Theory
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%% Created for Pierre-Francois Loos at 2019-05-25 17:51:22 +0200
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%% Created for Pierre-Francois Loos at 2019-05-28 13:36:42 +0200
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@article{BarDelPerMat-JMS-97,
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||||
Author = {Rodney J. Bartlett and Janet E. Del Bene and S.Ajith Perera and Renee-Peloquin Mattie},
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Date-Added = {2019-05-28 13:34:13 +0200},
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Date-Modified = {2019-05-28 13:35:03 +0200},
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Doi = {https://doi.org/10.1016/S0166-1280(97)90277-3},
|
||||
Issn = {0166-1280},
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||||
Journal = {J. Mol. Struct. (THEOCHEM)},
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||||
Keywords = {Ammonia, Spectra, Heat of formation, Properties, Correlation effects},
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||||
Pages = {157--168},
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||||
Title = {Ammonia: The Prototypical Lone Pair Molecule},
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||||
Url = {http://www.sciencedirect.com/science/article/pii/S0166128097902773},
|
||||
Volume = {400},
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||||
Year = {1997},
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||||
Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0166128097902773},
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||||
Bdsk-Url-2 = {https://doi.org/10.1016/S0166-1280(97)90277-3}}
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||||
|
||||
@article{SchGoe-JCTC-17,
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||||
Author = {Schwabe, Tobias and Goerigk, Lars},
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||||
Date-Added = {2019-05-28 13:33:10 +0200},
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||||
Date-Modified = {2019-05-28 13:33:22 +0200},
|
||||
Doi = {10.1021/acs.jctc.7b00386},
|
||||
Eprint = {https://doi.org/10.1021/acs.jctc.7b00386},
|
||||
Journal = {J. Chem. Theory Comput.},
|
||||
Number = {9},
|
||||
Pages = {4307--4323},
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||||
Title = {Time-Dependent Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling},
|
||||
Url = {https://doi.org/10.1021/acs.jctc.7b00386},
|
||||
Volume = {13},
|
||||
Year = {2017},
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||||
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.7b00386}}
|
||||
|
||||
@article{RubSerMer-JCP-08,
|
||||
Author = {Mercedes Rubio and Luis Serrano-Andr{\'e}s and Manuela Merch{\'a}n},
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||||
Date-Added = {2019-05-28 12:21:04 +0200},
|
||||
Date-Modified = {2019-05-28 12:21:20 +0200},
|
||||
Doi = {10.1063/1.2837827},
|
||||
Eprint = {https://doi.org/10.1063/1.2837827},
|
||||
Journal = {J. Chem. Phys.},
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||||
Number = {10},
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||||
Pages = {104305},
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||||
Title = {Excited States of the Water Molecule: Analysis of the Valence and Rydberg Character},
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||||
Url = {https://doi.org/10.1063/1.2837827},
|
||||
Volume = {128},
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||||
Year = {2008},
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||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.2837827}}
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||||
|
||||
@article{LiPal-JCP-11,
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||||
Author = {Xiangzhu Li and Josef Paldus},
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||||
Date-Added = {2019-05-28 12:20:10 +0200},
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||||
Date-Modified = {2019-05-28 12:20:19 +0200},
|
||||
Doi = {10.1063/1.3595513},
|
||||
Eprint = {https://doi.org/10.1063/1.3595513},
|
||||
Journal = {J. Chem. Phys.},
|
||||
Number = {21},
|
||||
Pages = {214118},
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||||
Title = {Multi-Reference State-Universal Coupled-Cluster Approaches to Electronically Excited States},
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||||
Url = {https://doi.org/10.1063/1.3595513},
|
||||
Volume = {134},
|
||||
Year = {2011},
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||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.3595513}}
|
||||
|
||||
@article{CaiTozRei-JCP-00,
|
||||
Author = {Zheng-Li Cai and David J. Tozer and Jeffrey R. Reimers},
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||||
Date-Added = {2019-05-28 12:19:14 +0200},
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||||
Date-Modified = {2019-05-28 12:19:44 +0200},
|
||||
Doi = {10.1063/1.1312826},
|
||||
Eprint = {https://doi.org/10.1063/1.1312826},
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||||
Journal = {J. Chem. Phys.},
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||||
Number = {17},
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||||
Pages = {7084--7096},
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||||
Title = {Time-Dependent Density-Functional Determination of Arbitrary Singlet and Triplet Excited-State Potential Energy Surfaces: Application to the Water Molecule},
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||||
Url = {https://doi.org/10.1063/1.1312826},
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||||
Volume = {113},
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||||
Year = {2000},
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||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.1312826}}
|
||||
|
||||
@article{PurZhaKra-JCP-09,
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||||
Author = {Purwanto, Wirawan and Zhang, Shiwei and Krakauer, Henry},
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||||
Date-Added = {2019-05-28 12:00:39 +0200},
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||||
Date-Modified = {2019-05-28 12:00:56 +0200},
|
||||
Doi = {10.1063/1.3077920},
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||||
File = {/Users/loos/Zotero/storage/JDM6C32K/Purwanto et al. - 2009 - Excited state calculations using phaseless auxilia.pdf},
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||||
Issn = {0021-9606, 1089-7690},
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||||
Journal = {J. Chem. Phys.},
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||||
Language = {en},
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||||
