Electron correlation in Hooke’s law atom in the high-density limit

Closed-form expressions for the first three terms in the perturbation expansion of the exact energy and Hartree-Fock energy of the lowest singlet and triplet states of the Hooke's law atom are found. These yield elementary formulas for the exact correlation energies (-49.7028 and -5.807 65 mE(h)) of the two states in the high-density limit and lead to a pair of necessary conditions on the exact correlation kernel G(w) in Hartree-Fock-Wigner theory.The authors also thank Professor John D. Morgan III for advice concerning Eq. s1d and both EPSRC sGrant No. GR/R81121d and the Research School of Chemistry at ANU for funding

Depletion of DNMT1 in differentiated human cells highlights key classes of sensitive genes and an interplay with polycomb repression

Additional file 3: Figure S2. Changes in methylation levels by genomic element. (A) Protein levels in knockdown lines by western blotting. As a control HCT116 colon cancer cells which are WT or have a homozygous mutation in DNMT1 (KO) are shown: the DNMT1-specific top band is indicated by the arrowhead at right. (B) Median levels of methylation are shown for each genomic element (listed at top). The positions of medians are also indicated at right (arrowheads). The differences between WT and KD medians were used to plot Fig. 1d. (C) Density distribution of methylation at the three main elements involved in gene regulation, shown by cell line. Demethylation seems most marked at gene bodies (Genes), indicated by increased density of probes at low methylation (β) values

Effectiveness of a biopsychosocial e-learning intervention on the clinical judgements of medical students and GP trainees regarding future risk of disability in patients with chronic lower back pain: study protocol for a randomised controlled trial

Introduction Chronic lower back pain (CLBP) is a major healthcare problem with wide ranging effects. It is a priority for appropriate management of CLBP to get individuals back to work as early as possible. Interventions that identify biopsychosocial barriers to recovery have been observed to lead to successfully reduced pain-related work absences and increased return to work for individuals with CLBP. Modern conceptualisations of pain adopt a biopsychosocial approach, such as the flags approach. Biopsychosocial perspectives have been applied to judgements about future adjustment, recovery from pain and risk of long-term disability; and provide a helpful model for understanding the importance of contextual interactions between psychosocial and biological variables in the experience of pain. Medical students and general practitioner (GP) trainees are important groups to target with education about biopsychosocial conceptualisations of pain and related clinical implications. Aim The current study will compare the effects of an e-learning intervention that focuses on a biopsychosocial model of pain, on the clinical judgements of medical students and trainees. Methods and analysis Medical student and GP trainee participants will be randomised to 1 of 2 study conditions: (1) a 20 min e-learning intervention focused on the fundamentals of the flags approach to clinical judgement-making regarding risk of future pain-related disability; compared with a (2) wait-list control group on judgement accuracy and weighting (ie, primary outcomes); flags approach knowledge, attitudes and beliefs towards pain, judgement speed and empathy (ie, secondary outcomes). Participants will be assessed at preintervention and postintervention. Ethics and dissemination The study will be performed in agreement with the Declaration of Helsinki and is approved by the National University of Ireland Galway Research Ethics Committee. The results of the trial will be published according to the CONSORT statement and will be presented at conferences and reported in peer-reviewed journals

Wave functions and two-electron probability distributions of the Hooke's-law atom and helium

The wave functions and two-electron probability distributions of the Hooke's-law atom (hookium) and helium were studied. The intracules for hookium and helium were presented using both exact and Hartree-Fock wave functions. The Coulomb holes in position

Benchmark correlation energies for small molecules

We present estimates of the exact correlation energies for 56 small molecules whose experimental atomization energies are known accurately. These should prove useful in the assessment and parameterization of new quantum chemical methods

Self-Consistent Hartree-Fock-Wigner Calculations: A Two-Electron-Density Functional Theory

We recently presented a correlation method based on the Wigner intracule, in which correlation energies are calculated directly from a Hartree-Fock wavefunction. We now describe a self-consistent form of this approach which we term the Hartree-Fock-Wigner method. The efficacy of the new scheme is demonstrated using a simple weight function to reproduce the correlation energies of the first- and second-row atoms with a mean absolute deviation of 2.5 mEh

Wigner intracule for the Kellner helium-like ions

The Kellner wavefunction for a helium-like ion is the Hartree-Fock solution wherein the orbital is a Slater-type function with the variationally optimal exponent ζ= Z - 5/16. The Wigner intracule W(u, v) of a system gives the joint quasiprobability of f

Two-electron distribution functions and intracules

Two-electron distribution functions and intracules are functions of electronic coordinates and occupy an important, and frequently overlooked, middle ground between the beguiling simplicity of electron densities and the bewildering complexity of wavefunctions. We survey the functions that have been considered by earlier workers and introduce two new ones, the Wigner intracule and the action intracule, that have not previously been discussed. To illustrate their usefulness, we consider the intracules of jellium, a few small atoms and the dissociating hydrogen molecule