Theoretical predictions of nuclear magnetic resonance parameters in a novel organo-xenon species: chemical shifts and nuclear quadrupole couplings in HXeCCH

We calibrate the methodology for the calculation of nuclear magnetic resonance (NMR) properties in novel organo-xenon compounds. The available state-of-the-art quantum-chemical approaches are combined and applied to the HXeCCH molecule as the model system. The studied properties are (129)Xe, (1)H, and (13)C chemical shifts and shielding anisotropies, as well as (131)Xe and (2)H nuclear quadrupole coupling constants. The aim is to obtain, as accurately as currently possible, converged results with respect to the basis set, electron correlation, and relativistic effects, including the coupling of relativity and correlation. This is done, on one hand, by nonrelativistic correlated ab initio calculations up to the CCSD(T) level and, on the other hand, for chemical shifts and shielding anisotropies by the leading-order relativistic Breit-Pauli perturbation theory (BPPT) with correlated ab initio and density-functional theory (DFT) reference states. BPPT at the uncorrelated Hartree-Fock level as well as the corresponding fully relativistic Dirac-Hartree-Fock method are found to be inapplicable due to a dramatic overestimation of relativistic effects, implying the influence of triplet instability in this multiply bonded system. In contrast, the fully relativistic second-order Moller-Plesset perturbation theory method can be applied for the quadrupole coupling, which is a ground-state electric property. The performance of DFT with various exchange-correlation functionals is found to be inadequate for the nonrelativistic shifts and shielding anisotropies as compared to the CCSD(T) results. The relativistic BPPT corrections to these quantities can, however, be reasonably predicted by DFT, due to the improved triplet excitation spectrum as compared to the Hartree-Fock method, as well as error cancellation within the five main BPPT contributions. We establish three computationally feasible models with characteristic error margins for future calculations of larger organo-xenon compounds to guide forthcoming experimental NMR efforts. The predicted (129)Xe chemical shift in HXeCCH is in a novel range for this nucleus, between weakly bonded or solvated atomic xenon and xenon in the hitherto characterized molecules.     

Relativistic heavy-atom effects on heavy-atom nuclear shieldings

The principal relativistic heavy-atom effects on the nuclear magnetic resonance (NMR) shielding tensor of the heavy atom itself (HAHA effects) are calculated using ab initio methods at the level of the Breit-Pauli Hamiltonian. This is the first systematic study of the main HAHA effects on nuclear shielding and chemical shift by perturbational relativistic approach. The dependence of the HAHA effects on the chemical environment of the heavy atom is investigated for the closed-shell X(2+), X(4+), XH(2), and XH(3) (-) (X=Si-Pb) as well as X(3+), XH(3), and XF(3) (X=P-Bi) systems. Fully relativistic Dirac-Hartree-Fock calculations are carried out for comparison. It is necessary in the Breit-Pauli approach to include the second-order magnetic-field-dependent spin-orbit (SO) shielding contribution as it is the larger SO term in XH(3) (-), XH(3), and XF(3), and is equally large in XH(2) as the conventional, third-order field-independent spin-orbit contribution. Considering the chemical shift, the third-order SO mechanism contributes two-thirds of the difference of approximately 1500 ppm between BiH(3) and BiF(3). The second-order SO mechanism and the numerically largest relativistic effect, which arises from the cross-term contribution of the Fermi contact hyperfine interaction and the relativistically modified spin-Zeeman interaction (FC/SZ-KE), are isotropic and practically independent of electron correlation effects as well as the chemical environment of the heavy atom. The third-order SO terms depend on these factors and contribute both to heavy-atom shielding anisotropy and NMR chemical shifts. While a qualitative picture of heavy-atom chemical shifts is already obtained at the nonrelativistic level of theory, reliable shifts may be expected after including the third-order SO contributions only, especially when calculations are carried out at correlated level. The FC/SZ-KE contribution to shielding is almost completely produced in the s orbitals of the heavy atom, with values diminishing with the principal quantum number. The relative contributions converge to universal fractions for the core and subvalence ns shells. The valence shell contribution is negligible, which explains the HAHA characteristics of the FC/SZ-KE term. Although the nonrelativistic theory gives correct chemical shift trends in present systems, the third-order SO-I terms are necessary for more reliable predictions. All of the presently considered relativistic corrections provide significant HAHA contributions to absolute shielding in heavy atoms.     

