M?ssbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury

The electrostatic contribution to the M?ssbauer isomer shift of mercury for the series HgF _n (n?=?1,?2,?4) with respect to the neutral atom has been investigated in the framework of four- and two-component relativistic theory. Replacing the integration of the electron density over the nuclear volume by the contact density (that is, the electron density at the nucleus) leads to a 10% overestimation of the isomer shift. The systematic nature of this error suggests that it can be incorporated into a correction factor, thus justifying the use of the contact density for the calculation of the M?ssbauer isomer shift. The performance of a large selection of density functionals for the calculation of contact densities has been assessed by comparing with finite-field four-component relativistic coupled-cluster with single and double and perturbative triple excitations [CCSD(T)] calculations. For the absolute contact density of the mercury atom, the Density Functional Theory (DFT) calculations are in error by about 0.5%, a result that must be judged against the observation that the change in contact density along the series HgF _n (n?=?1,?2,?4), relevant for the isomer shift, is on the order of 50?ppm with respect to absolute densities. Contrary to previous studies of the ⁵⁷Fe isomer shift (F Neese, Inorg Chim Acta 332:181, 2002), for mercury, DFT is not able to reproduce the trends in the isomer shift provided by reference data, in our case CCSD(T) calculations, notably the non-monotonous decrease in the contact density along the series HgF _n (n?=?1,?2,?4). Projection analysis shows the expected reduction of the 6s _1/2 population at the mercury center with an increasing number of ligands, but also brings into light an opposing effect, namely the increasing polarization of the 6s _1/2 orbital due to increasing effective charge of the mercury atom, which explains the non-monotonous behavior of the contact density along the series. The same analysis shows increasing covalent contributions to bonding along the series with the effective charge of the mercury atom reaching a maximum of around +2 for HgF₄ at the DFT level, far from the formal charge +4 suggested by the oxidation state of this recently observed species. Whereas the geometries for the linear HgF₂ and square-planar HgF₄ molecules were taken from previous computational studies, we optimized the equilibrium distance of HgF at the four-component Fock-space CCSD/aug-cc-pVQZ level, giving spectroscopic constants r _e = 2.007 ? and ?? _e = 513.5?cm^?1.     

Rapid reagentless quantification of alginate biosynthesis in Pseudomonas fluorescens bacteria mutants using FT-IR spectroscopy coupled to multivariate partial least squares regression

Alginate is an important medical and commercial product and currently is isolated from seaweeds. Certain microorganisms also produce alginate and these polymers have the potential to replace seaweed alginates in some applications, mainly because such production will allow much better and more reproducible control of critical qualitative polymer properties. The research conducted here presents the development of a new approach to this problem by analysing a transposon insertion mutant library constructed in an alginate-producing derivative of the Pseudomonas fluorescens strain SBW25. The procedure is based on the non-destructive and reagent-free method of Fourier transform infrared (FT-IR) spectroscopy which is used to generate a complex biochemical infrared fingerprint of the medium after bacterial growth. First, we investigate the potential differences caused by the growth media fructose and glycerol on the bacterial phenotype and alginate synthesis in 193 selected P. fluorescens mutants and show that clear phenotypic differences are observed in the infrared fingerprints. In order to quantify the level of the alginate we also report the construction and interpretation of multivariate partial least squares regression models which were able to quantify alginate levels successfully with typical normalized root-mean-square error in predictions of only approximately 14%. We have demonstrated that this high-throughput approach can be implemented in alginate screens and we believe that this FT-IR spectroscopic methodology, when combined with the most appropriate chemometrics, could easily be modified for the quantification of other valuable microbial products and play a valuable screening role for synthetic biology.     

Four-component relativistic Kohn-Sham theory

A four-component relativistic implementation of Kohn-Sham theory for molecular systems is presented. The implementation is based on a nonredundant exponential parametrization of the Kohn-Sham energy, well suited to studies of molecular static and dynamic properties as well as of total electronic energies. Calculations are presented of the bond lengths and the harmonic and anharmonic vibrational frequencies of Au(2), Hg(2+)(2), HgAu(+), HgPt, and AuH. All calculations are based on the full four-component Dirac-Coulomb Hamiltonian, employing nonrelativistic local, gradient-corrected, and hybrid density functionals. The relevance of the Coulomb and Breit operators for the construction of relativistic functionals is discussed; it is argued that, at the relativistic level of density-functional theory and in the absence of a vector potential, the neglect of current functionals follows from the neglect of the Breit operator.     

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.     

Unconditional ideals of finite rank operators

Let X be a Banach space. We give characterizations of when is a u-ideal in for every Banach space Y in terms of nets of finite rank operators approximating weakly compact operators. Similar characterizations are given for the cases when is a u-ideal in for every Banach space Y, when is a u-ideal in for every Banach space Y, and when is a u-ideal in for every Banach space Y.     

Quadratic response functions in the relativistic four-component Kohn-Sham approximation

A formulation and implementation of the quadratic response function in the adiabatic four-component Kohn-Sham approximation is presented. The noninteracting reference state is time-reversal symmetric and formed from Kramers pair spinors, and the energy density is gradient corrected. Example calculations are presented for the optical properties of disubstituted halobenzenes in their meta and ortho conformations. It is demonstrated that correlation and relativistic effects are not additive, and it is shown that relativity alone reduces the mubeta-response signal by 62% and 75% for meta- and ortho-bromobenzene, respectively, and enhances the same response by 17% and 21% for meta- and ortho-iodobenzene, respectively. Of the employed functionals, CAM-B3LYP shows the best performance and gives hyperpolarizabilities beta distinctly different from B3LYP.     

Local and superlinear convergence for truncated iterated projections methods

Least change secant updates can be obtained as the limit of iterated projections based on other secant updates. We show that these iterated projections can be terminated or truncated after any positive number of iterations and the local and the superlinear rate of convergence are still maintained. The truncated iterated projections method is used to find sparse and symmetric updates that are locally and superlinearly convergent. A part of this paper was presented at the Third International Workshop on Numerical Analysis, IIMAS, University of Mexico, January 1981 and ORSA-TIMS National Meeting, Houston, October 1981.