful for future experimental characterizations of J tensors in systems having symmetry properties that do not force J to be axially symmetric or coincident with the dipolar coupling tensor.

Measurement of delta(1)J((199)Hg, (31)P) in [HgPCy3(OAc)2]2 and relativistic ZORA DFT investigations of mercury-phosphorus coupling tensors

Using 31P solid-state NMR spectroscopy, anisotropy in the indirect 199Hg-31P spin-spin coupling tensor (DeltaJ) for powdered [HgPCy3(OAc)2]2 (1) has been measured as 4700 +/- 300 Hz. Zeroth-order regular approximation (ZORA) density functional theory (DFT) calculations, including scalar and spin-orbit relativistic effects, performed on 1 and a series of other related compounds show that DeltaJ(199Hg, (31)P) arises entirely from the ZORA Fermi-contact-spin-dipolar cross term. The calculations validate assumptions made in the spectral analysis of 1 and in previous determinations of DeltaJ in powder samples, namely that J is axially symmetric and shares its principal axis system with the direct dipolar coupling tensor (D). Agreement between experiment and theory for various 199Hg, 31P spin-spin coupling anisotropies is reasonable; however, experimental values of 1J(199Hg, 31P)(iso) are significantly underestimated by the calculations. The most important improvements in the agreement were obtained as a result of including more of the crystal lattice in the model used for the calculations, e.g., a change of 43% was noted for 1J(199Hg, 31P)(iso) in [HgPPh3(NO3)2]2 depending on whether the two or three nearest nitrate ions are included in the model. Finally, we have written a computer program to simulate the effects of non-axial symmetry in J and of non-coincidence of the J and D on powder NMR spectra. Simulations clearly show that both of these effects have a pronounced impact on the 31P NMR spectrum of 199Hg-31P spin pairs, suggesting that the effects should be observable experimentally if a suitable compound can be identified.

NMR line shapes from AB spin systems in solids — The role of antisymmetric spin–spin coupling

NMR parameters such as indirect nuclear spin–spin coupling (J), nuclear magnetic shielding (σ), direct dipolar coupling (D), and electric field gradient (V) are properly described by second-rank tensors. Each may be decomposed into isotropic, symmetric, and antisymmetric components; the number of these three components which may be nonzero is a distinguishing attribute of each interaction tensor. The rank-1 antisymmetric portion of J (Janti) holds the distinction of remaining the only nonzero part of these fundamental NMR interaction tensors which has never been observed experimentally. Accordingly, effects from Janti are usually ignored, but it is important to consider when this is valid. An experimental strategy for observing Janti in powdered samples of tightly coupled homonuclear spin pairs, based on ideas originally presented by Andrew and Farnell ( Mol. Phys. 1968, 15, 157 ), is described. The theory of Andrew and Farnell is extended to powder samples, and methods for analyzing NMR spectra from powdered samples are presented. It is found that, in certain rare cases, Janti has the potential to affect the NMR line shapes from AB spin systems, but that even in these systems, the most intense features of the spectra are not affected and may be analyzed independently of Janti. Furthermore, Janti will only have an observable effect on the NMR spectra when its magnitude is comparable with that of Jiso and with the difference in chemical shifts (in Hz) between the two sites. Finally, the first experimental attempts to measure Janti are reported, and experimental proof that no elements of Janti(119Sn,119Sn) in hexa(p-tolyl)ditin are larger than 2900 Hz is given. The benefits of modern double-quantum filtering NMR pulse sequences in isolating effects from Janti are also illustrated.

Computed EOM-CCSD 19F-19F Spin-Spin Coupling Constants in Small Organic Molecules

Two-, three-, and four-bond 19F-19F spin-spin coupling constants ( nJ FF) for a set of small fluoro-substituted organic molecules have been computed using ab initio equation-of-motion coupled cluster singles and doubles (EOM-CCSD) theory. The computed values reproduce the experimental signs and magnitudes of nJ FF. The straight line that relates the experimental and computed coupling constants has a slope of approximately 1 and passes through the point (0,0 Hz) within the uncertainties of the fit. Hence, EOM-CCSD values of nJ FF should be excellent predictors of experimental values when these are not available. All of the components of nJ FF except for the diamagnetic spin-orbit term may be large and must be evaluated if agreement between theory and experiment is to be obtained.

Relativistic hybrid density functional calculations of indirect nuclear spin–spin coupling tensors — Comparison with experiment for diatomic alkali metal halides,

The accurate calculation of the isotropic (Jiso) and anisotropic (ΔJ) parts of indirect nuclear spin–spin coupling tensors is a stringent test for quantum chemistry, particularly for couplings involving heavy isotopes where relativistic effects and relativity – electron correlation cross terms are expected to play an important role. Experimental measurements on diatomic molecules in the gas phase offer ideal data for testing the success of computational approaches, since the data are essentially free from intermolecular effects, and precise coupling anisotropies may be reliably extracted in favourable cases. On the basis of available experimental molecular-beam coupling-tensor parameters for diatomic alkali metal halides, we tabulate known values of Jiso and, taking rotational–vibrational corrections to the direct dipolar coupling constant into account, precise values of ΔJ are determined for the ground rovibrational state. First-principles calculations of the coupling tensors were performed using a recently developed program based on hybrid density functional theory using the two-component relativistic zeroth-order regular approximation (ZORA). Experimental trends in Jiso and ΔJ are reproduced with correlation coefficients of 0.993 and 0.977, respectively. Periodic trends in the coupling constants and their dependence on the product of the atomic numbers of the coupled nuclei are discussed. Finally, the hybrid functional method is also successfully tested against experimental data for a series of polyatomic xenon fluorides and group-17 fluorides.

