Direct relativistic MP2: properties of ground state CuF, AgF and AuF

A computer program for the calculation of the MP2 energy correction for a Kramers-restricted Dirac-Hartree-Fock four component wave-function is presented. In the spirit of the integral-driven direct SCF scheme the algorithm has been developed as direct MP2, calculating integrals as they are needed and avoiding the integral storage bottle-neck of conventional MP2. Relativistic MP2 is applied to ground state (¹Σ⁺) CuF, AgF and AuF. Received: 15 December 1996 / Accepted: 2 April 1997     

Synthesis of methyl (5Z,8Z,10E,12E,14Z)-eicosapentaenoate

The first total synthesis of methyl (5Z,8Z,10E,12E,14Z)-eicosapentaenoate has been achieved in seven steps and in 16% overall yield. The synthesis confirmed the assigned structure of this polyunsaturated natural product.     

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.     

Langmuir films of naphthenic acids at different pH and electrolyte concentrations

Langmuir films of naphthenic acids at different pH and electrolyte concentrations are reported. The polydisperse naphthenic acids were commercially available, while two single-component naphthenic acids [5#(H)-cholanoic acid and 1-naphthalenepentanoic acid, decahydro- (9CI)] were synthesized. 1-naphthalenepentanoic acid, decahydro- is too water-soluble to form stable monolayers. 5#(H)-Cholanoic acid and Fluka naphthenic acid form stable films when cations are present in the aqueous subphase. At lower pH the cations are less influential since the naphthenic acids are not protolysed and metal naphthenates cannot be formed. pK_a^s for 5#(H)-cholanoic acid is determined to 5.65. The micellisation of the naphthenates at high pH is described.     

On diagonally structured problems in unconstrained optimization using an inexact super Halley method

We consider solving the unconstrained minimization problem using an iterative method derived from the third order super Halley method. Each iteration of the super Halley method requires the solution of two linear systems of equations. We show a practical implementation using an iterative method to solve the linear systems. This paper introduces an array of arrays (jagged) data structure for storing the second and third derivative of a multivariate function and suitable termination criteria for the (inner) iterative method to achieve a cubic rate of convergence. Using a jagged compressed diagonal storage of the Hessian matrices and for the tensor, numerical results show that storing the diagonals are more efficient than the row or column oriented approach when we use an iterative method for solving the linear systems of equations.     

Matrix-valued Schrödinger operators over local fields

We consider quantum systems that have as their configuration spaces finite dimensional vector spaces over local fields. The quantum Hilbert space is taken to be a space with complex coefficients and we include in our model particles with internal symmetry. The Hamiltonian operator is a pseudo-differential operator that is initially only formally defined. For a wide class of potentials we prove that this Hamiltonian is well-defined as an unbounded self-adjoint operator. The free part of the operator gives rise to ameasure on the Skorokhod space of paths,D[0,∞), and with respect to this measure there is a path integral representation for the semigroup associated to the Hamiltonian. We prove this Feynman-Kac formula in the local field setting as a consequence of the Hille-Yosida theory of semi-groups. The text was submitted by the authors in English.     

Time discretization of an evolution equation via Laplace transforms

Following earlier work by Sheen, Sloan, and Thomée concerningparabolic equations we study the discretization in time of aVolterra type integro-differential equation in which the integraloperator is a convolution of a weakly singular function andan elliptic differential operator in space. The time discretizationis accomplished by using a modified Laplace transform in timeto represent the solution as an integral along a smooth curveextending into the left half of the complex plane, which isthen evaluated by quadrature. This reduces the problem to afinite set of elliptic equations with complex coefficients,which may be solved in parallel. Stability and error boundsof high order are derived for two different choices of the quadraturerule. The method is combined with finite-element discretizationin the spatial variables.