Preconditioned Iterative Methods for Scattered Data Interpolation

The scattered data interpolation problem in two space dimensions is formulated as a partial differential equation with interpolating side conditions. The system is discretized by the Morley finite element space. The focus of this paper is to study preconditioned iterative methods for the corresponding discrete systems. We introduce block diagonal preconditioners, where a multigrid operator is used for the differential equation part of the system, while we propose an operator constructed from thin plate radial basis functions for the equations corresponding to the interpolation conditions. The effect of the preconditioners are documented by numerical experiments.     

Thermal conductivity of KCl up to 19 kbar

The pressure dependency of the thermal conductivity of KCl has been measured at room temperature up to 19kbar. The high pressure tool was of the “belt” type and a solid medium was used. The specimen was cylindrical and was heated along its axis. The conductivity was found to increase linearly at a rate of (3·3 ± 0·3) per cent/kbar.     

Photoinduced fission of the doubly even uranium isotopes 234U, 236U and 238U

A measurement of the angular distributions and yields of fission fragments in the photofission of ²³⁴U has been performed between 5.2 and 6.4 MeV. As γ-source, the bremsstrahlung from a microtron was used. For the detection of the fission fragments, solid-state track detectors were used. The present data for ²³⁴U have been analysed together with earlier obtained data for ²³⁶U and ²³⁸U. The values of the fission barrier parameters obtained are compared to results in theoretical macroscopic and microscopic fission potential energy calculations.     

Instrumental correction of time dependent counting losses in high rate gamma-ray spectrometry

A CAMAC system was installed for pulse height analysis and correction of counting losses due to the dead-time of a multichannel analyzer and the pulse pile-up. A computer program was developed to control the whole system, and to collect and store data in both conventional and cyclic measurement modes.     

Quadratic response functions in a second-order polarization propagator framework

The linear and quadratic response functions have been derived for an exact state, based on an exponential parametrization of the time evolution consisting of products of exponentials for orbital rotations and for higher-order excitations. Truncating the linear response function such that the response function itself and its pole structure is correct to second order in M?ller-Plesset perturbation theory, we arrive at the second-order polarization propagator approximation (SOPPA). Previous derivations of SOPPA have used the superoperator formalism, making the extension of SOPPA to quadratic and higher order response functions difficult. The derivation of the quadratic response function is described in detail, allowing molecular properties such as hyperpolarizabilities, two-photon cross sections, and excited-state properties to be calculated using the SOPPA model.     

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.     

Configuration-interaction energy derivatives in a fully variational formulation

A configuration-interaction energy function (Lagrange) which is variational in all variables, including the orbital rotational parameters, is constructed. When this Lagrangian is used for obtaining configuration-interaction derivatives, all the important simplifications which occur for derivatives of variational wave functions carry over in a straightforward way. In particular, the state and orbital rotational response parameters obey the 2n+1 rule and the Lagrange multipliers obey the somewhat stronger 2n+2 rule. The simplifications which are normally obtained by invoking the Handy-Schaefer technique are automatically incorporated to all orders. Simple expressions for energy derivatives up to third order are presented. The relationship between the numerical errors in the variational parameters and the errors in the calculated energy derivatives is discussed.     

Linear-scaling formation of Kohn-Sham Hamiltonian: application to the calculation of excitation energies and polarizabilities of large molecular systems

We present calculations of excitation energies and polarizabilities in large molecular systems at the local-density and generalized-gradient approximation levels of density-functional theory (DFT). Our results are obtained using a linear-scaling DFT implementation in the program system DALTON for the formation of the Kohn-Sham Hamiltonian. For the Coulomb contribution, we introduce a modification of the fast multipole method to calculations over Gaussian charge distributions. It affords a simpler implementation than the original continuous fast multipole method by partitioning the electrostatic Coulomb interactions into "classical" and "nonclassical" terms which are explicitly evaluated by linear-scaling multipole techniques and a modified two-electron integral code, respectively. As an illustration of the code, we have studied the singlet and triplet excitation energies as well as the static and dynamic polarizabilities of polyethylenes, polyenes, polyynes, and graphite sheets with an emphasis on the trends observed with system size.     

Ab initio calculation of electronic circular dichroism fortrans-cyclooctene using London atomic orbitals

Summary The second-quantization magnetic dipole operator that arises when London atomic orbitals are used as basis functions is derived. In atomic units, the magnetic dipole operator is defined as the negative of the first derivative of the electronic Hamiltonian containing the interaction with the external magnetic field. It is shown that for finite basis sets, the gauge origin dependence of the resulting magnetic dipole operator is analogous to that of the exact operator, and that the derived operator converges to the exact operator in the limit of a complete basis set. It is also demonstrated that the length expression for the rotatory strength in linear response calculations gives gauge-origin-independent results. Sample calculations ontrans-cyclooctene and its fragments are presented. Compared to conventional orbitals, the basis set convergence of the rotatory strengths calculated in the length form using London atomic orbitals is favourable. The rotatory strength calculated fortrans-cyclooctene agrees nicely with the corresponding experimental circular dichroism spectrum, but the spectra for the fragment molecules show little resemblance with that oftrans-cyclooctene.Dedicated to Prof. Jan Linderberg