Probing lead(II) bonding environments in 4-substituted pyridine adducts of (2,6-Me2C6H3S)2Pb: an X-ray structural and solid-state 207Pb NMR study

The effect of subtle changes in the sigma-electron donor ability of 4-substituted pyridine ligands on the lead(II) coordination environment of (2,6-Me(2)C(6)H(3)S)(2)Pb (1) adducts has been examined. The reaction of 1 with a series of 4-substituted pyridines in toluene or dichloromethane results in the formation of 1:1 complexes [(2,6-Me(2)C(6)H(3)S)(2)Pb(pyCOH)](2) (3), [(2,6-Me(2)C(6)H(3)S)(2)Pb(pyOMe)](2) (4), and (2,6-Me(2)C(6)H(3)S)(2)Pb(pyNMe(2)) (5) (pyCOH = 4-pyridinecarboxaldehyde; pyOMe = 4-methoxypyridine; pyNMe2 = 4-dimethylaminopyridine), all of which have been structurally characterized by X-ray crystallography. The structures of 3 and 4 are dimeric and have psi-trigonal bipyramidal S(3)N bonding environments, with the 4-substituted pyridine nitrogen and bridging sulfur atoms in axial positions and two thiolate sulfur atoms in equatorial sites. Conversely, compound 5 is monomeric and exhibits a psi-trigonal pyramidal S(2)N bonding environment at lead(II). The observed structures may be rationalized in terms of a simple valence bond model and the sigma-electron donor ability of the 4-pyridine ligands as derived from the analysis of proton affinity values. Solid-state (207)Pb NMR experiments are applied in combination with density functional theory (DFT) calculations to provide further insight into the nature of bonding in 4, 5, and (2,6-Me(2)C(6)H(3)S)(2)Pb(py)(2) (2). The lead chemical shielding (CS) tensor parameters of 2, 4, and 5 reveal some of the largest chemical shielding anisotropies (CSA) observed in lead coordination complexes to date. DFT calculations using the Amsterdam Density Functional (ADF) program, which take into account relativistic effects using the zeroth-order regular approximation (ZORA), yield lead CS tensor components and orientations. Paramagnetic contributions to the lead CS tensor from individual pairs of occupied and virtual molecular orbitals (MOs) are examined to gain insight into the origin of the large CSA. The CS tensor is primarily influenced by mixing of the occupied MOs localized on the sulfur and lead atoms with virtual MOs largely comprised of lead 6p orbitals.

Microwave spectroscopy and nuclear magnetic resonance spectroscopy--what is the connection?

The history and development of microwave spectroscopy and nuclear magnetic resonance (NMR) spectroscopy have much in common. In this Account, we discuss the less widely appreciated connections between the parameters measured using the two techniques. Selected examples from our laboratory and from the recent literature attest to the utility and importance of these connections. For example, how are nuclear spin-rotation tensors and NMR chemical shifts related? Why should chemists be interested in absolute magnetic shielding scales? What can chemists learn about trends in spin-spin coupling constants from the hyperfine parameters measured in microwave and molecular beam experiments? The increasingly important role of quantum-chemical calculations in the interpretation of the microwave and NMR data is also highlighted.

A theoretical study of the large Hg-Hg spin-spin coupling constants in Hg(2)(2+), Hg(3)(2+), and Hg(2)(2+)-crown ether complexes

Nuclear spin-spin coupling constants (1)J(Hg-Hg) in the systems Hg(2)(2+) and Hg(3)(2+) represent the largest coupling constants so far observed in NMR experiments. We have performed a computational study on these ions, on Hg(2)(2+) complexes with 18-crown-6 and 15-crown-5, and on Hg(3)(2+) with solvent molecules and counterions. The results obtained with our recently developed program for the density functional computation of heavy nucleus spin-spin coupling constants are in good agreement with experiments. The data reveal that the bare ions Hg(2)(2+) and Hg(3)(2+) would afford much larger coupling constants than those experimentally observed, with an upper limit of approximately 0.9 MHz for Hg(2)(2+). This limit is much larger than that previously estimated by Hückel theory. It is demonstrated that in solution or due to complexation the experimentally determined values are much smaller than the free ion's coupling constants. With the help of intuitive MO arguments, it is illustrated how the environment strongly reduces the coupling constants in Hg(2)(2+) and Hg(3)(2+). The two-bond coupling constant (2)J(Hg-Hg) in Hg(3)(2+) is also examined.

