Variational finite-difference representation of the kinetic energy operator

A potential disadvantage of real-space-grid electronic structure methods is the lack of a variational principle and the concomitant increase of total energy with grid refinement. We show that the origin of this feature is the systematic underestimation of the kinetic energy by the finite difference representation of the Laplacian operator. We present an alternative representation that provides a rigorous upper bound estimate of the true kinetic energy and we illustrate its properties with a harmonic oscillator potential. For a more realistic application, we study the convergence of the total energy of bulk silicon using a real-space-grid density-functional code and employing both the conventional and the alternative representations of the kinetic energy operator.Comment: 3 pages, 3 figures, 1 table. To appear in Phys. Rev. B. Contribution for the 10th anniversary of the eprint serve

Prognostic value of the ratio between prothesis area and indexed annulus area measured by multiSlice-CT for transcatheter aortic valve implantation procedures

Background Postprocedural aortic regurgitations following transcatheter aortic valve implantation (TAVI) procedures remain an is- sue. Benefit of oversizing strategies to prevent them isn’t well established. We compared different level of oversizing in our cohort of con- secutive patients to address if severe oversizing compared to normal sizing had an impact on post-procedural outcomes. Methods From January 2010 to August 2013, consecutive patients were referred for TAVI with preoperative Multislice-CT (MSCT) and the procedures were achieved using Edwards Sapien® or Corevalve devices®. Retrospectively, according to pre-procedural MSCT and the valve size, pa- tients were classified into three groups: normal, moderate and severe oversizing; depending on the ratio between the prosthesis area and the annulus area indexed and measured on MSCT. Main endpoint was mid-term mortality and secondary endpoints were the Valve Academic Research Consortium (VARC-2) endpoints. Results Two hundred and sixty eight patients had a MSCT and underwent TAVI procedure, with mainly Corevalve®. While all-cause and cardiovascular mortality rates were similar in all groups, post-procedural new pacemaker (PM) implantation rate was significantly higher in the severe oversizing group (P = 0.03), while we observed more in-hospital congestive heart-failure (P = 0.02) in the normal sizing group. There was a trend toward more moderate to severe aortic regurgitation (AR) in the normal sizing group (P = 0.07). Conclusions Despite a higher rate of PM implantation, oversizing based on this ratio reduces aortic leak with lower rates of post-procedural complications and a similar mid-term survival

Accurate Results from Perturbation Theory for Strongly Frustrated S=1/2S=1/2 Heisenberg Spin Clusters

We investigate the use of perturbation theory in finite sized frustrated spin systems by calculating the effect of quantum fluctuations on coherent states derived from the classical ground state. We first calculate the ground and first excited state wavefunctions as a function of applied field for a 12-site system and compare with the results of exact diagonalization. We then apply the technique to a 20-site system with the same three fold site coordination as the 12-site system. Frustration results in asymptotically convergent series for both systems which are summed with Pad\'e approximants. We find that at zero magnetic field the different connectivity of the two systems leads to a triplet first excited state in the 12-site system and a singlet first excited state in the 20-site system, while the ground state is a singlet for both. We also show how the analytic structure of the Pad\'e approximants at $|\lambda| \simeq 1$ evolves in the complex $\lambda$ plane at the values of the applied field where the ground state switches between spin sectors and how this is connected with the non-trivial dependence of the $$ number on the strength of quantum fluctuations. We discuss the origin of this difference in the energy spectra and in the analytic structures. We also characterize the ground and first excited states according to the values of the various spin correlation functions.Comment: Final version, accepted for publication in Physical review

Comparison of Global and Local Adaptive Coordinates for Density Functional Calculations

A globally-adaptive curvilinear coordinate formalism is shown to be easily convertible to a class of curvilinear transformations locally optimized around atom sites by a few parameters. Parameter transferability is established for a demanding test case, and the results of the two methods are shown to be comparable. Computational efficiencies realized in the local method are discussed.Comment: 21 pages, 4 figure

Variational Hilbert space truncation approach to quantum Heisenberg antiferromagnets on frustrated clusters

