Excitations and benchmark ensemble density functional theory for two electrons

A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two electron systems, exploring the behavior of exact ensemble density functional theory. The issue of separating the Hartree energy and the choice of degenerate eigenstates is explored. A new approximation, spin eigenstate Hartree-exchange (SEHX), is derived. Exact conditions that are proven include the signs of the correlation energy components, the virial theorem for both exchange and correlation, and the asymptotic behavior of the potential for small weights of the excited states. Many energy components are given as a function of the weights for two electrons in a one-dimensional flat box, in a box with a large barrier to create charge transfer excitations, in a three-dimensional harmonic well (Hooke's atom), and for the He atom singlet-triplet ensemble, singlet-triplet-singlet ensemble, and triplet bi-ensemble.Comment: 15 pages, supplemental material pd

Quantum Monte Carlo study of the energetics of the rutile, anatase, brookite, and columbite TiO2_{2} polymorphs

The relative energies of the low-pressure rutile, anatase, and brookite polymorphs and the high-pressure columbite polymorph of TiO$_{2}$ have been calculated as a function of temperature using the diffusion quantum Monte Carlo (DMC) method and density functional theory (DFT). The vibrational energies are found to be important on the scale of interest and significant quartic anharmonicity is found in the rutile phase. Static-lattice DFT calculations predict that anatase is lower in energy than rutile, in disagreement with experiment. The accurate description of electronic correlations afforded by DMC calculations and the inclusion of anharmonic vibrational effects contribute to stabilizing rutile with respect to anatase. Our calculations predict a phase transition from anatase to rutile TiO$_{2}$ at 630±210 K.J.R.T., P.L.R., and R.J.N. acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant No. EP/J017639/1. B.M. acknowledges support from Robinson College, Cambridge, and the Cambridge Philosophical Society for a Henslow Research Fellowship. R.M. is grateful for financial support from MEXT-KAKENHI Grants No. 26287063, No. 25600156, and No. 22104011, and a grant from the Asahi Glass Foundation. Computational resources were provided by the Archer facility of the U.K.'s national high-performance computing service (for which access was obtained via the UKCP consortium, EPSRC Grant No. EP/K014560/1), by the Center for Information Science of the JAIST, and by the K-computer (supported by the Computational Materials Science Initiative, CMSI/Japan, under Projects No. hp120086, No. hp140150, and No. hp150014)

Observation of B-c(+) -> J/psi D-(*()) K-(*()) decays

A search for the decays $B_c^+ \to J/\psi D^{(*)0} K^+$ and $B_c^+ \to J/\psi D^{(*)+} K^{*0}$ is performed with data collected at the LHCb experiment corresponding to an integrated luminosity of 3 fb$^{-1}$. The decays $B_c^+ \to J/\psi D^0 K^+$ and $B_c^+ \to J/\psi D^{*0} K^+$ are observed for the first time, while first evidence is reported for the $B_c^+ \to J/\psi D^{*+} K^{*0}$ and $B_c^+ \to J/\psi D^+ K^{*0}$ decays. The branching fractions of these decays are determined relative to the $B_c^+ \to J/\psi \pi^+$ decay. The $B_c^+$ mass is measured, using the $J/\psi D^0 K^+$ final state, to be $6274.28 \pm 1.40 (stat) \pm 0.32 (syst)$ MeV/$c^2$. This is the most precise single measurement of the $B_c^+$ mass to date.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2016-055.htm

The IDENTIFY study: the investigation and detection of urological neoplasia in patients referred with suspected urinary tract cancer - a multicentre observational study

Objective To evaluate the contemporary prevalence of urinary tract cancer (bladder cancer, upper tract urothelial cancer [UTUC] and renal cancer) in patients referred to secondary care with haematuria, adjusted for established patient risk markers and geographical variation. Patients and Methods This was an international multicentre prospective observational study. We included patients aged ≥16 years, referred to secondary care with suspected urinary tract cancer. Patients with a known or previous urological malignancy were excluded. We estimated the prevalence of bladder cancer, UTUC, renal cancer and prostate cancer; stratified by age, type of haematuria, sex, and smoking. We used a multivariable mixed-effects logistic regression to adjust cancer prevalence for age, type of haematuria, sex, smoking, hospitals, and countries. Results Of the 11 059 patients assessed for eligibility, 10 896 were included from 110 hospitals across 26 countries. The overall adjusted cancer prevalence (n = 2257) was 28.2% (95% confidence interval [CI] 22.3–34.1), bladder cancer (n = 1951) 24.7% (95% CI 19.1–30.2), UTUC (n = 128) 1.14% (95% CI 0.77–1.52), renal cancer (n = 107) 1.05% (95% CI 0.80–1.29), and prostate cancer (n = 124) 1.75% (95% CI 1.32–2.18). The odds ratios for patient risk markers in the model for all cancers were: age 1.04 (95% CI 1.03–1.05; P < 0.001), visible haematuria 3.47 (95% CI 2.90–4.15; P < 0.001), male sex 1.30 (95% CI 1.14–1.50; P < 0.001), and smoking 2.70 (95% CI 2.30–3.18; P < 0.001). Conclusions A better understanding of cancer prevalence across an international population is required to inform clinical guidelines. We are the first to report urinary tract cancer prevalence across an international population in patients referred to secondary care, adjusted for patient risk markers and geographical variation. Bladder cancer was the most prevalent disease. Visible haematuria was the strongest predictor for urinary tract cancer

Excitations and benchmark ensemble density functional theory for two electrons.

A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two-electron systems, exploring the behavior of exact ensemble density functional theory. The issue of separating the Hartree energy and the choice of degenerate eigenstates is explored. A new approximation, spin eigenstate Hartree-exchange, is derived. Exact conditions that are proven include the signs of the correlation energy components and the asymptotic behavior of the potential for small weights of the excited states. Many energy components are given as a function of the weights for two electrons in a one-dimensional flat box, in a box with a large barrier to create charge transfer excitations, in a three-dimensional harmonic well (Hooke's atom), and for the He atom singlet-triplet ensemble, singlet-triplet-singlet ensemble, and triplet bi-ensemble