From d3e011084ea74daaee181200f49eef453ccb32f4 Mon Sep 17 00:00:00 2001 From: Hugh Burton Date: Fri, 4 Dec 2020 14:55:26 +0000 Subject: [PATCH] Modified conclusions --- Manuscript/EPAWTFT.bbl | 143 ++++++++++++++++++++++++++++++++++++++++- Manuscript/EPAWTFT.bib | 97 ++++++++++++++++++++++++++++ Manuscript/EPAWTFT.tex | 14 ++-- 3 files changed, 247 insertions(+), 7 deletions(-) diff --git a/Manuscript/EPAWTFT.bbl b/Manuscript/EPAWTFT.bbl index a1ea818..84d6eb4 100644 --- a/Manuscript/EPAWTFT.bbl +++ b/Manuscript/EPAWTFT.bbl @@ -6,7 +6,7 @@ %Control: page (0) single %Control: year (1) truncated %Control: production of eprint (0) enabled -\begin{thebibliography}{159}% +\begin{thebibliography}{174}% \makeatletter \providecommand \@ifxundefined [1]{% \@ifx{#1\undefined} @@ -1364,6 +1364,147 @@ {journal} {\bibinfo {journal} {Theor. Chem. 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Pulay and Hans-Joachim Werner}, + journal={J. Comp. Chem.}, + year ={1998}, + volume ={19}, + pages ={1241}, + title ={Integral transformation with low‐order scaling for large local second‐order {M\oller--Plesset} calculations}, + doi ={10.1002/(SICI)1096-987X(199808)19:11<1241::AID-JCC4>3.0.CO;2-K}, +} +@article{Schutz_1999, + author ={M. Sch{\"u}tz and G. Hetzer and Hans-Joachim Werner}, + journal={J. Chem. Phys.}, + year ={1999}, + volume ={111}, + pages ={5691}, + title ={Low-order scaling local electron correlation methods. I. Linear scaling local MP2}, + doi ={10.1063/1.479957} +} +@article{Takeshita_2017, + author ={T. Y. Takeshita and W. A. {de Jong} and D. Neuhauser and R. Baer and E. Rabani}, + journal={J. Chem. Theory Comput.}, + year ={2017}, + volume ={13}, + pages ={4605}, + title ={Stochastic Formulation of the Resolution of Identity: Application to Second Order {M\oller--Plesset} Perturbation Theory}, + doi ={10.1021/acs.jctc.7b00343}, +} +@article{Li_2019, + author ={Zhendong Li}, + journal={J. Chem. Phys.}, + year ={2019}, + volume ={151}, + pages ={244114}, + title ={Stochastic many-body perturbation theory for electron correlation energies}, + doi ={10.1063/1.5128719}, +} +@article{Thom_2007, + author ={A. J. W. Thom and A. Alavi}, + journal={Phys. Rev. Lett.}, + year ={2007}, + pages ={143001}, + volume ={99}, + title ={Stochastic Perturbation Theory: A Low-Scaling Approach to Correlated Electronic Energies}, + doi ={10.1103/PhysRevLett.99.143001}, +} +@article{Willow_2012, + author ={S. Y. Willow and K. S. Kim and S. Hirata}, + journal={J. Chem. Phys.}, + year ={2012}, + volume ={137}, + pages ={204122}, + title ={Stochastic evaluation of second-order many-body perturbation energies}, + doi ={10.1063/1.4768697}, +} +@article{Neuhauser_2012, + author ={D. Neuhauser and E. Rabani and R. Baer}, + journal={J. Chem. Theory Comput.}, + year ={2012}, + pages ={24}, + volume ={9}, + title ={Expeditious Stochastic Approach for MP2 Energies in Large Electronic Systems}, + doi ={10.1021/ct.300946j}, +} +@article{Lee_2018, + author ={J. Lee and M. Head-Gordon}, + journal={J. Chem. Theory Comput.}, + year ={2018}, + pages ={5203}, + title ={Regularized Orbital-Optimized Second-Order Møller–Plesset Perturbation Theory: A Reliable Fifth-Order-Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers}, + doi ={10.1021/acs.jctc.8b00731}, +} +@article{Bertels_2019, + author ={L. W. Bertels and J. Lee and M. Head-Gordon}, + journal={J. Phys. Chem. Lett.}, + year ={2019}, + volume ={10}, + pages ={4170}, + title ={Third-Order {M\oller–Plesset} Perturbation Theory Made Useful? Choice of Orbitals and Scaling Greatly Improves Accuracy for Thermochemistry, Kinetics, and Intermolecular Interactions}, + doi ={10.1021/acs.jpclett.9b01641}, +} +@article{CarterFenk_2020, + author ={K. Carter-Fenk and J. M. Herbert}, + journal={J. Chem. Teory Comput.