Reducing the Many-Electron Self-Interaction Error in the Second-Order Screened Exchange Method

2019 ◽  
Vol 15 (12) ◽  
pp. 6607-6616 ◽  
Author(s):  
Pál D. Mezei ◽  
Adrienn Ruzsinszky ◽  
Mihály Kállay
2010 ◽  
Vol 132 (9) ◽  
pp. 094103 ◽  
Author(s):  
Joachim Paier ◽  
Benjamin G. Janesko ◽  
Thomas M. Henderson ◽  
Gustavo E. Scuseria ◽  
Andreas Grüneis ◽  
...  

1985 ◽  
Vol 63 (3) ◽  
pp. 327-334
Author(s):  
H. R. Zaidi

A general formulation, developed earlier, is applied to the problem of optical bistability in a sample with dimensions that are small compared with the wavelength of light. A self-consistent model of radiative relaxation is introduced in which atom–atom correlations are taken into account. This is based on the screened interaction approximation of the many-body theory. The degree of correlation is internally determined by the dynamics of the system. The validity of the S-conservation approximation is investigated; it is concluded that this approximation may be valid only in the weak-field limit, since the local-field fluctuations become appreciable as the pump-field strength is increased. As a result, the system undergoes a first-order phase transition, in contrast to the second-order transition predicted by the S-conserving model. The method is quite general, and it can be applied to other damping mechanisms. As an illustration, a simple collision model is also considered. In the limit of a zero external field and thermodynamic equilibrium, our results reduce to the results of existing theories; the system exhibits a second-order phase transition.


2018 ◽  
pp. 71
Author(s):  
Nina Mendelson

In resolving questions of statutory meaning, the lion’s share of Roberts Court opinions considers and applies at least one interpretive canon, whether the rule against surplusage or the presumption against state law preemption. This is part of a decades-long turn toward textualist statutory interpretation in the Supreme Court. Commentators have debated how to justify canons, since they are judicially created rules that reside outside the statutory text. Earlier studies have cast substantial doubt on whether these canons can be justified as capturing congressional practices or preferences; commentators have accordingly turned toward second-order justifications, arguing that canons usefully make interpretation constrained and predictable, supplying Congress with a stable interpretive background. Based on an extensive study tracking the use of over 30 interpretive canons in the first 10 years of the Roberts Court, this Article attempts to contribute evidence to the debate over canons. The data raise substantial questions regarding stability and predictability. Despite a long tradition of use, some canons have essentially disappeared; meanwhile, the Court has created others out of whole cloth. In addition, application is erratic. The Roberts Court Justices have declined to apply even the most widely engaged canons 20–30% or more of the time, often for difficult-to-anticipate reasons; some well-known canons, such as the rule of lenity and the presumption against preemption, were applied roughly at a 50–50 rate. The story is worse in the many cases in which multiple canons are considered. Based on these and other findings, this Article accordingly argues that predictability and stability arguments cannot supply a firm foundation for canon use. The study also reveals troubling mismatches between canons actually in use and congressional staff acceptance of canons. The Article concludes by suggesting some future directions for investigation and reform.


2021 ◽  
Vol 9 ◽  
Author(s):  
Fabien Bruneval ◽  
Nike Dattani ◽  
Michiel J. van Setten

We use the GW100 benchmark set to systematically judge the quality of several perturbation theories against high-level quantum chemistry methods. First of all, we revisit the reference CCSD(T) ionization potentials for this popular benchmark set and establish a revised set of CCSD(T) results. Then, for all of these 100 molecules, we calculate the HOMO energy within second and third-order perturbation theory (PT2 and PT3), and, GW as post-Hartree-Fock methods. We found GW to be the most accurate of these three approximations for the ionization potential, by far. Going beyond GW by adding more diagrams is a tedious and dangerous activity: We tried to complement GW with second-order exchange (SOX), with second-order screened exchange (SOSEX), with interacting electron-hole pairs (WTDHF), and with a GW density-matrix (γGW). Only the γGW result has a positive impact. Finally using an improved hybrid functional for the non-interacting Green’s function, considering it as a cheap way to approximate self-consistency, the accuracy of the simplest GW approximation improves even more. We conclude that GW is a miracle: Its subtle balance makes GW both accurate and fast.


2010 ◽  
Vol 133 (17) ◽  
pp. 179902 ◽  
Author(s):  
Joachim Paier ◽  
Benjamin G. Janesko ◽  
Thomas M. Henderson ◽  
Gustavo E. Scuseria ◽  
Andreas Grüneis ◽  
...  

2017 ◽  
Vol 147 (20) ◽  
pp. 204107 ◽  
Author(s):  
Matthias Beuerle ◽  
Christian Ochsenfeld

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Gorm Harste

The world of the future will not be one without wars. The many hopes we have about a future peace governed by a more or less confederal state will not make wars obsolete. Regular wars and irregular wars will continue and probably on different subjects than we are used to. The article proposes that the form of war will be more about temporalities, i.e. fast interchanges or, rather, more risky protracted wars of attrition and exhaustion and less on tactical well defined territories. The West can neither dominate such wars nor establish one world that is ruled or even governed. The risk is that we have the systems we have. They have their own path dependencies, their temporal bindings and their own stories to tell. In the worst case, the West sticks to an imaginary of almighty power – and then it will lose. We tend to forget that our present past will be experienced and told differently in the future. The “extreme 20th century” will have another history and another impact. Its extremes will be narrated as more extreme, and its temporal bindings become easier to observe. The much celebrated “revolutions in military affairs” will not dominate future war systems. Unipolarity is fading away. Kantian convergences may appear.


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