Logarithm second-order many-body perturbation method for extended systems

2010 ◽  
Vol 133 (3) ◽  
pp. 034106 ◽  
Author(s):  
Yu-ya Ohnishi ◽  
So Hirata
Keyword(s):  
Perturbation Method ◽  
Second Order ◽  
Many Body ◽  
Extended Systems

scholarly journals Regularized Second-Order Correlation Methods for Extended Systems

2021 ◽  
Author(s):  
Elisabeth Keller ◽  
Theodoros Tsatsoulis ◽  
Karsten Reuter ◽  
Johannes T. Margraf
Keyword(s):  
Computational Cost ◽  
Cost Effective ◽  
Strongly Correlated Systems ◽  
Second Order ◽  
Strongly Correlated ◽  
Many Body ◽  
Correlated Systems ◽  
Extended Systems ◽  
Moller Plesset ◽  
The One

While many-body wavefunction theory has long been established as a powerful framework for highly accurate molecular quantum chemistry, these methods have only fairly recently been applied to extended systems in a significant scale. This is due to the high computational cost of such calculations, requiring efficient implementations and ample computing resources. To further aggravate this, second-order Møller-Plesset perturbation theory (MP2) (the most cost effective wavefuntion method) is known to diverge or fail for some prototypical condensed matter systems like the homogeneous electron gas (HEG). In this paper, we explore how the issues of MP2 for metallic and strongly correlated systems can be ameliorated through regularization. To this end, two regularized second-order methods (including a new, size-extensive Brillioun-Wigner approach) are applied to the HEG, the one-dimensional Hubbard model and the graphene-water interaction energy. We find that regularization consistently leads to improvements over the MP2 baseline and that different regularizers are appropriate for metallic and strongly correlated systems, respectively.

Divergence of Many-Body Perturbation Theory for Noncovalent Interactions of Large Molecules

2019 ◽  
Author(s):  
Brian Nguyen ◽  
Guo P Chen ◽  
Matthew M. Agee ◽  
Asbjörn M. Burow ◽  
Matthew Tang ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
System Size ◽  
State Density ◽  
Second Order ◽  
Binding Energies ◽  
Basis Set ◽  
Many Body ◽  
Many Body Perturbation Theory ◽  
Relative Errors ◽  
Ground State Density

Prompted by recent reports of large errors in noncovalent interaction (NI) energies obtained from many-body perturbation theory (MBPT), we compare the performance of second-order Møller–Plesset MBPT (MP2), spin-scaled MP2, dispersion-corrected semilocal density functional approximations (DFA), and the post-Kohn–Sham random phase approximation (RPA) for predicting binding energies of supramolecular complexes contained in the S66, L7, and S30L benchmarks. All binding energies are extrapolated to the basis set limit, corrected for basis set superposition errors, and compared to reference results of the domain-based local pair-natural orbital coupled-cluster (DLPNO-CCSD(T)) or better quality. Our results confirm that MP2 severely overestimates binding energies of large complexes, producing relative errors of over 100% for several benchmark compounds. RPA relative errors consistently range between 5-10%, significantly less than reported previously using smaller basis sets, whereas spin-scaled MP2 methods show limitations similar to MP2, albeit less pronounced, and empirically dispersion-corrected DFAs perform almost as well as RPA. Regression analysis reveals a systematic increase of relative MP2 binding energy errors with the system size at a rate of approximately 1‰ per valence electron, whereas the RPA and dispersion-corrected DFA relative errors are virtually independent of the system size. These observations are corroborated by a comparison of computed rotational constants of organic molecules to gas-phase spectroscopy data contained in the ROT34 benchmark. To analyze these results, an asymptotic adiabatic connection symmetry-adapted perturbation theory (AC-SAPT) is developed which uses monomers at full coupling whose ground-state density is constrained to the ground-state density of the complex. Using the fluctuation–dissipation theorem, we obtain a nonperturbative “screened second-order” expression for the dispersion energy in terms of monomer quantities which is exact for non-overlapping subsystems and free of induction terms; a first-order RPA-like approximation to the Hartree, exchange, and correlation kernel recovers the macroscopic Lifshitz limit. The AC-SAPT expansion of the interaction energy is obtained from Taylor expansion of the coupling strength integrand. Explicit expressions for the convergence radius of the AC-SAPT series are derived within RPA and MBPT and numerically evaluated. Whereas the AC-SAPT expansion is always convergent for nondegenerate monomers when RPA is used, it is found to spuriously diverge for second-order MBPT, except for the smallest and least polarizable monomers. The divergence of the AC-SAPT series within MBPT is numerically confirmed within RPA; prior numerical results on the convergence of the SAPT expansion for MBPT methods are revisited and support this conclusion once sufficiently high orders are included. The cause of the failure of MBPT methods for NIs of large systems is missing or incomplete “electrodynamic” screening of the Coulomb interaction due to induced particle–hole pairs between electrons in different monomers, leaving the effective interaction too strong for AC-SAPT to converge. Hence, MBPT cannot be considered reliable for quantitative predictions of NIs, even in moderately polarizable molecules with a few tens of atoms. The failure to accurately account for electrodynamic polarization makes MBPT qualitatively unsuitable for applications such as NIs of nanostructures, macromolecules, and soft materials; more robust non-perturbative approaches such as RPA or coupled cluster methods should be used instead whenever possible.<br>

scholarly journals Second Approximate Solution of Duffing Equation with Strong Nonlinearity by Homotopy Perturbation Method

1970 ◽  
Vol 30 ◽  
pp. 59-75
Author(s):  
M Alhaz Uddin ◽  
M Abdus Sattar
Keyword(s):  
Approximate Solution ◽  
Nonlinear Systems ◽  
Perturbation Method ◽  
Differential System ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Second Order ◽  
Strong Nonlinearity ◽  
Analytical Technique ◽  
Homotopy Perturbation

 In this paper, the second order approximate solution of a general second order nonlinear ordinary differential system, modeling damped oscillatory process is considered. The new analytical technique based on the work of He’s homotopy perturbation method is developed to find the periodic solution of a second order ordinary nonlinear differential system with damping effects. Usually the second or higher order approximate solutions are able to give better results than the first order approximate solutions. The results show that the analytical approximate solutions obtained by homotopy perturbation method are uniformly valid on the whole solutions domain and they are suitable not only for strongly nonlinear systems, but also for weakly nonlinear systems. Another advantage of this new analytical technique is that it also works for strongly damped, weakly damped and undamped systems. Figures are provided to show the comparison between the analytical and the numerical solutions. Keywords: Homotopy perturbation method; damped oscillation; nonlinear equation; strong nonlinearity. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 59-75  DOI: http://dx.doi.org/10.3329/ganit.v30i0.8504

scholarly journals Finite-size errors in quantum many-body simulations of extended systems

1999 ◽  
Vol 59 (3) ◽  
pp. 1917-1929 ◽  
Author(s):  
P. R. C. Kent ◽  
Randolph Q. Hood ◽  
A. J. Williamson ◽  
R. J. Needs ◽  
W. M. C. Foulkes ◽  
...  
Keyword(s):  
Finite Size ◽  
Many Body ◽  
Extended Systems
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