The quadrupole moment of the 3/2+ nuclear ground state of 197Au from electric field gradient relativistic coupled cluster and density-functional theory of small molecules and the solid state

An attempt is made to improve the currently accepted muonic value for the 197Au nuclear quadrupole moment [+0.547(16)x10(-28) m2] for the 3/2+ nuclear ground state obtained by Powers et al. [Nucl. Phys. A230, 413 (1974)]. From both measured Mossbauer electric quadrupole splittings and solid-state density-functional calculations for a large number of gold compounds a nuclear quadrupole moment of +0.60x10(-28) m2 is obtained. Recent Fourier transform microwave measurements for gas-phase AuF, AuCl, AuBr, and AuI give accurate bond distances and nuclear quadrupole coupling constants for the 197Au isotope. However, four-component relativistic density-functional calculations for these molecules yield unreliable results for the 197Au nuclear quadrupole moment. Relativistic singles-doubles coupled cluster calculations including perturbative triples [CCSD(T) level of theory] for these diatomic systems are also inaccurate because of large cancellation effects between different field gradient contributions subsequently leading to very small field gradients. Here one needs very large basis sets and has to go beyond the standard CCSD(T) procedure to obtain any reliable field gradients for gold. From recent microwave experiments by Gerry and co-workers [Inorg. Chem. 40, 6123 (2001)] a significantly enhanced (197)Au nuclear quadrupole coupling constant in (CO)AuF compared to free AuF is observed. Here, these cancellation effects are less important, and relativistic CCSD(T) calculations finally give a nuclear quadrupole moment of +0.64x10(-28) m2 for 197Au. It is argued that it is currently very difficult to improve on the already published muonic value for the 197Au nuclear quadrupole moment.     

Nuclear quadrupole moment of 197Au from high-accuracy atomic calculations

The electric field gradient (EFG) at the gold nucleus is calculated using a finite field approach, to make the extraction of the nuclear quadrupole moment Q from experimental nuclear quadrupole coupling constants possible. The four-component Dirac-Coulomb Hamiltonian serves as the framework, 51 of the 79 electrons are correlated by the relativistic Fock-space coupled cluster method with single and double excitations, and the contribution of the Gaunt term, the main part of the Breit interaction, is evaluated. Large basis sets (up to 26s22p18d12f8g5h uncontracted Gaussians) are employed. Energy splittings of the 2D5/2 and 2D3/2 levels, rather than level shifts, are used to extract the EFG constants, as the former remain linear with Q up to 10(-5) a.u., whereas the latter display significant nonlinearity even at Q=10(-8) a.u. Larger Q values lead to larger energy changes and better precision. Excellent agreement (0.1%) is obtained between Q values derived from 2D5/2 and 2D3/2 data. Systematic errors connected with neglecting triple and higher excitations, truncating the basis and orbital active space, and approximating the Gaunt contribution are evaluated. The final value of Q(197Au) is 521(7) mb. It is lower than the muonic 547(16) mb and agrees within error bounds with the recent value of 510(15) mb obtained from molecular calculations.     

XeAuF

XeAuF has been detected and characterized using microwave rotational spectroscopy. It was prepared by laser ablation of Au in the presence of Xe and SF(6), and stabilized in a supersonic jet of Ar. The spectrum was measured with a cavity pulsed jet Fourier transform microwave spectrometer, in the frequency range 6-26 GHz. Rotational constants, centrifugal distortion constants, and (131)Xe and (197)Au nuclear quadrupole coupling constants have been evaluated. The molecule is linear, with a short XeAu bond (2.54 A), and is rigid. The (131)Xe nuclear quadrupole coupling constant (NQCC) is large (-135 MHz). The (197)Au NQCC differs radically from that of uncomplexed AuF. The results are supported by those of ab initio calculations which have given an XeAu dissociation energy approximately 100 kJ mol(-1), plus Mulliken and natural bond orbital populations, MOLDEN plots of valence orbitals, and an energy density distribution. All evidence is consistent with XeAu covalent bonding in XeAuF.     