Month = mar,
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||||
Number = {9},
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||||
Pages = {094107},
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||||
Shorttitle = {Excited State Calculations Using Phaseless Auxiliary-Field Quantum {{Monte Carlo}}},
|
||||
Title = {Excited State Calculations Using Phaseless Auxiliary-Field Quantum {{Monte Carlo}}: {{Potential}} Energy Curves of Low-Lying {{C2}} Singlet States},
|
||||
Volume = {130},
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||||
Year = {2009},
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||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.3077920}}
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|
||||
@article{Var-JCP-08,
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||||
Author = {Varandas, A. J. C.},
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Date-Added = {2019-05-28 11:58:55 +0200},
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Date-Modified = {2019-05-28 11:59:09 +0200},
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||||
Doi = {10.1063/1.3036115},
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||||
Issn = {0021-9606, 1089-7690},
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||||
Journal = {J. Chem. Phys.},
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||||
Language = {en},
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||||
Month = dec,
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||||
Number = {23},
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||||
Pages = {234103},
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||||
Shorttitle = {Extrapolation to the Complete-Basis-Set Limit and the Implications of Avoided Crossings},
|
||||
Title = {Extrapolation to the Complete-Basis-Set Limit and the Implications of Avoided Crossings: {{The X $\Sigma$1g}}+, {{B $\Delta$1g}}, and {{B}}${'}$ {{$\Sigma$1g}}+ States of {{C2}}},
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Volume = {129},
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||||
Year = {2008},
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||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.3036115}}
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||||
|
||||
@article{VarRoc-PTRSMPES-18,
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||||
Author = {Varandas, A. J. C. and Rocha, C. M. R.},
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||||
Date-Added = {2019-05-28 11:58:55 +0200},
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||||
Date-Modified = {2019-05-28 11:59:35 +0200},
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||||
Doi = {10.1098/rsta.2017.0145},
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||||
File = {/Users/loos/Zotero/storage/VP3T2AAG/Varandas and Rocha - 2018 - iCi sub ini sub ( ini =2−4) c.pdf},
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||||
Issn = {1364-503X, 1471-2962},
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||||
Journal = {Philos. Trans. R. Soc. Math. Phys. Eng. Sci.},
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||||
Language = {en},
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||||
Month = mar,
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||||
Number = {2115},
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||||
Pages = {20170145},
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||||
Shorttitle = {{\emph{C}} {\textsubscript{ {\emph{n}} }} ( {\emph{n}} =2-4)},
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||||
Title = {{\emph{C}} {\textsubscript{ {\emph{n}} }} ( {\emph{n}} =2-4): Current Status},
|
||||
Volume = {376},
|
||||
Year = {2018},
|
||||
Bdsk-Url-1 = {https://doi.org/10.1098/rsta.2017.0145}}
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||||
|
||||
@article{SokCha-JCP-16,
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||||
Author = {Sokolov, Alexander Yu. and Chan, Garnet Kin-Lic},
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||||
Date-Added = {2019-05-28 11:57:29 +0200},
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||||
Date-Modified = {2019-05-28 11:58:02 +0200},
|
||||
Doi = {10.1063/1.4941606},
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||||
Issn = {0021-9606, 1089-7690},
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||||
Journal = {J. Chem. Phys.},
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||||
Language = {en},
|
||||
Month = feb,
|
||||
Number = {6},
|
||||
Pages = {064102},
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||||
Title = {A Time-Dependent Formulation of Multi-Reference Perturbation Theory},
|
||||
Volume = {144},
|
||||
Year = {2016},
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||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.4941606}}
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||||
|
||||
@article{Sha-JCP-15,
|
||||
Author = {Sharma, Sandeep},
|
||||
Date-Added = {2019-05-28 11:56:29 +0200},
|
||||
Date-Modified = {2019-05-28 11:56:44 +0200},
|
||||
Doi = {10.1063/1.4905237},
|
||||
Issn = {0021-9606, 1089-7690},
|
||||
Journal = {J. Chem. Phys.},
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||||
Language = {en},
|
||||
Month = jan,
|
||||
Number = {2},
|
||||
Pages = {024107},
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||||
Title = {A General Non-{{Abelian}} Density Matrix Renormalization Group Algorithm with Application to the {{C}} {\textsubscript{2}} Dimer},
|
||||
Volume = {142},
|
||||
Year = {2015},
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||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.4905237}}
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||||
|
||||
@article{AbrShe-JCP-04,
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||||
Author = {Abrams, Micah L. and Sherrill, C. David},
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||||
Date-Added = {2019-05-28 11:54:44 +0200},
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||||
Date-Modified = {2019-05-28 11:55:26 +0200},
|
||||
Doi = {10.1063/1.1804498},
|
||||
Issn = {0021-9606, 1089-7690},
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||||
Journal = {J. Chem. Phys.},
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||||
Language = {en},
|
||||
Month = nov,
|
||||
Number = {19},
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||||
Pages = {9211-9219},
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||||
Shorttitle = {Full Configuration Interaction Potential Energy Curves for the {{X 1$\Sigma$g}}+, {{B 1$\Delta$g}}, and {{B}}${'}$ {{1$\Sigma$g}}+ States of {{C2}}},
|
||||
Title = {Full Configuration Interaction Potential Energy Curves for the {{X 1$\Sigma_g^+$}}, {{B 1$\Delta_g$}}, and {{B}}${'}$ {{1$\Sigma_g^+$}} States of {{C$_2$}}: {{A}} Challenge for Approximate Methods},