A solid-state NMR investigation of single-source precursors for group 12 metal selenides; M[N(iPr2PSe)2]2 (M = Zn, Cd, Hg)

The first solid-state NMR investigation of dichalcogenoimidodiphosphinato complexes, M[N(R(2)PE)(2)](n), is presented. The single-source precursors for metal-selenide materials, M[N((i)Pr(2)PSe)(2)](2) (M = Zn, Cd, Hg), were studied by solid-state (31)P, (77)Se, (113)Cd, and (199)Hg NMR at 4.7, 7.0, and 11.7 T, representing the only (77)Se NMR measurements, and in the case of Cd[N((i)Pr(2)PSe)(2)](2)(113)Cd NMR measurements, to have been performed on these complexes. Residual dipolar coupling between (14)N and (31)P was observed in solid-state (31)P NMR spectra at 4.7 and 7.0 T yielding average values of R((31)P,(14)N)(eff) = 880 Hz, C(Q)((14)N) = 3.0 MHz, (1)J((31)P,(14)N)(iso) = 15 Hz, alpha = 90 degrees , beta = 26 degrees . The solid-state NMR spectra obtained were used to determine the respective phosphorus, selenium, cadmium, and mercury chemical shift tensors along with the indirect spin-spin coupling constants: (1)J((77)Se,(31)P)(iso), (1)J((111/113)Cd,(77)Se)(iso), (1)J((199)Hg,(77)Se)(iso), and (2)J((199)Hg,(31)P)(iso). Density functional theory magnetic shielding tensor calculations were performed yielding the orientations of the corresponding chemical shift tensors. For this series of complexes the phosphorus magnetic shielding tensors are essentially identical, the selenium magnetic shielding tensors are also very similar with respect to each other, and the magnetic shielding tensors of the central metals, cadmium and mercury, display near axial symmetry demonstrating an expected deviation from local S(4) symmetry.     

Nuclear magnetic resonance shielding constants and chemical shifts in linear 199Hg compounds: a comparison of three relativistic computational methods

We investigate the importance of relativistic effects on NMR shielding constants and chemical shifts of linear HgL(2) (L = Cl, Br, I, CH(3)) compounds using three different relativistic methods: the fully relativistic four-component approach and the two-component approximations, linear response elimination of small component (LR-ESC) and zeroth-order regular approximation (ZORA). LR-ESC reproduces successfully the four-component results for the C shielding constant in Hg(CH(3))(2) within 6 ppm, but fails to reproduce the Hg shielding constants and chemical shifts. The latter is mainly due to an underestimation of the change in spin-orbit contribution. Even though ZORA underestimates the absolute Hg NMR shielding constants by ～2100 ppm, the differences between Hg chemical shift values obtained using ZORA and the four-component approach without spin-density contribution to the exchange-correlation (XC) kernel are less than 60 ppm for all compounds using three different functionals, BP86, B3LYP, and PBE0. However, larger deviations (up to 366 ppm) occur for Hg chemical shifts in HgBr(2) and HgI(2) when ZORA results are compared with four-component calculations with non-collinear spin-density contribution to the XC kernel. For the ZORA calculations it is necessary to use large basis sets (QZ4P) and the TZ2P basis set may give errors of ～500 ppm for the Hg chemical shifts, despite deceivingly good agreement with experimental data. A Gaussian nucleus model for the Coulomb potential reduces the Hg shielding constants by ～100-500 ppm and the Hg chemical shifts by 1-143 ppm compared to the point nucleus model depending on the atomic number Z of the coordinating atom and the level of theory. The effect on the shielding constants of the lighter nuclei (C, Cl, Br, I) is, however, negligible.     