Microwave spectra and structures of KrAuF, KrAgF, and KrAgBr; 83Kr nuclear quadrupole coupling and the nature of noble gas-noble metal halide bonding

Microwave spectra of the complexes KrAuF and KrAgBr have been measured for the first time using a cavity pulsed jet Fourier transform microwave spectrometer. The samples were prepared by laser ablation of the metal from its solid and allowing the resulting plasma to react with an appropriate precursor (Kr, plus SF6 or Br2) contained in the backing gas of the jet (usually Ar). Rotational constants; geometries; centrifugal distortion constants; vibration frequencies; and 197Au, 79Br, and 81Br nuclear quadrupole coupling constants have all been evaluated. The complexes are unusually rigid and have short Kr-Au and Kr-Ag bonds. The 197Au nuclear quadrupole coupling constant differs radically from its value in an AuF monomer. In addition 83Kr hyperfine structure has been measured for KrAuF and the previously reported complex KrAgF. The geometry of the latter has been reevaluated. Large values for the 83Kr nuclear quadrupole coupling constants have been found for both complexes. Both the 197Au and 83Kr hyperfine constants indicate a large reorganization of the electron distribution on complex formation. A thorough assessment of the nature of the noble gas-noble metal bonding in these and related complexes (NgMX; Ng is a noble gas, M is a noble metal, and X is a halogen) has been carried out. The bond lengths are compared with sums of standard atomic and ionic radii. Ab initio calculations have produced dissociation energies along with Mulliken populations and other data on the electron distributions in the complexes. The origins of the rigidity, dissociation energies, and nuclear quadrupole coupling constants are considered. It is concluded that there is strong evidence for weak noble gas-noble metal chemical bonding in the complexes.     

Has AuF7 been made?

Quantum chemical calculations at DFT (BP86, B3LYP, BHLYP), MP2, CCSD, and CCSD(T) levels have been carried out on various fluoro complexes of gold in oxidation states +V through +VII to evaluate the previously claimed existence of AuF7. The calculations indicate clearly that elimination of F2 from AuF7 is a strongly exothermic reaction with a low activation barrier. This is inconsistent with the reported stability of AuF7 up to room temperature. A reported experimental vibrational frequency at 734 cm(-1) for AuF7 could not be verified computationally. It is concluded that the reported observation of AuF7 was probably erroneous. As the calculations indicate also an extremely large electron affinity and little stability for AuF6, Au(V) remains the highest well-established gold oxidation state.     

The stability of gold iodides in the gas phase and the solid state

The stability of gold iodides in the oxidation state +I and +III is investigated at the ab initio and density functional level using relativistic and nonrelativistic energy-adjusted pseudopotentials for gold and iodine. The calculations reveal that relativistic effects stabilize the higher oxidation state of gold as expected, that is Au2I6 is thermodynamically stable at the relativistic level, whilst at the nonrelativistic level the complex of two iodine molecules weakly bound to both gold atoms in Au2I2 is energetically preferred. The rather low stability of AuI3 with respect to dissociation into AuI and I2 will make it difficult to isolate this species in the solid state as (possibly) Au2I6 or detect it by matrix-isolation techniques. The monomer AuI3 is Jahn-Teller distorted from the ideal trigonal planar (D3h) form, but adopts a Y-shaped structure (in contrast to AuF3 and AuCl3), and in the nonrelativistic case can be described as I2 weakly bound to AuI. Relativistic effects turn AuI3 from a static Jahn-Teller system to a dynamic one. For the yet undetected gas-phase species AuI accurate coupled-cluster calculations for the potential energy curve are used to predict vibrational-rotational constants. Solid-state density functional calculations are performed for AuI and Au2I6 in order to predict cohesive energies.     

