12 research outputs found
A One-Dimensional Model for Many-Electron Atoms in Extremely Strong Magnetic Fields: Maximum Negative Ionization
We consider a one-dimensional model for many-electron atoms in strong
magnetic fields in which the Coulomb potential and interactions are replaced by
one-dimensional regularizations associated with the lowest Landau level. For
this model we show that the maximum number of electrons is bounded above by
2Z+1 + c sqrt{B}.
We follow Lieb's strategy in which convexity plays a critical role. For the
case of two electrons and fractional nuclear charge, we also discuss the
critical value at which the nuclear charge becomes too weak to bind two
electrons.Comment: 23 pages, 5 figures. J. Phys. A: Math and General (in press) 199
Lieb-Thirring inequalities for geometrically induced bound states
We prove new inequalities of the Lieb-Thirring type on the eigenvalues of
Schr\"odinger operators in wave guides with local perturbations. The estimates
are optimal in the weak-coupling case. To illustrate their applications, we
consider, in particular, a straight strip and a straight circular tube with
either mixed boundary conditions or boundary deformations.Comment: LaTeX2e, 14 page
Analytic structure factors and pair-correlation functions for the unpolarized homogeneous electron gas
We propose a simple and accurate model for the electron static structure
factors (and corresponding pair-correlation functions) of the 3D unpolarized
homogeneous electron gas. Our spin-resolved pair-correlation function is built
up with a combination of analytic constraints and fitting procedures to quantum
Monte Carlo data, and, in comparison to previous attempts (i) fulfills more
known integral and differential properties of the exact pair-correlation
function, (ii) is analytic both in real and in reciprocal space, and (iii)
accurately interpolates the newest, extensive diffusion-Monte Carlo data of
Ortiz, Harris and Ballone [Phys. Rev. Lett. 82, 5317 (1999)]. This can be of
interest for the study of electron correlations of real materials and for the
construction of new exchange and correlation energy density functionals.Comment: 14 pages, 5 figures, submitted to Phys. Rev.
New Dynamic Rotamer Libraries: Data-Driven Analysis of Side-Chain Conformational Propensities
NoMost rotamer libraries are generated from subsets of the PDB and do not fully represent the conformational scope of protein side chains. Previous attempts to rectify this sparse coverage of conformational space have involved application of weighting and smoothing functions. We resolve these limitations by using physics-based molecular dynamics simulations to determine more accurate frequencies of rotameric states. This work forms part of our Dynameomics initiative and uses a set of 807 proteins selected to represent 97% of known autonomous protein folds, thereby eliminating the bias toward common topologies found within the PDB. Our Dynameomics derived rotamer libraries encompass 4.8 × 10(9) rotamers, sampled from at least 51,000 occurrences of each of 93,642 residues. Here, we provide a backbone-dependent rotamer library, based on secondary structure ϕ/ψ regions, and an update to our 2011 backbone-independent library that addresses the doubling of our dataset since its original publication.NI