Indirect Nuclear Spin−Spin Coupling Tensors in Diatomic Molecules: A Comparison of Results Obtained by Experiment and First Principles Calculations

Quantum Chemical Approaches to the Calculation of NMR Parameters: From Fundamentals to Recent Advances

Quantum chemical methods for the calculation of indirect NMR spin–spin coupling constants and chemical shifts are always in progress. They never stay the same due to permanently developing computational facilities, which open new perspectives and create new challenges every now and then. This review starts from the fundamentals of the nonrelativistic and relativistic theory of nuclear magnetic resonance parameters, and gradually moves towards the discussion of the most popular common and newly developed methodologies for quantum chemical modeling of NMR spectra.

Calculated coupling constants 1 J(X-Y) and 1 K(X-Y), and fundamental relationships among the reduced coupling constants for molecules Hm X-YHn , with X, Y ═ 1 H, 7 Li, 9 Be, 11 B, 13 C, 15 N, 17 O, 19 F, 31 P, 33 S, and 35 Cl

Equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) calculations have been performed to determine coupling constants ¹ J(X-Y) for 65 molecules H_m X-YH_n , with X,Y ═ ¹ H, ⁷ Li, ⁹ Be, ¹¹ B, ¹³ C, ¹⁵ N, ¹⁷ O, ¹⁹ F, ³¹ P, ³³ S, and ³⁵ Cl. The computed ¹ J(X-Y) values are in good agreement with available experimental data. The reduced coupling constants ¹ K(X-Y) have been derived from ¹ J(X-Y) by removing the dependence on the magnetogyric ratios of X and Y. Patterns are found for the reduced coupling constants on a ¹ K(X-Y) surface that are related to the positions of X and Y in the periodic table.

Solid-State NMR Techniques for the Structural Characterization of Cyclic Aggregates Based on Borane-Phosphane Frustrated Lewis Pairs

Modern solid-state NMR techniques offer a wide range of opportunities for the structural characterization of frustrated Lewis pairs (FLPs), their aggregates, and the products of cooperative addition reactions at their two Lewis centers. This information is extremely valuable for materials that elude structural characterization by X-ray diffraction because of their nanocrystalline or amorphous character, (pseudo-)polymorphism, or other types of disordering phenomena inherent in the solid state. Aside from simple chemical shift measurements using single-pulse or cross-polarization/magic-angle spinning NMR detection techniques, the availability of advanced multidimensional and double-resonance NMR methods greatly deepened the informational content of these experiments. In particular, methods quantifying the magnetic dipole-dipole interaction strengths and indirect spin-spin interactions prove useful for the measurement of intermolecular association, connectivity, assessment of FLP-ligand distributions, and the stereochemistry of adducts. The present review illustrates several important solid-state NMR methods with some insightful applications to open questions in FLP chemistry, with a particular focus on supramolecular associates.

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.

Optimized basis sets for the calculation of indirect nuclear spin-spin coupling constants involving the atoms B, Al, Si, P, and Cl

The aug-cc-pVTZ-J series of basis sets for indirect nuclear spin-spin coupling constants has been extended to the atoms B, Al, Si, P, and Cl. The basis sets were obtained according to the scheme previously described by Provasi et al. [J. Chem. Phys. 115, 1324 (2001)]. First, the completely uncontracted correlation consistent aug-cc-pVTZ basis sets were extended with four tight s and three tight d functions. Second, the s and p basis functions were contracted with the molecular orbital coefficients of self-consistent-field calculations performed with the uncontracted basis sets on the simplest hydrides of each atom. As a first illustration, we have calculated the one-bond indirect spin-spin coupling constants in BH(4)(-), BF, AlH, AlF, SiH(4), SiF(4), PH(3), PF(3), H(2)S, SF(6), HCl, and ClF at the level of density functional theory using the Becke three parameter Lee-Yang-Parr and the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes.

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.

