one more ref to Hirata
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\begin{thebibliography}{174}%
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\begin{thebibliography}{175}%
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\makeatletter
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\providecommand \@ifxundefined [1]{%
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\@ifx{#1\undefined}
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@ -1546,6 +1546,17 @@
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}\href {\doibase 10.1063/1.4926327} {\bibfield {journal} {\bibinfo
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{journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {143}},\ \bibinfo
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{pages} {024108} (\bibinfo {year} {2015})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Hirata}\ \emph {et~al.}(2015)\citenamefont {Hirata},
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\citenamefont {Hermes}, \citenamefont {Simons},\ and\ \citenamefont
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{Ortiz}}]{Hirata_2015}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {S.}~\bibnamefont
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{Hirata}}, \bibinfo {author} {\bibfnamefont {M.~R.}\ \bibnamefont {Hermes}},
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\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Simons}}, \ and\ \bibinfo
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{author} {\bibfnamefont {J.~V.}\ \bibnamefont {Ortiz}},\ }\href {\doibase
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10.1021/acs.jctc.5b00005} {\bibfield {journal} {\bibinfo {journal} {J.
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Chem. Theory Comput.}\ }\textbf {\bibinfo {volume} {11}},\ \bibinfo {pages}
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{1595} (\bibinfo {year} {2015})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Tarantino}\ \emph {et~al.}(2017)\citenamefont
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{Tarantino}, \citenamefont {Romaniello}, \citenamefont {Berger},\ and\
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\citenamefont {Reining}}]{Tarantino_2017}%
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@ -1,136 +1,175 @@
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%% This BibTeX bibliography file was created using BibDesk.
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%% http://bibdesk.sourceforge.net/
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%% Created for Pierre-Francois Loos at 2020-12-04 09:51:06 +0100
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%% Created for Pierre-Francois Loos at 2020-12-04 17:07:40 +0100
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@article{Hirata_2017,
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author = {Hirata, So and Doran, Alexander E. and Knowles, Peter J. and Ortiz, J. V.},
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date-added = {2020-12-04 17:07:30 +0100},
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date-modified = {2020-12-04 17:07:40 +0100},
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doi = {10.1063/1.4994837},
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journal = {J. Chem. Phys.},
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pages = {044108},
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title = {One-Particle Many-Body {{Green}}'s Function Theory: {{Algebraic}} Recursive Definitions, Linked-Diagram Theorem, Irreducible-Diagram Theorem, and General-Order Algorithms},
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volume = {147},
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year = {2017},
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Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4994837}}
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@article{Hirata_2015,
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author = {Hirata, So and Hermes, Matthew R. and Simons, Jack and Ortiz, J. V.},
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date-added = {2020-12-04 17:07:12 +0100},
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date-modified = {2020-12-04 17:07:20 +0100},
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doi = {10.1021/acs.jctc.5b00005},
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journal = {J. Chem. Theory Comput.},
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language = {en},
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pages = {1595--1606},
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title = {General-{{Order Many}}-{{Body Green}}'s {{Function Method}}},
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volume = {11},
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year = {2015},
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Bdsk-Url-1 = {https://dx.doi.org/10.1021/acs.jctc.5b00005}}
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@article{Rauhut_1998,
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author ={G. Rauhut, P. Pulay and Hans-Joachim Werner},
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journal={J. Comp. Chem.},
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year ={1998},
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volume ={19},
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pages ={1241},
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title ={Integral transformation with low‐order scaling for large local second‐order {M\oller--Plesset} calculations},
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doi ={10.1002/(SICI)1096-987X(199808)19:11<1241::AID-JCC4>3.0.CO;2-K},
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}
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@article{Schutz_1999,
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author ={M. Sch{\"u}tz and G. Hetzer and Hans-Joachim Werner},
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journal={J. Chem. Phys.},
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year ={1999},
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volume ={111},
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pages ={5691},
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title ={Low-order scaling local electron correlation methods. I. Linear scaling local MP2},
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doi ={10.1063/1.479957}
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}
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@article{Takeshita_2017,
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author ={T. Y. Takeshita and W. A. {de Jong} and D. Neuhauser and R. Baer and E. Rabani},
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journal={J. Chem. Theory Comput.},
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year ={2017},
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volume ={13},
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pages ={4605},
