Experimental and Theoretical ab Initio Study of the 13C−13C Spin−Spin Coupling and 1H and 13C Shielding Tensors in Ethane, Ethene, and Ethyne

On the performance of HRPA(D) for NMR spin-spin coupling constants: Smaller molecules, aromatic and fluoroaromatic compounds

In this study, the performance of the doubles-corrected higher random-phase approximation [HRPA(D)] has been investigated in calculations of nuclear magnetic resonance spin-spin coupling constants (SSCCs) for 58 molecules with the experimental values used as the reference values. HRPA(D) is an approximation to the second-order polarization propagator approximation (SOPPA) and is, therefore, computationally less expensive than SOPPA. HRPA(D) performs comparable and sometimes even better than SOPPA, and therefore, when calculating SSCCs, it should be considered as an alternative to SOPPA. Furthermore, it was investigated whether a coupled-cluster singles, doubles and perturbative triples [CCSD(T)] or Møller-Plesset second order (MP2) geometry optimization was optimal for a SOPPA and a HRPA(D) SSCC calculation for eight smaller molecules. CCSD(T) is the optimal geometry optimization for the SOPPA calculation, and MP2 was optimal for HRPA(D) SSCC calculations.

Linking the Interatomic Exchange-Correlation Energy to Experimental J-Coupling Constants

The main aim of the current work is to find an experimental connection to the interatomic exchange-correlation energy as defined by the energy decomposition method Interacting Quantum Atoms (IQA). A suitable candidate as (essentially) experimental quantity is the nuclear magnetic resonance (NMR) J-coupling constant denoted ³J(H,H'), which a number of previous studies showed to correlate well with QTAIM's delocalization index (DI), which is essentially a bond order. Inspired by Karplus equations, here, we investigate correlations between ³J(H,H') and a relevant dihedral angle in six simple initial compounds of the shape H₃C-YH_n (Y = C, N, O, Si, P, and S), N-methylacetamide (as prototype of the peptide bond), and five peptide-capped amino acids (Gly, Ala, Val, Ile, and Leu) because of the protein direction of the force field FFLUX. In conclusion, except for methanol, the inter-hydrogen exchange-correlation energy V_xc(H,H') makes the best contact with experiment, through ³J(H,H'), when multiplied with the internuclear distance R_HH'.

Symmetry Constraints on Spin Order Transfer in Parahydrogen-Induced Polarization (PHIP)

It is well known that the association of parahydrogen (pH2) with an unsaturated molecule or a transient metalorganic complex can enhance the intensity of NMR signals; the effect is known as parahydrogen-induced polarization (PHIP). During recent decades, numerous methods were proposed for converting pH2-derived nuclear spin order to the observable magnetization of protons or other nuclei of interest, usually 13C or 15N. Here, we analyze the constraints imposed by the topological symmetry of the spin systems on the amplitude of transferred polarization. We find that in asymmetric systems, heteronuclei can be polarized to 100%. However, the amplitude drops to 75% in A2BX systems and further to 50% in A3B2X systems. The latter case is of primary importance for biological applications of PHIP using sidearm hydrogenation (PHIP-SAH). If the polarization is transferred to the same type of nuclei, i.e., 1H, symmetry constraints impose significant boundaries on the spin-order distribution. For AB, A2B, A3B, A2B2, AA’(AA’) systems, the maximum average polarization for each spin is 100%, 50%, 33.3%, 25%, and 0, respectively, (where A and B (or A’) came from pH2). Remarkably, if the polarization of all spins in a molecule is summed up, the total polarization grows asymptotically with ~1.27 and can exceed 2 in the absence of symmetry constraints (where is the number of spins). We also discuss the effect of dipole–dipole-induced pH2 spin-order distribution in heterogeneous catalysis or nematic liquid crystals. Practical examples from the literature illustrate our theoretical analysis.

NMR Coupling Constants Based on the Bethe-Salpeter Equation in the GW Approximation

