diff --git a/g.bib b/g.bib index 366b738..67a49ec 100644 --- a/g.bib +++ b/g.bib @@ -1,2029 +1,1907 @@ -%% This BibTeX bibliography file was created using BibDeslippk. +%% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ -%% Created for Pierre-Francois Loos at 2017-11-17 16:14:44 +0100 +%% Created for Pierre-Francois Loos at 2022-09-15 09:22:25 +0200 %% Saved with string encoding Unicode (UTF-8) -79. M. Caffarel, T. Applencourt, E. Giner, and A. Scemama Using CIPSI nodes -in diffusion Monte Carlo'' Recent Progress in Quantum Monte Carlo -ACS Symposium Series, Vol. 1234 Chapter 2, pp 15-46 -and arXiv:1607.06742v2 [physics.chem-ph] (2016). - -Hurley_1987,Hammond_1987 - -M. Caffarel, R. Assaraf A pedagogical introduction -to quantum Monte Carlo Mathematical models and methods for ab initio Quantum Chemistry in -Lecture Notes in Chemistry, Ed. by M. Defranceschi and C. Le Bris, Springer p.45 (2000). - -Lee M A, Schmidt K E, Kalos M H and Chester G V 1981, Phys. Rev. Lett. 46 728 -[12] Holzmann M, Bernu B and Ceperley D M 2006 Phys. Rev. B 74 104510 @article{Zhang_2003, - title = {Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants}, - author = {Zhang, Shiwei and Krakauer, Henry}, - journal = {Phys. Rev. Lett.}, - volume = {90}, - issue = {13}, - pages = {136401}, - numpages = {4}, - year = {2003}, - month = {Apr}, - publisher = {American Physical Society}, - doi = {10.1103/PhysRevLett.90.136401}, - url = {https://link.aps.org/doi/10.1103/PhysRevLett.90.136401} -} + author = {Zhang, Shiwei and Krakauer, Henry}, + doi = {10.1103/PhysRevLett.90.136401}, + issue = {13}, + journal = {Phys. Rev. Lett.}, + month = {Apr}, + numpages = {4}, + pages = {136401}, + publisher = {American Physical Society}, + title = {Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants}, + url = {https://link.aps.org/doi/10.1103/PhysRevLett.90.136401}, + volume = {90}, + year = {2003}, + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.90.136401}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.90.136401}} @article{Cleland_2010, -author = {Cleland,Deidre and Booth,George H. and Alavi,Ali }, -title = {Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo}, -journal = {The Journal of Chemical Physics}, -volume = {132}, -number = {4}, -pages = {041103}, -year = {2010}, -doi = {10.1063/1.3302277}, - -URL = { - https://doi.org/10.1063/1.3302277 - -}, -eprint = { - https://doi.org/10.1063/1.3302277 - -} - -} - - - + author = {Cleland,Deidre and Booth,George H. and Alavi,Ali}, + doi = {10.1063/1.3302277}, + eprint = {https://doi.org/10.1063/1.3302277}, + journal = {The Journal of Chemical Physics}, + number = {4}, + pages = {041103}, + title = {Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo}, + url = {https://doi.org/10.1063/1.3302277}, + volume = {132}, + year = {2010}, + bdsk-url-1 = {https://doi.org/10.1063/1.3302277}} @article{Chan_2011, -author = {Chan, Garnet Kin-Lic and Sharma, Sandeep}, -title = {The Density Matrix Renormalization Group in Quantum Chemistry}, -journal = {Annual Review of Physical Chemistry}, -volume = {62}, -number = {1}, -pages = {465-481}, -year = {2011}, -doi = {10.1146/annurev-physchem-032210-103338}, - note ={PMID: 21219144}, - -URL = { - https://doi.org/10.1146/annurev-physchem-032210-103338 - -}, -eprint = { - https://doi.org/10.1146/annurev-physchem-032210-103338 - -} -, - abstract = { The density matrix renormalization group is a method that is useful for describing molecules that have strongly correlated electrons. Here we provide a pedagogical overview of the basic challenges of strong correlation, how the density matrix renormalization group works, a survey of its existing applications to molecular problems, and some thoughts on the future of the method. } -} - + abstract = { The density matrix renormalization group is a method that is useful for describing molecules that have strongly correlated electrons. Here we provide a pedagogical