Nuclear spin–spin coupling constants from regular approximate relativistic density functional calculations. II. Spin–orbit coupling effects and anisotropies

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.

Analysis of one-bond Se-Se nuclear couplings in diselenides and 1,2-diselenoles on the basis of molecular orbital theory: torsional angular dependence, electron density influence, and origin in j(Se, Se)

Nuclear couplings for the Se-Se bonds, ¹J(Se, Se), are analyzed on the basis of the molecular orbital (MO) theory. The values are calculated by employing the triple ζ basis sets of the Slater type at the DFT level. ¹J(Se, Se) are calculated modeled by MeSeSeMe (1a), which shows the typical torsional angular dependence on ϕ(C_MeSeSeC_Me). The dependence explains well the observed ¹J_obsd (Se, Se) of small values (≤ 64 Hz) for RSeSeR′ (1) (simple derivatives of 1a) and large values (330–380 Hz) observed for 4-substituted naphto[1,8-c, d]-1,2-diselenoles (2) which correspond to symperiplanar diselenides. ¹J (Se, Se: 2) becomes larger as the electron density on Se increases. The paramagnetic spin-orbit terms contribute predominantly. The contributions are evaluated separately from each MO (ψ_i) and each ψ_i → ψ_a transition, where ψ_i and ψ_a are occupied and unoccupied MO's, respectively. The separate evaluation enables us to recognize and visualize the origin and the mechanism of the couplings.

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.

A solid-state 31P NMR study of 1:1 silver–triphenylphosphine complexes — Interpretation of 1J(107,109Ag,31P) values,

High-resolution solid-state 31P NMR spectroscopy was used to investigate a series of 1:1 silver–triphenylphosphine complexes, [Ph3PAgX]n, where X is a monovalent anion and n = 1, 2, 3, 4, or ∞. The 31P CP MAS NMR spectra reveal the number of distinct phosphorus sites in these complexes as well as the |1J(109Ag,31P)| values, which range from 401 ± 10 Hz (X = N3–) to 869 ± 10 Hz (X = SO3CF3–). The data obtained here and in earlier investigations indicate that |1J(109Ag,31P)| values for silver–tertiary phosphine complexes decrease as Ag–P bond lengths increase. This experimental conclusion is supported by DFT calculations, which also indicate that the Fermi-contact mechanism is the only important spin–spin coupling mechanism for 1J(109Ag,31P) in these complexes. In addition, the crystal structure of a silver–triphenylphosphine trifluoroacetate tetramer was determined using X-ray crystallography, and the structure of a silver–triphenylphosphine chloride tetramer was reinvestigated.

Solid-state 13C and 59Co NMR spectroscopy of 13C-methylcobalt(iii) complexes with amine ligands

Five octahedral Co(iii) cations, [trans-Co(en)(2)(X)((13)CH(3))](n+) where en = ethylenediamine, X = CN(-), N(3)(-), NH(3), NO(2)(-) or H(2)O and n = 1 or 2, as well as [Co(NH(3))(5)(13)CH(3)](2+), have been investigated by solid-state (13)C and (59)Co NMR spectroscopy. We show that the determination of the (59)Co nuclear quadrupolar parameters both directly via(59)Co NMR and indirectly via(13)C NMR provide complementary information that is unavailable if one investigates only one nucleus. Specifically, (1)J((59)Co,(13)C) and the orientation of the largest component of the EFG were determined via(13)C NMR spectroscopy, which also established the negative sign of C(Q)((59)Co). Cobalt-59 NMR spectroscopy was used to characterize the cobalt magnetic shielding tensor, to verify the magnitudes of C(Q)((59)Co) and to establish the value of eta(Q), which is difficult to determine indirectly. The measurements show that the EFG tensors are either axially symmetric or close to being so, but there is a wide range of C(Q) values, from -40 MHz for the complex with X = H(2)O to -105 MHz with X = CN(-). The Co chemical shift tensors are approximately axially symmetric with the spans, delta(11)-delta(33), ranging from 3700 to 5600 ppm for X = H(2)O and CN(-), respectively. The latter measurements also established the relative orientations of the Co EFG and chemical shift tensors. Density functional theory calculations of the (59)Co EFG and magnetic shielding tensors as well as of (1)J((59)Co,(13)C) for the NO(2)(-) and N(3)(-) complexes were undertaken. These calculations confirm the experimental observation that the sign of C(Q) is negative and that the largest component of the EFG is along the Co-methyl-carbon bond.