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title ={Stochastic Formulation of the Resolution of Identity: Application to Second Order {M\oller--Plesset} Perturbation Theory},
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doi ={10.1021/acs.jctc.7b00343},
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}
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@article{Li_2019,
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author ={Zhendong Li},
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journal={J. Chem. Phys.},
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year ={2019},
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volume ={151},
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pages ={244114},
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title ={Stochastic many-body perturbation theory for electron correlation energies},
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doi ={10.1063/1.5128719},
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}
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@article{Thom_2007,
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author ={A. J. W. Thom and A. Alavi},
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journal={Phys. Rev. Lett.},
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year ={2007},
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pages ={143001},
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volume ={99},
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title ={Stochastic Perturbation Theory: A Low-Scaling Approach to Correlated Electronic Energies},
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doi ={10.1103/PhysRevLett.99.143001},
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}
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@article{Willow_2012,
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author ={S. Y. Willow and K. S. Kim and S. Hirata},
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journal={J. Chem. Phys.},
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year ={2012},
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volume ={137},
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pages ={204122},
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title ={Stochastic evaluation of second-order many-body perturbation energies},
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doi ={10.1063/1.4768697},
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}
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@article{Neuhauser_2012,
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author ={D. Neuhauser and E. Rabani and R. Baer},
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journal={J. Chem. Theory Comput.},
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year ={2012},
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pages ={24},
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volume ={9},
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title ={Expeditious Stochastic Approach for MP2 Energies in Large Electronic Systems},
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doi ={10.1021/ct.300946j},
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}
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@article{Lee_2018,
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author ={J. Lee and M. Head-Gordon},
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journal={J. Chem. Theory Comput.},
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year ={2018},
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author = {G. Rauhut, P. Pulay and Hans-Joachim Werner},
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doi = {10.1002/(SICI)1096-987X(199808)19:11<1241::AID-JCC4>3.0.CO;2-K},
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journal = {J. Comp. Chem.},
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pages = {1241},
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title = {Integral transformation with low‐order scaling for large local second‐order {M\oller--Plesset} calculations},
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volume = {19},
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year = {1998},
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Bdsk-Url-1 = {https://doi.org/10.1002/(SICI)1096-987X(199808)19:11%3C1241::AID-JCC4%3E3.0.CO;2-K}}
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@article{Schutz_1999,
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author = {M. Sch{\"u}tz and G. Hetzer and Hans-Joachim Werner},
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doi = {10.1063/1.479957},
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journal = {J. Chem. Phys.},
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pages = {5691},
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title = {Low-order scaling local electron correlation methods. I. Linear scaling local MP2},
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volume = {111},
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year = {1999},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.479957}}
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@article{Takeshita_2017,
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author = {T. Y. Takeshita and W. A. {de Jong} and D. Neuhauser and R. Baer and E. Rabani},
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doi = {10.1021/acs.jctc.7b00343},
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journal = {J. Chem. Theory Comput.},
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pages = {4605},
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title = {Stochastic Formulation of the Resolution of Identity: Application to Second Order {M\oller--Plesset} Perturbation Theory},
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volume = {13},
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year = {2017},
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Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.7b00343}}
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@article{Li_2019,
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author = {Zhendong Li},
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doi = {10.1063/1.5128719},
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journal = {J. Chem. Phys.},
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pages = {244114},
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title = {Stochastic many-body perturbation theory for electron correlation energies},
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volume = {151},
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year = {2019},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.5128719}}
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@article{Thom_2007,
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author = {A. J. W. Thom and A. Alavi},
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doi = {10.1103/PhysRevLett.99.143001},
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journal = {Phys. Rev. Lett.},