Characterization of indirect 31P-31P spin-spin coupling and phosphorus chemical shift tensors in pentaphenylphosphinophosphonium tetrachlorogallate, [Ph3P-PPh2][GaCl4]

Phosphorus chemical shift and 31P,31P spin-spin coupling tensors have been characterized for pentaphenylphosphinophosphonium tetrachlorogallate, [Ph3P-PPh2][GaCl4], using solid-state 31P NMR spectroscopy. Spectra obtained with magic-angle spinning yield the isotropic value of the indirect spin-spin coupling, |1J(31P,31P)iso|, 323 ± 2 Hz, while 2D spin-echo and rotational resonance experiments provide the effective dipolar coupling constant, Reff, 1.70 ± 0.02 kHz, and demonstrate that Jiso is negative. Within experimental error, the effective dipolar coupling constant and Jiso are unchanged at –120°C. The anisotropy in 1J(31P,31P), ΔJ, has been estimated by comparison of Reff and the value of the dipolar coupling constant, RDD, calculated from the P—P bond length as determined by X-ray diffraction. It is concluded that |ΔJ| is small, with an upper limit of 300 Hz. Calculations of 1J(31P,31P) for model systems H3P-PH+2 and (CH3)3P-P(CH3)+2 using density functional theory as well as multiconfigurational self-consistent field theory (H3P-PH+2) support this conclusion. The experimental spin-spin coupling parameters were used to analyze the 31P NMR spectrum of a stationary powder sample and provide information about the phosphorus chemical shift tensors. The principal components of the phosphorus chemical shift tensor for the phosphorus nucleus bonded to three phenyl groups are δ11 = 36 ppm, δ22 = 23 ppm, and δ33 = –14 ppm with an experimental error of ±2 ppm for each component. The components are oriented such that δ33 is approximately perpendicular to the P—P bond while δ11 forms an angle of 31° with the P—P bond. For the phosphorus nucleus bonded to two phenyl groups, the principal components of the phosphorus chemical shift tensor are δ11 = 23 ppm, δ22 = –8 ppm, and δ33 = –68 ppm with experimental errors of ±2 ppm. In this case, δ33 is also approximately perpendicular to the P—P bond; however, δ22 is close to the P—P bond for this phosphorus nucleus, forming an angle of 13°. The dihedral angle between the δ33 components of the two phosphorus chemical shift tensors is 25°. Results from ab initio calculations are in good agreement with experiment and suggest orientations of the phosphorus chemical shift tensors in the molecular frame of reference.Key words: Nuclear magnetic resonance spectroscopy, phosphorus chemical shift tensors, 31P-31P J-coupling tensors, density functional theory, multiconfigurational self-consistent field theory, phosphinophosphonium salts.

Interpretation of indirect nuclear spin-spin coupling tensors for polyatomic xenon fluorides and group 17 fluorides: results from relativistic density-functional calculations

Significant improvements have been made recently in the calculation of NMR indirect nuclear spin-spin coupling tensors (J). In particular, the relativistic zeroth-order regular approximation density-functional theory (ZORA-DFT) approach holds great promise for the calculation of spin-spin coupling constants for a variety of chemical systems containing heavy nuclei. In the present work, the ZORA-DFT method is applied to the calculation of the complete reduced coupling tensors, K, for a range of chlorine-, bromine-, iodine-, and xenon-containing species: K(Cl,F) for ClF(2)(+), ClF(3), ClF(4)(+), ClF(5), ClF(6)(-), and ClF(6)(+); K(Br,F) for BrF(3), BrF(6)(-), and BrF(6)(+); K(I,F) for IF(4)(+) and IF(6)(+); K(Xe,F) for XeF(+), XeF(2), XeF(3)(+), XeF(4), XeF(5)(-), XeF(5)(+), and XeF(7)(+). These species represent a wide variety of geometrical bonding arrangements. Agreement between the calculated coupling constants and available experimental data is excellent, and the absolute sign of the coupling constants is provided. It is shown that (1)K(iso) may be positive or negative even within the same molecule, e.g., K(Cl,F)(iso) may be of either sign, depending on the local environment. Periodic trends in (1)K(iso) for isovalent and isostructural molecules are evident. The spin-spin coupling anisotropies, Delta K, and the orientations of the K tensors are also determined. The success of the calculations is a direct result of employing reliable geometries and considering both scalar and spin-orbit relativistic effects. The dependence of K(Cl,F)(iso) and K(Xe,F)(iso) on the local molecular and electronic structure is discussed in terms of the paramagnetic spin-orbit (PSO) and combined Fermi-contact spin-dipolar (FC+SD) coupling mechanisms. The PSO term depends strongly on the number of valence shell electron lone pairs on the central heavy atom, and the FC+SD contribution increases with the Cl[bond]F or Xe[bond]F bond length for a given series of compounds. This interpretation allows for the successful rationalization of the existing experimental data.