Relativistic two-component geometric approximation of the electron-positron contribution to magnetic properties in terms of Breit-Pauli spinors

An alternative approach for the calculation of the electron-positron (e-p) contribution to magnetic properties based on two-component Breit-Pauli spinors is presented. In it, the elimination of the small component scheme is applied to the inverse propagator matrix of e-p pairs. The effect of the positronic manifold is expressed as an operator acting on Breit-Pauli spinors. The operator form thus obtained sums up the relativistic correction as a geometric series and as a result a totally different behavior in the vicinity of a nucleus is obtained as compared to the one of the linear response approximation. This feature has deep influence in numerical values of the e-p contribution to the nuclear magnetic shielding of heavy atoms. Numerical calculations carried out for Kr, Xe, and I show that with this approach, the e-p contributions to this property are in good agreement with those of four-component methods.

Analyzing Pt chemical shifts calculated from relativistic density functional theory using localized orbitals: the role of Pt 5d lone pairs

Pt chemical shifts were calculated from two-component relativistic density functional theory (DFT). The shielding tensors were analyzed by using a recently developed method to decompose the spin-orbit DFT results into contributions from spin-free localized orbitals (here: natural localized molecular orbitals (NLMOs) and natural bond orbitals (NBOs)). Seven chemical shifts in six Pt complexes with Pt oxidation states II, III, and IV; and halide, amino, and amidate ligands were analyzed, with particular focus on the role of nonbonding Pt 5d orbitals. A simple d-orbital 'rotation' model has been used to rationalize some of the observed trends such as the main difference between Pt(II) and Pt(IV) chemical shifts. The localized orbital analysis data showed that most of this difference as well as trends among different Pt complexes with similar coordination can be rationalized by comparing properties of the nonbonding Pt 5d orbitals. We have also analyzed the spin-orbit effects on the chemical shifts of [PtCl4](2-) compared to [PtBr4](2-).

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.

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

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

Experimental and Theoretical Analysis of Vicinal and Long-Range Proton−Proton Coupling Constants for Anthracene Derivatives

We studied vicinal and long-range coupling constants for 9-anthracene derivatives, e.g., Br, CN, CHO, NO2, CH2Cl, CH2OH, and OCH3. We performed the accurate measurements using modified J doubling in the frequency domain, even for the smallest couplings immersed within the line width. Density functional theory allowed us to reproduce and exhaustively analyze the physical contributions to the values of these spectroscopic parameters. The theory of atoms in molecules defines a delocalization index that correlates linearly with vicinal and long-range coupling constants when they are grouped in terms of the number of bonds between the coupled nuclei. An exception to this behavior is obtained for 4J(H4,H10) values, which have a negative Fermi contact and the largest delocalization index for each molecule. This observation can be explained by a characteristic "gable roof" arrangement formed by the five nuclei involved in the coupling.

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.

Vicinal fluorine-fluorine coupling constants: Fourier analysis

Stereochemical dependences of vicinal fluorine-fluorine nuclear magnetic resonance coupling constants (3JFF) have been studied with the multiconfigurational self-consistent field in the restricted active space approach, with the second-order polarization propagator approximation (SOPPA), and with density functional theory. The SOPPA results show the best overall agreement with experimental couplings. The relationship with the dihedral angle between the coupled fluorines has been studied by Fourier analysis, the result is very different from that of proton-proton couplings. The Fourier coefficients do not resemble those of a typical Karplus equation. The four nonrelativistic contributions to the coupling constants of 1,2-difluoroethane configurations have been studied separately showing that up to six Fourier coefficients are required to reproduce the calculated values satisfactorily. Comparison with Fourier coefficients for matching hydrogen fluoride dimer configurations suggests that the higher order Fourier coefficients (Cn> or =3) originate mainly from through-space Fermi contact interaction. The through-space interaction is the main reason 3JFF do not follow the Karplus equation.

