Relativistic four-component calculations of indirect nuclear spin–spin couplings in MH4 (M=C, Si, Ge, Sn, Pb) and Pb(CH3)3H

Relativistic calculation of indirect NMR spin-spin couplings using the Douglas-Kroll-Hess approximation

We have employed the Douglas-Kroll-Hess approximation to derive the perturbative Hamiltonians involved in the calculation of NMR spin-spin couplings in molecules containing heavy elements. We have applied this two-component quasirelativistic approach using finite perturbation theory in combination with a generalized Kohn-Sham code that includes the spin-orbit interaction self-consistently and works with Hartree-Fock and both pure and hybrid density functionals. We present numerical results for one-bond spin-spin couplings in the series of tetrahydrides CH(4), SiH(4), GeH(4), and SnH(4). Our two-component Hartree-Fock results are in good agreement with four-component Dirac-Hartree-Fock calculations, although a density-functional treatment better reproduces the available experimental data.

Temperature and Isotope Substitution Effects on the Structure and NMR Properties of the Pertechnetate Ion in Water

The uniquely well-resolved (99)Tc NMR spectrum of the pertechnetate ion in liquid water poses a stringent test of the accuracy of ab initio calculations. The displacement of the (99)Tc chemical shift as a function of temperature has been measured over the range 10-45 degrees C for the three isotopomers Tc((16)O)(4)(-), Tc((16)O)(3)((18)O)(-), and Tc((16)O)(3)((17)O)(-) at natural oxygen isotope abundance levels, and in addition the temperature dependence of the Tc-O scalar coupling was determined for the Tc((16)O)(3)((17)O)(-) isotopomer. Values for these parameters were computed using relativistic spin-orbit density functional theory with an unsolvated ion approximation and with treatments of the solvated ion based on the COnductor-like Screening MOdel (COSMO) approach. The temperature and isotope dependence of (99)Tc NMR parameters inferred by these methods were in good quantitative agreement with experimental observations. The change in the Tc-O bond length associated with the changes in temperatures considered here was determined to be of the order of 10(-)(4) A. Vibrational energies and Tc-O bond lengths derived from these models also compare favorably with previous experimental studies.

Electric field effects on the shielding constants of noble gases: A four-component relativistic Hartree-Fock study

Second derivatives of nuclear shielding constants with respect to an electric field, i.e., shielding polarizabilities, have been calculated for the noble gas atoms from helium to xenon. The calculations have been carried out using the four-component relativistic Hartree-Fock method. In order to assess the importance of the individual relativistic corrections, the shielding polarizabilities have also been calculated at the nonrelativistic Hartree-Fock level, with spin-orbit and scalar (Darwin and mass-velocity) effects having been established by perturbative methods. Electron correlation effects have been estimated using the second-order polarization propagator approach. The relativistic effects on the tensor components of the shielding polarizabilities are found to be larger and changing less regularly with the atomic number than for the shielding constant itself. However, there is a partial cancellation of the contributions to the parallel and perpendicular components of the shielding polarizability and as a consequence the mean shielding polarizability is far less affected than the individual components.

Calculation of indirect nuclear spin–spin coupling constants within the regular approximation for relativistic effects

A new method for calculating the indirect nuclear spin-spin coupling constant within the regular approximation to the exact relativistic Hamiltonian is presented. The method is completely analytic in the sense that it does not employ numeric integration for the evaluation of relativistic corrections to the molecular Hamiltonian. It can be applied at the level of conventional wave function theory or density functional theory. In the latter case, both pure and hybrid density functionals can be used for the calculation of the quasirelativistic spin-spin coupling constants. The new method is used in connection with the infinite-order regular approximation with modified metric (IORAmm) to calculate the spin-spin coupling constants for molecules containing heavy elements. The importance of including exact exchange into the density functional calculations is demonstrated.

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.

Theoretical investigation of the apparently irregular behavior of pt-pt nuclear spin-spin coupling constants

One-bond Pt-Pt nuclear spin-spin coupling constants J(Pt-Pt) for closely related dinuclear Pt complexes can differ by an order of magnitude without any obvious correlation with Pt-Pt distances. As representative examples, the spin-spin couplings of the dinuclear Pt(I) complexes [Pt(2)(CO)(6)](2+) (1) and [Pt(2)(CO)(2)Cl(4)](2-) (2) have been computationally studied with a recently developed relativistic density functional method. The experimental values are (1)J((195)Pt-(195)Pt) = 5250 Hz for 2 but 551 Hz for 1. Many other examples are known in the literature. The experimental trends are well reproduced by the computations and can be explained based on the nature of the ligands that are coordinated to the Pt-Pt fragment. The difference for J(Pt-Pt) of an order of magnitude is caused by a sensitive interplay between the influence of different ligands on the Pt-Pt bond, and relativistic effects on metal-metal and metal-ligand bonds as well as on "atomic orbital contributions" to the nuclear spin-spin coupling constants. The results can be intuitively rationalized with the help of a simple qualitative molecular orbital diagram.

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.

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

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

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.