Relativistic DFT Research Articles

The Chemical Bond between Au(I) and the Noble Gases. Comparative Study of NgAuF and NgAu+ (Ng = Ar, Kr, Xe) by Density Functional and Coupled Cluster Methods

The nature of the chemical bond between gold and the noble gases in the simplest prototype of Au(I) complexes (NgAuF and NgAu+, where Ng = Ar, Kr, Xe), has been theoretically investigated by state of art all-electron fully relativistic DC-CCSD(T) and DFT calculations with extended basis sets. The main properties of the molecules, including dipole moments and polarizabilities, have been computed and a detailed study of the electron density changes upon formation of the Ng-Au bond has been made. The Ar-Au dissociation energy is found to be nearly the same in both Argon compounds. It almost doubles along the NgAuF series and nearly triples in the corresponding NgAu+ series. The formation of the Ng-Au(I) bonds is accompanied by a large and very complex charge redistribution pattern which not only affects the outer valence region but reaches deep into the core-electron region. The charge transfer from the noble gas to Au taking place in the NgAu+ systems is largely reduced in the fluorides but the Ng-Au chemical bond in the latter systems is found to be tighter near the equilibrium distance. The density difference analysis shows, for all three noble gases, a qualitatively identical nature of the Ng-Au bond, characterized by the pronounced charge accumulation in the middle of the Ng-Au internuclear region which is typical of a covalent bond. This bonding density accumulation is more pronounced in the fluorides, where the Au-F bond is found to become more ionic, while the overall density deformation is more evident and less localized in the NgAu+ systems. Accurate density difference maps and charge-transfer curves help explain very subtle features of the chemistry of Au(I), including its peculiar preference for tight linear bicordination.

Metal-Mediated J Coupling in DNA Base Pairs: Relativistic DFT Predictions

Relativistic DFT calculations of NMR properties (metal-mediated JNN couplings) support the proposed coordination motif of Hg(II) to DNA bases and allow for predictions of other useful NMR parameters.

Computational Modeling of Polyoxotungstates by Relativistic DFT Calculations of 183W NMR Chemical Shifts.

AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract, please click on HTML or PDF.

Computational Modeling of Polyoxotungstates by Relativistic DFT Calculations of 183W 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.

Reactions of Th and U Atoms with C2H2: Infrared Spectra and Relativistic Calculations of the Metallacyclopropene, Actinide Insertion, and Ethynyl Products

Reactions of laser-ablated Th and U atoms with C(2)H(2) during condensation with excess argon at 7 K give several new product species. The metallacyclopropene, inserted hydride, and actinide ethynyl are identified from isotopic frequencies and relativistic DFT calculations. The higher-energy vinylidine isomer was not observed. These actinide metallacyclopropenes exhibit substantially stronger bonding interactions than found recently for the Pd and Pt metals. In the case of Th(C(2)H(2)) the argon matrix interaction is strong enough to reverse the computed order of states (MR-CISD) in favor of a triplet ground state for the (Ar)(n)(Th(C(2)H(2))) complex. The nature of the electronic interactions between various metal atoms and acetylene is compared and the origin of the particularly strong interaction for U and Th is traced to the higher energy of their 6d orbitals. The ThCCH and UCCH actinide ethynyl products are also observed and characterized by C[triple bond]C stretching modes 38+/-2 cm(-1) lower than acetylene itself.

The Prediction of the Nuclear Quadrupole Splitting of 119Sn Mössbauer Spectroscopy Data by Scalar Relativistic DFT Calculations

The electric field gradient components for the tin nucleus of 34 tin compounds of experimentally known structures and (119)Sn Mössbauer spectroscopy parameters were computed at the scalar relativistic density functional theory level of approximation. The theoretical values of the electric field gradient components were used to determine a quantity, V, which is proportional to the nuclear quadrupole splitting parameter (DeltaE). In a subsequent linear regression analysis the effective nuclear quadrupole moment, Q, was evaluated. The value of (11.9+/-0.1) fm(2) is a significant improvement over the non-relativistic result of (15.2+/-4.4) fm(2) and is in agreement with the experimental value of (10.9+/-0.8) fm(2). The average mean square error DeltaE(calcd)-DeltaE(exptl)=+/-0.3 mm s(-1) is a factor of two smaller than in the non-relativistic case. Thus, the approach has a quality which provides accurate support for the structure interpretation by (119)Sn spectroscopy. It was noted that geometry optimization at the relativistic level does not significantly increase the quality of the results compared with non-relativistic optimized structures. The accuracy in the approach called on us to consider the singlet-triplet state nature of the electronic structure of one of the investigated compounds.

