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The correlation energy functional within the GW-RPA approximation: exact forms, approximate forms and challenges
Sohrab Ismail-Beigi
Physics , 2010, DOI: 10.1103/PhysRevB.81.195126
Abstract: In principle, the Luttinger-Ward Green's function formalism allows one to compute simultaneously the total energy and the quasiparticle band structure of a many-body electronic system from first principles. We present approximate and exact expressions for the correlation energy within the GW-RPA approximation that are more amenable to computation and allow for developing efficient approximations to the self-energy operator and correlation energy. The exact form is a sum over differences between plasmon and interband energies. The approximate forms are based on summing over screened interband transitions. We also demonstrate that blind extremization of such functionals leads to unphysical results: imposing physical constraints on the allowed solutions (Green's functions) is necessary. Finally, we present some relevant numerical results for atomic systems.
Justifying quasiparticle self-consistent schemes via gradient optimization in Luttinger-Ward theory
Sohrab Ismail-Beigi
Physics , 2014,
Abstract: The question of which non-interacting Green's function "best" describes an interacting many-body electronic system is both of fundamental interest as well as of practical importance in describing electronic properties of materials in a realistic manner. Here, we study this question within the framework of Luttinger-Ward theory, an approach where one extremizes a total energy functional of the one-particle Green's function in order to find the total ground-state energy as well as all one-particle properties such as the density matrix, chemical potential, or the quasiparticle energy spectrum and quasiparticle wave functions. Our basic finding is that minimizing the length of the gradient of the total energy functional over non-interacting Green's functions yields a set of self-consistent equations for quasiparticles that is identical to those of the Quasiparticle Self-Consistent GW (QSGW) approach, thereby providing an a priori justification for such an approach to electronic structure calculations. In fact, this result is general, applies to any self-energy operator, and is not restricted to any particular approximation, e.g. the GW approximation for the self-energy. The approach also naturally shows why solving the diagonal part of the self-consistent equations is of primary importance while the off-diagonals are of secondary importance, a common prior observation in the literature of electronic structure calculations based on self-energy calculations.
Truncation of Periodic Image Interactions for Confined Systems
Sohrab Ismail-Beigi
Physics , 2006, DOI: 10.1103/PhysRevB.73.233103
Abstract: First principles methods based on periodic boundary conditions are used extensively by materials theorists. However, applying these methods to systems with confined electronic states entails the use of large unit cells in order to avoid artificial image interactions. We present a general approach for truncating the Coulomb interaction that removes image effects directly and leads to well converged results for modest-sized periodic cells. As an illustration, we find the lowest-energy quasiparticle and exciton states in two-dimensional hexagonal GaN sheets. These sheets have been proposed as parent materials for single-walled GaN nanotubes which may be of interest for optoelectronics.
Severe hypoglycemia symptoms, antecedent behaviors, immediate consequences and association with glycemia medication usage: Secondary analysis of the ACCORD clinical trial data
Denise E Bonds, Michael E Miller, Jim Dudl, Mark Feinglos, Faramarz Ismail-Beigi, Saul Malozowski, Elizabeth Seaquest, Debra L Simmons, Ajay Sood
BMC Endocrine Disorders , 2012, DOI: 10.1186/1472-6823-12-5
Abstract: Information about symptoms, antecedents, and consequences was collected at the time participants reported an episode of severe hypoglycemia. Data on medications prescribed during the clinical trial was used to determine the association of particular diabetes drug classes and severe hypoglycemia.The most frequently reported symptoms in both glycemia group were weakness/fatigue (Int 29%; Std 30%) and sweating (Int 26%; Std 27%), followed by confusion/disorientation (Int 22%; Std 29%) and shakiness (Int 21%; Std 19%). Approximately half of all events were preceded by a variation in food intake (Int 48%; Std 58%). The most common consequences were confusion (Int 37%; Std 34%), loss of consciousness (Int 25%; Std 25%), and hospitalization (Int 18%; Std 24%). The highest rates of hypoglycemia were found among those participants treated with insulin only (Int 6.09/100 person yrs; Std 2.64/100 person yrs) while the lowest were among those prescribed oral agents only (Int 1.93/100 person yrs; Std 0.20/100 person yrs).Severe hypoglycemia episodes were frequently preceded by a change in food intake, making many episodes potentially preventable. Symptoms of confusion/disorientation and loss of consciousness were frequently seen. The highest rates of hypoglycemia were seen with prescription of insulin, either alone or in combination with other medications.Number: NCT00000620
Novel Precursors for Boron Nanotubes: The Competition of Two-Center and Three-Center Bonding in Boron Sheets
Hui Tang,Sohrab Ismail-Beigi
Physics , 2007, DOI: 10.1103/PhysRevLett.99.115501
Abstract: We present a new class of boron sheets, composed of triangular and hexagonal motifs, that are more stable than structures considered to date and thus are likely to be the precursors of boron nanotubes. We describe a simple and clear picture of electronic bonding in boron sheets and highlight the importance of three-center bonding and its competition with two-center bonding, which can also explain the stability of recently discovered boron fullerenes. Our findings call for reconsideration of the literature on boron sheets, nanotubes, and clusters.
