Design and optimization of modified simplex methods

Four test functions are used to evaluate different modifications of the modified simplex method and to optimize the contraction, reflection and expansion parameters. The evaluation shows that some of the modifications and the optimization of the parameters result in a simplex method that has gained in convergence ability, with some improvement in speed.     

X-ray emission spectroscopy of hydrogen bonding and electronic structure of liquid water

We use x-ray emission spectroscopy to examine the influence of the intermolecular interaction on the local electronic structure of liquid water. By comparing x-ray emission spectra of the water molecule and liquid water, we find a strong involvement of the a(1)-symmetry valence-orbital in the hydrogen bonding. The local electronic structure of water molecules, where one hydrogen bond is broken at the hydrogen site, is separately determined. Our results provide an illustration of the important potential of x-ray emission spectroscopy for elucidating basic features of liquids.     

Double excitations of helium in weak static electric fields

A dramatic electric field dependence has been observed in the fluorescence yield spectrum of the doubly excited states in helium, where a rich phenomenology is encountered below the threshold. Fluorescence yields of certain states can be tuned to zero, while other dipole-forbidden states are significantly enhanced, for fields much weaker than 1 kV/cm. Using an R-matrix multichannel quantum defect theory, spherical-to-parabolic frame transformation method, we are able to reproduce the main features of the observed spectrum, and we discuss the qualitative behavior in terms of weak electric field mixing.     

Recursive inverse factorization

A recursive algorithm for the inverse factorization S(-1)=ZZ(*) of Hermitian positive definite matrices S is proposed. The inverse factorization is based on iterative refinement [A.M.N. Niklasson, Phys. Rev. B 70, 193102 (2004)] combined with a recursive decomposition of S. As the computational kernel is matrix-matrix multiplication, the algorithm can be parallelized and the computational effort increases linearly with system size for systems with sufficiently sparse matrices. Recent advances in network theory are used to find appropriate recursive decompositions. We show that optimization of the so-called network modularity results in an improved partitioning compared to other approaches. In particular, when the recursive inverse factorization is applied to overlap matrices of irregularly structured three-dimensional molecules.     

Truncation of small matrix elements based on the Euclidean norm for blocked data structures

Methods for the removal of small symmetric matrix elements based on the Euclidean norm of the error matrix are presented in this article. In large scale Hartree-Fock and Kohn-Sham calculations it is important to be able to enforce matrix sparsity while keeping errors under control. Truncation based on some unitary-invariant norm allows for control of errors in the occupied subspace as described in (Rubensson et al. J Math Phys 49, 032103). The Euclidean norm is unitary-invariant and does not grow intrinsically with system size and is thus suitable for error control in large scale calculations. The presented truncation schemes repetitively use the Lanczos method to compute the Euclidean norms of the error matrix candidates. Ritz value convergence patterns are utilized to reduce the total number of Lanczos iterations.