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pages = {143001},
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title = {Stochastic Perturbation Theory: A Low-Scaling Approach to Correlated Electronic Energies},
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volume = {99},
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year = {2007},
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Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.99.143001}}
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@article{Willow_2012,
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author = {S. Y. Willow and K. S. Kim and S. Hirata},
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doi = {10.1063/1.4768697},
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journal = {J. Chem. Phys.},
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pages = {204122},
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title = {Stochastic evaluation of second-order many-body perturbation energies},
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volume = {137},
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year = {2012},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.4768697}}
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@article{Neuhauser_2012,
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author = {D. Neuhauser and E. Rabani and R. Baer},
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doi = {10.1021/ct.300946j},
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journal = {J. Chem. Theory Comput.},
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pages = {24},
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title = {Expeditious Stochastic Approach for MP2 Energies in Large Electronic Systems},
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volume = {9},
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year = {2012},
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Bdsk-Url-1 = {https://doi.org/10.1021/ct.300946j}}
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@article{Lee_2018,
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author = {J. Lee and M. Head-Gordon},
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doi = {10.1021/acs.jctc.8b00731},
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journal = {J. Chem. Theory Comput.},
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pages = {5203},
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title = {Regularized Orbital-Optimized Second-Order M{\o}ller--Plesset Perturbation Theory: A Reliable Fifth-Order-Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers},
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year = {2018},
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Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00731}}
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pages ={5203},
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title ={Regularized Orbital-Optimized Second-Order Møller–Plesset Perturbation Theory: A Reliable Fifth-Order-Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers},
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doi ={10.1021/acs.jctc.8b00731},
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}
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@article{Bertels_2019,
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author ={L. W. Bertels and J. Lee and M. Head-Gordon},
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journal={J. Phys. Chem. Lett.},
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year ={2019},
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volume ={10},
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pages ={4170},
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title ={Third-Order {M\oller–Plesset} Perturbation Theory Made Useful? Choice of Orbitals and Scaling Greatly Improves Accuracy for Thermochemistry, Kinetics, and Intermolecular Interactions},
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doi ={10.1021/acs.jpclett.9b01641},
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}
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author = {L. W. Bertels and J. Lee and M. Head-Gordon},
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doi = {10.1021/acs.jpclett.9b01641},
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journal = {J. Phys. Chem. Lett.},
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pages = {4170},
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title = {Third-Order {M\oller--Plesset} Perturbation Theory Made Useful? Choice of Orbitals and Scaling Greatly Improves Accuracy for Thermochemistry, Kinetics, and Intermolecular Interactions},
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volume = {10},
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year = {2019},
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Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.9b01641}}
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@article{CarterFenk_2020,
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author ={K. Carter-Fenk and J. M. Herbert},
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journal={J. Chem. Teory Comput.},
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year ={2020},
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volume ={16},
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pages ={5067},
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title ={State-Targeted Energy Projection: A Simple and Robust Approach to Orbital Relaxation of Non-Aufbau Self-Consistent Field Solutions},
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doi ={10.1021/acs.jctc.0c00502},
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}
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author = {K. Carter-Fenk and J. M. Herbert},
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doi = {10.1021/acs.jctc.0c00502},
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journal = {J. Chem. Teory Comput.},
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pages = {5067},
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title = {State-Targeted Energy Projection: A Simple and Robust Approach to Orbital Relaxation of Non-Aufbau Self-Consistent Field Solutions},
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volume = {16},
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year = {2020},
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Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.0c00502}}
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@article{Rettig_2020,
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author ={A. Rettig and D. Hait and L. W. Bertels and M. Head-Gordon},
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journal={J. Chem. Teory Comput.},
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year ={2020},
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title ={Third-Order {M\oller--Plesset} Theory Made More Useful? The Role of Density Functional Theory Orbitals},