We present the first steps to extend the Green's function GW method and the Bethe-Salpeter equation (BSE) to molecular response properties such as nuclear magnetic resonance (NMR) indirect spin-spin coupling constants. We discuss both a nonrelativistic one-component and a quasi-relativistic two-component formalism. The latter describes scalar-relativistic and spin-orbit effects and allows us to study heavy-element systems with reasonable accuracy. Efficiency is maintained by the application of the resolution of the identity approximation throughout. The performance is demonstrated using conventional central processing units (CPUs) and modern graphics processing units (GPUs) for molecules involving several thousand basis functions. Our results show that a large amount of Hartree-Fock exchange is vital to provide a sufficient Kohn-Sham starting point to compute the GW quasi-particle energies. As the GW-BSE approach is generally less accurate for triplet excitations or related properties such as the Fermi-contact interaction, the admixture of the Kohn-Sham correlation kernel through the contracted BSE (cBSE) method improves the results for NMR coupling constants. This leads to remarkable results when combined with the eigenvalue-only self-consistent variant (evGW) and Becke's half and half functional (BH&HLYP) or the CAM-QTP family. The developed methodology is used to calculate the Karplus curve of tin molecules, illustrating its applicability to extended chemically relevant molecules. Here, the GW-cBSE method improves upon the chosen BH&HLYP Kohn-Sham starting points.

Insertion, protonolysis and photolysis reactivity of a thorium monoalkyl amidinate complex

The reactivity of the thorium monoalkyl complex Th(CH2SiMe3)(BIMA)3 [1, BIMA = MeC(NiPr)2] with various small molecules is described. While steric congestion prohibits the insertion of N,N'-diisopropylcarbodiimide into the Th-C bond in 1, the first thorium tetrakis(amidinate) complex, Th(BIMA)4 (2), is synthesized via an alternative salt metathesis route. Insertion of p-tolyl azide leads to the triazenido complex Th[(p-tolyl)NNN(CH2SiMe3)-κ2N1,2](BIMA)3 (3), which then undergoes thermal decomposition to the amido species Th[(p-tolyl)N(SiMe3)](BIMA)3 (4). The reaction of 1 with 2,6-dimethylphenylisocyanide results in the thorium iminoacyl complex Th[η2-(C[double bond, length as m-dash]N)-2,6-Me2-C6H3(CH2SiMe3)](BIMA)3 (5), while the reaction with isoelectronic CO leads to the products Th[OC([double bond, length as m-dash]CH2)SiMe3](BIMA)3 (6) and Th[OC(NiPr)C(CH2SiMe3)(C(Me)N(iPr))O-κ2O,O'](BIMA)2 (7), the latter being the result of CO coupling and insertion into an amidinate ligand. Protonolysis is achieved with several substrates, producing amido (9), aryloxide (10), phosphido (11a,b), acetylide (12), and cationic (13) complexes. Ligand exchange with 9-borabicyclo[3.3.1]nonane (9-BBN) results in formation of the thorium borohydride complex (BIMA)3Th(μ-H)2[B(C8H14)] (14). Complex 1 also reacts under photolytic conditions to eliminate SiMe4 and produce Th(BIMA)2(BIMA*) [15, BIMA* = (iPr)NC(CH2)N(iPr)], featuring a rare example of a dianionic amidinate ligand. Complexes 2, 3, 5, 6, 11a, and 12-15 were characterized by 1H and 13C{1H} NMR spectroscopy, FTIR, EA, melting point and X-ray crystallography. All other complexes were identified by one or more of these spectroscopic techniques.

Evaluating the accuracy of theoretical one-bond 13 C─13 C scalar couplings and their ability to predict structure in a natural product

This study explores the feasibility of using a combination of experimental and theoretical 1-bond ¹³ C─¹³ C scalar couplings (¹ J_CC ) to establish structure in organic compounds, including unknowns. Historically, ⁿ J_CC and ⁿ J_CH studies have emphasized 2 and 3-bond couplings, yet ¹ J_CC couplings exhibit significantly larger variations. Moreover, recent improvements in experimental measurement and data processing methods have made ¹ J_CC data more available. Herein, an approach is evaluated in which a collection of theoretical structures is created from a partial nuclear magnetic resonance structural characterization. Computed ¹ J_CC values are compared to experimental data to identify candidates giving the best agreement. This process requires knowledge of the error in theoretical methods, thus the B3LYP, B3PW91, and PBE0 functionals are evaluated by comparing to 27 experimental values from INADEQUATE. Respective errors of ±1.2, ±3.8, and ±2.3 Hz are observed. An initial test of this methodology involves the natural product 5-methylmellein. In this case, only a single candidate matches experimental data with high statistical confidence. This analysis establishes the intramolecular hydrogen-bonding arrangement, ring heteroatom identity, and conformation at one position. This approach is then extended to hydroheptelidic acid, a natural product not fully characterized in prior studies. The experimental/theoretical approach proposed herein identifies a single best-fit structure from among 26 candidates and establishes, for the first time, 1 configuration and 3 conformations to complete the characterization. These results suggest that accurate and complete structural characterizations of many moderately sized organic structures (<800 Da) may be possible using only ¹ J_CC data.