We study the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on a series of finite-size clusters with features inspired by the fullerenes. Frustration due to the presence of pentagonal rings makes such structures challenging in the context of quantum Monte-Carlo methods. We use an exact diagonalization approach combined with a truncation method in which only the most important basis states of the Hilbert space are retained. We describe an efficient variational method for finding an optimal truncation of a given size which minimizes the error in the ground state energy. Ground state energies and spin-spin correlations are obtained for clusters with up to thirty-two sites without the need to restrict the symmetry of the structures. The results are compared to full-space calculations and to unfrustrated structures based on the honeycomb lattice.Comment: 22 pages and 12 Postscript figure

A novel multigrid method for electronic structure calculations

A general real-space multigrid algorithm for the self-consistent solution of the Kohn-Sham equations appearing in the state-of-the-art electronic-structure calculations is described. The most important part of the method is the multigrid solver for the Schroedinger equation. Our choice is the Rayleigh quotient multigrid method (RQMG), which applies directly to the minimization of the Rayleigh quotient on the finest level. Very coarse correction grids can be used, because there is no need to be able to represent the states on the coarse levels. The RQMG method is generalized for the simultaneous solution of all the states of the system using a penalty functional to keep the states orthogonal. The performance of the scheme is demonstrated by applying it in a few molecular and solid-state systems described by non-local norm-conserving pseudopotentials.Comment: 9 pages, 3 figure

Band Structure of InGaAsN Alloys and Effects of Presure

InGaAsN is a new semiconductor alloy system with the remarkable property that the inclusion of only 2% nitrogen reduces the bandgap by more than 30%. In order to help understand the physical origin of this extreme deviation from the typically observed nearly linear dependence of alloy properties on concentration, we have investigated the pressure dependence of state energies using both experimental and theoretical methods. the excited We report measurements of the low temperature photoluminescence of the material for pressures between ambient and 110 kbar. We also describe a simple, density- functional-theory-based approach to calculating the pressure dependence of low lying excitation energies for low concentration alloys. The theoretically predicted pressure dependence of the bandgap is in excellent agreement with the experimental data. Based on the results of our calculations, we suggest an explanation for the strongly non-linear pressure dependence of the bandgap that, surprisingly, does not involve a nitrogen impurity state

Evaluation of Exchange-Correlation Energy, Potential, and Stress

We describe a method for calculating the exchange and correlation (XC) contributions to the total energy, effective potential, and stress tensor in the generalized gradient approximation. We avoid using the analytical expressions for the functional derivatives of E_xc*rho, which depend on discontinuous second-order derivatives of the electron density rho. Instead, we first approximate E_xc by its integral in a real space grid, and then we evaluate its partial derivatives with respect to the density at the grid points. This ensures the exact consistency between the calculated total energy, potential, and stress, and it avoids the need of second-order derivatives. We show a few applications of the method, which requires only the value of the (spin) electron density in a grid (possibly nonuniform) and returns a conventional (local) XC potential.Comment: 7 pages, 3 figure

Optical Properties of InGaAsN: A New 1eV Bandgap Material System

InGaAsN is a new semiconductor alloy system with the remarkable property that the inclusion of only 2% nitrogen reduces the bandgap by more than 30%. In order to help understand the physical origin of this extreme deviation from the typically observed nearly linear dependence of alloy properties on concentration, we have investigated the pressure dependence of the excited state energies using both experimental and theoretical methods. We report measurements of the low temperature photohnninescence energy of the material for pressures between ambient and 110 kbar. We describe a simple, density-functional-theory-based approach to calculating the pressure dependence of low lying excitation energies for low concentration alloys. The theoretically predicted pressure dependence of the bandgap is in excellent agreement with the experimental data. Based on the results of our calculations, we suggest an explanation for the strongly non-linear pressure dependence of the bandgap that, surprisingly, does not involve a nitrogen impurity band. Addhionally, conduction-band mass measurements, measured by three different techniques, will be described and finally, the magnetoluminescence determined pressure coefficient for the conduction-band mass is measured