Excited-state Forces within a First-principles Green's Function Formalism
Sohrab Ismail-Beigi Steven G. Louie
Physics , 2002, DOI: 10.1103/PhysRevLett.90.076401
Abstract: We present a new first-principles formalism for calculating forces for optically excited electronic states using the interacting Green's function approach with the GW-Bethe Salpeter Equation method. This advance allows for efficient computation of gradients of the excited-state Born-Oppenheimer energy, allowing for the study of relaxation, molecular dynamics, and photoluminescence of excited states. The approach is tested on photoexcited carbon dioxide and ammonia molecules, and the calculations accurately describe the excitation energies and photoinduced structural deformations.
New Algebraic Formulation of Density Functional Calculation
Sohrab Ismail-Beigi,T. A. Arias
Physics , 1999, DOI: 10.1016/S0010-4655(00)00072-2
Abstract: This article addresses a fundamental problem faced by the ab initio community: the lack of an effective formalism for the rapid exploration and exchange of new methods. To rectify this, we introduce a novel, basis-set independent, matrix-based formulation of generalized density functional theories which reduces the development, implementation, and dissemination of new ab initio techniques to the derivation and transcription of a few lines of algebra. This new framework enables us to concisely demystify the inner workings of fully functional, highly efficient modern ab initio codes and to give complete instructions for the construction of such for calculations employing arbitrary basis sets. Within this framework, we also discuss in full detail a variety of leading-edge ab initio techniques, minimization algorithms, and highly efficient computational kernels for use with scalar as well as shared and distributed-memory supercomputer architectures.
Generalized slave-particle method for extended Hubbard models
Alexandru B. Georgescu,Sohrab Ismail-Beigi
Physics , 2015, DOI: 10.1103/PhysRevB.92.235117
Abstract: We introduce a set of generalized slave-particle models for extended Hubbard models that treat localized electronic correlations using slave-boson decompositions. Our models automatically include two slave-particle methods of recent interest, the slave-rotor and slave-spin methods, as well as a ladder of new intermediate models where one can choose which of the electronic degrees of freedom (e.g., spin or orbital labels) are treated as correlated degrees of freedom by the slave bosons. In addition, our method removes the aberrant behavior of the slave-rotor model at weak correlation strength by removing the contribution of unphysical states from the bosonic Hilbert space. The flexibility of our formalism permits one to separate and isolate the effect of correlations on the key degrees of freedom.
On the Locality of Physics in Metals, Semiconductors, and Insulators
Sohrab Ismail-Beigi,Tomas Arias
Physics , 1998,
Abstract: We present an analytical study of the spatial decay rate $\gamma$ of the one-particle density matrix $\rho(\vec r,\vec r')\sim\exp(-\gamma|\vec r-\vec r'|)$ for systems described by single particle orbitals in periodic potentials in arbitrary dimensions. This decay reflects electronic locality in condensed matter systems and is also crucial for O(N) density functional methods. We find that $\gamma$ behaves contrary to the conventional wisdom that generically $\gamma\propto\sqrt{\Delta}$ in insulators and $\gamma\propto\sqrt{T}$ in metals, where $\Delta$ is the direct band gap and $T$ the temperature. Rather, in semiconductors $\gamma\propto\Delta$, and in metals at low temperature $\gamma\propto T$.
Edge-driven transition in surface structure of nanoscale silicon
Sohrab Ismail-Beigi,T. A. Arias
Physics , 1998, DOI: 10.1103/PhysRevB.57.11923
Abstract: We present an ab initio exploration of the phenomena which will become important for freestanding structures of silicon as they are realized on the nanoscale. We find that not only surface but also edge effects are important considerations in structures of dimensions on the order of 3 nm. Specifically, for long nanoscale silicon bars, we find two competing low-energy reconstructions with a transition from one to the other as the cross section of the bar decreases. We predict that this size-dependent phase transition has a signature in the electronic structure of the bar but little effect on elastic properties.
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