EPR properties of Au atoms adsorbed on various sites of the MgO(1 0 0) surface from relativistic DFT calculations

Using all electron fully relativistic DFT calculations we have computed the EPR properties of Au atoms bound to various sites of the MgO surface. Changes in g-tensor and hyperfine coupling constants provide a way to identify the gold adsorption site and to map the surface morphology by comparison of measured and calculated EPR spectra. We found a strong reduction of the isotropic hyperfine coupling constant, a iso(Au), for adsorbed gold compared to the free atom; this reduction, which is about 45% for terrace sites, is more pronounced when Au interacts with low-coordinated sites like steps, edges and corners where it is about 60%. The reduction of a iso(Au) is accompanied by a corresponding increase of the superhyperfine interaction with the surface oxygen sites, as measured by a iso( 17O). Large anisotropies in the g-tensor are computed for all sites.

Density‐Functional Calculation of the 183W and 17O NMR Chemical Shifts for Large Polyoxotungstates

AbstractA phosphane sulfate relativistic DFT method (ZORA)has been used to calculate the 183W and 17O NMR chemicalshifts for large polyoxotungstates, including W6O192–,CH3OTiW5O183–, W5O18WIINO3–, W10O324–, α‐δ‐γ‐XW12O40n–, β‐PW9O28Br63–, P2W18O626–, PW2O143–, and W7O246–, based on their optimized molecular structures. Despite sizeable deviations between the calculated and experimental values, the calculations correctly reproduce the trends in the change of the chemical shift for both nuclei. As expected, the diamagnetic term is almost constant throughout the whole series. The change in the chemical shifts is shown to be determined by the paramagnetic term, which depends on the electronic structure of the whole anion under study and, in particular, on the local geometry around a given tungsten atom. On the other hand, there is no correlation between the chemical shift and HOMO–LUMO gap, showing that deeper occupied levels and several unoccupied orbitals play an important role in the paramagnetic term. However, analysis of the components of the paramagnetic shielding has shown that the most significant transitions determining the change of both 183W and 17O NMR chemical shifts for anions consisting of tungsten and oxygen atoms are the occupied–occupied and not the occupied–virtual ones.(© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2006)

DFT Calculations of the 183W NMR Chemical Shifts in Reduced Polyoxotungstates

AbstractA relativistic DFT method (ZORA) is used to calculate the 183W and 17O NMR chemical shifts for the reduced polyoxotungstates W5O18WIINO3–, γ‐SiW12O406–, P2W18O628–, and W10O326– with different degrees of (de)localization of the electrons introduced. Despite some discrepancies in the calculated and experimental data, the calculations adequately describe the changes in the chemical shifts upon reduction. The reduction of a fully oxidized anion is accompanied by an expansion of the geometry. The effect of the charge localization and change in geometry on the chemical shift is evaluated. The shift of the resonance of the tungsten atoms largely depends on the reduced charge acquired upon reduction. On the other hand, those tungsten atoms that do not increase the electron density upon reduction have a negative shift. The calculations also reproduce the negative shifts of all the 17O NMR resonances upon reduction of the polyoxotungstates. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2006)

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).

