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Pierre-Francois Loos 2020-08-25 18:35:40 +02:00
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44
benzene.bib
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@ -1,13 +1,36 @@
%% This BibTeX bibliography file was created using BibDesk. %% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/ %% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2020-08-24 16:21:19 +0200 %% Created for Pierre-Francois Loos at 2020-08-25 18:15:28 +0200
%% Saved with string encoding Unicode (UTF-8) %% Saved with string encoding Unicode (UTF-8)
@article{Eriksen_2019b,
Author = {J. J. Eriksen and J. Gauss},
Date-Added = {2020-08-25 18:14:27 +0200},
Date-Modified = {2020-08-25 18:15:20 +0200},
Doi = {10.1021/acs.jpclett.9b02968},
Journal = {J. Phys. Chem. Lett.},
Pages = {7910--7915},
Title = {Generalized Many-Body Expanded Full Configuration Interaction Theory},
Volume = {27},
Year = {2019}}
@article{Eriksen_2017,
Author = {J. J. Eriksen and F. Lipparini and J. Gauss},
Date-Added = {2020-08-25 18:12:46 +0200},
Date-Modified = {2020-08-25 18:13:55 +0200},
Doi = {10.1021/acs.jpclett.7b02075},
Journal = {J. Phys. Chem. Lett.},
Pages = {4633--4639},
Title = {Virtual Orbital Many-Body Expansions: A Possible Route towards the Full Configuration Interaction Limit},
Volume = {8},
Year = {2017},
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.7b02075}}
@article{Sauer_2009, @article{Sauer_2009,
Author = {Sauer, Stephan P. A. and Schreiber, Marko and Silva-Junior, Mario R. and Thiel, Walter}, Author = {Sauer, Stephan P. A. and Schreiber, Marko and Silva-Junior, Mario R. and Thiel, Walter},
Date-Added = {2020-08-24 16:15:18 +0200}, Date-Added = {2020-08-24 16:15:18 +0200},
@ -18,7 +41,8 @@
Pages = {555--564}, Pages = {555--564},
Title = {Benchmarks for Electronically Excited States: A Comparison of Noniterative and Iterative Triples Corrections in Linear Response Coupled Cluster Methods: CCSDR(3) versus CC3}, Title = {Benchmarks for Electronically Excited States: A Comparison of Noniterative and Iterative Triples Corrections in Linear Response Coupled Cluster Methods: CCSDR(3) versus CC3},
Volume = {5}, Volume = {5},
Year = {2009}} Year = {2009},
Bdsk-Url-1 = {https://doi.org/10.1021/ct800256j}}
@article{Schreiber_2008, @article{Schreiber_2008,
Author = {Schreiber, M. and Silva-Junior, M. R. and Sauer, S. P. A. and Thiel, W.}, Author = {Schreiber, M. and Silva-Junior, M. R. and Sauer, S. P. A. and Thiel, W.},
@ -29,7 +53,8 @@
Pages = {134110}, Pages = {134110},
Title = {Benchmarks for Electronically Excited States: CASPT2, CC2, CCSD and CC3}, Title = {Benchmarks for Electronically Excited States: CASPT2, CC2, CCSD and CC3},
Volume = 128, Volume = 128,
Year = 2008} Year = 2008,
Bdsk-Url-1 = {https://doi.org/10.1063/1.2889385}}
@article{Silva-Junior_2010a, @article{Silva-Junior_2010a,
Author = {Silva-Junior, M. R. and Schreiber, M. and Sauer, S. P. A. and Thiel, W.}, Author = {Silva-Junior, M. R. and Schreiber, M. and Sauer, S. P. A. and Thiel, W.},
@ -40,7 +65,8 @@
Pages = {104103}, Pages = {104103},
Title = {Benchmarks for Electronically Excited States: Time-Dependent Density Functional Theory and Density Functional Theory Based Multireference Configuration Interaction}, Title = {Benchmarks for Electronically Excited States: Time-Dependent Density Functional Theory and Density Functional Theory Based Multireference Configuration Interaction},
Volume = 129, Volume = 129,
Year = 2008} Year = 2008,
Bdsk-Url-1 = {https://doi.org/10.1063/1.2973541}}
@article{Silva-Junior_2010b, @article{Silva-Junior_2010b,
Author = {Silva-Junior, M. R. and Sauer, S. P. A. and Schreiber, M. and Thiel, W.}, Author = {Silva-Junior, M. R. and Sauer, S. P. A. and Schreiber, M. and Thiel, W.},
@ -51,7 +77,8 @@
Pages = {453--465}, Pages = {453--465},
Title = {Basis Set Effects on Coupled Cluster Benchmarks of Electronically Excited States: CC3, CCSDR(3) and CC2}, Title = {Basis Set Effects on Coupled Cluster Benchmarks of Electronically Excited States: CC3, CCSDR(3) and CC2},
Volume = 108, Volume = 108,
Year = 2010} Year = 2010,
Bdsk-Url-1 = {https://doi.org/10.1080/00268970903549047}}
@article{Silva-Junior_2010c, @article{Silva-Junior_2010c,
