Nodal surfaces and interdimensional degeneracies

The aim of this paper is to shed light on the topology and properties of the nodes (i.e., the zeros of the wave function) in electronic systems. Using the "electrons on a sphere" model, we study the nodes of two-, three-, and four-electron systems in various ferromagnetic configurations (sp, p2, sd, pd, p3, sp2, and sp3). In some particular cases (sp, p2, sd, pd, and p3), we rigorously prove that the non-interacting wave function has the same nodes as the exact (yet unknown) wave function. The number of atomic and molecular systems for which the exact nodes are known analytically is very limited and we show here that this peculiar feature can be attributed to interdimensional degeneracies. Although we have not been able to prove it rigorously, we conjecture that the nodes of the non-interacting wave function for the sp3 configuration are exact

Natural occupation numbers in two-electron quantum rings

Natural orbitals (NOs) are central constituents for evaluating correlation energies through efficient approximations. Here, we report the closed-form expression of the NOs of two-electron quantum rings, which are prototypical finite-extension systems and new starting points for the development of exchange-correlation functionals in density functional theory. We also show that the natural occupation numbers for these two-electron paradigms are in general non-vanishing and follow the same power law decay as atomic and molecular two-electron systems. C 2016 AIP Publishing LLC

The uniform electron gas

The uniform electron gas or UEG (also known as jellium) is one of the most fundamental models in condensed-matter physics and the cornerstone of the most popular approximation—the local-density approximation—within density- functional theory. In this article, we provide a detailed review on the energetics of the UEG at high, intermediate, and low densities, and in one, two, and three dimensions. We also report the best quantum Monte Carlo and symmetry-broken Hartree-Fock calculations available in the literature for the UEG and discuss the phase diagrams of jellium.P.F.L. thanks the Australian Research Council for a Discovery Early Career Researcher Award (Grant No. DE130101441) and a Discovery Project grant (DP140104071). P.M.W.G. thanks the Australian Research Council for funding (Grants No. DP120104740 and DP140104071)

Spin adaptation with determinant-based selected configuration interaction

Selected configuration interaction (sCI) methods, when complemented with a second order perturbative correction, provide near full configuration interaction (FCI) quality energies with only a small fraction of the Slater determinants of the FCI space. The selection of the determinants is often implemented in a determinant-based formalism, and therefore does not provide spin adapted wave functions. In other words, sCI wave functions are not eigenfunctions of the $\widehat{S^2}$ operator. In some situations, having a spin adapted wave function is essential for the proper convergence of the method. We propose an efficient algorithm which, given an arbitrary determinant space, generates all the missing Slater determinants allowing one to obtain spin adapted wave functions while avoiding working with configuration state functions. For example, generating all the possible determinants with 6 up-spin and 6 down-spin electrons in 12 open shells takes 21 CPU cycles per generated Slater determinant. We also propose a modification of the denominators in the Epstein-Nesbet perturbation theory reducing significantly the non-invariance of the second order correction with respect to different values of the spin quantum number $m_s$. The computational cost of this correction is also negligible

Communication: Three-electron coalescence points in two and three dimensions

The form of the wave function at three-electron coalescence points is examined for several spin states using an alternative method to the usual Fock expansion. We find that, in two- and three-dimensional systems, the non-analytical nature of the wave function is characterized by the appearance of logarithmic terms, reminiscent of those that appear as both electrons approach the nucleus of the helium atom. The explicit form of these singularities is given in terms of the interelectronic distances for a doublet and two quartet states of three electrons in a harmonic well

