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.     

DFT study of the NMR properties of xenon in covalent compounds and van der waals complexes-implications for the use of 129Xe as a molecular probe

The NMR properties (chemical shift and spin-spin coupling constants) of (129)Xe in covalent compounds and weakly bound complexes have been investigated by DFT methods including relativistic effects. For covalent species, a good agreement between experimental and calculated results is achieved without scalar relativistic effects, but their inclusion (with a triple-zeta, double-polarization basis set) leads to some improvement in the quality of the correlation. The spin-orbit coupling term has a significant effect on the shielding constant, but makes a small contribution to the chemical shift. Coupling constants contain substantial contributions from the Fermi contact and paramagnetic spin-orbit terms; unlike light nuclei the spin-dipole term is also large, whereas the diamagnetic spin-orbit term is negligible. For van der Waals dimers, the dependence of the xenon chemical shift and anisotropy is calculated as a function of the distance. Small (<1 Hz) but non-negligible through-space coupling constants between (129)Xe and (13)C or (1)H are predicted. Much larger couplings, of the order of few Hz, are calculated between xenon and (17)O in a model silicate residue.     

Thermal and solvent effects on NMR indirect spin-spin coupling constants of a prototypical Chagas disease drug

NMR J-couplings across hydrogen bonds reflect the static and dynamic character of hydrogen bonding. They are affected by thermal and solvent effects and can therefore be used to probe such effects. We have applied density functional theory (DFT) to compute the NMR (n)J(N,H) scalar couplings of a prototypical Chagas disease drug (metronidazole). The calculations were done for the molecule in vacuo, in microsolvated cluster models with one or few water molecules, in snapshots obtained from molecular dynamics simulations with explicit water solvent, and in a polarizable dielectric continuum. Hyperconjugative and electrostatic effects on spin-spin coupling constants were assessed through DFT calculations using natural bond orbital (NBO) analysis and atoms in molecules (AIM) theory. In the calculations with explicit solvent molecules, special attention was given to the nature of the hydrogen bonds formed with the solvent molecules. The results highlight the importance of properly incorporating thermal and solvent effects into NMR calculations in the condensed phase.     

Indirect relativistic bridge and substituent effects from the ‘heavy’ environment on the one‐bond and two‐bond 13C1H spin–spin coupling constants

Indirect relativistic bridge effect (IRBE) and indirect relativistic substituent effect (IRSE) induced by the ‘heavy’ environment of the IV‐th, V‐th and VI‐th main group elements on the one‐bond and geminal ¹³C? ¹H spin–spin coupling constants are observed, and spin‐orbit parts of these two effects were interpreted in terms of the third‐order Rayleigh–Schrödinger perturbation theory. Both effects, IRBE and IRSE, rapidly increase with the total atomic charge of the substituents at the coupled carbon. The accumulation of IRSE for geminal coupling constants is not linear with respect to the number of substituents in contrast to the one‐bond couplings where IRSE is an essentially additive quantity. Copyright © 2015 John Wiley & Sons, Ltd.     

Magnitude of Finite‐Nucleus‐Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin–Spin Coupling Constants

A spherical Gaussian nuclear charge distribution model has been implemented for spin‐free (scalar) and two‐component (spin–orbit) relativistic density functional calculations of indirect NMR nuclear spin–spin coupling (J‐coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J‐couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg₂²⁺, and Tl? X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite‐nucleus effects.     

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.     

Ab initio study of dynamical E × e Jahn-Teller and spin-orbit coupling effects in the transition-metal trifluorides TiF3, CrF3, and NiF3

Multiconfiguration ab initio methods have been employed to study the effects of Jahn-Teller (JT) and spin-orbit (SO) coupling in the transition-metal trifluorides TiF(3), CrF(3), and NiF(3), which possess spatially doubly degenerate excited states ((M)E) of even spin multiplicities (M = 2 or 4). The ground states of TiF(3), CrF(3), and NiF(3) are nondegenerate and exhibit minima of D(3h) symmetry. Potential-energy surfaces of spatially degenerate excited states have been calculated using the state-averaged complete-active-space self-consistent-field method. SO coupling is described by the matrix elements of the Breit-Pauli operator. Linear and higher order JT coupling constants for the JT-active bending and stretching modes as well as SO-coupling constants have been determined. Vibronic spectra of JT-active excited electronic states have been calculated, using JT Hamiltonians for trigonal systems with inclusion of SO coupling. The effect of higher order (up to sixth order) JT couplings on the vibronic spectra has been investigated for selected electronic states and vibrational modes with particularly strong JT couplings. While the weak SO couplings in TiF(3) and CrF(3) are almost completely quenched by the strong JT couplings, the stronger SO coupling in NiF(3) is only partially quenched by JT coupling.     

