Sequential decoupling of negative-energy states in Douglas-Kroll-Hess theory

Here, we review the historical development, current status, and prospects of Douglas--Kroll--Hess theory as a quantum chemical relativistic electrons-only theory.Comment: 15 page

Complete-Graph Tensor Network States: A New Fermionic Wave Function Ansatz for Molecules

We present a new class of tensor network states that are specifically designed to capture the electron correlation of a molecule of arbitrary structure. In this ansatz, the electronic wave function is represented by a Complete-Graph Tensor Network (CGTN) ansatz which implements an efficient reduction of the number of variational parameters by breaking down the complexity of the high-dimensional coefficient tensor of a full-configuration-interaction (FCI) wave function. We demonstrate that CGTN states approximate ground states of molecules accurately by comparison of the CGTN and FCI expansion coefficients. The CGTN parametrization is not biased towards any reference configuration in contrast to many standard quantum chemical methods. This feature allows one to obtain accurate relative energies between CGTN states which is central to molecular physics and chemistry. We discuss the implications for quantum chemistry and focus on the spin-state problem. Our CGTN approach is applied to the energy splitting of states of different spin for methylene and the strongly correlated ozone molecule at a transition state structure. The parameters of the tensor network ansatz are variationally optimized by means of a parallel-tempering Monte Carlo algorithm

Block-Diagonalization of Operators with Gaps, with Applications to Dirac Operators

We present new results on the block-diagonalization of Dirac operators on three-dimensional Euclidean space with unbounded potentials. Classes of admissible potentials include electromagnetic potentials with strong Coulomb singularities and more general matrix-valued potentials, even non-self-adjoint ones. For the Coulomb potential, we achieve an exact diagonalization up to nuclear charge Z=124 and prove the convergence of the Douglas-Kroll-He\ss\ approximation up to Z=62, thus improving the upper bounds Z=93 and Z=51, respectively, by H.\ Siedentop and E.\ Stockmeyer considerably. These results follow from abstract theorems on perturbations of spectral subspaces of operators with gaps, which are based on a method of H.\ Langer and C.\ Tretter and are also of independent interest

Glamdring: automatic application partitioning for Intel SGX

Trusted execution support in modern CPUs, as offered by Intel SGX enclaves , can protect applications in untrusted environments. While prior work has shown that legacy applications can run in their entirety inside enclaves, this results in a large trusted computing base (TCB). Instead, we explore an approach in which we partition an applica- tion and use an enclave to protect only security-sensitive data and functions, thus obtaining a smaller TCB. We describe Glamdring , the first source-level parti- tioning framework that secures applications written in C using Intel SGX. A developer first annotates security- sensitive application data. Glamdring then automatically partitions the application into untrusted and enclave parts: (i) to preserve data confidentiality, Glamdring uses dataflow analysis to identify functions that may be ex- posed to sensitive data; (ii) for data integrity, it uses back- ward slicing to identify functions that may affect sensitive data. Glamdring then places security-sensitive functions inside the enclave, and adds runtime checks and crypto- graphic operations at the enclave boundary to protect it from attack. Our evaluation of Glamdring with the Mem- cached store, the LibreSSL library, and the Digital Bitbox bitcoin wallet shows that it achieves small TCB sizes and has acceptable performance overheads

Quantum information analysis of electronic states at different molecular structures

We have studied transition metal clusters from a quantum information theory perspective using the density-matrix renormalization group (DMRG) method. We demonstrate the competition between entanglement and interaction localization. We also discuss the application of the configuration interaction based dynamically extended active space procedure which significantly reduces the effective system size and accelerates the speed of convergence for complicated molecular electronic structures to a great extent. Our results indicate the importance of taking entanglement among molecular orbitals into account in order to devise an optimal orbital ordering and carry out efficient calculations on transition metal clusters. We propose a recipe to perform DMRG calculations in a black-box fashion and we point out the connections of our work to other tensor network state approaches

Toward in silico Catalyst Optimization

In this minireview, we overview a computational pipeline developed within the framework of NCCR Catalysis that can be used to successfully reproduce the enantiomeric ratios of homogeneous catalytic reactions. At the core of this pipeline is the SCINE Molassembler module, a graph-based software that provides algorithms for molecular construction of all periodic table elements. With this pipeline, we are able to simultaneously functionalizenand generate ensembles of transition state conformers, which permits facile exploration of the influencenof various substituents on the overall enantiomeric ratio. This allows preconceived back-of-the-envelope designnmodels to be tested and subsequently refined by providing quick and reliable access to energetically low-lyingntransition states, which represents a key step in undertaking in silico catalyst optimization

Length of carotid stenosis predicts peri-procedural stroke or death and restenosis in patients randomized to endovascular treatment or endarterectomy.

BACKGROUND: The anatomy of carotid stenosis may influence the outcome of endovascular treatment or carotid endarterectomy. Whether anatomy favors one treatment over the other in terms of safety or efficacy has not been investigated in randomized trials. METHODS: In 414 patients with mostly symptomatic carotid stenosis randomized to endovascular treatment (angioplasty or stenting; n = 213) or carotid endarterectomy (n = 211) in the Carotid and Vertebral Artery Transluminal Angioplasty Study (CAVATAS), the degree and length of stenosis and plaque surface irregularity were assessed on baseline intraarterial angiography. Outcome measures were stroke or death occurring between randomization and 30 days after treatment, and ipsilateral stroke and restenosis ≥50% during follow-up. RESULTS: Carotid stenosis longer than 0.65 times the common carotid artery diameter was associated with increased risk of peri-procedural stroke or death after both endovascular treatment [odds ratio 2.79 (1.17-6.65), P = 0.02] and carotid endarterectomy [2.43 (1.03-5.73), P = 0.04], and with increased long-term risk of restenosis in endovascular treatment [hazard ratio 1.68 (1.12-2.53), P = 0.01]. The excess in restenosis after endovascular treatment compared with carotid endarterectomy was significantly greater in patients with long stenosis than with short stenosis at baseline (interaction P = 0.003). Results remained significant after multivariate adjustment. No associations were found for degree of stenosis and plaque surface. CONCLUSIONS: Increasing stenosis length is an independent risk factor for peri-procedural stroke or death in endovascular treatment and carotid endarterectomy, without favoring one treatment over the other. However, the excess restenosis rate after endovascular treatment compared with carotid endarterectomy increases with longer stenosis at baseline. Stenosis length merits further investigation in carotid revascularisation trials

Entanglement Measures for Single- and Multi-Reference Correlation Effects

Electron correlation effects are essential for an accurate ab initio description of molecules. A quantitative a priori knowledge of the single- or multi-reference nature of electronic structures as well as of the dominant contributions to the correlation energy can facilitate the decision regarding the optimum quantum chemical method of choice. We propose concepts from quantum information theory as orbital entanglement measures that allow us to evaluate the single- and multi-reference character of any molecular structure in a given orbital basis set. By studying these measures we can detect possible artifacts of small active spaces.Comment: 14 pages, 4 figure