Intermolecular Potential of the Methane Dimer and Trimer

The Heitler–London (HL) exchange energy is responsible for the anisotropy of the pair potential in methane. The equilibrium dimer structure is that which minimizes steric repulsion between hydrogens belonging to opposite subsystems. Dispersion energy, which represents a dominating attractive contribution, displays an orientation dependence which is the mirror image of that for HL exchange. The three‐body correction to the pair potential is a superposition of HL and second‐order exchange nonadditivities combined with the Axilrod–Teller dispersion nonadditivity. A great deal of cancellation between these terms results in near additivity of methane interactions in the long and intermediate regions

Derivation of the Supermolecular Interaction Energy from the Monomer Densities in the Density Functional Theory

The density functional theory (DFT) interaction energy of a dimer is rigorously derived from the monomer densities. To this end, the supermolecular energy bifunctional is formulated in terms of mutually orthogonal sets of orbitals of the constituent monomers. The orthogonality condition is preserved in the solution of the Kohn-Sham equations through the Pauli blockade method. Numerical implementation of the method provides interaction energies which agree with those obtained from standard supermolecular calculations within less than 0.1% error for three example functionals: Slater-Dirac, PBE0 and B3LYP, and for two model van der Waals dimers: Ne2 and (C2H4)2, and two model H-bond complexes: (HF)2 and (NH3)2.Comment: 6 pages, 1 figure, REVTeX

Entropic Uncertainty Relations in Quantum Physics

Uncertainty relations have become the trademark of quantum theory since they were formulated by Bohr and Heisenberg. This review covers various generalizations and extensions of the uncertainty relations in quantum theory that involve the R\'enyi and the Shannon entropies. The advantages of these entropic uncertainty relations are pointed out and their more direct connection to the observed phenomena is emphasized. Several remaining open problems are mentionedComment: 35 pages, review pape

Density Functional Theory Approach to Noncovalent Interactions via Interacting Monomer Densities

A recently proposed "DFT+dispersion" treatment (Rajchel et al., Phys. Rev. Lett., 2010, 104, 163001) is described in detail and illustrated by more examples. The formalism derives the dispersion-free density functional theory (DFT) interaction energy and combines it with the dispersion energy from separate DFT calculations. It consists in the self-consistent polarization of DFT monomers restrained by the exclusion principle via the Pauli blockade technique. Within the monomers a complete exchange-correlation potential should be used, but between them only the exact exchange operates. The applications to wide range of molecular complexes from rare-gas dimers to H-bonds to pi-electron interactions show good agreement with benchmark values.Comment: 9 pages, 5 figures, 2 tables, REVTeX

Rare germline variants in DNA repair genes and the angiogenesis pathway predispose prostate cancer patients to develop metastatic disease

Background Prostate cancer (PrCa) demonstrates a heterogeneous clinical presentation ranging from largely indolent to lethal. We sought to identify a signature of rare inherited variants that distinguishes between these two extreme phenotypes. Methods We sequenced germline whole exomes from 139 aggressive (metastatic, age of diagnosis < 60) and 141 non-aggressive (low clinical grade, age of diagnosis ≥60) PrCa cases. We conducted rare variant association analyses at gene and gene set levels using SKAT and Bayesian risk index techniques. GO term enrichment analysis was performed for genes with the highest differential burden of rare disruptive variants. Results Protein truncating variants (PTVs) in specific DNA repair genes were significantly overrepresented among patients with the aggressive phenotype, with BRCA2, ATM and NBN the most frequently mutated genes. Differential burden of rare variants was identified between metastatic and non-aggressive cases for several genes implicated in angiogenesis, conferring both deleterious and protective effects. Conclusions Inherited PTVs in several DNA repair genes distinguish aggressive from non-aggressive PrCa cases. Furthermore, inherited variants in genes with roles in angiogenesis may be potential predictors for risk of metastases. If validated in a larger dataset, these findings have potential for future clinical application

Early Science with the Large Millimeter Telescope: COOL BUDHIES I - a pilot study of molecular and atomic gas at z~0.2

An understanding of the mass build-up in galaxies over time necessitates tracing the evolution of cold gas (molecular and atomic) in galaxies. To that end, we have conducted a pilot study called CO Observations with the LMT of the Blind Ultra-Deep H I Environment Survey (COOL BUDHIES). We have observed 23 galaxies in and around the two clusters Abell 2192 (z = 0.188) and Abell 963 (z = 0.206), where 12 are cluster members and 11 are slightly in the foreground or background, using about 28 total hours on the Redshift Search Receiver (RSR) on the Large Millimeter Telescope (LMT) to measure the $^{12}$CO J = 1 --> 0 emission line and obtain molecular gas masses. These new observations provide a unique opportunity to probe both the molecular and atomic components of galaxies as a function of environment beyond the local Universe. For our sample of 23 galaxies, nine have reliable detections (S/N$\geq$3.6) of the $^{12}$CO line, and another six have marginal detections (2.0 < S/N < 3.6). For the remaining eight targets we can place upper limits on molecular gas masses roughly between $10^9$ and $10^{10} M_\odot$. Comparing our results to other studies of molecular gas, we find that our sample is significantly more abundant in molecular gas overall, when compared to the stellar and the atomic gas component, and our median molecular gas fraction lies about $1\sigma$ above the upper limits of proposed redshift evolution in earlier studies. We discuss possible reasons for this discrepancy, with the most likely conclusion being target selection and Eddington bias.Comment: MNRAS, submitte