Revisiting the geometry of nd10 (n+1)s0 [M(H2O)]p+ complexes using four‐component relativistic DFT calculations and scalar relativistic correlated CSOV energy decompositions (Mp+ = Cu+, Zn2+, Ag+, Cd2+, Au+, Hg2+)

Hartree-Fock and DFT (B3LYP) nonrelativistic (scalar relativistic pseudopotentials for the metallic cation) and relativistic (molecular four-component approach coupled to an all-electron basis set) calculations are performed on a series of six nd10 (n+1)s0 [M(H2O)]p+ complexes to investigate their geometry, either planar C2v or nonplanar C(s). These complexes are, formally, entities originating from the complexation of a water molecule to a metallic cation: in the present study, no internal reorganization has been found, which ensures that the complexes can be regarded as a water molecule interacting with a metallic cation. For [Au(H2O)]+ and [Hg(H2O)]2+, it is observed that both electronic correlation and relativistic effects are required to recover the C(s) structures predicted by the four-component relativistic all-electron DFT calculations. However, including the zero-point energy corrections makes these shallow C(s) minima vanish and the systems become floppy. In all other systems, namely [Cu(H2O)]+, [Zn(H2O)]2+, [Ag(H2O)]+, and [Cd(H2O)]2+, all calculations predict a C2v geometry arising from especially flat potential energy surfaces related to the out-of-plane wagging vibration mode. In all cases, our computations point to the quasi-perfect transferability of the atomic pseudopotentials considered toward the molecular species investigated. A rationalization of the shape of the wagging potential energy surfaces (i.e., single well vs. double well) is proposed based on the Constrained Space Orbital Variation decompositions of the complexation energies. Any way of stabilizing the lowest unoccupied orbital of the metallic cation is expected to favor charge-transfer (from the highest occupied orbital(s) of the water ligand), covalence, and, consequently, C(s) structures. The CSOV complexation energy decompositions unambiguously reveal that such stabilizations are achieved by means of relativistic effects for [Au(H2O)]+, and, to a lesser extent, for [Hg(H2O)]2+. Such analyses allow to numerically quantify the rule of thumb known for Au+ which, once again, appears as a better archetype of a relativistic cation than Hg2+. This observation is reinforced due to the especially high contribution of the nonadditive correlation/relativity terms to the total complexation energy of [Au(H2O)]+.

Relativistic DFT Calculation of (119)Sn Chemical Shifts and Coupling Constants in Tin Compounds.

The nuclear shielding and spin-spin coupling constants of (119)Sn in stannane, tetramethylstannane, methyltin halides Me4-nSnXn (X = Cl, Br, I; n = 1-3), tin halides, and some stannyl cations have been investigated computationally by DFT methods and Slater all-electron basis sets, including relativistic effects by means of the zeroth order regular approximation (ZORA) method up to spin-orbit coupling. Calculated (119)Sn chemical shifts generally correlate well with experimental values, except when several heavy halogen atoms, especially iodine, are bound to tin. In such cases, calculated chemical shifts are almost constant at the scalar (spin-free) ZORA level; only at the spin-orbit level is a good correlation, which holds for all compounds examined, attained. A remarkable "heavy-atom effect", analogous to that observed for analogous alkyl halides, is evident. The chemical shift of the putative stannyl cation (SnH3(+)) has also been examined, and it is concluded that the spectrum of the species obtained in superacids is inconsistent with a simple SnH3(+) structure; strong coordination to even weak nucleophiles such as FSO3H leads to a very satisfactory agreement. On the contrary, the calculated (119)Sn chemical shift of the trimesitylstannyl cation is in very good agreement with the experimental value. Coupling constants between (119)Sn and halogen nuclei are also well-modeled in general (taking into account the large uncertainties in the experimental values); relativistic spin-orbit effects are again quite evident. Couplings to (13)C and (1)H also fall, on the average, on the same correlation line, but individual values show a significant deviation from the expected unit slope.

Spin–orbit density functional theory calculations for IX (X=F, Cl, Br and I) molecules

Two-component spin–orbit density functional theory (SODFT) calculations for spectroscopic constants of IX (X=F, Cl, Br and I) molecules have been performed with several functionals using shape-consistent relativistic effective core potentials (RECPs) with effective one-electron spin–orbit operator. The SODFT results obtained with the B3LYP functional are in very good accord with the results of previous two-component CCSD(T) calculations with the same RECP and basis sets. Results of two-component SODFT calculations with RECPs are also in good agreement with reported all-electron relativistic DFT calculations with the same functionals. The spectroscopic constants obtained with ACM and PBE0 functionals display the best agreement with the experimental values among the functionals tested. Spin–orbit effects from the SODFT calculations result in increases of bond lengths and decreases of dissociation energies and harmonic vibrational frequencies and the magnitudes are in reasonable agreement with those from two-component CCSD(T) calculations. Spin–orbit effects appear to be quite insensitive to the choice of functionals for the bond lengths and harmonic vibrational frequencies, but those of the dissociation energies somewhat deviate with the differing class of functionals.