Nuclear magnetic shielding of the 113Cd(II) ion in aqua solution: a combined molecular dynamics/density functional theory study

We present a combined molecular dynamics simulation and density functional theory investigation of the nuclear magnetic shielding constant of the (113)Cd(II) ion solvated in aqueous solution. Molecular dynamics simulations are carried out for the cadmium-water system in order to produce instantaneous geometries for subsequent determination of the nuclear magnetic shielding constant at the density functional theory level. The nuclear magnetic shielding constant is computed using a perturbation theory formalism, which includes nonrelativistic and leading order relativistic contributions to the nuclear magnetic shielding tensor. Although the NMR shielding constant varies significantly with respect to simulation time, the value averaged over increasing number of snapshots remains almost constant. The paramagnetic nonrelativistic contribution is found to be most sensitive to dynamical changes in the system and is mainly responsible for the thermal and solvent effects in solution. The relativistic correction features very little sensitivity to the chemical environment, and can be disregarded in theoretical calculations when a Cd complex is used as reference compound in (113)Cd NMR experiments, due to the mutual cancelation between individual relativistic corrections.     

Four-component relativistic calculations of NMR shielding constants of the transition metal complexes. Part 1: Pentaammines of cobalt,rhodium, and iridium

The nonrelativistic and four-component fully relativistic calculations of ¹H, ¹⁵N, ⁵⁹Co, ¹⁰³Rh, and ¹⁹³Ir shielding constants of pentaammineaquacomplexes of cobalt(III), rhodium(III), and iridium(III) were carried out at the density functional theory (DFT) level of theory. The noticeable deshielding relativistic corrections were observed for nitrogen shielding constants (chemical shifts), whereas those corrections were found to be negligible for protons. For the transition metals cobalt, rhodium, and iridium, relativistic corrections to their nuclear magnetic resonance (NMR) shielding constants were found to be rather small for cobalt and rhodium (some 5–10%), whereas they are essentially larger for iridium (up to 70%).     

NMR shielding constants in PH3, absolute shielding scale, and the nuclear magnetic moment of 31P

Ab initio values of the absolute shielding constants of phosphorus and hydrogen in PH(3) were determined, and their accuracy is discussed. In particular, we analyzed the relativistic corrections to nuclear magnetic resonance (NMR) shielding constants, comparing the constants computed using the four-component Dirac-Hartree-Fock approach, the four-component density functional theory (DFT), and the Breit-Pauli perturbation theory (BPPT) with nonrelativistic Hartree-Fock or DFT reference functions. For the equilibrium geometry, we obtained σ(P) = 624.309 ppm and σ(H) = 29.761 ppm. Resonance frequencies of both nuclei were measured in gas-phase NMR experiments, and the results were extrapolated to zero density to provide the frequency ratio for an isolated PH(3) molecule. This ratio, together with the computed shielding constants, was used to determine a new value of the nuclear magnetic dipole moment of (31)P: μ(P) = 1.1309246(50) μ(N).     

NMR shielding calculations across the periodic table: diamagnetic uranium compounds. 2. Ligand and metal NMR