The quadrupole moment of the Sb nucleus from molecular microwave data and calculated relativistic electric-field gradients

The recently determined accurate values of the nuclear quadrupole coupling constant of the Sb nucleus in SbN, SbP, SbF, and SbCl and the calculated electric-field gradients at Sb in these molecules are used to obtain the nuclear quadrupole moment of 121Sb and 123Sb. The calculation of the electric-field gradient has been carried out by using the infinite-order two-component relativistic method in the scalar approximation. The accompanying change of picture of the electric-field gradient operator has been accounted for by employing the shifted nucleus model of nuclear quadrupoles. The electron correlation effects are calculated at the level of the coupled cluster approximation. The present calculations give the "molecular" value of the nuclear quadrupole moment of 121Sb equal to -556+/-24 mb which is considerably different from the old "recommended" value of -360+/-40 mb and also differs from the recent "solid-state" result (-669+/-15 mb). The validation of the present data is comprehensively discussed.     

After 20 years, theoretical evidence that "AuF(7)" is actually AuF(5) x F(2)

Quantum-chemical calculations at the DFT (BP86, PBE, TPSS, B3LYP, PBE0), MP2, CCSD, and CCSD(T) levels have been carried out to characterize the putative AuF(7) reported in 1986 by Timakov et al. Our calculations indicate clearly that the species claimed to be AuF(7) had not been synthesized. Instead, a new gold fluoride complex AuF(7) x F2 was prepared. This complex is 205 kJ mol(-1) more stable than the proposed AuF(7) species, and the elimination of F(2) is calculated to be endothermic. This is consistent with the reported stability of the product. A reported experimental vibrational frequency at 734 cm(-1) was verified computationally to be the F-F stretching mode of the end-on coordinated F2 molecule. This result is in line with the recently published trends in the highest attainable oxidation states of the 5d transition metals where Au(V) remains the highest oxidation state of gold.     

An investigation of lanthanum coordination compounds by using solid-state 139La NMR spectroscopy and relativistic density functional theory

Lanthanum-139 NMR spectra of stationary samples of several solid La(III) coordination compounds have been obtained at applied magnetic fields of 11.75 and 17.60 T. The breadth and shape of the 139La NMR spectra of the central transition are dominated by the interaction between the 139La nuclear quadrupole moment and the electric field gradient (EFG) at that nucleus; however, the influence of chemical-shift anisotropy on the NMR spectra is non-negligible for the majority of the compounds investigated. Analysis of the experimental NMR spectra reveals that the 139La quadrupolar coupling constants (C(Q)) range from 10.0 to 35.6 MHz, the spans of the chemical-shift tensor (Omega) range from 50 to 260 ppm, and the isotropic chemical shifts (delta(iso)) range from -80 to 178 ppm. In general, there is a correlation between the magnitudes of C(Q) and Omega, and delta(iso) is shown to depend on the La coordination number. Magnetic-shielding tensors, calculated by using relativistic zeroth-order regular approximation density functional theory (ZORA-DFT) and incorporating scalar only or scalar plus spin-orbit relativistic effects, qualitatively reproduce the experimental chemical-shift tensors. In general, the inclusion of spin-orbit coupling yields results that are in better agreement with those from the experiment. The magnetic-shielding calculations and experimentally determined Euler angles can be used to predict the orientation of the chemical-shift and EFG tensors in the molecular frame. This study demonstrates that solid-state 139La NMR spectroscopy is a useful characterization method and can provide insight into the molecular structure of lanthanum coordination compounds.     

Calculations of nuclear quadrupole coupling in noble gas-noble metal fluorides: interplay of relativistic and electron correlation effects