Computational Modeling of Polyoxotungstates by Relativistic DFT Calculations of183W NMR Chemical Shifts

The (183)W nuclear shielding in a variety of tungsten polyoxometalates (POM) (Lindqvist, Anderson, decatungstates, Keggin) of different shapes and charges has been modeled by DFT calculations that take into account relativistic effects, by means of the zero-order regular approximation (ZORA), and solvent effects, by the conductor-like screening model (COSMO) continuum method. The charge/surface area ratio (q/A) is proposed as an indicator of the charge density to which the solvation energies of all POMs are correlated in a satisfactory way. Among the various theoretical levels tested (ZORA scalar or spin-orbit, frozen-core or all-electron basis set, geometry optimization in the gas phase or in the continuum solvent, etc.), the best results are obtained when both geometry optimization in solvent and spin-orbit shielding are included (mean absolute error of delta=35 ppm). The quality of the computed chemical shifts depends systematically on the charge density as expressed by q/A; thus, POMs with low q/A ratios display the best agreement with experimental data. The performance of the method is such that computed values can aid the assignment of the (183)W NMR spectra of polyoxotungstates, as shown by the case of alpha-[PW(11)TiO(40)](5-), whose six signals are ranked computationally so as to almost reproduce the experimental ordering even though the signals are spaced by as little as 5 ppm.

Calculation of zero-field splitting parameters: Comparison of a two-component noncolinear spin-density-functional method and a one-component perturbational approach

Two different sets of approaches for the density-functional calculation of the spin-orbit contributions to zero-field splitting (ZFS) parameters of high-spin systems have been implemented within the same quantum chemistry code ReSpect and have been validated and compared for a series of model systems. The first approach includes spin-orbit coupling variationally in a two-component calculation, using either an all-electron Douglas-Kroll-Hess ansatz or two-component relativistic pseudopotentials. The ZFS parameters are computed directly from energy differences between different relativistic states. Additionally, an approximate second-order perturbation theory approach has been implemented, based on nonrelativistic or scalar relativistic wave functions. For a series of group 16 triplet diatomics and for the octet GdH3 molecules, two-component density functional calculations underestimate the zero-field splitting D systematically by a factor of 2. This may be rationalized readily by the incomplete description of states with absolute value MJ < J by a single-determinantal wave function built from two-component spinors. In the case of two 3d transition metal complexes and for GdH3, the results depend furthermore sensitively on exchange-correlation functional. Results of the alternative one-component approach agree strikingly with the two-component data for systems with small spin-orbit effects and start to deviate from them only for heavier systems with large spin-orbit effects. These results have fundamental implications for the achievable accuracy of one-component density-functional approaches used widely to compute ZFS parameters in the field of molecular magnetism. Possible refinements of both one-and two-component approaches are discussed.

Spectral and Structural Characterization of Amidate-Bridged Platinum−Thallium Complexes with Strong Metal−Metal Bonds

The reactions of [Pt(NH3)2(NHCOtBu)2] and TlX3 (X = NO3-, Cl-, CF3CO2-) yielded dinuclear [{Pt(ONO2)(NH3)2(NHCOtBu)}Tl(ONO2)2(MeOH)] (2) and trinuclear complexes [{PtX(RNH2)2(NHCOtBu)2}2Tl]+ [X = NO3- (3), Cl- (5), CF3CO2- (6)], which were spectroscopically and structurally characterized. Strong Pt-Tl interaction in the complexes in solutions was indicated by both 195Pt and 205Tl NMR spectra, which exhibit very large one-bond spin-spin coupling constants between the heteronuclei (1J(PtTl)), 146.8 and 88.84 kHz for 2 and 3, respectively. Both the X-ray photoelectron spectra and the 195Pt chemical shifts reveal that the complexes have Pt centers whose oxidation states are close to that of Pt(III). Characterization of these complexes by X-ray diffraction analysis confirms that the Pt and Tl atoms are held together by very short Pt-Tl bonds and are supported by the bridging amidate ligands. The Pt-Tl bonds are shorter than 2.6 Angstrom, indicating a strong metal-metal attraction between these two metals. Compound 2 was found to activate the C-H bond of acetone to yield a platinum(IV) acetonate complex. This reactivity corresponds to the property of Pt(III) complexes. Density functional theory calculations were able to reproduce the large magnitude of the metal-metal spin-spin coupling constants. The couplings are sensitive to the computational model because of a delicate balance of metal 6s contributions in the frontier orbitals. The computational analysis reveals the role of the axial ligands in the magnitude of the coupling constants.