overview of the basic challenges of strong correlation, how the density matrix renormalization group works, a survey of its existing applications to molecular problems, and some thoughts on the future of the method. }, + author = {Chan, Garnet Kin-Lic and Sharma, Sandeep}, + doi = {10.1146/annurev-physchem-032210-103338}, + eprint = {https://doi.org/10.1146/annurev-physchem-032210-103338}, + journal = {Annual Review of Physical Chemistry}, + note = {PMID: 21219144}, + number = {1}, + pages = {465-481}, + title = {The Density Matrix Renormalization Group in Quantum Chemistry}, + url = {https://doi.org/10.1146/annurev-physchem-032210-103338}, + volume = {62}, + year = {2011}, + bdsk-url-1 = {https://doi.org/10.1146/annurev-physchem-032210-103338}} @article{White_1999, -author = {White,Steven R. and Martin,Richard L. }, -title = {Ab initio quantum chemistry using the density matrix renormalization group}, -journal = {The Journal of Chemical Physics}, -volume = {110}, -number = {9}, -pages = {4127-4130}, -year = {1999}, -doi = {10.1063/1.478295}, -URL = { - https://doi.org/10.1063/1.478295 -}, -eprint = { - https://doi.org/10.1063/1.478295 -} -} + author = {White,Steven R. and Martin,Richard L.}, + doi = {10.1063/1.478295}, + eprint = {https://doi.org/10.1063/1.478295}, + journal = {The Journal of Chemical Physics}, + number = {9}, + pages = {4127-4130}, + title = {Ab initio quantum chemistry using the density matrix renormalization group}, + url = {https://doi.org/10.1063/1.478295}, + volume = {110}, + year = {1999}, + bdsk-url-1 = {https://doi.org/10.1063/1.478295}} @article{Booth_2009, -author = {Booth,George H. and Thom,Alex J. W. and Alavi,Ali }, -title = {Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space}, -journal = {The Journal of Chemical Physics}, -volume = {131}, -number = {5}, -pages = {054106}, -year = {2009}, -doi = {10.1063/1.3193710}, -URL = { - https://aip.scitation.org/doi/abs/10.1063/1.3193710 -}, -eprint = { - https://aip.scitation.org/doi/pdf/10.1063/1.3193710 -} -} + author = {Booth,George H. and Thom,Alex J. W. and Alavi,Ali}, + doi = {10.1063/1.3193710}, + eprint = {https://aip.scitation.org/doi/pdf/10.1063/1.3193710}, + journal = {The Journal of Chemical Physics}, + number = {5}, + pages = {054106}, + title = {Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space}, + url = {https://aip.scitation.org/doi/abs/10.1063/1.3193710}, + volume = {131}, + year = {2009}, + bdsk-url-1 = {https://aip.scitation.org/doi/abs/10.1063/1.3193710}, + bdsk-url-2 = {https://doi.org/10.1063/1.3193710}} @article{Tubman_2020, -author = {Tubman, Norm M. and Freeman, C. Daniel and Levine, Daniel S. and Hait, Diptarka and Head-Gordon, Martin and Whaley, K. Birgitta}, -title = {Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method}, -journal = {Journal of Chemical Theory and Computation}, -volume = {16}, -number = {4}, -pages = {2139-2159}, -year = {2020}, -doi = {10.1021/acs.jctc.8b00536}, - note ={PMID: 32159951}, -URL = { - https://doi.org/10.1021/acs.jctc.8b00536 -}, -eprint = { - https://doi.org/10.1021/acs.jctc.8b00536 -} -} + author = {Tubman, Norm M. and Freeman, C. Daniel and Levine, Daniel S. and Hait, Diptarka and Head-Gordon, Martin and Whaley, K. Birgitta}, + doi = {10.1021/acs.jctc.8b00536}, + eprint = {https://doi.org/10.1021/acs.jctc.8b00536}, + journal = {Journal of Chemical Theory and Computation}, + note = {PMID: 32159951}, + number = {4}, + pages = {2139-2159}, + title = {Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method}, + url = {https://doi.org/10.1021/acs.jctc.8b00536}, + volume = {16}, + year = {2020}, + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.8b00536}} @article{Schriber_2016, -author = {Schriber,Jeffrey B. and Evangelista,Francesco A. }, -title = {Communication: An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy}, -journal = {The Journal of Chemical Physics}, -volume = {144}, -number = {16}, -pages = {161106}, -year = {2016}, -doi = {10.1063/1.4948308}, -URL = { - https://doi.org/10.1063/1.4948308 -}, -eprint = { - https://doi.org/10.1063/1.4948308 -} -} + author = {Schriber,Jeffrey B. and Evangelista,Francesco A.