Theoretical study on solvation effects in chemical reactions: A vibrational coupling model

A vibrational coupling model to treat the solvation effects in chemical reaction rate calculations is proposed and applied to the intramolecular hydrogen transfer reaction CH₃O· → ·CH₂OH in the condensed phase. The effect of solvation is taken into account in two ways: (1) the solvent effect on the activation energy of the reaction is simulated by including 39 surrounding water molecules, represented by fractional charges at the assumed atomic positions, in the potential energy surface calculation; and (2) the vibrational couplings between the 10 nearest solvent molecules and the molecules constituting the reaction system are explicitly included in a vibrational frequency calculation. RRKM theory with Miller's tunneling correction included is employed to calculate the rate constants. The effect of solvation causes a significant change in the chemical reaction rate, mainly through a lowering of the activation energy. The vibrational coupling causes a slight increase of the rate constant in the tunneling region by perturbing the vibrational frequencies of the reactant and transition states, which appear in the rate-constant expression, but has little effect at higher temperatures.     

Effects of static and dynamic perturbations on isotropic hyperfine coupling constants in some quinone radicals

The effects of solvent dielectric response on the isotropic hyperfine coupling constants of the 1,4-benzoquinone, 1,4-naphthoquinone and 9,10-anthraquinone anions and 1,4-naphthalenediol cation radicals were studied by electron spin resonance (ESR) spectroscopy and by the theoretical density functional method within the polarizable continuum model. Experimental results demonstrate that the isotropic hyperfine coupling constants can be obtained with high accuracy and that the effects of solvent impurities can be minimized by careful sample preparation. The results obtained correlate well with theoretical predictions from density functional theory calculations. For 1,4-naphthalenediol both the solvent dielectric response as well as rotational averaging of the hydroxy groups were calculated. The overall results highlight the importance of static and dynamic perturbations to the couplings and aid in the assignation process of the couplings to specific magnetic nuclei.     

Scalar relativistic calculations of hyperfine coupling tensors using the Douglas-Kroll-Hess method with a finite-size nucleus model

A scalar relativistic method to calculate hyperfine coupling tensors at the Douglas-Kroll-Hess level has been extended to incorporate a finite-size nucleus model using a Gaussian charge and magnetic moment distribution. Density functional calculations at gradient-corrected and hybrid functional levels have been carried out for the group 11 atoms and for a set of small group 12 molecules, comparing nonrelativistic as well as scalar relativistic results at second-order Douglas-Kroll-Hess level with and without finite-size nucleus. While nonrelativistic calculations underestimate isotropic hyperfine couplings increasingly with increasing nuclear charge, scalar relativistic calculations with point nucleus provide somewhat overestimated values. Inclusion of the finite-size nuclear model in the calculation of the wavefunction, and in the transformed hyperfine operators both decrease the magnitude of the hyperfine couplings. The effects, which are cumulative, improve agreement with experiment.     

A theoretical study of the NMR spin-spin coupling constants of the complexes [(NC)(5)Pt-Tl(CN)(n)](n-) (n = 0-3) and [(NC)(5)Pt-Tl-Pt(CN)(5)](3-): a lesson on environmental effects

The molecular geometries and the nuclear spin-spin coupling constants of the complexes [(NC)(5)Pt-Tl(CN)(n)](n-), n = 0-3, and the related system [(NC)(5)Pt-Tl-Pt(CN)(5)](3-) are studied. These complexes have received considerable interest since the first characterization of the n = 1 system by Glaser and co-workers in 1995 [J. Am. Chem. Soc. 1995, 117, 7550-7551]. For instance, these systems exhibit outstanding NMR properties, such as extremely large Pt-Tl spin-spin coupling constants. For the present work, all nuclear spin-spin coupling constants J(Pt-Tl), J(Pt-C), and J(Tl-C) have been computed by means of a two-component relativistic density functional approach. It is demonstrated by the application of increasingly accurate computational models that both the huge J(Pt-Tl) for the complex (NC)(5)Pt-Tl and the whole experimental trend among the series are entirely due to solvent effects. An approximate inclusion of the bulk solvent effects by means of a continuum model, in addition to the direct coordination, proves to be crucial. Similarly drastic effects are reported for the coupling constants between the heavy atoms and the carbon nuclei. A computational model employing the statistical average of orbital-dependent model potentials (SAOP) in addition to the solvent effects allows to accurately reproduce the experimental coupling constants within reasonable limits.     