Author = {Silva-Junior, M. R. and Schreiber, M. and Sauer, S. P. A. and Thiel, W.}, Author = {Silva-Junior, M. R. and Schreiber, M. and Sauer, S. P. A. and Thiel, W.},
@ -62,7 +89,8 @@
Pages = {174318}, Pages = {174318},
Title = {Benchmarks of Electronically Excited States: Basis Set Effecs on {{CASPT2}} Results}, Title = {Benchmarks of Electronically Excited States: Basis Set Effecs on {{CASPT2}} Results},
Volume = 133, Volume = 133,
Year = 2010} Year = 2010,
Bdsk-Url-1 = {https://doi.org/10.1063/1.3499598}}
@article{Boys_1960, @article{Boys_1960,
Author = {J. M. Foster and S. F. Boys}, Author = {J. M. Foster and S. F. Boys},
@ -424,10 +452,10 @@
Year = {2018}, Year = {2018},
Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.121.113001}} Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.121.113001}}
@article{Eriksen_2019, @article{Eriksen_2019a,
Author = {J. J. Eriksen and J. Gauss}, Author = {J. J. Eriksen and J. Gauss},
Date-Added = {2020-08-16 13:35:02 +0200}, Date-Added = {2020-08-16 13:35:02 +0200},
Date-Modified = {2020-08-16 13:35:51 +0200}, Date-Modified = {2020-08-25 18:15:28 +0200},
Doi = {10.1021/acs.jctc.9b00456}, Doi = {10.1021/acs.jctc.9b00456},
Journal = {J. Chem. Theory Comput.}, Journal = {J. Chem. Theory Comput.},
Pages = {4873}, Pages = {4873},

36
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5
benzene.tex
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@ -59,7 +59,7 @@ Following a similar goal, we have recently proposed a large set of highly-accura
% The context % The context
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. 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.
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: 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:
(i) the many-body expansion FCI (MBE-FCI), \cite{Eriksen_2018,Eriksen_2019} (i) the many-body expansion FCI (MBE-FCI), \cite{Eriksen_2017,Eriksen_2018,Eriksen_2019a,Eriksen_2019b}
(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}), (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}),
(iii) a selected coupled-cluster theory method which also includes a second-order perturbative correction (FCCR), \cite{Xu_2018} (iii) a selected coupled-cluster theory method which also includes a second-order perturbative correction (FCCR), \cite{Xu_2018}
(iv) the density-matrix renornalization group approach (DMRG), \cite{White_1992} and (iv) the density-matrix renornalization group approach (DMRG), \cite{White_1992} and
@ -69,7 +69,7 @@ Soon after, Lee \textit{et al.}~reported phaseless auxiliary-field quantum Monte
% The system % The system
The target application is the non-relativistic frozen-core correlation energy of the ground state of the benzene molecule in the cc-pVDZ basis. The target application is the non-relativistic frozen-core correlation energy of the ground state of the benzene molecule in the cc-pVDZ basis.
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}. 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.
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. 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.
Needless to say that this size of Hilbert space cannot be tackled by exact diagonalization with current architectures. Needless to say that this size of Hilbert space cannot be tackled by exact diagonalization with current architectures.
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. 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.
@ -91,6 +91,7 @@ The outcome of this work is nicely summarized in the abstract of Ref.~\onlinecit
CCSDTQ & $-862.4$ & \onlinecite{Eriksen_2020} \\ CCSDTQ & $-862.4$ & \onlinecite{Eriksen_2020} \\
DMRG & $-862.8(7)$ & \onlinecite{Eriksen_2020} \\ DMRG & $-862.8(7)$ & \onlinecite{Eriksen_2020} \\
FCCR(2) & $-863.0$ & \onlinecite{Eriksen_2020} \\ FCCR(2) & $-863.0$ & \onlinecite{Eriksen_2020} \\
MBE-FCI & $-863.0$ & \onlinecite{Eriksen_2020} \\
CAD-FCIQMC & $-863.4$ & \onlinecite{Eriksen_2020} \\ CAD-FCIQMC & $-863.4$ & \onlinecite{Eriksen_2020} \\
AS-FCIQMC & $-863.7(3)$ & \onlinecite{Eriksen_2020} \\ AS-FCIQMC & $-863.7(3)$ & \onlinecite{Eriksen_2020} \\
SHCI & $-864.2(2)$ & \onlinecite{Eriksen_2020} \\ SHCI & $-864.2(2)$ & \onlinecite{Eriksen_2020} \\