|
||||
Volume = {121},
|
||||
Year = {2004},
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||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.1804498}}
|
||||
|
||||
@article{AbrShe-CPL-05,
|
||||
Author = {Abrams, Micah L. and Sherrill, C. David},
|
||||
Date-Added = {2019-05-28 11:54:44 +0200},
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Date-Modified = {2019-05-28 11:55:38 +0200},
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||||
Doi = {10.1016/j.cplett.2005.06.107},
|
||||
Issn = {0009-2614},
|
||||
Journal = {Chem. Phys. Lett.},
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||||
Month = {Aug},
|
||||
Number = {1-3},
|
||||
Pages = {121--124},
|
||||
Publisher = {Elsevier BV},
|
||||
Title = {Important configurations in configuration interaction and coupled-cluster wave functions},
|
||||
Url = {http://dx.doi.org/10.1016/j.cplett.2005.06.107},
|
||||
Volume = {412},
|
||||
Year = {2005},
|
||||
Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.cplett.2005.06.107}}
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||||
@article{AngCimPas-MP-12,
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||||
Author = {Angeli, Celestino and Cimiraglia, Renzo and Pastore, Mariachiara},
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Date-Added = {2019-05-28 11:53:10 +0200},
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Date-Modified = {2019-05-28 11:53:28 +0200},
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Doi = {10.1080/00268976.2012.689872},
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||||
Journal = {Mol. Phys.},
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||||
Language = {en},
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||||
Month = dec,
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||||
Number = {23},
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||||
Pages = {2963-2968},
|
||||
Shorttitle = {A Comparison of Various Approaches in Internally Contracted Multireference Configuration Interaction},
|
||||
Title = {A Comparison of Various Approaches in Internally Contracted Multireference Configuration Interaction: The Carbon Dimer as a Test Case},
|
||||
Volume = {110},
|
||||
Year = {2012},
|
||||
Bdsk-Url-1 = {https://doi.org/10.1080/00268976.2012.689872}}
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||||
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||||
@article{SchSilSauThi-JCP-08,
|
||||
Author = {Schreiber, M. and Silva-Junior, M. R. and Sauer, S. P. A. and Thiel, W.},
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||||
Date-Added = {2019-05-28 11:41:37 +0200},
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Date-Modified = {2019-05-28 11:42:24 +0200},
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Doi = {10.1063/1.2889385},
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||||
Journal = {J. Chem. Phys.},
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||||
Pages = {134110},
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||||
Title = {Benchmarks for Electronically Excited States: CASPT2, CC2, CCSD and CC3},
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||||
Volume = 128,
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||||
Year = 2008,
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||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.2889385}}
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@article{SilSauSchThi-MP-10,
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||||
Author = {Silva-Junior, M. R. and Sauer, S. P. A. and Schreiber, M. and Thiel, W.},
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Date-Added = {2019-05-28 11:41:37 +0200},
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Date-Modified = {2019-05-28 11:42:05 +0200},
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Doi = {10.1080/00268970903549047},
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||||
Journal = {Mol. Phys.},
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||||
Pages = {453--465},
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||||
Title = {Basis Set Effects on Coupled Cluster Benchmarks of Electronically Excited States: CC3, CCSDR(3) and CC2},
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||||
Volume = 108,
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||||
Year = 2010,
|
||||
Bdsk-Url-1 = {https://doi.org/10.1080/00268970903549047}}
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||||
|
||||
@article{SilSchSauThi-JCP-10,
|
||||
Author = {Silva-Junior, M. R. and Schreiber, M. and Sauer, S. P. A. and Thiel, W.},
|
||||
Date-Added = {2019-05-28 11:41:37 +0200},
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Date-Modified = {2019-05-28 11:42:45 +0200},
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Journal = {J. Chem. Phys.},
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||||
Pages = {174318},
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||||
Title = {Benchmarks of Electronically Excited States: Basis Set Effecs Benchmarks of Electronically Excited States: Basis Set Effects on CASPT2 Results},
|
||||
Volume = 133,
|
||||
Year = 2010,
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||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.3499598}}
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||||
@article{Ang-JCC-08,
|
||||
Author = {C. Angeli},
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||||
Date-Added = {2019-05-28 11:37:39 +0200},
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Date-Modified = {2019-05-28 11:39:34 +0200},
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Doi = {10.1002/jcc.21155},
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||||
Journal = {J. Comput. Chem.},
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||||
Pages = {1319--1333},
|
||||
Title = {On the Nature of the $\pi \rightarrow \pi^*$ Ionic Excited States: The V State of Ethene as a Prototype},
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||||
Volume = {30},
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||||
Year = {2008},
|
||||
Bdsk-Url-1 = {https://doi.org/10.1002/jcc.21155}}
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||||
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||||
@article{Ang-IJQC-10,
|
||||
Author = {Angeli, Celestino},
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||||
Date-Added = {2019-05-28 11:37:39 +0200},
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Date-Modified = {2019-05-28 11:38:19 +0200},
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Doi = {10.1002/qua.22597},
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Issn = {00207608, 1097461X},
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||||