Excited-state Wigner crystals

Wigner crystals (WCs) are electronic phases peculiar to low-density systems, particularly in the uniform electron gas. Since its introduction in the early twentieth century, this model has remained essential to many aspects of electronic structure theory and condensed-matter physics. Although the (lowest-energy) ground-state WC (GSWC) has been thoroughly studied, the properties of excited-state WCs (ESWCs) are basically unknown. To bridge this gap, we present a well-defined procedure to obtain an entire family of ESWCs in a one-dimensional electron gas using a symmetry-broken mean-field approach. While the GSWC is a commensurate crystal (i.e., the number of density maxima equals the number of electrons), these ESWCs are incommensurate crystals exhibiting more or less maxima. Interestingly, they are lower in energy than the (uniform) Fermi fluid state. For some of these ESWCs, we have found asymmetrical band gaps, which would lead to anisotropic conductivity. These properties are associated with unusual characteristics in their electronic structure.The NCI National Facility for generous grants of supercomputer tim

Uniform electron gases. III. Low-density gases on three-dimensional spheres

By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGF centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids - the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) - and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy

Iterative stochastic subspace self-consistent field method

We propose a new self-consistent field (SCF) algorithm based on an iterative, partially stochastic “Divide & Conquer”-type approach. This new SCF algorithm is a simple variant of the usual SCF procedure and can be easily implemented in parallel. A detailed description of the algorithm is reported. We illustrate this new method on one-dimensional hydrogen chains and three-dimensional hydrogen clusters.PFL thanks the NCI National Facility for a generous grant of supercomputer time, and the Australian Research Council for funding (Grant DP140104071) and a Discovery Early Career Researcher Award (Grant DE130101441). XA would like to thank the Research School of Chemistry of the Australian National University for a visiting fellowship during the construction of this manuscript

Novel Blood Pressure Locus and Gene Discovery Using Genome-Wide Association Study and Expression Data Sets From Blood and the Kidney.

Elevated blood pressure is a major risk factor for cardiovascular disease and has a substantial genetic contribution. Genetic variation influencing blood pressure has the potential to identify new pharmacological targets for the treatment of hypertension. To discover additional novel blood pressure loci, we used 1000 Genomes Project-based imputation in 150 134 European ancestry individuals and sought significant evidence for independent replication in a further 228 245 individuals. We report 6 new signals of association in or near HSPB7, TNXB, LRP12, LOC283335, SEPT9, and AKT2, and provide new replication evidence for a further 2 signals in EBF2 and NFKBIA Combining large whole-blood gene expression resources totaling 12 607 individuals, we investigated all novel and previously reported signals and identified 48 genes with evidence for involvement in blood pressure regulation that are significant in multiple resources. Three novel kidney-specific signals were also detected. These robustly implicated genes may provide new leads for therapeutic innovation

Causal effect of plasminogen activator inhibitor type 1 on coronary heart disease

Background--Plasminogen activator inhibitor type 1 (PAI-1) plays an essential role in the fibrinolysis system and thrombosis. Population studies have reported that blood PAI-1 levels are associated with increased risk of coronary heart disease (CHD). However, it is unclear whether the association reflects a causal influence of PAI-1 on CHD risk. Methods and Results--To evaluate the association between PAI-1 and CHD, we applied a 3-step strategy. First, we investigated the observational association between PAI-1 and CHD incidence using a systematic review based on a literature search for PAI-1 and CHD studies. Second, we explored the causal association between PAI-1 and CHD using a Mendelian randomization approach using summary statistics from large genome-wide association studies. Finally, we explored the causal effect of PAI-1 on cardiovascular risk factors including metabolic and subclinical atherosclerosis measures. In the systematic meta-analysis, the highest quantile of blood PAI-1 level was associated with higher CHD risk comparing with the lowest quantile (odds ratio=2.17; 95% CI: 1.53, 3.07) in an age- and sex-adjusted model. The effect size was reduced in studies using a multivariable-adjusted model (odds ratio=1.46; 95% CI: 1.13, 1.88). The Mendelian randomization analyses suggested a causal effect of increased PAI-1 level on CHD risk (odds ratio=1.22 per unit increase of log-transformed PAI-1; 95% CI: 1.01, 1.47). In addition, we also detected a causal effect of PAI-1 on elevating blood glucose and high-density lipoprotein cholesterol. Conclusions--Our study indicates a causal effect of elevated PAI-1 level on CHD risk, which may be mediated by glucose dysfunction