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benzene.bib
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benzene.bib
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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 2020-08-24 16:21:19 +0200
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%% Created for Pierre-Francois Loos at 2020-08-25 18:15:28 +0200
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%% Saved with string encoding Unicode (UTF-8)
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@article{Eriksen_2019b,
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Author = {J. J. Eriksen and J. Gauss},
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Date-Added = {2020-08-25 18:14:27 +0200},
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Date-Modified = {2020-08-25 18:15:20 +0200},
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Doi = {10.1021/acs.jpclett.9b02968},
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Journal = {J. Phys. Chem. Lett.},
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Pages = {7910--7915},
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Title = {Generalized Many-Body Expanded Full Configuration Interaction Theory},
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Volume = {27},
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Year = {2019}}
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@article{Eriksen_2017,
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Author = {J. J. Eriksen and F. Lipparini and J. Gauss},
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Date-Added = {2020-08-25 18:12:46 +0200},
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Date-Modified = {2020-08-25 18:13:55 +0200},
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Doi = {10.1021/acs.jpclett.7b02075},
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Journal = {J. Phys. Chem. Lett.},
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Pages = {4633--4639},
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Title = {Virtual Orbital Many-Body Expansions: A Possible Route towards the Full Configuration Interaction Limit},
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Volume = {8},
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Year = {2017},
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Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.7b02075}}
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@article{Sauer_2009,
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Author = {Sauer, Stephan P. A. and Schreiber, Marko and Silva-Junior, Mario R. and Thiel, Walter},
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Date-Added = {2020-08-24 16:15:18 +0200},
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@ -18,7 +41,8 @@
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Pages = {555--564},
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Title = {Benchmarks for Electronically Excited States: A Comparison of Noniterative and Iterative Triples Corrections in Linear Response Coupled Cluster Methods: CCSDR(3) versus CC3},
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Volume = {5},
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Year = {2009}}
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Year = {2009},
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Bdsk-Url-1 = {https://doi.org/10.1021/ct800256j}}
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@article{Schreiber_2008,
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Author = {Schreiber, M. and Silva-Junior, M. R. and Sauer, S. P. A. and Thiel, W.},
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@ -29,7 +53,8 @@
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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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Year = 2008,
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Bdsk-Url-1 = {https://doi.org/10.1063/1.2889385}}
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@article{Silva-Junior_2010a,
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Author = {Silva-Junior, M. R. and Schreiber, M. and Sauer, S. P. A. and Thiel, W.},
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@ -40,7 +65,8 @@
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Pages = {104103},
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Title = {Benchmarks for Electronically Excited States: Time-Dependent Density Functional Theory and Density Functional Theory Based Multireference Configuration Interaction},
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Volume = 129,
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Year = 2008}
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Year = 2008,
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Bdsk-Url-1 = {https://doi.org/10.1063/1.2973541}}
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@article{Silva-Junior_2010b,
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Author = {Silva-Junior, M. R. and Sauer, S. P. A. and Schreiber, M. and Thiel, W.},
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@ -51,7 +77,8 @@
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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}
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Year = 2010,
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Bdsk-Url-1 = {https://doi.org/10.1080/00268970903549047}}
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@article{Silva-Junior_2010c,
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Author = {Silva-Junior, M. R. and Schreiber, M. and Sauer, S. P. A. and Thiel, W.},
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@ -62,7 +89,8 @@
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Pages = {174318},
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Title = {Benchmarks of Electronically Excited States: Basis Set Effecs on {{CASPT2}} Results},
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Volume = 133,
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Year = 2010}
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Year = 2010,
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Bdsk-Url-1 = {https://doi.org/10.1063/1.3499598}}
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@article{Boys_1960,
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Author = {J. M. Foster and S. F. Boys},
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@ -424,10 +452,10 @@
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Year = {2018},
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Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.121.113001}}
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@article{Eriksen_2019,
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@article{Eriksen_2019a,
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Author = {J. J. Eriksen and J. Gauss},
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Date-Added = {2020-08-16 13:35:02 +0200},
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Date-Modified = {2020-08-16 13:35:51 +0200},
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Date-Modified = {2020-08-25 18:15:28 +0200},
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Doi = {10.1021/acs.jctc.9b00456},
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Journal = {J. Chem. Theory Comput.},
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Pages = {4873},
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36
benzene.nb
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benzene.nb
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@ -59,7 +59,7 @@ Following a similar goal, we have recently proposed a large set of highly-accura
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% The context
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In a recent preprint, \cite{Eriksen_2020} Eriksen \textit{et al.}~have proposed a blind test for a particular electronic structure problem inviting several groups around the world to contribute to this endeavour.
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In addition to coupled cluster theory with singles, doubles, triples, and quadruples (CCSDTQ), \cite{Oliphant_1991,Kucharski_1992} a large panel of highly-accurate, emerging electronic structure methods were considered:
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(i) the many-body expansion FCI (MBE-FCI), \cite{Eriksen_2018,Eriksen_2019}
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(i) the many-body expansion FCI (MBE-FCI), \cite{Eriksen_2017,Eriksen_2018,Eriksen_2019a,Eriksen_2019b}
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(ii) three SCI methods including a second-order perturbative correction (ASCI, \cite{Tubman_2016,Tubman_2018,Tubman_2020} iCI, \cite{Liu_2016} and SHCI \cite{Holmes_2016,Holmes_2017,Sharma_2017}),
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(iii) a selected coupled-cluster theory method which also includes a second-order perturbative correction (FCCR), \cite{Xu_2018}
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(iv) the density-matrix renornalization group approach (DMRG), \cite{White_1992} and
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@ -69,7 +69,7 @@ Soon after, Lee \textit{et al.}~reported phaseless auxiliary-field quantum Monte
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% The system
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The target application is the non-relativistic frozen-core correlation energy of the ground state of the benzene molecule in the cc-pVDZ basis.
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The geometry of benzene has been computed at the MP2/6-31G* level and it can be found in the supporting information of Ref.~\onlinecite{Eriksen_2020}.
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The geometry of benzene has been computed at the MP2/6-31G* level and it can be found in the supporting information of Ref.~\onlinecite{Eriksen_2020} alongside its nuclear repulsion and Hartree-Fock energies.
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This corresponds to an active space of 30 electrons and 108 orbitals, \ie, the Hilbert space of benzene is of the order of $10^{35}$ Slater determinants.
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Needless to say that this size of Hilbert space cannot be tackled by exact diagonalization with current architectures.
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The correlation energies reported in Ref.~\onlinecite{Eriksen_2020} are gathered in Table \ref{tab:energy} alongside the best ph-AFQMC estimate from Ref.~\onlinecite{Lee_2020} based on a CAS(6,6) trial wave function.
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@ -91,6 +91,7 @@ The outcome of this work is nicely summarized in the abstract of Ref.~\onlinecit
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CCSDTQ & $-862.4$ & \onlinecite{Eriksen_2020} \\
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DMRG & $-862.8(7)$ & \onlinecite{Eriksen_2020} \\
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FCCR(2) & $-863.0$ & \onlinecite{Eriksen_2020} \\
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MBE-FCI & $-863.0$ & \onlinecite{Eriksen_2020} \\
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CAD-FCIQMC & $-863.4$ & \onlinecite{Eriksen_2020} \\
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AS-FCIQMC & $-863.7(3)$ & \onlinecite{Eriksen_2020} \\
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SHCI & $-864.2(2)$ & \onlinecite{Eriksen_2020} \\
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