Journal = {Int. J. Quantum Chem.},
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||||
Language = {en},
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||||
Pages = {2436-2447},
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||||
Title = {An Analysis of the Dynamic $\sigma$ Polarization in the {{V}} State of Ethene},
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||||
Year = {2010},
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||||
Bdsk-Url-1 = {https://doi.org/10.1002/qua.22597}}
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||||
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||||
@article{DadSmaBooAlaFil-JCTC-12,
|
||||
Author = {Daday, Csaba and Smart, Simon and Booth, George H. and Alavi, Ali and Filippi, Claudia},
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||||
Date-Added = {2019-05-28 11:37:39 +0200},
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Date-Modified = {2019-05-28 11:39:00 +0200},
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||||
Doi = {10.1021/ct300486d},
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||||
File = {/Users/loos/Zotero/storage/APCJKTM8/Daday et al. - 2012 - Full Configuration Interaction Excitations of Ethe.pdf},
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Issn = {1549-9618, 1549-9626},
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||||
Journal = {J. Chem. Theory. Comput.},
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||||
Language = {en},
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Month = nov,
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||||
Number = {11},
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||||
Pages = {4441-4451},
|
||||
Shorttitle = {Full {{Configuration Interaction Excitations}} of {{Ethene}} and {{Butadiene}}},
|
||||
Title = {Full {{Configuration Interaction Excitations}} of {{Ethene}} and {{Butadiene}}: {{Resolution}} of an {{Ancient Question}}},
|
||||
Volume = {8},
|
||||
Year = {2012},
|
||||
Bdsk-Url-1 = {https://doi.org/10.1021/ct300486d}}
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||||
@article{SerMarNebLinRoo-JCP-93,
|
||||
Author = {{Serrano-Andr\'es}, Luis and Merch\'an, Manuela and Nebot-Gil, Ignacio and Lindh, Roland and Roos, Bj\"orn O.},
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Date-Added = {2019-05-28 11:37:39 +0200},
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Doi = {10.1063/1.465071},
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Issn = {0021-9606, 1089-7690},
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Journal = {J. Chem. Phys.},
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||||
Language = {en},
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||||
Month = feb,
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Number = {4},
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||||
Pages = {3151-3162},
|
||||
Shorttitle = {Towards an Accurate Molecular Orbital Theory for Excited States},
|
||||
Title = {Towards an Accurate Molecular Orbital Theory for Excited States: {{Ethene}}, Butadiene, and Hexatriene},
|
||||
Volume = {98},
|
||||
Year = {1993},
|
||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.465071}}
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@article{WibOliTru-JPCA-02,
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||||
Author = {Wiberg, K. B. and de Oliveria, A. E. and Trucks, G.},
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Date-Added = {2019-05-28 11:37:39 +0200},
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Date-Modified = {2019-05-28 11:38:07 +0200},
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Doi = {10.1021/jp014123x},
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Journal = {J. Phys. Chem. A},
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||||
Pages = {4192--4199},
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||||
Title = {A Comparison of the Electronic Transition Energies for Ethene, Isobutene, Formaldehyde, and Acetone Calculated Using RPA, TDDFT, and EOM-CCSD. Effect of Basis Sets},
|
||||
Volume = {106},
|
||||
Year = 2002,
|
||||
Bdsk-Url-1 = {https://doi.org/10.1021/jp014123x}}
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@article{BarPaiLis-JCP-04,
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||||
Author = {M. Barbatti and J. Paier and H. Lischka},
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Date-Added = {2019-05-28 11:32:07 +0200},
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Date-Modified = {2019-05-28 11:36:03 +0200},
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Doi = {10.1063/1.1807378},
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Journal = {J. Chem. Phys.},
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Pages = {11614},
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Title = {Photochemistry Of Ethylene: A Multireference Configuration Interaction Investigation Of The Excited-State Energy Surfaces},
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Volume = {121},
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Year = {20004},
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||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.1807378}}
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@article{ChiHolAdaOttUmrShaZim-JPCA-18,
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Author = {Chien, Alan D. and Holmes, Adam A. and Otten, Matthew and Umrigar, C. J. and Sharma, Sandeep and Zimmerman, Paul M.},
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Date-Added = {2019-05-28 11:32:07 +0200},
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Date-Modified = {2019-05-28 11:33:45 +0200},
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Doi = {10.1021/acs.jpca.8b01554},
|
||||
File = {/Users/loos/Zotero/storage/J96RZ7JP/Chien et al. - 2018 - Excited States of Methylene, Polyenes, and Ozone f.pdf},
|
||||
Issn = {1089-5639, 1520-5215},
|
||||
Journal = {J. Phys. Chem. A},
|
||||
Language = {en},
|
||||
Month = mar,
|
||||
Number = {10},
|
||||
Pages = {2714--2722},
|
||||
Title = {Excited {{States}} of {{Methylene}}, {{Polyenes}}, and {{Ozone}} from {{Heat}}-{{Bath Configuration Interaction}}},
|
||||
Volume = {122},
|
||||
Year = {2018},
|
||||
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpca.8b01554}}
|
||||
|
||||
@article{FelPetDav-JCP-14,
|
||||
Author = {David Feller and Kirk A. Peterson and Ernest R. Davidson},
|
||||
Date-Added = {2019-05-28 11:32:07 +0200},
|
||||
Date-Modified = {2019-05-28 11:34:05 +0200},
|
||||
Doi = {10.1063/1.4894482},
|
||||
Journal = {J. Chem. Phys.},
|
||||
Number = {10},
|
||||
Pages = {104302},
|
||||
Title = {A Systematic Approach to Vertically Excited States of Ethylene Using Configuration Interaction and Coupled Cluster Techniques},
