Absolutely Continuous Spectrum for the Anderson Model on Some Tree-like Graphs

We prove persistence of absolutely continuous spectrum for the Anderson model on a general class of tree-like graphs.Comment: Some clarifications were added in the introduction and an extra appendix was adde

Symmetry Breaking of Relativistic Multiconfiguration Methods in the Nonrelativistic Limit

The multiconfiguration Dirac-Fock method allows to calculate the state of relativistic electrons in atoms or molecules. This method has been known for a long time to provide certain wrong predictions in the nonrelativistic limit. We study in full mathematical details the nonlinear model obtained in the nonrelativistic limit for Be-like atoms. We show that the method with sp+pd configurations in the J=1 sector leads to a symmetry breaking phenomenon in the sense that the ground state is never an eigenvector of L^2 or S^2. We thereby complement and clarify some previous studies.Comment: Final version, to appear in Nonlinearity. Nonlinearity (2010) in pres

Exchange-assisted tunneling in the classical limit

The exchange interaction and correlations may produce a power-law decay instead of the usual exponential decrease of the wave function under potential barrier. The exchange-assisted tunneling vanishes in the classical limit, however, the dependence on the Planck constant h is different from that for a conventional single-particle tunneling

Exploring Biorthonormal Transformations of Pair-Correlation Functions in Atomic Structure Variational Calculations

Multiconfiguration expansions frequently target valence correlation and correlation between valence electrons and the outermost core electrons. Correlation within the core is often neglected. A large orbital basis is needed to saturate both the valence and core-valence correlation effects. This in turn leads to huge numbers of CSFs, many of which are unimportant. To avoid the problems inherent to the use of a single common orthonormal orbital basis for all correlation effects in the MCHF method, we propose to optimize independent MCHF pair-correlation functions (PCFs), bringing their own orthonormal one-electron basis. Each PCF is generated by allowing single- and double- excitations from a multireference (MR) function. This computational scheme has the advantage of using targeted and optimally localized orbital sets for each PCF. These pair-correlation functions are coupled together and with each component of the MR space through a low dimension generalized eigenvalue problem. Nonorthogonal orbital sets being involved, the interaction and overlap matrices are built using biorthonormal transformation of the coupled basis sets followed by a counter-transformation of the PCF expansions. Applied to the ground state of beryllium, the new method gives total energies that are lower than the ones from traditional CAS-MCHF calculations using large orbital active sets. It is fair to say that we now have the possibility to account for, in a balanced way, correlation deep down in the atomic core in variational calculations

Efficient Algorithm for Asymptotics-Based Configuration-Interaction Methods and Electronic Structure of Transition Metal Atoms

Asymptotics-based configuration-interaction (CI) methods [G. Friesecke and B. D. Goddard, Multiscale Model. Simul. 7, 1876 (2009)] are a class of CI methods for atoms which reproduce, at fixed finite subspace dimension, the exact Schr\"odinger eigenstates in the limit of fixed electron number and large nuclear charge. Here we develop, implement, and apply to 3d transition metal atoms an efficient and accurate algorithm for asymptotics-based CI. Efficiency gains come from exact (symbolic) decomposition of the CI space into irreducible symmetry subspaces at essentially linear computational cost in the number of radial subshells with fixed angular momentum, use of reduced density matrices in order to avoid having to store wavefunctions, and use of Slater-type orbitals (STO's). The required Coulomb integrals for STO's are evaluated in closed form, with the help of Hankel matrices, Fourier analysis, and residue calculus. Applications to 3d transition metal atoms are in good agreement with experimental data. In particular we reproduce the anomalous magnetic moment and orbital filling of Chromium in the otherwise regular series Ca, Sc, Ti, V, Cr.Comment: 14 pages, 1 figur

Chaos and localization in the wavefunctions of complex atoms NdI, PmI and SmI

Wavefunctions of complex lanthanide atoms NdI, PmI and SmI, obtained via multi-configuration Dirac-Fock method, are analyzed for density of states in terms of partial densities, strength functions ($F_k(E)$), number of principal components ($\xi_2(E)$) and occupancies (\lan n_\alpha \ran^E) of single particle orbits using embedded Gaussian orthogonal ensemble of one plus two-body random matrix ensembles [EGOE(1+2)]. It is seen that density of states are in general multi-modal, $F_k(E)$'s exhibit variations as function of the basis states energy and $\xi_2(E)$'s show structures arising from localized states. The sources of these departures from EGOE(1+2) are investigated by examining the partial densities, correlations between $F_k(E)$, $\xi_2(E)$ and \lan n_\alpha \ran^E and also by studying the structure of the Hamiltonian matrices. These studies point out the operation of EGOE(1+2) but at the same time suggest that weak admixing between well separated configurations should be incorporated into EGOE(1+2) for more quantitative description of chaos and localization in NdI, PmI and SmI.Comment: There are 9 figure

On the secondly quantized theory of many-electron atom

Traditional theory of many-electron atoms and ions is based on the coefficients of fractional parentage and matrix elements of tensorial operators, composed of unit tensors. Then the calculation of spin-angular coefficients of radial integrals appearing in the expressions of matrix elements of arbitrary physical operators of atomic quantities has two main disadvantages: (i) The numerical codes for the calculation of spin-angular coefficients are usually very time-consuming; (ii) f-shells are often omitted from programs for matrix element calculation since the tables for their coefficients of fractional parentage are very extensive. The authors suppose that a series of difficulties persisting in the traditional approach to the calculation of spin-angular parts of matrix elements could be avoided by using this secondly quantized methodology, based on angular momentum theory, on the concept of the irreducible tensorial sets, on a generalized graphical method, on quasispin and on the reduced coefficients of fractional parentage

Implementation of screened hybrid functionals based on the Yukawa potential within the LAPW basis set

The implementation of screened hybrid functionals into the WIEN2k code, which is based on the LAPW basis set, is reported. The Hartree-Fock exchange energy and potential are screened by means of the Yukawa potential as proposed by Bylander and Kleinman [Phys. Rev. B 41, 7868 (1990)] for the calculation of the electronic structure of solids with the screened-exchange local density approximation. Details of the formalism, which is based on the method of Massidda, Posternak, and Baldereschi [Phys. Rev. B 48, 5058 (1993)] for the unscreened Hartree-Fock exchange are given. The results for the transition-energy and structural properties of several test cases are presented. Results of calculations of the Cu electric-field gradient in Cu2O are also presented, and it is shown that the hybrid functionals are much more accurate than the standard local-density or generalized gradient approximations

Diffraction in low-energy electron scattering from DNA: bridging gas phase and solid state theory

Using high-quality gas phase electron scattering calculations and multiple scattering theory, we attempt to gain insights on the radiation damage to DNA induced by secondary low-energy electrons in the condensed phase, and to bridge the existing gap with the gas phase theory and experiments. The origin of different resonant features (arising from single molecules or diffraction) is discussed and the calculations are compared to existing experiments in thin films.Comment: 40 pages preprint, 12 figures, submitted to J. Chem. Phy

Spin-other-orbit operator in the tensorial form of second quantization

The tensorial form of the spin-other-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements according to an approach, based on a combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin), and a generalized graphical technique. One of the basic features of this approach is the use of tables of standard quantities, without which the process of obtaining matrix elements of spin-other-orbit interaction operator between any electron configurations is much more complicated. Some special cases are shown for which the tensorial structure of the spin-other-orbit interaction operator reduces to an unusually simple form