The nuclear quadrupole coupling constants (NQCCs) of noble gas and noble metal nuclei in the recently found noble gas-noble metal fluorides (NgMF, where Ng=Ar,Kr,Xe and M=Cu,Ag,Au) are obtained theoretically by high-level ab initio calculations, where both relativistic and electron correlation effects are included, and compared to experimental results. Fully relativistic four-component Dirac-Hartree-Fock (DHF) calculations are carried out at the basis set limit for electric field gradient that couples with the electric quadrupole moment of the nucleus, and uncorrelated relativistic effects are extracted by comparing DHF results to nonrelativistic (NR) HF calculations. Electron correlation effects are investigated both at fully relativistic second-order Moller-Plesset (DMP2) and at NR MP2 levels of theory, as well as at the NR coupled-cluster singles and doubles with perturbational triples [CCSD(T)] level. The validity of the approximation where relativistic effects, on the one hand, and nonrelativistically obtained correlation effects, on the other hand, are evaluated separately and assumed to be additive, is investigated by comparison with the DMP2 results. Inclusion of relativistic effects is shown to be necessary for obtaining the correct NQCC trends as the nucleus of interest and/or its neighbors become heavier. Electron correlation treatment is needed for approaching quantitative agreement with the experimental NQCCs. The assumption of additive electron correlation and relativistic effects, corresponding to the NR correlation treatment added on top of relativistic DHF data, gives qualitatively correct noble gas NQCCs. For noble metal NQCCs, correlation treatment at the relativistic level of theory is mandatory for reaching agreement with experimental results. Current work also confirms the experimental trends of NQCCs, which have been taken as an indication of nearly covalent interaction between noble gas and noble metal in the heaviest present systems, especially in XeAuF.     

Fully relativistic coupled cluster and DFT study of electric field gradients at Hg in 199Hg compounds

We investigate the magnitude and interplay of relativistic and electron correlation effects on the electric field gradient (EFG) at the position of Hg in linear and bent HgL(2) (L = CH(3), Cl, Br, I) and trigonal planar [HgCl(3)](-) compounds using four-component relativistic Dirac-Coulomb (DC) and non-relativistic (NR) calculations at the Hartree-Fock (HF), DFT, MP2 and coupled cluster (CC) levels. The relativistic and electron correlation contributions to EFG have opposite signs and are not additive, demonstrating the importance of taking into account relativistic and electron correlation contributions on an equal footing. DC-MP2 overestimates the electron correlation correction by 0.48-0.56 a.u. for Hg-halides and by 0.8 a.u. for Hg(CH(3))(2), respectively, while DC-CCSD underestimates the correlation correction by 0.57-0.66 a.u. compared to the reference DC-CCSD-T data. EFGs obtained at the DC-DFT level vary considerably with the functional; DC-CAMB3LYP and DC-BH&H reproduce DC-CCSD-T results within 0.08-0.24 a.u. (1%-3%) for Hg(CH(3))(2) and Hg-halides, respectively. An updated value of the nuclear quadrupole moment of the I = 5/2 excited state of (199)Hg, Q((199)Hg) = 0.675(12) b is derived from the literature. This value compares well with that derived from our calculated EFG at the DC-CCSD-T level and the experimental data for Hg(CH(3))(2); Q((199)Hg) = 0.650 b.     

NMR shielding constants of CuX,AgX, and AuX (X = F,Cl, Br,and I) investigated by density functional theory based on the Douglas–Kroll–Hess Hamiltonian

Two‐component relativistic density functional theory (DFT) with the second‐order Douglas–Kroll–Hess (DKH2) one‐electron Hamiltonian was applied to the calculation of nuclear magnetic resonance (NMR) shielding constant. Large basis set dependence was observed in the shielding constant of Xe atom. The DKH2‐DFT‐calculated shielding constants of I and Xe in HI, I₂, CuI, AgI, and XeF₂ agree well with those obtained by the four‐component relativistic theory and experiments. The Au NMR shielding constant in AuF is extremely more positive than in AuCl, AuBr, and AuI, as reported recently. This extremely positive shielding constant arises from the much larger Fermi contact (FC) term of AuF than in others. Interestingly, the absolute values of the paramagnetic and the FC terms are considerably larger in CuF and AuF than in others. The large paramagnetic term of AuF arises from the large d‐components in the Au d_π –F p_π and Au sd_σ–F p_σ molecular orbitals (MOs). The large FC term in AuF arises from the small energy difference between the Au sd_σ + F p_σ and Au sd_σ–F p_σ MOs. The second‐order magnetically relativistic effect, which is the effect of DKH2 magnetic operator, is important even in CuF. This effect considerably improves the overestimation of the spin‐orbit effect calculated by the Breit–Pauli magnetic operator. © 2013 Wiley Periodicals, Inc.     