Reactions of Laser‐Ablated Uranium Atoms with H2O in Excess Argon: A Matrix Infrared and Relativistic DFT Investigation of Uranium Oxyhydrides.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Vicinal Tungsten–Tungsten Coupling Constants in Polyoxotungstates: DFT Calculations Challenge an Empirical Rule

Smaller than expected: The empirical rule that edge and corner junctions give rise to small and large vicinal NMR tungsten–tungsten coupling constants, respectively, in polyoxometalates has led to the assumption that the W-O-W angle is the sole factor involved. Why then is the corner 2JWW coupling in γ-[SiW10O36]8− (see picture) so small? Relativistic DFT calculations show why this is indeed expected.

Reactions of Laser-Ablated Uranium Atoms with H2O in Excess Argon: A Matrix Infrared and Relativistic DFT Investigation of Uranium Oxyhydrides

Laser-ablated U atoms react with H2O during condensation in excess argon. Infrared absorptions at 1416.3, 1377.1, and 859.4 cm(-1) are assigned to symmetric H-U-H, antisymmetric H-U-H, and U=O stretching vibrations of the primary reaction product H(2)UO. Uranium monoxide, UO, also formed in the reaction, inserts into H2O to produce HUO(OH), which absorbs at 1370.5, 834.3, and 575.7 cm(-1). The HUO(OH) uranium(IV) product undergoes ultraviolet photoisomerization to a more stable H2UO2 uranium(VI) molecule, which absorbs at 1406.4 and 885.9 cm(-1). Several of these species, particularly H2UO2, appear to form weak Ar-coordinated complexes. The predicted vibrational frequencies, relative absorption intensities, and isotopic shifts from relativistic DFT calculations are in good agreement with observed spectra, which further supports the identification of novel uranium oxyhydrides from matrix infrared spectra.

Determination of theg-Tensors and Their Orientations forcis,trans-(L-N2S2)MoVOX (X = Cl, SCH2Ph) by Single-Crystal EPR Spectroscopy and Molecular Orbital Calculations

A single-crystal study of cis,trans-(L-N2S2)MoVOCl (1) doped into cis,trans-(N2S2)MoVIO2 (3) has enabled the g-tensor of 1 and its orientation with respect to the molecular structure to be determined. The EPR parameters (g1, 2.004; g2, 1.960; g3, 1.946; A1, 71.7 x 10(-4) cm(-1); A2, 11.7 x 10(-4) cm(-1); A3, 32.0 x 10(-4) cm(-1)) of cis,trans-(L-N2S2)MoVOCl [L-N2S2H2 = N,N'-dimethyl-N,N'-bis(mercaptophenyl)ethylenediamine] mimic those of the low-pH form of sulfite oxidase and the "very rapid" species of xanthine oxidase. The principal axis that corresponds to g1 is rotated approximately 10 degrees from the Mo[triple bond]O vector, while the principal axis that corresponds to g3 is located in the equatorial plane and approximately 38 degrees from the Mo-Cl vector. Independent theoretical calculations of the g-tensor of 1 were performed using two types of techniques: (1) the spectroscopically parametrized intermediate neglect of differential overlap technique (INDO/S) combined with single-excitation configuration interaction (CIS); (2) a scalar relativistic DFT (BP86 and B3LYP functionals) treatment using the zeroth order regular approximation to relativistic effects (ZORA) in combination with recently developed accurate multicenter mean field spin-orbit operators (RI-SOMF) and the estimation of solvent effects using dielectric continuum theory at the conductor-like screening model (COSMO) level. The excellent agreement between experiment and theory, as well as the high consistency between the INDO/S and BP86/ZORA results, provides a sound basis for analysis of the calculated orientation of the g-tensor for cis,trans-(L-N2S2)MoVO(SCH2Ph) (2), for which single-crystal EPR data are not available but which contains three equatorial sulfur donor atoms, as occurs in sulfite oxidase and xanthine oxidase. The implications of these results for the EPR spectra of the Mo(V) centers of enzymes are discussed.