}, + doi = {10.1063/1.4948308}, + eprint = {https://doi.org/10.1063/1.4948308}, + journal = {The Journal of Chemical Physics}, + number = {16}, + pages = {161106}, + title = {Communication: An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy}, + url = {https://doi.org/10.1063/1.4948308}, + volume = {144}, + year = {2016}, + bdsk-url-1 = {https://doi.org/10.1063/1.4948308}} @article{Holmes_2016, -author = {Holmes, Adam A. and Tubman, Norm M. and Umrigar, C. J.}, -title = {Heat-Bath Configuration Interaction: An Efficient Selected Configuration Interaction Algorithm Inspired by Heat-Bath Sampling}, -journal = {Journal of Chemical Theory and Computation}, -volume = {12}, -number = {8}, -pages = {3674-3680}, -year = {2016}, -doi = {10.1021/acs.jctc.6b00407}, - note ={PMID: 27428771}, -URL = { - https://doi.org/10.1021/acs.jctc.6b00407 -}, -eprint = { - https://doi.org/10.1021/acs.jctc.6b00407 -} -} - + author = {Holmes, Adam A. and Tubman, Norm M. and Umrigar, C. J.}, + doi = {10.1021/acs.jctc.6b00407}, + eprint = {https://doi.org/10.1021/acs.jctc.6b00407}, + journal = {Journal of Chemical Theory and Computation}, + note = {PMID: 27428771}, + number = {8}, + pages = {3674-3680}, + title = {Heat-Bath Configuration Interaction: An Efficient Selected Configuration Interaction Algorithm Inspired by Heat-Bath Sampling}, + url = {https://doi.org/10.1021/acs.jctc.6b00407}, + volume = {12}, + year = {2016}, + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.6b00407}} @article{Harrison_1991, -author={Robert J. Harrison}, -title={Approximating full configuration interaction with selected configuration interaction and perturbation theory}, -journal={J. Chem. Phys.}, -volume={94}, -pages={5021-5031}, -year={1991} -} + author = {Robert J. Harrison}, + journal = {J. Chem. Phys.}, + pages = {5021-5031}, + title = {Approximating full configuration interaction with selected configuration interaction and perturbation theory}, + volume = {94}, + year = {1991}} @article{Gutzwiller_1963, - title = {Effect of Correlation on the Ferromagnetism of Transition Metals}, - author = {Gutzwiller, Martin C.}, - journal = {Phys. Rev. Lett.}, - volume = {10}, - issue = {5}, - pages = {159--162}, - numpages = {0}, - year = {1963}, - month = {Mar}, - publisher = {American Physical Society}, - doi = {10.1103/PhysRevLett.10.159}, - url = {https://link.aps.org/doi/10.1103/PhysRevLett.10.159} -} + author = {Gutzwiller, Martin C.}, + doi = {10.1103/PhysRevLett.10.159}, + issue = {5}, + journal = {Phys. Rev. Lett.}, + month = {Mar}, + numpages = {0}, + pages = {159--162}, + publisher = {American Physical Society}, + title = {Effect of Correlation on the Ferromagnetism of Transition Metals}, + url = {https://link.aps.org/doi/10.1103/PhysRevLett.10.159}, + volume = {10}, + year = {1963}, + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.10.159}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.10.159}} @techreport{Kalos_2000, - author = {M. H. Kalos}, - title = {Domain Green's Function Sampling in Diffusion Monte Carlo}, - institution = {University of North Texas Libraries, UNT Digital Library}, - year = {2000} -} + author = {M. H. Kalos}, + institution = {University of North Texas Libraries, UNT Digital Library}, + title = {Domain Green's Function Sampling in Diffusion Monte Carlo}, + year = {2000}} -@phdthesis{Assaraf_1999B, - author = {R. Assaraf}, - title = {M\'ethodes Monte Carlo quantique. D\'eveloppements et applications \`a quelques probl\`emes quantiques fortement corr\'el\'es.}, - school = {Universit\'e d Pierre et Marie Curie}, - year = {1999}, - address = {Paris} -} +@phdthesis{Assaraf_PhD, + address = {Paris}, + author = {R. Assaraf}, + date-modified = {2022-09-15 09:18:33 +0200}, + school = {Universit\'e d Pierre et Marie Curie}, + title = {M\'ethodes Monte Carlo quantique. D\'eveloppements et applications \`a quelques probl\`emes quantiques fortement corr\'el\'es.