In this and a previous article (J. Phys. Chem. A 2000, 104, 8244), the range of application for relativistic density functional theory (DFT) is extended to the calculation of nuclear magnetic resonance (NMR) shieldings and chemical shifts in diamagnetic actinide compounds. Two relativistic DFT methods are used, ZORA ("zeroth-order regular approximation") and the quasirelativistic (QR) method. In the given second paper, NMR shieldings and chemical shifts are calculated and discussed for a wide range of compounds. The molecules studied comprise uranyl complexes, [UO(2)L(n)](+/-)(q); UF(6); inorganic UF(6) derivatives, UF(6-n)Cl(n), n = 0-6; and organometallic UF(6) derivatives, UF(6-n)(OCH(3))(n), n = 0-5. Uranyl complexes include [UO(2)F(4)](2-), [UO(2)Cl(4)](2-), [UO(2)(OH)(4)](2-), [UO(2)(CO(3))(3)](4-), and [UO(2)(H(2)O)(5)](2+). For the ligand NMR, moderate (e.g., (19)F NMR chemical shifts in UF(6-n)Cl(n)) to excellent agreement [e.g., (19)F chemical shift tensor in UF(6) or (1)H NMR in UF(6-n)(OCH(3))(n)] has been found between theory and experiment. The methods have been used to calculate the experimentally unknown (235)U NMR chemical shifts. A large chemical shift range of at least 21,000 ppm has been predicted for the (235)U nucleus. ZORA spin-orbit appears to be the most accurate method for predicting actinide metal chemical shifts. Trends in the (235)U NMR chemical shifts of UF(6-n)L(n) molecules are analyzed and explained in terms of the calculated electronic structure. It is argued that the energy separation and interaction between occupied and virtual orbitals with f-character are the determining factors.     

Quasirelativistic theory for the magnetic shielding constant. III. Quasirelativistic second-order Møller-Plesset perturbation theory and its application to tellurium compounds

The quasirelativistic (QR) generalized unrestricted Hartree-Fock method for the magnetic shielding constant [R. Fukuda, M. Hada, and H. Nakatsuji, J. Chem. Phys. 118, 1015 (2003); R. Fukuda, M. Hada, and H. Nakatsuji, J. Chem. Phys.118, 1027 (2003)] has been extended to include the electron correlation effect in the level of the second-order M?ller-Plesset perturbation theory (MP2). We have implemented the energy gradient and finite-perturbation methods to calculate the magnetic shielding constant at the QR MP2 level and applied to the magnetic shielding constants and the NMR chemical shifts of 125Te nucleus in various tellurium compounds. The calculated magnetic shielding constants and NMR chemical shifts well reproduced the experimental values. The relations of the chemical shifts with the natures of ligands, and the tellurium oxidation states were investigated. The chemical shifts in different valence states were explained by the paramagnetic shielding and spin-orbit terms. The tellurium 5p electrons are the dominant origin of the chemical shifts in the Te I and Te II compounds and the chemical shifts were explained by the p-hole mechanism. The tellurium d electrons also play an important role in the chemical shifts of the hypervalent compounds.     

A computational and experimental study of the structures and Raman and 77Se NMR spectra of SeX3+ and SeX2 (X = Cl, Br, I): FT-Raman spectrum of (SeI3)[AsF6

The ability of MP2, B3PW91 and PBE0 methods to produce reliable predictions in structural and spectroscopic properties of small selenium-halogen molecules and cations has been demonstrated by using 6-311G(d) and cc-pVTZ basis sets. Optimized structures and vibrational frequencies agree closely with the experimental information, where available. Raman intensities are also well reproduced at all levels of theory. Calculated GIAO isotropic shielding tensors yield a reasonable linear correlation with the experimental chemical shift data at each level of theory. The largest deviations between calculated and experimental chemical shifts are found for selenium-iodine species. The agreement between observed and calculated chemical shifts for selenium-iodine species can be improved by inclusion of relativistic effects using the ZORA method. The best results are achieved by adding spin-orbit correction terms from ZORA calculations to nonrelativistic GIAO isotropic shielding tensors. The calculated isotropic shielding tensors can be utilized in the spectroscopic assignment of the 77Se chemical shifts of novel selenium-halogen molecules and cations. The experimental FT-Raman spectra of (SeI3)[AsF6] in the solid state and in SO2(l) solution are also reported.     