Rovibrational and Temperature Effects in Theoretical Studies of NMR Parameters

The demand for high precision calculations of NMR shieldings (or their related values, chemical shifts δ) and spin–spin coupling constants facilitating and supporting detailed interpretations of NMR spectra increases hand in hand with the development of computational techniques and hardware resources. Highly sophisticated calculations including even relativistic effects are nowadays possible for these properties. However, NMR parameters depend not only on molecular structure and environment but also on molecular flexibility and temperature and the apparent success of theoretical predictions for molecular equilibrium geometries creates a demand for zero-point vibrational and temperature corrections. In this chapter we describe briefly the theory behind rovibrational corrections and review then some important contributions to this field.

On the truncation of the number of excited states in density functional theory sum-over-states calculations of indirect spin spin coupling constants

It is investigated, whether the number of excited (pseudo)states can be truncated in the sum-over-states expression for indirect spin-spin coupling constants (SSCCs), which is used in the Contributions from Localized Orbitals within the Polarization Propagator Approach and Inner Projections of the Polarization Propagator (IPPP-CLOPPA) approach to analyzing SSCCs in terms of localized orbitals. As a test set we have studied the nine simple compounds, CH4, NH3, H2O, SiH4, PH3, SH2, C2H2, C2H4, and C2H6. The excited (pseudo)states were obtained from time-dependent density functional theory (TD-DFT) calculations with the B3LYP exchange-correlation functional and the specialized core-property basis set, aug-cc-pVTZ-J. We investigated both how the calculated coupling constants depend on the number of (pseudo)states included in the summation and whether the summation can be truncated in a systematic way at a smaller number of states and extrapolated to the total number of (pseudo)states for the given one-electron basis set. We find that this is possible and that for some of the couplings it is sufficient to include only about 30% of the excited (pseudo)states.

Influence of Density Functionals and Basis Sets on One-Bond Carbon-Carbon NMR Spin-Spin Coupling Constants

The basis set and the functional dependence of one-bond carbon-carbon NMR spin-spin coupling constants (SSCC) have been analyzed using density functional theory. Four basis sets (6-311G**, TZVP, EPR-III, and aug-cc-pVTZ-J) and four functionals (PBE, PW91, B3LYP, and B3P86) are tested by comparison with 70 experimental values corresponding to 49 molecules that represent multiple types of hybridization of the carbon atoms. The two hybrid functionals B3P86 and B3LYP combined either EPR-III or aug-cc-pVTZ-J basis sets lead to the best accuracy of calculated SSCC. However, a simple linear regression allows for the obtaining of scaled coupling constants that fit much better with the experimental data and where the differences between the different basis sets and/or functional results are significantly reduced. For large molecules the TZVP basis set can be an appropriate election presenting a good compromise between quality of results and computational cost.

Sulfur-containing stable five-membered “cycloallene” complexes: 1-thia-2-zircona- and 1-thia-2-titanacyclopenta-3,4-dienes

Stable five-membered sulfur-containing metallacyclic allenes, 1-thia-2-metallacyclopenta-3,4-diene, were synthesized from the reactions of low-valent zirconocene or titanocene with alkynylthioamides.

A Magic-Angle Spinning NMR Method for the Site-Specific Measurement of Proton Chemical-Shift Anisotropy in Biological and Organic Solids

Proton chemical shifts are a rich probe of structure and hydrogen bonding environments in organic and biological molecules. Until recently, measurements of ¹H chemical shift tensors have been restricted to either solid systems with sparse proton sites or were based on the indirect determination of anisotropic tensor components from cross-relaxation and liquid-crystal experiments. We have introduced an MAS approach that permits site-resolved determination of CSA tensors of protons forming chemical bonds with labeled spin-1/2 nuclei in fully protonated solids with multiple sites, including organic molecules and proteins. This approach, originally introduced for the measurements of chemical shift tensors of amide protons, is based on three RN-symmetry based experiments, from which the principal components of the ¹H CS tensor can be reliably extracted by simultaneous triple fit of the data. In this article, we expand our approach to a much more challenging system involving aliphatic and aromatic protons. We start with a review of the prior work on experimental-NMR and computational-quantum-chemical approaches for the measurements of ¹H chemical shift tensors and for relating these to the electronic structures. We then present our experimental results on U-¹³C,¹⁵N-labeled histdine demonstrating that ¹H chemical shift tensors can be reliably determined for the ¹H¹⁵N and ¹H¹³C spin pairs in cationic and neutral forms of histidine. Finally, we demonstrate that the experimental ¹H(C) and ¹H(N) chemical shift tensors are in agreement with Density Functional Theory calculations, therefore establishing the usefulness of our method for characterization of structure and hydrogen bonding environment in organic and biological solids.