}, + year = {1999}} @article{Kalos_1974, - title = {Helium at zero temperature with hard-sphere and other forces}, - author = {Kalos, M. H. and Levesque, D. and Verlet, L.}, - journal = {Phys. Rev. A}, - volume = {9}, - issue = {5}, - pages = {2178--2195}, - numpages = {0}, - year = {1974}, - month = {May}, - publisher = {American Physical Society}, - doi = {10.1103/PhysRevA.9.2178}, - url = {https://link.aps.org/doi/10.1103/PhysRevA.9.2178} -} + author = {Kalos, M. H. and Levesque, D. and Verlet, L.}, + doi = {10.1103/PhysRevA.9.2178}, + issue = {5}, + journal = {Phys. Rev. A}, + month = {May}, + numpages = {0}, + pages = {2178--2195}, + publisher = {American Physical Society}, + title = {Helium at zero temperature with hard-sphere and other forces}, + url = {https://link.aps.org/doi/10.1103/PhysRevA.9.2178}, + volume = {9}, + year = {1974}, + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.9.2178}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevA.9.2178}} - -@article{Assaraf_1999, - title = {Zero-Variance Principle for Monte Carlo Algorithms}, - author = {Assaraf, Roland and Caffarel, Michel}, - journal = {Phys. Rev. Lett.}, - volume = {83}, - issue = {23}, - pages = {4682--4685}, - numpages = {0}, - year = {1999}, - month = {Dec}, - publisher = {American Physical Society}, - doi = {10.1103/PhysRevLett.83.4682}, - url = {https://link.aps.org/doi/10.1103/PhysRevLett.83.4682} -} +@article{Assaraf_1999A, + author = {Assaraf, Roland and Caffarel, Michel}, + date-modified = {2022-09-15 09:18:50 +0200}, + doi = {10.1103/PhysRevLett.83.4682}, + issue = {23}, + journal = {Phys. Rev. Lett.}, + month = {Dec}, + numpages = {0}, + pages = {4682--4685}, + publisher = {American Physical Society}, + title = {Zero-Variance Principle for Monte Carlo Algorithms}, + url = {https://link.aps.org/doi/10.1103/PhysRevLett.83.4682}, + volume = {83}, + year = {1999}, + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.83.4682}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.83.4682}} @article{Caffarel_1988, -author = {Caffarel,Michel and Claverie,Pierre }, -title = {Development of a pure diffusion quantum Monte Carlo method using a full generalized Feynman–Kac formula. I. Formalism}, -journal = {The Journal of Chemical Physics}, -volume = {88}, -number = {2}, -pages = {1088-1099}, -year = {1988}, -doi = {10.1063/1.454227}, -URL = { - https://doi.org/10.1063/1.454227 -}, -eprint = { - https://doi.org/10.1063/1.454227 -} -} + author = {Caffarel,Michel and Claverie,Pierre}, + doi = {10.1063/1.454227}, + eprint = {https://doi.org/10.1063/1.454227}, + journal = {The Journal of Chemical Physics}, + number = {2}, + pages = {1088-1099}, + title = {Development of a pure diffusion quantum Monte Carlo method using a full generalized Feynman--Kac formula. I. Formalism}, + url = {https://doi.org/10.1063/1.454227}, + volume = {88}, + year = {1988}, + bdsk-url-1 = {https://doi.org/10.1063/1.454227}} @article{Baroni_1999, - title = {Reptation Quantum Monte Carlo: A Method for Unbiased Ground-State Averages and Imaginary-Time Correlations}, - author = {Baroni, Stefano and Moroni, Saverio}, - journal = {Phys. Rev. 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Lett.}, + month = {May}, + numpages = {0}, + pages = {4558--4561}, + publisher = {American Physical Society}, + title = {Green Function Monte Carlo with Stochastic Reconfiguration}, + url = {https://link.aps.org/doi/10.1103/PhysRevLett.80.4558}, + volume = {80}, + year = {1998}, + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.80.4558}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.80.4558}} + +@book{Golub_2012, + author = {Golub, Gene H. and Van Loan, Charles F.