Relativistic spin-orbit coupling effects on secondary isotope shifts of (13)C nuclear shielding in CX(2) (X = O, S, Se, Te)

Rovibrational corrections, temperature dependence, and secondary isotope shifts of the (13)C nuclear shielding in CX(2) (X = O, S, Se, Te) are calculated taking into account the relativistic spin-orbit (SO) interaction. The SO effect is considered for the first time for the secondary isotope shifts. The nuclear shielding hypersurface in terms of nuclear displacements is calculated by using a density-functional theory method. Ab initio multiconfiguration self-consistent field calculations are done at the equilibrium geometry for comparison. (13)C NMR measurements are carried out for CS(2). The calculated results are compared with both present and earlier experimental data on CO(2), CS(2), and CSe(2). The heavy-atom SO effects on the rovibrational corrections of (13)C shielding are shown to be significant. For CSe(2) and CTe(2), reliable prediction of secondary isotope effects and their temperature dependence requires the inclusion of the SO corrections. In particular, earlier discrepancies of theory and experiment for CSe(2) are fully resolved by taking the SO interactions into account.     

Simulations of 129Xe NMR chemical shift of atomic xenon dissolved in liquid benzene

The isotropic ¹²⁹Xe NMR chemical shift of atomic Xe dissolved in liquid benzene was simulated by combining classical molecular dynamics and quantum chemical calculations of ¹²⁹Xe nuclear magnetic shielding. Snapshots from the molecular dynamics trajectory of xenon atom in a periodic box of benzene molecules were used for the quantum chemical calculations of isotropic ¹²⁹Xe chemical shift using nonrelativistic density functional theory as well as relativistic Breit?CPauli perturbation corrections. Thus, the correlation and relativistic effects as well as the temperature and dynamics effects could be included in the calculations. Theoretical results are in a very good agreement with the experimental data. The most of the experimentally observed isotropic ¹²⁹Xe shift was recovered in the nonrelativistic dynamical region, while the relativistic effects explain of about 8% of the total ¹²⁹Xe chemical shift.     

Density functional computations of 99Ru chemical shifts: relativistic effects, influence of the density functional, and study of solvent effects on fac-[Ru(CO)3I3]-

Solvent effects on the 99Ru NMR chemical shift of the complex fac-[Ru(CO)3I3]- are investigated computationally using density functional theory. Further, benchmark calculations of the 99Ru shift for a set of ten Ru complexes have been performed in order to calibrate the computational model and to determine the importance of relativistic effects on the 99Ru nuclear magnetic shielding and on the chemical shift. A computational model for fac-[Ru(CO)3I3]- that includes both explicit solvent molecules and a continuum model is shown to yield the best agreement with experiment. Relativistic corrections are shown to be of minor importance for determining 99Ru chemical shifts. On the other hand, the nature of the density functional is of importance. In agreement with literature data for ligand trends of 99Ru chemical shifts, the chemical shift range for different solvents is also best reproduced by a hybrid functional.     

Calculation of binary magnetic properties and potential energy curve in xenon dimer: second virial coefficient of (129)Xe nuclear shielding

Quantum chemical calculations of the nuclear shielding tensor, the nuclear quadrupole coupling tensor, and the spin-rotation tensor are reported for the Xe dimer using ab initio quantum chemical methods. The binary chemical shift delta, the anisotropy of the shielding tensor Delta sigma, the nuclear quadrupole coupling tensor component along the internuclear axis chi( parallel ), and the spin-rotation constant C( perpendicular ) are presented as a function of internuclear distance. The basis set superposition error is approximately corrected for by using the counterpoise correction (CP) method. Electron correlation effects are systematically studied via the Hartree-Fock, complete active space self-consistent field, second-order M?ller-Plesset many-body perturbation, and coupled-cluster singles and doubles (CCSD) theories, the last one without and with noniterative triples, at the nonrelativistic all-electron level. We also report a high-quality theoretical interatomic potential for the Xe dimer, gained using the relativistic effective potential/core polarization potential scheme. These calculations used valence basis set of cc-pVQZ quality supplemented with a set of midbond functions. The second virial coefficient of Xe nuclear shielding, which is probably the experimentally best-characterized intermolecular interaction effect in nuclear magnetic resonance spectroscopy, is computed as a function of temperature, and compared to experiment and earlier theoretical results. The best results for the second virial coefficient, obtained using the CCSD(CP) binary chemical shift curve and either our best theoretical potential or the empirical potentials from the literature, are in good agreement with experiment. Zero-point vibrational corrections of delta, Delta sigma, chi (parallel), and C (perpendicular) in the nu=0, J=0 rovibrational ground state of the xenon dimer are also reported.     