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).

Relativistic two-component calculations of electronic g-tensors that include spin polarization

The first two-component relativistic density-functional approach for the calculation of electronic g-tensors is reported that includes spin polarization using noncollinear spin-density functionals. The method is based on the relativistic Douglas-Kroll-Hess Hamiltonian and has been implemented into the ReSpect program package. Using three self-consistent-field calculations with orthogonal orientations of total magnetization J, the full g-matrix may be obtained. In contrast to previous spin-restricted two-component treatments, results with the new approach agree excellently with spin-polarized one-component calculations for light-atom radicals. Additionally, unlike one-component approaches, the method also reproduces successfully the negative deltag(parallel)-values of heavy-atom 2sigma radicals and the negative deltag(perpendicular) components in cysteinyl. The new method removes effectively the dilemma existing up to now regarding the simultaneous inclusion of spin polarization and higher-order spin-orbit effects in g-tensor calculations. It is straightforwardly applicable to higher than doublet spin multiplicities and has been implemented with hybrid functionals.

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.

Density functional theory study of indirect nuclear spin-spin coupling constants with spin-orbit corrections

This work outlines the calculation of indirect nuclear spin-spin coupling constants with spin-orbit corrections using density functional response theory. The nonrelativistic indirect nuclear spin-spin couplings are evaluated using the linear response method, whereas the relativistic spin-orbit corrections are computed using quadratic response theory. The formalism is applied to the homologous systems H2X (X=O,S,Se,Te) and XH4 (X=C,Si,Ge,Sn,Pb) to calculate the indirect nuclear spin-spin coupling constants between the protons. The results confirm that spin-orbit corrections are important for compounds of the H2X series, for which the electronic structure allows for an efficient coupling between the nuclei mediated by the spin-orbit interaction, whereas in the case of the XH4 series the opposite situation is encountered and the spin-orbit corrections are negligible for all compounds of this series. In addition we analyze the performance of the density functional theory in the calculations of nonrelativistic indirect nuclear spin-spin coupling constants.

Structural and spectroscopic studies on mercury(II) tribenzylphosphine complexes

The tribenzylphosphine (PBz3) complexes of mercury(II), [Hg(PBz3)2](BF4)2, [Hg(PBz3)2(NO3)2] and [HgX(NO3)(PBz3)](X = Cl, Br, I and SCN), have been synthesised and their structures determined by single-crystal X-ray crystallography. [Hg(PBz3)2](BF4)2 contains [Hg(PBz3)2]2+ cations with linear P-Hg-P coordination, the first example of a truly two-coordinate [Hg(PR3)2]2+ complex. The mercury coordination in [Hg(PBz3)2(NO3)2] can be described as distorted tetrahedral, with a significant deviation of the P-Hg-P angle from linearity as a result of coordination of the nitrate groups. Nitrate coordination is also observed in [HgX(NO3)(PBz3)](X = Cl, Br, I), resulting in significantly non-linear P-Hg-X coordination. The thiocyanate complex is a centrosymmetric thiocyanate-bridged dimer with distorted trigonal-pyramidal mercury coordination to the P atom of PBz3, to the S and N atoms of two bridging thiocyanate groups, and to the O atom of one nitrate group. For all the nitrato complexes, secondary mercury-nitrate interactions (Hg-O 2.7-3.1 A) effectively raise the coordination number of the Hg(II) centres to six. High-resolution 31P solid-state NMR spectra of the six tribenzylphosphine mercury(II)-complexes, obtained by combining magic-angle spinning, proton dipolar decoupling and proton-phosphorus cross-polarization (CP-MAS), have been recorded. The spectra of [Hg(PBz3)2](BF4)2 and [HgX(NO3)(PBz3)](X = Cl, Br, I and SCN) exhibit a single line, due to species that contain non-magnetic isotopes of mercury, and satellite lines, due to 1J(31P-199Hg) coupling. The asymmetric unit of [Hg(PBz3)2(NO3)2] contains two molecules with four phosphorus environments, resulting in two AB spectra with 2J(31P-31P) coupling, due to species that contain non-magnetic isotopes of mercury, and satellite lines consisting of two ABX spectra, due to 1J(31P-199Hg) coupling. These spectra have been analysed to yield all of the chemical shifts and coupling constants involved. A remarkable increase in 1J(31P-199Hg) is observed from [Hg(PBz3)2](BF4)2 to [Hg(PBz3)2(NO3)2] as a consequence of the incorporation of the nitrate group into the Hg coordination sphere in the latter case. Several of the spectra also exhibit broader satellites due to the presence of scalar spin-spin coupling between 31P and the quadrupolar 201Hg nucleus. Slow-spinning methods have been used to analyze the spinning-sideband intensities of the NMR spectra, in order to obtain the 31P shielding anisotropy and asymmetry parameters Deltasigma and eta. The 199Hg and 31P NMR shielding tensors of PMe3 models of the above six compounds have been calculated using relativistic density functional theory. The 31P results are in good agreement with experiment and assist in the assignment of some of the signals.