|
||||
Volume = {141},
|
||||
Year = {2014},
|
||||
Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4894482}}
|
||||
|
||||
@article{WatGwaBar-JCP-96,
|
||||
Author = {Watts, John D. and Gwaltney, Steven R. and Bartlett, Rodney J.},
|
||||
Date-Added = {2019-05-28 11:32:07 +0200},
|
||||
Date-Modified = {2019-05-28 11:34:37 +0200},
|
||||
Doi = {10.1063/1.471988},
|
||||
Issn = {0021-9606, 1089-7690},
|
||||
Journal = {J. Chem. Phys.},
|
||||
Language = {en},
|
||||
Month = oct,
|
||||
Number = {16},
|
||||
Pages = {6979-6988},
|
||||
Title = {Coupled-cluster Calculations of the Excitation Energies of Ethylene, Butadiene, and Cyclopentadiene},
|
||||
Volume = {105},
|
||||
Year = {1996},
|
||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.471988}}
|
||||
|
||||
@article{Koh-JCP-09,
|
||||
Author = {A. Kohn},
|
||||
Date-Added = {2019-05-25 17:49:32 +0200},
|
||||
@ -17,7 +395,8 @@
|
||||
Pages = {104104},
|
||||
Title = {A modified ansatz for explicitly correlated coupled-cluster wave functions that is suitable for response theory},
|
||||
Volume = {130},
|
||||
Year = {2009}}
|
||||
Year = {2009},
|
||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.3079543}}
|
||||
|
||||
@article{ShiWer-JCP-11,
|
||||
Author = {T. Shiozaki and H.-J. Werner},
|
||||
@ -64,7 +443,8 @@
|
||||
Pages = {607--630},
|
||||
Title = {Multireference explicitly correlated F12 theories},
|
||||
Volume = {111},
|
||||
Year = {2013}}
|
||||
Year = {2013},
|
||||
Bdsk-Url-1 = {https://doi.org/10.1080/00268976.2013.779393}}
|
||||
|
||||
@article{NeiHatKlo-JCP-06,
|
||||
Author = {C. Neiss and C. Hattig and W. Klopper},
|
||||
@ -75,7 +455,8 @@
|
||||
Pages = {064111},
|
||||
Title = {Extensions of r12 corrections to CC2-R12 for excited states},
|
||||
Volume = {125},
|
||||
Year = {2006}}
|
||||
Year = {2006},
|
||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.2335443%F4%8F%B0%83}}
|
||||
|
||||
@article{HanKoh-JCP-09,
|
||||
Author = {M. Hanauer and A. Kohn},
|
||||
@ -86,7 +467,8 @@
|
||||
Pages = {124118},
|
||||
Title = {Response properties with explicitly correlated coupled-cluster methods using a Slater-type correlation factor and cusp conditions},
|
||||
Volume = {131},
|
||||
Year = {2009}}
|
||||
Year = {2009},
|
||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.3238237%F4%8F%B0%83}}
|
||||
|
||||
@article{FliHatKlo-JCP-06,
|
||||
Author = {H. Fliegl and C. Hattig and W. Klopper},
|
||||
@ -97,7 +479,8 @@
|
||||
Pages = {044112},
|
||||
Title = {Coupled-cluster response theory with linear-r12 corrections: The CC2-R12 model for excitation energies},
|
||||
Volume = {124},
|
||||
Year = {2006}}
|
||||
Year = {2006},
|
||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.2161183%F4%8F%B0%83}}
|
||||
|
||||
@article{LooPraSceTouGin-JPCL-19,
|
||||
Author = {P. F. Loos and B. Pradines and A. Scemama and J. Toulouse and E. Giner},
|
||||
@ -8989,13 +9372,6 @@
|
||||
Volume = {17},
|
||||
Year = {1969}}
|
||||
|
||||
@article{PurZhaKra-JCP-09,
|
||||
Author = {W. Purwanto and S. Zhang and H. Krakauer},
|
||||
Journal = {J. Chem. Phys.},
|
||||
Pages = {094107},
|
||||
Volume = {130},
|
||||
Year = {2009}}
|
||||
|
||||
@misc{Qmc-PROG-XX,
|
||||
Note = {QMCMOL, a quantum Monte Carlo program written by R. Assaraf, F. Colonna, X. Krokidis, P. Reinhardt and coworkers.},
|
||||
Url = {http://www.lct.jussieu.fr/pagesequipe/qmcmol/qmcmol/},
|
||||
|
||||
@ -83,7 +83,9 @@
|
||||
\newcommand{\n}[2]{n_{#1}^{#2}}
|
||||
\newcommand{\Ec}{E_\text{c}}
|
||||
\newcommand{\E}[2]{E_{#1}^{#2}}
|
||||
\newcommand{\DE}[2]{\Delta E_{#1}^{#2}}
|
||||
\newcommand{\bE}[2]{\Bar{E}_{#1}^{#2}}
|
||||
\newcommand{\DbE}[2]{\Delta \Bar{E}_{#1}^{#2}}
|
||||
\newcommand{\bEc}[1]{\Bar{E}_\text{c,md}^{#1}}
|
||||
\newcommand{\e}[2]{\varepsilon_{#1}^{#2}}
|
||||
\newcommand{\be}[2]{\Bar{\varepsilon}_{#1}^{#2}}
|
||||
@ -218,6 +220,45 @@ Contrary to our recent study on atomization and correlation energies, \cite{LooP
|
||||
\label{sec:theory}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
The present basis set correction assumes that we have, in a given (finite) basis set $\Bas$, the ground-state and the $k$th excited-state energies, $\E{0}{\Bas}$ and $\E{k}{\Bas}$, their one-electron densities, $\n{k}{\Bas}$ and $\n{0}{\Bas}$, as well as their opposite-spin on-top pair densities, $\n{2,0}{\Bas}(\br{},\br{})$ and $\n{2,k}{\Bas}(\br{},\br{})$,
|
||||
Therefore, the complete basis set (CBS) energy of the ground and excited states may be approximated as
|
||||
\begin{align}
|
||||
\label{eq:ECBS}
|
||||
\E{0}{\CBS} & \approx \E{0}{\Bas} + \bE{}{\Bas}[\n{0}{\Bas}],
|
||||
&
|
||||
\E{k}{\CBS} & \approx \E{k}{\Bas} + \bE{}{\Bas}[\n{k}{\Bas}],
|
||||
\end{align}
|
||||
where
|
||||
\begin{equation}
|
||||
\label{eq:E_funcbasis}
|
||||
\bE{}{\Bas}[\n{}{}]
|
||||
= \min_{\wf{}{} \rightsquigarrow \n{}{}} \mel*{\wf{}{}}{\hT + \hWee{}}{\wf{}{}}
|
||||
- \min_{\wf{}{\Bas} \rightsquigarrow \n{}{}} \mel*{\wf{}{\Bas}}{\hT + \hWee{}}{\wf{}{\Bas}}
|
||||
\end{equation}
|
||||
is the basis-dependent complementary density functional,
|
||||
\begin{align}
|
||||
\hT & = - \frac{1}{2} \sum_{i}^{\Ne} \nabla_i^2,
|
||||
&
|
||||
\hWee{} & = \sum_{i<j}^{\Ne} r_{ij}^{-1},
|
||||
\end{align}
|
||||
are the kinetic and interelectronic repulsion operators, respectively, and $\wf{}{\Bas}$ and $\wf{}{}$ are two general $\Ne$-electron normalized wave functions belonging to the Hilbert space spanned by $\Bas$ and the complete basis set (CBS), respectively.
|
||||
The notation $\wf{}{} \rightsquigarrow \n{}{}$ states that $\wf{}{}$ yield the density $\n{}{}$.
|
||||
|
||||
Hence, the CBS excitation energy reads
|
||||
\begin{equation}
|
||||
\DE{k}{\CBS} = \E{k}{\CBS} - \E{0}{\CBS} = \DE{k}{\Bas} + \DbE{}{\Bas}[\n{0}{\Bas},\n{k}{\Bas}],
|
||||
\end{equation}
|
||||
where
|
||||
\begin{equation}
|
||||
\label{eq:DEB}
|
||||
\DE{k}{\Bas} = \E{k}{\Bas} - \E{0}{\Bas}
|
||||
\end{equation}
|
||||
is the excitation energy in $\Bas$ and
|
||||
\begin{equation}
|
||||
\label{eq:DbE}
|
||||
\DbE{}{\Bas}[\n{0}{\Bas},\n{k}{\Bas}] = \bE{}{\Bas}[\n{k}{\Bas}] - \bE{}{\Bas}[\n{0}{\Bas}]
|
||||
\end{equation}
|
||||
its basis set correction.
|
||||
|
||||
%Let us assume that we have reasonable approximations of the FCI energy and density of a $\Ne$-electron system in an incomplete basis set $\Bas$, say the CCSD(T) energy $\E{\CCSDT}{\Bas}$ and the Hartree-Fock (HF) density $\n{\HF}{\Bas}$.
|
||||
%According to Eq.~(15) of Ref.~\citenum{GinPraFerAssSavTou-JCP-18}, the exact ground-state energy $\E{}{}$ may be approximated as
|
||||
@ -333,75 +374,47 @@ Contrary to our recent study on atomization and correlation energies, \cite{LooP
|
||||
%Indeed, the two functionals coincide if $\wf{}{\Bas} = \wf{}{\rsmu{}{}}$.