Experimental assessment of the vibration-reorientation contribution to liquid crystal NMR dipolar couplings: the case of tetramethylallene dissolved in a nematic mesophase

In the present paper, the peculiar orientational behavior, studied by liquid crystal NMR (LXNMR) spectroscopy, of the D(2d) symmetry quasi-spherical molecule of tetramethylallene (TMA) dissolved in the nematic solvent I52 is exploited to attempt a quantitative experimental assessment of the correlation between molecular vibrations and overall rotations in weakly oriented molecules. The analysis of the very small D(HH) and (1)D((13)C-H) dipolar couplings, available from the natural abundance LXNMR spectra of TMA at different temperatures, allows for a derivation leading (by making a few approximations) to the quantification of the vibration-reorientation (also called nonrigid) contribution affecting the observed direct (1)D((13)C-H) dipolar coupling. The obtained results show that, under the particular conditions of the studied system (very weak orientational ordering of a highly symmetric molecule), this contribution is particularly important, in order to reproduce the whole value of the "observed" dipolar coupling. This issue is discussed and commented on at length in the work, also, by making reference to the analogy with perfectly symmetric molecules (such as methane and analogues) dissolved in liquid crystalline phases.

On the unusual 2J(C2-H(f)) coupling dependence on syn/anti CHO conformation in 5-X-furan-2-carboxaldehydes

A remarkable difference for (2)J(C(2)-H(f)) coupling constant in syn and anti conformers of 5-X-furan-2-carboxaldehydes (X = CH(3), Ph, NO(2), Br) and a rationalization of this difference are reported. On the basis of the current knowledge of the Fermi-contact term transmission, a rather unusual dual-coupling pathway in the syn conformer is presented. The additional coupling pathway resembles somewhat that of the J(H-H) in homoallylic couplings, which are transmitted by hyperconjugative interactions involving the pi(C=C) electronic system. The homoallylic coupling pathway can be labeled as sigma*(C-H) <-- pi(C=C) --> sigma*(C-H). In the present case, this additional coupling pathway, using an analogous notation, can be labeled as sigma*(C(2)-C(C)) <-- LP(1)(O(1))...LP(2)(O(C)) --> sigma*(C(C)-H(f)) (sigma*(C(2)-C(C))) where O(1) and O(C) stand for the ring and carbonyl O atoms, respectively. This additional coupling pathway is not activated in the anti conformers since both oxygen lone pairs do not overlap.

Theory and computation of nuclear magnetic resonance parameters

The art of quantum chemical electronic structure calculation has over the last 15 years reached a point where systematic computational studies of magnetic response properties have become a routine procedure for molecular systems. One of their most prominent areas of application are the spectral parameters of nuclear magnetic resonance (NMR) spectroscopy, due to the immense importance of this experimental method in many scientific disciplines. This article attempts to give an overview on the theory and state-of-the-art of the practical computations in the field, in terms of the size of systems that can be treated, the accuracy that can be expected, and the various factors that would influence the agreement of even the most accurate imaginable electronic structure calculation with experiment. These factors include relativistic effects, thermal effects, as well as solvation/environmental influences, where my group has been active. The dependence of the NMR spectra on external magnetic and optical fields is also briefly touched on.

Acetylenic Carbon-13 Chemical Shift Tensors for Diphenylacetylene and (η2-Diphenylacetylene)Pt(PPh3)2: A Solid-State NMR and Theoretical Study

The structure of (eta2-diphenylacetylene)Pt(PPh3) (2), as well as those of its dichloromethane and benzene solvates, is determined via X-ray crystallography. An investigation of the chemical shift (CS) tensors of the 13C-labeled carbons in Ph13C13CPh and (eta2-Ph13C13CPh)Pt(PPh3)2.(C6H6) is carried out via analysis of 13C NMR spectra from stationary solid samples. The principal components of the CS tensors as well as their orientations with respect to the 13C,13C internuclear vector are determined. DFT calculations of these CS tensors are in close agreement with the experimental values. For diphenylacetylene (tolane), the orientations and principal-component magnitudes of the alkynyl carbon CS tensors are comparable to those for other alkynyl carbons, although the CS tensor is not axially symmetric in this case. Coordination to platinum causes a change in the CS tensor orientation and a net increase in the isotropic chemical shift, resulting from a significant increase in two principal components (delta11 and delta33) while the third (delta22) decreases only slightly. The measured carbon CS tensors in the platinum complex bear a striking similarity to those of the alkenyl carbons in trans-Ph(H)C=C(H)Ph, and a short theoretical discussion of these observations is presented.