The ?Invisible?13C NMR Chemical Shift of the Central Carbon Atom in [(Ph3PAu)6C]2+: A Theoretical Investigation

The experimental 13C NMR chemical shift of the central carbon atom in the octahedral [(Ph3PAu)6C]2+ cluster was investigated on the basis of relativistic density functional calculations. In order to arrive at independent model conclusions regarding the value of the chemical shift, a systematic study of the dependence of the cluster structure on the phosphine ligands, the chosen density functionals, and the basis set size was conducted. The best structures obtained were then used in the NMR calculations. Because of the cage-like cluster structure a pronounced deshielding of the central carbon nucleus could have been expected. However, upon comparison with the 13C NMR properties of the related complex [C{Au[P(C6H5)2(p-C6H4NMe2)]}6]2+, Schmidbaur et al. have assigned a signal at delta=135.2 ppm to the interstitial carbon atom. Our calculations confirm this value in the region of the aromatic carbon atoms of the triphenylphosphine ligands. The close-lying signals of the 108 phenyl carbon atoms can explain the difficulties of assigning them experimentally.

Oxidative addition of iodo-acetonitrile and of elemental halogens to [Pt3(µ-CO)3(PCy3)3]

The reaction of [Pt3(mu-CO)3(PCy3)3](1) with one mole-equivalent of iodo-acetonitrile was quantitative at -70 degrees C giving the oxidative addition product [Pt3(mu-CO)3(PCy3)3(I)(CH2CN)](2). Fragmentation of was observed in solution giving [Pt2I(CH2CN)(CO)2(PCy3)2](3) which is the major product at room temperature if the starting cluster/reactant ratio is equal to or less than 1 to 1.5. Dimer 3 decomposes slowly in solution giving [Pt2I2(CO)2(PCy3)2](4a) and succinonitrile. Monomer [PtI(CH2CN)(CO)(PCy3)] was the final product of the reaction when using excess of iodo-acetonitrile. The reactions of with one mole-equivalent of halogens X2 gave the new 44-electron clusters [Pt3X(micro-CO)2(micro-X)(PCy3)3](X = I2(7a) or Br2(7b)) by oxidative addition followed by substitution of CO by X-. Fragmentation of and took place in solution when using one and a half mole-equivalents of X2 giving dimers 4a and [Pt2Br2(CO)2(PCy3)2](4b) as well as [Pt2X2(mu-X)2(CO)2(PCy3)2]. Monomers cis-[PtX2(CO)(PCy3)] were the final products of the reaction of with excess of halogens. Insertion of SnCl2 was observed into the Pt-Pt bond but not into the Pt-X bond, when equimolar amounts of SnCl2 x 2H2O were added to a solution of 4a or its chloro-analogue giving [Pt2X2(micro-SnCl2)(CO)2(PCy3)2]. The Pt(I) dimers have unusually small J(Pt-Pt) values as observed by 195Pt NMR and calculated by DFT. These values showed periodic changes comparing 4a and its analogues with other halides and mixed halide dimers.

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.