|
||||
%Therefore, we approximate $\bE{}{\Bas}[\n{}{}]$ by ECMD functionals evaluated with the range-separation function $\rsmu{}{\Bas}(\br{})$.
|
||||
|
||||
%The local-density approximation (LDA) of the ECMD complementary functional is defined as
|
||||
%\begin{equation}
|
||||
% \label{eq:def_lda_tot}
|
||||
% \bE{\LDA}{\Bas}[\n{}{},\rsmu{}{\Bas}] = \int \n{}{}(\br{}) \be{\text{c,md}}{\sr,\LDA}\qty(\n{}{}(\br{}),\zeta(\br{}),\rsmu{}{\Bas}(\br{})) \dbr{},
|
||||
%\end{equation}
|
||||
%where $\zeta = (\n{\uparrow}{} - \n{\downarrow}{})/\n{}{}$ is the spin polarization and $\be{\text{c,md}}{\sr,\LDA}(\n{}{},\zeta,\rsmu{}{})$ is the ECMD short-range correlation energy per electron of the uniform electron gas (UEG) \cite{LooGil-WIRES-16} parameterized in Ref.~\citenum{PazMorGorBac-PRB-06}.
|
||||
%The short-range LDA correlation functional relies on the transferability of the physics of the UEG which is certainly valid for large $\mu$ but is known to over correlate for small $\mu$.
|
||||
%In order to correct such a defect, inspired by the recent functional proposed by some of the authors~\cite{FerGinTou-JCP-18}, we propose here a new Perdew-Burke-Ernzerhof (PBE)-based ECMD functional
|
||||
%Inspired by the recent functional proposed by some of the authors~\cite{FerGinTou-JCP-18}, we propose here a new Perdew-Burke-Ernzerhof (PBE)-based ECMD functional
|
||||
%\begin{equation}
|
||||
% \label{eq:def_pbe_tot}
|
||||
% \bE{\PBE}{\Bas}[\n{}{},\rsmu{}{\Bas}] =
|
||||
% \int \n{}{}(\br{}) \be{\text{c,md}}{\sr,\PBE}\qty(\n{}{}(\br{}),s(\br{}),\zeta(\br{}),\rsmu{}{\Bas}(\br{})) \dbr{},
|
||||
%\end{equation}
|
||||
%where \titou{$\zeta = (\n{\uparrow}{} - \n{\downarrow}{})/\n{}{}$ is the spin polarization and} $s=\abs{\nabla \n{}{}}/\n{}{4/3}$ is the reduced density gradient.
|
||||
%$\be{\text{c,md}}{\sr,\PBE}\qty(\n{}{},s,\zeta,\rsmu{}{})$ interpolates between the usual PBE correlation functional, \cite{PerBurErn-PRL-96} $\e{\text{c}}{\PBE}(\n{}{},s,\zeta)$, at $\rsmu{}{}=0$ and the exact large-$\rsmu{}{}$ behavior, \cite{TouColSav-PRA-04, GorSav-PRA-06, PazMorGorBac-PRB-06} yielding
|
||||
%\begin{subequations}
|
||||
%\begin{gather}
|
||||
% \label{eq:epsilon_cmdpbe}
|
||||
% \be{\text{c,md}}{\sr,\PBE}(\n{}{},s,\zeta,\rsmu{}{}) = \frac{\e{\text{c}}{\PBE}(\n{}{},s,\zeta)}{1 + \beta(\n{}{},s,\zeta) \rsmu{}{3} },
|
||||
% \\
|
||||
% \label{eq:beta_cmdpbe}
|
||||
% \beta(\n{}{},s,\zeta) = \frac{3}{2\sqrt{\pi} (1 - \sqrt{2} )} \frac{\e{\text{c}}{\PBE}(\n{}{},s,\zeta)}{\n{2}{\UEG}(\n{}{},\zeta)}.
|
||||
%\end{gather}
|
||||
%\end{subequations}
|
||||
%The difference between the ECMD functional defined in Ref.~\citenum{FerGinTou-JCP-18} and the present expression \eqref{eq:epsilon_cmdpbe}-\eqref{eq:beta_cmdpbe} is that we approximate here the on-top pair density by its \titou{uniform electron gas \cite{LooGil-WIRES-16} (UEG)} version, i.e.~$\n{2}{\Bas}(\br{},\br{}) \approx \n{2}{\UEG}(\n{}{}(\br{}),\zeta(\br{}))$, where $\n{2}{\UEG}(\n{}{},\zeta) \approx \n{}{2} (1-\zeta^2) g_0(n)$ with the parametrization of the UEG on-top pair-distribution function $g_0(n)$ given in Eq.~(46) of Ref.~\citenum{GorSav-PRA-06}.
|
||||
%This represents a major computational saving without loss of accuracy for weakly correlated systems as we eschew the computation of $\n{2}{\Bas}(\br{},\br{})$.
|
||||
%The complementary functional $\bE{}{\Bas}[\n{\HF}{\Bas}]$ is approximated by $\bE{\PBE}{\Bas}[\n{\HF}{\Bas},\rsmu{}{\Bas}]$ where $\rsmu{}{\Bas}(\br{})$ is given by Eq.~\eqref{eq:mu_of_r}.
|
||||
|
||||
%As most WFT calculations are performed within the frozen-core (FC) approximation, it is important to define an effective interaction within a subset of MOs.