Rapid determination of gold in Romanian auriferous alluvial sands, concentrates and rocks by 14 MeV NAA

The nuclear and spectral interferences in the 14 MeV neutron activation analysis (NAA) of gold from Romanian auriferous alluvial sands, concentrates and rocks have been studied and the optimum of activation, cooling and measuring times was determined for a maximum peak-to-background ratio for gold. The contribution of the nuclear interfering elements in the samples, Hg and Pt, to the concentration of gold has been calculated and, concluded that the nuclear reactions ¹⁹⁷Au(n,2n)¹⁹⁶Au, ¹⁹⁷Au(n,2n)^196mAu and ¹⁹⁷Au(n,n')^197mAu can be used for gold determination, with minimal errors. Using the nuclear reactions ¹⁹⁷Au(n,n')^197mAu and ¹⁹⁷Au(n,2n)¹⁹⁶Au the spectral interferences are minimal and are due to Rb, Ti and V for a short irradiation and to Se for a long one. Two methods of fast gold determination were proposed for auriferous alluvial sands and rocks in the range of 20-2500 ppm, under the optimum conditions established so that the systematic errors of analysis due to the gold accompanying elements can be considerably diminished. For measuring the induced gamma-radioactivity in the samples either a short irradiation (25 seconds) with a NaI(Tl) detector or a long irradiation (3000 seconds) with a Ge(Li) detector were used. This revised version was published online in July 2006 with corrections to the Cover Date.     

Evolutionary Algorithm-based Crystal Structure Prediction for Gold(I) Fluoride

Solid gold(I) fluoride remains as an unsynthesized and uncharacterized compound. We have performed a search for potential gold(I) fluoride crystal structures using USPEX evolutionary algorithm and dispersion-corrected hybrid density functional methods. Over 4000 AuF crystal structures have been investigated. Behavior of the AuF crystal structures under pressure was studied up to 25 GPa, and we also evaluated the thermodynamic stability of the hypothetical AuF crystal structures with respect to AuF₃, AuF₅, and Au₃F₈. Mixed-valence compound Au₃[AuF₄] with Au atoms in various formal oxidation states emerged as the thermodynamically most stable AuF species.     

Evaluation of 27Al and 51V electric field gradients and the crystal structure for aluminum orthovanadate (AlVO4) by density functional theory calculations

Three sets of crystal-structure data reported for AlVO(4) from two powder-XRD studies and a density functional theory (DFT) investigation, employing the Vienna ab initio simulation package (VASP), have been examined and refined using the DFT structure-optimization scheme implemented in the WIEN2k software. The crystal structures are evaluated on the basis of (27)Al and (51)V quadrupole coupling parameters recently reported for AlVO(4), employing the corresponding electric-field gradient (EFG) tensor elements obtained from the DFT calculations. The DFT calculations provide a reliable assignment of the (27)Al/(51)V resonances from three distinct Al and three V environments to the specific crystallographic sites in the asymmetric unit for AlVO(4). An improved agreement between experimental quadrupole tensor elements and calculated EFG tensors is achieved after the DFT structure optimizations and consistent results are obtained using the three different structures as starting points. The improvement of the structural data is also supported by an evaluation of the Al-O and V-O bond lengths before and after DFT structure optimization. The (51)V nuclear quadrupole moment, |Q((51)V)| = 4.8 +/- 0.1 fm(2), derived from the present analysis, represents a value of higher accuracy than earlier reported Q((51)V) values. The origin of the (27)Al and (51)V EFGs are investigated by an evaluation of the orientations of the EFG tensors in the crystal frame and by an examination of the individual contributions from the valence electrons and the surrounding lattice. The latter investigation shows that the magnitude and orientation of the tensors are largely determined by the p-p((27)Al) and p-p, d-d((51)V) orbital contributions to the valence electrons, while the lattice part only gives a minor contribution for both nuclei.     