Quantum-mechanical studies of NMR properties of solutes in liquid crystals: A new strategy to determine orientational order parameters

We present a quantum-mechanical method to calculate the tensorial NMR magnetic properties of molecules in liquid crystals. The method exploits a density functional description for the solute and the integral equation formalism version of the polarizable continuum model to include the effects of the dielectric anisotropy of the solvent on the wave function of the solute molecule and on its response to an applied magnetic field. Taking into account the dependence of the calculated molecular tensors on the solute orientation, we have derived the necessary expressions to relate such tensors to the spectral observables. These equations are then used to determine order parameters by calculating the nuclear shieldings of various solutes in the nematic ZLI-1167. Comparisons with experimental data of the same parameters are finally presented.

Hartree-Fock and density functional complete basis-set (CBS) predicted nuclear shielding anisotropy and shielding tensor components

The nuclear shielding anisotropy and shielding tensor components calculated using the hybrid density functional B3PW91 are reported for a model set of compounds comprised of N2, NH3, CH4, C2H4, HCN and CH3CN. An estimation of density functional theory (DFT) and Hartree-Fock complete basis-set limit (CBS) parameters from a 2 (3) point exact fit vs. least-squares fit was obtained with the cc-pVxZ and aug-cc-pVxZ basis sets (x=D, T, Q, 5, 6). Both Hartree-Fock- and DFT-predicted CBS shielding anisotropies and shielding tensor components of the model molecules were in reasonable agreement with available experimental data. The utility of using a limited CBS approach for calculating accurate anisotropic shielding parameters of larger molecules as complementary methods to solid-state NMR is proposed.

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.

X-ray diffraction, Raman spectroscopic, and solid-state NMR studies of the group 14 metal-(tetracarbonyl)cobalt complexes Ph3MCo(CO)4 (M = Si, Sn, Pb)

Single-crystal X-ray diffraction studies illustrate that the three title compounds are isomorphous, belonging to the triclinic space group P[Formula: see text], with slightly distorted trigonal bipyramidal geometry about cobalt. The solid-state 29Si, 119Sn, and 207Pb cross-polarization magic angle spinning (CP MAS) NMR spectra are presented. The indirect spin–spin coupling constant (J), quadrupolar–dipolar shift (d), direct dipolar coupling constant (D' ), anisotropy in spin–spin coupling (ΔJ), and the chemical shift tensor were extracted. A plot of the reduced coupling constant vs. s-electron densities at the nucleus indicates that the Fermi contact term may be dominant for the tin and lead complexes; however, the large ΔJ for all complexes indicate that there are also significant anisotropic terms. Trends in the Raman scattering spectra are also discussed.Key words: 29Si, 119Sn, and 207Pb CP MAS NMR, tetracarbonyl cobalt, spin–spin coupling, chemical shift tensor, quadrupole coupling, Fermi contact, cobalt–group 14.

A 13C solid-state NMR investigation of the alkynyl carbon chemical shift tensors for 2-butyne-1,4-diol

The alkynyl carbon chemical shift (CS) tensors for 2-butyne-1,4-diol are reported, based on analyses of the carbon-13 NMR spectra of stationary-powder and slow magic-angle spinning (MAS) samples for which the alkynyl carbon nuclei are enriched in 13C. NMR spectra of slow MAS samples exhibit spinning-frequency-dependent fine structure typical of crystallographically equivalent but magnetically distinct nuclei. Simulated spectra of slow MAS samples of this two-spin system are particularly sensitive to the relative orientations of the CS tensors. In addition, the value of 1J(13C, 13C), +175 +/- 10 Hz, is determined by examination of the total NMR lineshape of slow MAS samples. The CS tensors are almost axially symmetric, delta11 = 158.9 +/- 1.0 ppm and delta22 = 155.7 +/- 1.0 ppm; the direction of greatest shielding is approximately along the alkynyl C-C bond, delta33 = -57.8 +/- 2.0 ppm. Both the magnitudes of the principal components of the CS tensors and their orientations are in agreement with those predicted from first-principles calculations at the HF and MP2 levels of theory. This study demonstrates the importance of examining the NMR spectra of homonuclear two-spin systems with and without MAS under a variety of conditions (e.g., two or more applied magnetic fields and slow MAS).