Understanding solvent effects on hyperfine coupling constants of cyclohexadienyl radicals

Quantum chemical calculations have been carried out to understand better solvent effects on the isotropic muon and proton hyperfine coupling constants in the C₆H₆Mu^• radical. Both polarizable continuum solvent models and explicit inclusion of water molecules into supermolecular complexes were used. Changes in the hyperfine couplings of in-plane hydrogen atoms are very small and difficult to discuss, partly due to relatively large experimental error bars. In contrast, the out-of-plane proton and muon hyperfine couplings exhibit more pronounced changes. These are partly due to structural changes of the radical and partly due to direct electronic polarization effects. Polarizable continuum solvent models agree well with experimental changes for benzene but overshoot the enhancement of the hyperfine couplings for water. Explicit inclusion of water molecules reduces this overestimated spin density increase and thereby tends to bring theory and experiment into closer agreement. The enhancement of the spin density on the out-of-plane hydrogen or muon atoms by the solvent environment is mainly due to an increased polarization of the singly occupied MO towards this side. Electronic Supplementary Material: Supplementary material is available in the online version of this article at dx.doi.org/10.1007/s00214-005-0680-x     

Modeling solvent effects on electron-spin-resonance hyperfine couplings by frozen-density embedding

In this study, we investigate the performance of the frozen-density embedding scheme within density-functional theory [J. Phys. Chem. 97, 8050 (1993)] to model the solvent effects on the electron-spin-resonance hyperfine coupling constants (hfcc's) of the H2NO molecule. The hfcc's for this molecule depend critically on the out-of-plane bending angle of the NO bond from the molecular plane. Therefore, solvent effects can have an influence on both the electronic structure for a given configuration of solute and solvent molecules and on the probability for different solute (plus solvent) structures compared to the gas phase. For an accurate modeling of dynamic effects in solution, we employ the Car-Parrinello molecular-dynamics (CPMD) approach. A first-principles-based Monte Carlo scheme is used for the gas-phase simulation, in order to avoid problems in the thermal equilibration for this small molecule. Calculations of small H2NO-water clusters show that microsolvation effects of water molecules due to hydrogen bonding can be reproduced by frozen-density embedding calculations. Even simple sum-of-molecular-densities approaches for the frozen density lead to good results. This allows us to include also bulk solvent effects by performing frozen-density calculations with many explicit water molecules for snapshots from the CPMD simulation. The electronic effect of the solvent at a given structure is reproduced by the frozen-density embedding. Dynamic structural effects in solution are found to be similar to the gas phase. But the small differences in the average structures still induce significant changes in the computed shifts due to the strong dependence of the hyperfine coupling constants on the out-of-plane bending angle.     

A new method to generate spin-orbit coupled potential energy surfaces: effective relativistic coupling by asymptotic representation

A new method has been developed to generate fully coupled potential energy surfaces including derivative and spin-orbit coupling. The method is based on an asymptotic (atomic) representation of the molecular fine structure states and a corresponding diabatization. The effective relativistic coupling is described by a constant spin-orbit coupling matrix and the geometry dependence of the coupling is accounted for by the diabatization. This approach is very efficient, particularly for certain systems containing a very heavy atom, and yields consistent results throughout nuclear configuration space. A first application to a diatomic system is presented as proof of principle and is compared to accurate ab initio calculations. However, the method is widely applicable to general polyatomic systems in full dimensionality, containing several relativistic atoms and treating higher order relativistic couplings as well.     

Molecular design for high-spin molecules in view of vibronic couplings

A high-spin ground state is possible if a molecule has degenerate or pseudo-degenerate frontier orbitals. Since strong vibronic couplings, or electron-vibration interactions give rise to reduce the degeneracy or pseudo degeneracy, a lower-spin state is the ground state in such a molecule. Therefore small vibronic couplings are desirable for designing molecules with a high-spin ground state. Vibronic coupling constants of derivatives of m-phenylene diamine are evaluated. The calculated results are analyzed based on vibronic coupling density which enables us to control the vibronic coupling constants. Based on the vibronic coupling density analysis, we succeed in recovering the high-spin ground state from the closed-shell singlet ground state of a methoxy derivative of m-phenylene diamine by introducing an appropriate substituent.     

A theoretical study of medium effects on the transmission mechanisms of the fermi contact term of spin–spin coupling constants in the acetamide molecule

Solvent effects on different transmission mechanisms of spin–spin coupling constants are analyzed from a theoretical viewpoint. Medium effects are introduced using the solvaton model, and the decomposition of coupling constants in σ- and π-electron transmitted components is accomplished with the PRMO method. Trends thus obtained are in fairly good agreement with experimental findings reported in the literature. In all types of couplings studied in this work, σ and π components show opposite behavior when increasing the polarity of the solvent.     

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.