Electric field gradients in the ionic crystals NaNO2, NaBF4, NaNO3, and Ba(NO3)2

The electric field gradients (EFG) at the sites of the cations and the “central” atoms of the anions in the ionic crystals NaNO₂, NaBF₄, NaNO₃ and Ba(NO₃)₂ are calculated by a method based on a combination of the semi-empirical INDO method for the charge distribution and the intramolecular EFG with a lattice summation in the framework of the extended multipole model. At some lattice sites the contribution of the induced dipole and quadrupole moments to the EFG is comparable with the contribution of the point charges. The charge distribution within the molecular ions is found by adjusting either the calculated asymmetry parameter η or the z-component of the EFG to the experimental value deduced from nuclear quadrupole coupling constants. These charge distributions are in good agreement with those gained from INDO calculations. The calculated and experimental quadrupole coupling constants of nuclei in anions and cations are compared.     

An explicit relationship between the dielectric anisotropy and the average electric field gradient in nematic solvents

Nowadays, the interaction between the electric quadrupole moment of a probe-solute and the so-called average electric field gradient (EFG) of the nematic medium is commonly suggested as an important long-range mechanism contributing to the ordering of small molecules dissolved in nematic solvents. Anyway, an explicit relationship between the solvent's EFG and some macroscopic property of the medium has never been established explicitly. In this work, a derivation is carried out leading to a simple formula that shows that the EFG of a nematic solvent is directly related to the dielectric permittivity of the medium (in particular, to its dielectric anisotropy, Deltaepsilon) and to the quadrupole moment of the solute. The obtained expression (a) allows for immediate considerations about the sign and the value of EFG (and could be very useful in designing proper nematic mixtures with null EFG) and (b) reconciles two existing conceptual ways of describing long-range orientational interactions, revealing they are only seemingly different.     

The nuclear electric quadrupole moment of antimony from the molecular method

Relativistic Dirac-Coulomb (DC) Hartree-Fock calculations are employed to obtain the analytic electric field gradient (EFG) on the antimony nucleus in the SbN, SbP, SbF, and SbCl molecules. The electronic correlation contribution to the EFGs is included with the DC-CCSD(T) and DC-CCSD-T approaches, also in the four-component framework, using a finite-difference method. The total EFG results, along with the experimental nuclear quadrupole coupling constants from microwave spectroscopy, allow to derive the nuclear quadrupole moments of (121)Sb and (123)Sb, respectively, as -543(11) and -692(14) mb.     

Structural variations and bonding in gold halides: a quantum chemical study of monomeric and dimeric gold monohalide and gold trihalide molecules, AuX, Au2X2, AuX3, and Au2X6 (X = F, Cl, Br, I)

The molecular structures of all gold mono- and trihalides and of their dimers have been calculated at the B3LYP, MP2, and CCSD(T) levels of theory by using relativistic pseudopotentials for all atoms except fluorine. Our computations support the experimental observation that the relative stability of the monohalides increases from the fluoride toward the iodide, while the stability trend of the trihalides is the opposite. The potential energy surface (PES) of all gold trihalides has been investigated. These molecules are typical Jahn-Teller systems; the trigonal planar D3h-symmetry geometry does not correspond to the minimum energy structure for any of them. At the same time, the amount and character of their Jahn-Teller distortion changes gradually from AuF3 to AuI3. The minimum energy geometry is a T-shaped structure for AuF3 and AuCl3, with a Y-shaped transition-state structure. For AuI3, the Y-shaped structure lies lower than the T-shaped structure on the PES. For AuBr3 and AuI3, neither of them is the global minimum but instead an L-shaped structure, which lies outside the Jahn-Teller PES. This structure can be considered to be a donor-acceptor system, or a closed-shell interaction, with I2 acting as donor and AuI as acceptor. The dimers of gold monohalides have very short gold-gold distances and demonstrate the aurophilic interaction. The dimers of the trihalides are planar molecules with two bridging halogen atoms.