|
||||
%We then naturally split the basis set as $\Bas = \Cor \bigcup \BasFC$ (where $\Cor$ and $\BasFC$ are the sets of core and active MOs, respectively) and define the FC version of the effective interaction as
|
||||
% \begin{equation}
|
||||
% \label{eq:WFC}
|
||||
% \WFC{}{\Bas}(\br{1},\br{2}) =
|
||||
% \begin{cases}
|
||||
% \fFC{}{\Bas}(\br{1},\br{2})/\nFC{2}{\Bas}(\br{1},\br{2}), & \text{if $\nFC{2}{\Bas}(\br{1},\br{2}) \ne 0$},
|
||||
% \\
|
||||
% \infty, & \text{otherwise,}
|
||||
% \end{cases}
|
||||
% \end{equation}
|
||||
%with
|
||||
%\begin{subequations}
|
||||
%\begin{gather}
|
||||
% \label{eq:fbasisval}
|
||||
% \fFC{}{\Bas}(\br{1},\br{2})
|
||||
% = \sum_{pq \in \Bas} \sum_{rstu \in \BasFC} \SO{p}{1} \SO{q}{2} \V{pq}{rs} \Gam{rs}{tu} \SO{t}{1} \SO{u}{2},
|
||||
% \\
|
||||
% \nFC{2}{\Bas}(\br{1},\br{2})
|
||||
% = \sum_{pqrs \in \BasFC} \SO{p}{1} \SO{q}{2} \Gam{pq}{rs} \SO{r}{1} \SO{s}{2},
|
||||
%\end{gather}
|
||||
%\end{subequations}
|
||||
%and the corresponding FC range-separation function $\rsmuFC{}{\Bas}(\br{}) = (\sqrt{\pi}/2) \WFC{}{\Bas}(\br{},\br{})$.
|
||||
%It is noteworthy that, within the present definition, $\WFC{}{\Bas}(\br{1},\br{2})$ still tends to the regular Coulomb interaction as $\Bas \to \CBS$.
|
||||
%Defining $\nFC{\HF}{\Bas}$ as the FC (i.e.~valence-only) $\HF$ one-electron density in $\Bas$, the FC contribution of the complementary functional is then approximated by $\bE{\PBE}{\Bas}[\nFC{\HF}{\Bas},\rsmuFC{}{\Bas}]$.
|
||||
|
||||
%The most computationally intensive task of the present approach is the evaluation of $\W{}{\Bas}(\br{},\br{})$ at each quadrature grid point.
|
||||
%In the general case (i.e.~$\wf{}{\Bas}$ is a multi-determinant expansion), we compute this embarrassingly parallel step in $\order*{\Ng \Nb^4}$ computational cost with a memory requirement of $\order*{ \Ng \Nb^2}$, where $\Nb$ is the number of basis functions in $\Bas$.
|
||||
%The computational cost can be reduced to $\order*{ \Ng \Ne^2 \Nb^2}$ with no memory footprint when $\wf{}{\Bas}$ is a single Slater determinant.
|
||||
%As shown in Ref.~\citenum{GinPraFerAssSavTou-JCP-18}, this choice for $\wf{}{\Bas}$ already provides, for weakly correlated systems, a quantitative representation of the incompleteness of $\Bas$.
|
||||
%Hence, we will stick to this choice throughout the present study.
|
||||
%In our current implementation, the computational bottleneck is the four-index transformation to get the two-electron integrals in the MO basis which appear in Eqs.~\eqref{eq:n2basis} and \eqref{eq:fbasis}.
|
||||
%Nevertheless, this step usually has to be performed for most correlated WFT calculations.
|
||||
|
||||
|
||||
%To conclude this section, we point out that, thanks to the definitions \eqref{eq:def_weebasis} and \eqref{eq:mu_of_r} as well as the properties \eqref{eq:lim_W} and \eqref{eq:large_mu_ecmd}, independently of the DFT functional, the present basis-set correction
|
||||
%i) can be applied to any WFT method that provides an energy and a density,
|
||||
%ii) does not correct one-electron systems, and
|
||||
%iii) vanishes in the CBS limit, hence guaranteeing an unaltered CBS limit for a given WFT method.
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Short-range correlation functionals}
|
||||
\label{sec:func}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
The local-density approximation (LDA) of the ECMD complementary functional is defined as
|
||||
\begin{equation}
|
||||
\label{eq:def_lda_tot}
|
||||
\bE{\LDA}{\Bas}[\n{}{},\rsmu{}{\Bas}] = \int \n{}{}(\br{}) \be{\text{c,md}}{\sr,\LDA}\qty(\n{}{}(\br{}),\zeta(\br{}),\rsmu{}{\Bas}(\br{})) \dbr{},
|
||||
\end{equation}
|
||||
where $\zeta = (\n{\uparrow}{} - \n{\downarrow}{})/\n{}{}$ is the spin polarization and $\be{\text{c,md}}{\sr,\LDA}(\n{}{},\zeta,\rsmu{}{})$ is the ECMD short-range correlation energy per electron of the uniform electron gas (UEG) \cite{LooGil-WIRES-16} parameterized in Ref.~\citenum{PazMorGorBac-PRB-06}.
|
||||
|
||||
To go beyond the LDA and cure its over correlation at small $\mu$, some of the authors recently proposed a Perdew-Burke-Ernzerhof (PBE)-based ECMD functional \cite{FerGinTou-JCP-18},
|
||||
\begin{equation}
|
||||
\label{eq:def_pbe_tot}
|
||||
\bE{\PBE}{\Bas}[\n{}{},\rsmu{}{\Bas}] =
|
||||
\int \n{}{}(\br{}) \be{\text{c,md}}{\sr,\PBE}\qty(\n{}{}(\br{}),s(\br{}),\zeta(\br{}),\rsmu{}{\Bas}(\br{})) \dbr{},
|
||||
\end{equation}
|
||||
where $s = \abs{\nabla \n{}{}}/\n{}{4/3}$ is the reduced density gradient.
|
||||
$\be{\text{c,md}}{\sr,\PBE}\qty(\n{}{},s,\zeta,\rsmu{}{})$ interpolates between the usual PBE correlation functional, \cite{PerBurErn-PRL-96} $\e{\text{c}}{\PBE}(\n{}{},s,\zeta)$, at $\rsmu{}{}=0$ and the exact large-$\rsmu{}{}$ behavior, \cite{TouColSav-PRA-04, GorSav-PRA-06, PazMorGorBac-PRB-06} yielding
|
||||
\begin{subequations}
|
||||
\begin{gather}
|
||||
\label{eq:epsilon_cmdpbe}
|
||||
\be{\text{c,md}}{\sr,\PBE}(\n{}{},s,\zeta,\rsmu{}{}) = \frac{\e{\text{c}}{\PBE}(\n{}{},s,\zeta)}{1 + \beta(\n{}{},s,\zeta) \rsmu{}{3} },
|
||||
\\
|
||||
\label{eq:beta_cmdpbe}
|
||||
\beta(\n{}{},s,\zeta) = \frac{3}{2\sqrt{\pi} (1 - \sqrt{2} )} \frac{\e{\text{c}}{\PBE}(\n{}{},s,\zeta)}{\n{2}{\Bas}(\br{},\br{})}.