129Xe NMR chemical shift in Xe@C60 calculated at experimental conditions: Essential role of the relativity,dynamics, and explicit solvent

The isotropic ¹²⁹Xe nuclear magnetic resonance (NMR) chemical shift (CS) in Xe@C₆₀ dissolved in liquid benzene was calculated by piecewise approximation to faithfully simulate the experimental conditions and to evaluate the role of different physical factors influencing the ¹²⁹Xe NMR CS. The ¹²⁹Xe shielding constant was obtained by averaging the ¹²⁹Xe nuclear magnetic shieldings calculated for snapshots obtained from the molecular dynamics trajectory of the Xe@C₆₀ system embedded in a periodic box of benzene molecules. Relativistic corrections were added at the Breit–Pauli perturbation theory (BPPT) level, included the solvent, and were dynamically averaged. It is demonstrated that the contribution of internal dynamics of the Xe@C₆₀ system represents about 8% of the total nonrelativistic NMR CS, whereas the effects of dynamical solvent add another 8%. The dynamically averaged relativistic effects contribute by 9% to the total calculated ¹²⁹Xe NMR CS. The final theoretical value of 172.7 ppm corresponds well to the experimental ¹²⁹Xe CS of 179.2 ppm and lies within the estimated errors of the model. The presented computational protocol serves as a prototype for calculations of ¹²⁹Xe NMR parameters in different Xe atom guest–host systems. © 2013 Wiley Periodicals, Inc.     

MP2 calculation of 77Se NMR chemical shifts taking into account relativistic corrections

The main factors affecting the accuracy and computational cost of the Second‐order Möller‐Plesset perturbation theory (MP2) calculation of ⁷⁷Se NMR chemical shifts (methods and basis sets, relativistic corrections, and solvent effects) are addressed with a special emphasis on relativistic effects. For the latter, paramagnetic contribution (390–466 ppm) dominates over diamagnetic term (192–198 ppm) resulting in a total shielding relativistic correction of about 230–260 ppm (some 15% of the total values of selenium absolute shielding constants). Diamagnetic term is practically constant, while paramagnetic contribution spans over 70–80 ppm. In the ⁷⁷Se NMR chemical shifts scale, relativistic corrections are about 20–30 ppm (some 5% of the total values of selenium chemical shifts). Solvent effects evaluated within the polarizable continuum solvation model are of the same order of magnitude as relativistic corrections (about 5%). For the practical calculations of ⁷⁷Se NMR chemical shifts of the medium‐sized organoselenium compounds, the most efficient computational protocols employing relativistic Dyall's basis sets and taking into account relativistic and solvent corrections are suggested. The best result is characterized by a mean absolute error of 17 ppm for the span of ⁷⁷Se NMR chemical shifts reaching 2500 ppm resulting in a mean absolute percentage error of 0.7%. Copyright © 2015 John Wiley & Sons, Ltd.     

Characterization of metal centers in bioinorganic complexes using ab initio calculations of 113Cd chemical shifts

Determination of (113)Cd chemical shift is of significant interest in NMR characterization of metal porphyrins, metal-histidine interactions, and other metal-ligand interactions in many bioinorganic complexes and metalloproteins. In this study, we present a detailed account of a number of quantum chemical investigations aimed at relating isotropic and anisotropic (113)Cd chemical shifts to the structure of several biologically relevant complexes with discrete and polymeric structures. Calculated and experimentally determined chemical shift values are compared to correlate the variation of the chemical shift values with the structural changes around the metal center. Our results infer that the density functional theory using the Sadlej basis set on the cadmium atom is a suitable method for estimating cadmium shielding values to a reasonable accuracy.