Analyzing molecular properties calculated with two-component relativistic methods using spin-free natural bond orbitals: NMR spin-spin coupling constants

An analysis method for static linear response properties employing two-component (spin-orbit) relativistic density functional theory along with scalar relativistic "natural localized molecular orbitals" (NLMOs) and "natural bond orbitals" (NBOs) has been developed. The spin-orbit NLMO/NBO analysis has been applied to study the indirect spin-spin coupling (J-coupling) constants in Tl-I, PbH(4), and a dinuclear Pt-Tl bonded complex with a very large Pt-Tl coupling constant (expt.: 146.8 kHz). For Tl-I it is shown that the analysis scheme based on scalar relativistic NLMOs is applicable even if spin-orbit coupling is responsible for most of the coupling's magnitude. For PbH(4) it is shown that electron delocalization plays a much larger role for the Pb-H coupling than it is the case for the C-H coupling in methane. For the Pt-Tl complex the analysis clearly demonstrates the strong influence of the ligands on the Pt-Tl coupling constant and quantifies the effect of the delocalization of the Pt-Tl bond on the Pt-Tl coupling constant.

Computed coupling constants in X(CH3)nH(4-n) moieties where X = 13C and 15N+, and n = 0-4: comparisons with experimental data

Seventy-three unique spin-spin coupling constants have been analyzed for the ten species in the two series X(CH3)nH(4-n), where the central atom X is 13C or 15N+. Thirty-seven experimental values have been obtained from the literature, and several new coupling constants have been measured for the methyl-substituted ammonium ions. Both DFT with the B3LYP functional and ab initio EOM-CCSD calculations have been carried out on these same systems. Coupling constants computed by these two methods are in agreement with experimental values. Some problems related to coupling constants for the cationic ammonium systems have been resolved when these were recomputed at EOM-CCSD for complexes in which NH4+ is hydrogen-bonded to H2O molecules.

Spin–spin coupling constants in homonuclear polynitrogen species

Quantum chemical calculations provide new insights into the dependence of J(N,N) coupling tensors on bonding environment in a series of polynitrogen species including N(5)(+).

An NMR and relativistic DFT investigation of one-bond nuclear spin–spin coupling in solid triphenyl group-14 chlorides

A solid-state nuclear magnetic resonance and zeroth-order regular approximation density functional theory, ZORA-DFT, study of one-bond nuclear spin-spin coupling between group-14 nuclei and quadrupolar 35/37Cl nuclei in triphenyl group-14 chlorides, Ph3XCl (X = C, Si, Ge, Sn and Pb), is presented. This represents the first combined experimental and theoretical systematic study of spin-spin coupling involving spin-pairs containing quadrupolar nuclei. Solid-state NMR spectra have been acquired for all compounds in which X has a spin-1/2 isotope--13C, 29Si, [117/119]Sn and 207Pb-at applied magnetic fields of 4.70, 7.05 and 11.75 T. From simulations of these spectra, values describing the indirect spin-spin coupling tensor-the isotropic indirect spin-spin coupling constant, 1J(X, 35/37Cl)iso and the anisotropy of the J tensor, Delta1J(X, 35/37Cl)--have been determined for all but the lead-chlorine spin-pair. To better compare the indirect spin-spin coupling parameters between spin-pairs, 1J(iso) and Delta1J values were converted to their reduced coupling constants, 1K(iso) and Delta1K. From experiment, the sign of 1K(iso) was found to be negative while the sign of Delta1K is positive for all spin-pairs investigated. The magnitude of both 1K(iso) and Delta1K was found to increase as one moves down group-14. Theoretical values of the magnitude and sign of 1K(iso) and Delta1K were obtained from ZORA-DFT calculations and are in agreement with the available experimental data. From the calculations, the Fermi-contact mechanism was determined to provide the largest contribution to 1K(iso) for all spin-pairs while spin-dipolar and paramagnetic spin-orbit mechanisms make significant contributions to the anisotropy of K. The inclusion of relativistic effects was found to influence K(Sn,Cl) and K(Pb,Cl).

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.

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.

Complete Prediction of the1H NMR Spectrum of Organic Molecules by DFT Calculations of Chemical Shifts and Spin-Spin Coupling Constants

1H NMR chemical shifts and coupling constants for several aromatic and aliphatic organic molecules have been calculated with DFT methods. In some test cases (furan, o-dichlorobenzene and n-butyl chloride) the performance of several functionals and basis sets has been analyzed, and the various contributions to spin-spin coupling (Fermi-contact, diamagnetic and paramagnetic spin-orbit) have been evaluated. The latter two components cancel each other, so that the calculation of the contact term only is sufficient for an accurate evaluation of proton-proton couplings. Such calculated values are used to simulate the 1H NMR spectra of organic molecules with complicated spin systems (e.g. naphthalene, o-bromochlorobenzene), obtaining a generally very good agreement with experimental spectra with no prior knowledge of the involved parameters.

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.