}, + year ={2020}, + volume ={16}, + pages ={5067}, + title ={State-Targeted Energy Projection: A Simple and Robust Approach to Orbital Relaxation of Non-Aufbau Self-Consistent Field Solutions}, + doi ={10.1021/acs.jctc.0c00502}, +} +@article{Rettig_2020, + author ={A. Rettig and D. Hait and L. W. Bertels and M. Head-Gordon}, + journal={J. Chem. Teory Comput.}, + year ={2020}, + title ={Third-Order {M\oller--Plesset} Theory Made More Useful? The Role of Density Functional Theory Orbitals}, + doi ={10.1021/acs.jctc.0c00986}, +} @article{Neese_2009, author ={F. Neese and T. Schwabe and S. Kossmann and B. Schirmer and S. Grimme}, journal={J. Chem. Teory Comput.}, diff --git a/Manuscript/EPAWTFT.tex b/Manuscript/EPAWTFT.tex index 0fd3bf0..5d7d394 100644 --- a/Manuscript/EPAWTFT.tex +++ b/Manuscript/EPAWTFT.tex @@ -1871,8 +1871,9 @@ worth highlighting. In Cremer and He's original classification, ``class A'' systems exhibit monotonic convergence and generally correspond to weakly correlated electron pairs, while ``class B'' systems show erratic convergence after initial oscillations and generally contain spatially dense electron clusters.\cite{Cremer_1996} -Further insights were provided by Olsen and coworkers\cite{Christiansen_1996,Olsen_1996,Olsen_2000,Olsen_2019} -who employed a two-state model to understand the various convergence behaviours of Hermitian and non-Hermitian perturbation series. +Further insights were provided by Olsen and coworkers +who employed a two-state model to understand the various convergence behaviours of Hermitian and non-Hermitian +perturbation series.\cite{Christiansen_1996,Olsen_1996,Olsen_2000,Olsen_2019} The careful analysis from Sergeev and Goodson later refined these classes depending on the position of the singularity closest to the origin, giving $\alpha$ singularities which have large imaginary component, and $\beta$ singularities which have a very small imaginary component.% @@ -1893,7 +1894,8 @@ systematically improvable series can dramatically improve the accuracy and appli \hugh{However, the application of these approaches requires the evaluation of higher-order MP coefficents (\eg, MP3, MP4, MP5, etc) that are generally expensive to compute in practice. There is therefore a strong demand for computationally efficient approaches to evaluate general terms in the MP -series, and the development of stochastic, resolution-of-the-identity, or linear-scaling approximations +series, and the development of stochastic,\cite{Thom_2007,Neuhauser_2012,Willow_2012,Takeshita_2017,Li_2019} +or linear-scaling approximations\cite{Rauhut_1998,Schutz_1999} may prove fruitful avenues in this direction. } @@ -1902,14 +1904,14 @@ may prove fruitful avenues in this direction. The present review has only considered the convergence of the MP series using the RHF or UHF reference orbitals. However, numerous recent studies have shown that the use of orbitals optimised in the presence of the MP2 -correction or using Kohn--Sham density-functional theory (DFT) orbitals -can significantly improve the accuracy of the MP3 correction, +correction\cite{Bozkaya_2011,Neese_2009,Lee_2018} or Kohn--Sham density-functional theory (DFT) orbitals +can significantly improve the accuracy of the MP3 correction,\cite{Bertels_2019,Rettig_2020} particularly in the presence of symmetry-breaking. Beyond intuitive heuristics, it is not clear why these alternative orbitals provide such accurate results, and a detailed investigation of their MP energy function in the complex plane is therefore bound to provide fascinating insights. Furthermore, the convergence properties of the excited-state MP series using orbital-optimised higher energy -HF solutions remains entirely unexplored. +HF solutions\cite{Gilbert_2008} remains entirely unexplored.\cite{Lee_2019,CarterFenk_2020} } % HUBBARD