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doi ={10.1021/acs.jctc.0c00986},
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}
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author = {A. Rettig and D. Hait and L. W. Bertels and M. Head-Gordon},
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doi = {10.1021/acs.jctc.0c00986},
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journal = {J. Chem. Teory Comput.},
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title = {Third-Order {M\oller--Plesset} Theory Made More Useful? The Role of Density Functional Theory Orbitals},
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year = {2020},
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Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.0c00986}}
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@article{Neese_2009,
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author ={F. Neese and T. Schwabe and S. Kossmann and B. Schirmer and S. Grimme},
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journal={J. Chem. Teory Comput.},
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volume ={5},
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pages ={3060},
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title ={Assessment of Orbital-Optimized, Spin-Component Scaled Second-Order Many-Body Perturbation Theory for Thermochemistry and Kinetics},
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year ={2009},
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doi ={10.1021/ct9003299}
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}
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author = {F. Neese and T. Schwabe and S. Kossmann and B. Schirmer and S. Grimme},
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doi = {10.1021/ct9003299},
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journal = {J. Chem. Teory Comput.},
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pages = {3060},
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title = {Assessment of Orbital-Optimized, Spin-Component Scaled Second-Order Many-Body Perturbation Theory for Thermochemistry and Kinetics},
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volume = {5},
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year = {2009},
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Bdsk-Url-1 = {https://doi.org/10.1021/ct9003299}}
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@article{Bozkaya_2011,
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author ={U. Bozkaya},
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journal={J. Chem. Phys.},
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volume ={135},
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pages ={224103},
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title ={Orbital-optimized third-order {M\oller--Plesset} perturbation theory and its spin-component and spin-opposite scaled variants: Application to symmetry breaking problems},
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year ={2011},
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doi ={10.1063/1.3665134},
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}
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author = {U. Bozkaya},
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doi = {10.1063/1.3665134},
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journal = {J. Chem. Phys.},
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pages = {224103},
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title = {Orbital-optimized third-order {M\oller--Plesset} perturbation theory and its spin-component and spin-opposite scaled variants: Application to symmetry breaking problems},
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volume = {135},
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year = {2011},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.3665134}}
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@article{Lee_2019,
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author ={Joonho Lee and David W. Small and Martin Head-Gordon},
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journal={J. Chem. Phys.},
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pages ={214103},
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title ={Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states},
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volume ={151},
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year ={2019},
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doi ={10.1063/1.5128795}
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}
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author = {Joonho Lee and David W. Small and Martin Head-Gordon},
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doi = {10.1063/1.5128795},
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journal = {J. Chem. Phys.},
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pages = {214103},
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title = {Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states},
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volume = {151},
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year = {2019},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.5128795}}
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@article{Shepherd_2016,
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author = {Shepherd,James J. and Henderson,Thomas M. and Scuseria,Gustavo E.},
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date-added = {2020-12-04 09:50:38 +0100},
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@ -1912,7 +1912,7 @@ on the symmetric (or asymmetric in one occasion) Hubbard dimer at half-filling.
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Although extremely simple, these illustrations highlight the incredible versatility of the Hubbard model
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for understanding the subtle features of perturbation theory in the complex plane, alongisde other examples
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such as Kohn-Sham DFT, \cite{Carrascal_2015,Cohen_2016} linear-response theory,\cite{Carrascal_2018}
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many-body perturbation theory,\cite{Romaniello_2009,Romaniello_2012,DiSabatino_2015,Tarantino_2017,Olevano_2019}
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many-body perturbation theory,\cite{Romaniello_2009,Romaniello_2012,DiSabatino_2015,Hirata_2015,Tarantino_2017,Olevano_2019}
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ensemble DFT, \cite{Deur_2017,Deur_2018,Senjean_2018,Sagredo_2018,Fromager_2020} thermal DFT,\cite{Smith_2016,Smith_2018}
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coupled cluster theory,\cite{Stein_2014,Henderson_2015,Shepherd_2016} and many more.
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In particular, we have shown that the Hubbard dimer contains sufficient flexibility to describe
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