Density Functional Theory and Low-Temperature Matrix Investigations of CO-Loss Photochemistry from [(C5R5)Ru(CO)2]2 (R = H, Me) Complexes

The photochemical CO-loss products of the diruthenium complexes [CpRu(CO) 2]2 (5; Cp = η5-C5H5), [Cp*Ru(CO)2]2 (5*; Cp* = η5-C5(CH3)5) and CpCp*[Ru(CO)2]2 (5′) have been studied experimentally in low-temperature (96 K) matrices in 3-methylpentane by using IR spectroscopy. It is proposed that all three complexes undergo single-CO-loss chemistry but that the products have different structures. The single-CO-loss product from 5 is proposed to have one bridging and two terminal carbonyl ligands, whereas 5* and 5′ generate triply bridged CO-loss products similar to that observed from [CpFe(CO)2]2 and [Cp*Fe(CO)2]2. Double-CO-loss from 5* and 5* 9′ is also apparently observed. Relativistic DFT calculations have been carried out on various isomers of the starting materials and on potential CO-loss products from 5. The calculations suggest that the triply bridged product Cp2Ru2(μ-CO)3 (6) might have a singlet ground state in contrast to the corresponding diiron complex Cp2Fe2(μ-CO)3 (3), which has a triplet ground state.

A relativistic DFT study of one-bond fluorine-X indirect spin-spin coupling tensors.

The relativistic zeroth-order regular approximation (ZORA) DFT method was employed to investigate indirect spin-spin coupling tensors involving fluorine, (1)J(X, F). The relative contributions of the mechanisms contributing to (1)J(X, F) are discussed, with special attention paid to the magnitude and origin of the anisotropy in this tensor, DeltaJ. This quantum chemical study demonstrates that, for the systems investigated, the ZORA-DFT method reproduces the magnitude of (1)J(X, F)(iso) and indicates that DeltaJ(X, F) is of the same order of magnitude as (1)J(X, F)(iso). Several examples are provided that demonstrate the importance of considering contributions of DeltaJ to the experimental measurement of effective dipolar coupling constants, R(eff). Given the difficulties with determining DeltaJ experimentally and the promising computational results, we suggest that the quantum chemical calculation of (1)J(X, F) be used as a complementary tool to aid in the analysis of data from NMR experiments designed to measure dipolar coupling constants.

Investigation of Magnetic Shielding in Xenon Difluoride Using Solid-State NMR Spectroscopy and Relativistic Density Functional Theory

The xenon and fluorine magnetic shielding tensors, σ, of XeF2 are characterized using solid-state 129Xe and 19F NMR spectroscopy and nonrelativistic and spin−orbit relativistic zeroth-order regular approximation density functional theory (ZORA DFT). Analysis of 129Xe and 19F NMR spectra acquired with magic-angle spinning at several spinning rates indicates that the Xe and F magnetic shielding tensors are axially symmetric, as dictated by the crystal symmetry. The isotropic 129Xe chemical shift is −1603 ± 5 ppm with respect to OXeF4 (neat liquid, 24 °C) and the Xe magnetic shielding anisotropy, Ω, is 4245 ± 20 ppm, the first anisotropy measured directly for a xenon compound. The parallel component of the experimentally determined xenon chemical shift tensor, δ∥ = −4433 ppm differs from δ(Xe(free atom)) by ∼1000 ppm, providing the first experimental demonstration that relativistic effects play an important role in the nuclear magnetic shielding for xenon. Both the sign and magnitude of the isotropic indirect 129Xe,19F nuclear spin−spin coupling constant are determined, −5560 ± 50 Hz. Analysis of the 19F NMR spectra yield Ω(F) = 150 ± 20 ppm. The ZORA DFT method has been employed to calculate σ(Xe) and σ(F) for isolated XeF2 and XeF4 molecules, as well as σ(Kr) and σ(F) for an isolated KrF2 molecule, at the relativistic and nonrelativistic levels of theory. Spin−orbit relativistic DFT results for Ω(Xe) are in very good agreement with those determined experimentally and highlight the importance of relativistic effects.