|
||||
\end{gather}
|
||||
\end{subequations}
|
||||
We will refer to this functional as the ``on top'' PBE (PBEot) ECMD functional.
|
||||
More recently, we have also proposed a simplified version of the PBEot functional where we replaced the on-top pair density by its UEG version, i.e.~$\n{2}{\Bas}(\br{},\br{}) \approx \n{2}{\UEG}(\n{}{}(\br{}),\zeta(\br{}))$, where $\n{2}{\UEG}(\n{}{},\zeta) \approx \n{}{2} (1-\zeta^2) g_0(n)$ with the parametrization of the UEG on-top pair-distribution function $g_0(n)$ given in Eq.~(46) of Ref.~\citenum{GorSav-PRA-06}.
|
||||
This computationally-lighter functional will be refer to as PBE.
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
@ -421,7 +434,12 @@ The geometries have been extracted from Refs.~\onlinecite{LooSceBloGarCafJac-JCT
|
||||
They are also reported in the {\SI}.
|
||||
Frozen-core calculations are systematically performed and defined as such: a \ce{He} core is frozen from \ce{Li} to \ce{Ne}, while a \ce{Ne} core is frozen from \ce{Na} to \ce{Ar}.
|
||||
The FC density-based correction is used consistently with the FC approximation in WFT methods.
|
||||
We refer the interested reader to Ref.~\onlinecite{LooPraSceTouGin-JPCL-19} for detailed explanations on how the previous equations have to be modified within the FC approximation.
|
||||
|
||||
The most computationally intensive task of the present approach is the evaluation of $\W{}{\Bas}(\br{},\br{})$ at each quadrature grid point.
|
||||
In the general case (i.e.~$\wf{}{\Bas}$ is a multi-determinant expansion), we compute this embarrassingly parallel step in $\order*{\Ng \Nb^4}$ computational cost with a memory requirement of $\order*{ \Ng \Nb^2}$, where $\Nb$ is the number of basis functions in $\Bas$.
|
||||
In our current implementation, the computational bottleneck is the four-index transformation to get the two-electron integrals in the MO basis which appear in Eqs.~\eqref{eq:n2basis} and \eqref{eq:fbasis}.
|
||||
Nevertheless, this step usually has to be performed for most correlated WFT calculations.
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%
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||||
\section{Results}
|
||||
@ -433,7 +451,7 @@ The FC density-based correction is used consistently with the FC approximation i
|
||||
\label{sec:CH2}
|
||||
%=======================
|
||||
|
||||
As a first test of the present basis set correction, we consider the adiabatic transitions of methylene which have been thourhoughly studied in the literature with high-level ab initio methods.
|
||||
As a first test of the present basis set correction, we consider the adiabatic transitions of methylene which have been thourhoughly studied in the literature with high-level ab initio methods. \cite{AbrShe-JCP-04, AbrShe-CPL-05, ZimTouZhaMusUmr-JCP-09, ChiHolAdaOttUmrShaZim-JPCA-18}
|
||||
|
||||
%%% TABLE 1 %%%
|
||||
\begin{squeezetable}
|
||||
@ -551,7 +569,7 @@ As a first test of the present basis set correction, we consider the adiabatic t
|
||||
\label{sec:H2O-NH3}
|
||||
%=======================
|
||||
|
||||
Water and ammonia are two interesting molecules with Rydberge excited states which are highly sensitive to the radial completeness of the one-electron basis set.
|
||||
Water \cite{CaiTozRei-JCP-00, RubSerMer-JCP-08, LiPal-JCP-11, LooSceBloGarCafJac-JCTC-18, SceBenJacCafLoo-JCP-18} and ammonia \cite{SchGoe-JCTC-17, BarDelPerMat-JMS-97, LooSceBloGarCafJac-JCTC-18} are two interesting molecules with Rydberg excited states which are highly sensitive to the radial completeness of the one-electron basis set.
|
||||
|
||||
%%% TABLE 2 %%%
|
||||
\begin{squeezetable}
|
||||
@ -801,7 +819,7 @@ Water and ammonia are two interesting molecules with Rydberge excited states whi
|
||||
\subsection{Doubly-Excited States of the Carbon Dimer}
|
||||
\label{sec:C2}
|
||||
%=======================
|
||||
It is also interesting to study doubly-excited states.
|
||||
It is also interesting to study doubly-excited states. \cite{AbrShe-JCP-04, AbrShe-CPL-05, Var-JCP-08, PurZhaKra-JCP-09, AngCimPas-MP-12, BooCleThoAla-JCP-11, Sha-JCP-15, SokCha-JCP-16, VarRoc-PTRSMPES-18}
|
||||
In the carbon dimer, these valence states are of $(\pi,\pi) \ra (\si,\si)$ character and they have been recently studied with state-of-the-art methods. \cite{LooBogSceCafJAc-JCTC-19}
|
||||
|
||||
%%% FIG 4 %%%
|
||||
@ -818,7 +836,7 @@ In the carbon dimer, these valence states are of $(\pi,\pi) \ra (\si,\si)$ chara
|
||||
\label{sec:C2H4}
|
||||
%=======================
|
||||
|
||||
Ethylene is an interesting molecules as it contains both valence and Rydberg excited states.
|
||||
Ethylene is an interesting molecules as it contains both valence and Rydberg excited states. \cite{SerMarNebLinRoo-JCP-93, WatGwaBar-JCP-96, WibOliTru-JPCA-02, BarPaiLis-JCP-04, Ang-JCC-08, SchSilSauThi-JCP-08, SilSchSauThi-JCP-10, SilSauSchThi-MP-10, Ang-IJQC-10, DadSmaBooAlaFil-JCTC-12, FelPetDav-JCP-14, ChiHolAdaOttUmrShaZim-JPCA-18}
|
||||
|
||||
%\begin{figure}
|
||||
% \includegraphics[width=\linewidth]{C2H2}
|
||||
|
||||
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Reference in New Issue
Block a user