}, + edition = {Fourth}, + publisher = {The Johns Hopkins University Press}, + title = {Matrix Computations}, + year = {2012}} + @article{Carlson_2007, - author={J. Carlson}, - journal={Nucl. Physics. A}, - volume={787}, - pages={516}, - year={2007} -} + author = {J. Carlson}, + journal = {Nucl. Physics. A}, + pages = {516}, + volume = {787}, + year = {2007}} @article{Davidson_1975, - author={Davidson E R}, - journal={Comput. 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Phys.}, + month = {Jan}, + numpages = {0}, + pages = {33--83}, + publisher = {American Physical Society}, + title = {Quantum Monte Carlo simulations of solids}, + url = {https://link.aps.org/doi/10.1103/RevModPhys.73.33}, + volume = {73}, + year = {2001}, + bdsk-url-1 = {https://link.aps.org/doi/10.1103/RevModPhys.73.33}, + bdsk-url-2 = {https://doi.org/10.1103/RevModPhys.73.33}} @article{Kolorenc_2011, - author={Kolorenc, J. and Mitas, L}, - journal={Rep. Prog. Phys.}, - volume={74}, - pages={026502}, - year={2011} -} - + author = {Kolorenc, J. and Mitas, L}, + journal = {Rep. Prog. Phys.}, + pages = {026502}, + volume = {74}, + year = {2011}} @article{Carlson_2015, - title = {Quantum Monte Carlo methods for nuclear physics}, - author = {Carlson, J. and Gandolfi, S. and Pederiva, F. and Pieper, Steven C. and Schiavilla, R. and Schmidt, K. E. and Wiringa, R. B.}, - journal = {Rev. Mod. Phys.}, - volume = {87}, - issue = {3}, - pages = {1067--1118}, - numpages = {52}, - year = {2015}, - month = {Sep}, - publisher = {American Physical Society}, - doi = {10.1103/RevModPhys.87.1067}, - url = {https://link.aps.org/doi/10.1103/RevModPhys.87.1067} -} + author = {Carlson, J. and Gandolfi, S. and Pederiva, F. and Pieper, Steven C. and Schiavilla, R. and Schmidt, K. E. and Wiringa, R. B.}, + doi = {10.1103/RevModPhys.87.1067}, + issue = {3}, + journal = {Rev. Mod. Phys.}, + month = {Sep}, + numpages = {52}, + pages = {1067--1118}, + publisher = {American Physical Society}, + title = {Quantum Monte Carlo methods for nuclear physics}, + url = {https://link.aps.org/doi/10.1103/RevModPhys.87.1067}, + volume = {87}, + year = {2015}, + bdsk-url-1 = {https://link.aps.org/doi/10.1103/RevModPhys.87.1067}, + bdsk-url-2 = {https://doi.org/10.1103/RevModPhys.87.1067}} -@article{assaraf_99, -author = { -R. Assaraf and P. Azaria and M. Caffarel and P. Lecheminant}, -title={Metal-insulator transition in the one-dimensional SU(N) Hubbard model}, -journal={Phys. Rev. B}, -volume={60}, -pages={ 2299}, -year={ 1999} -} +@article{Assaraf_1999B, + author = {R. Assaraf and P. Azaria and M. Caffarel and P. Lecheminant}, + date-modified = {2022-09-15 09:16:25 +0200}, + journal = {Phys. Rev. B}, + pages = {2299}, + title = {Metal-insulator transition in the one-dimensional SU(N) Hubbard model}, + volume = {60}, + year = {1999}} -@article{caffarel_00, -author = {M. Caffarel and R. Assaraf }, -title={ A pedagogical introduction to quantum Monte Carlo}, -journal={Lecture Notes in Chemistry}, -editor={M. Defranceschi and C. Le Bris Springer}, -pages={45}, -year={2000} -} +@article{Caffarel_2000, + author = {M. Caffarel and R. Assaraf}, + date-modified = {2022-09-15 09:15:59 +0200}, + editor = {M. Defranceschi and C. Le Bris Springer}, + journal = {Lecture Notes in Chemistry}, + pages = {45}, + title = {A pedagogical introduction to quantum Monte Carlo}, + year = {2000}} @article{rothstein_93, -author = {Peter Belohorec and Stuart M. Rothstein and Jan Vrbik}, -title = {Infinitesimal differential diffusion quantum Monte Carlo study of CuH spectroscopic constants}, -journal = {The Journal of Chemical Physics}, -volume = {98}, -number = {8}, -pages = {6401-6405}, -year = {1993}, -doi = {10.1063/1.464838}, -URL = { - https://doi.org/10.1063/1.464838 -}, -eprint = { - https://doi.org/10.1063/1.464838 -} -} + author = {Peter Belohorec and Stuart M. Rothstein and Jan Vrbik}, + doi = {10.1063/1.464838}, + eprint = {https://doi.org/10.1063/1.464838}, + journal = {The Journal of Chemical Physics}, + number = {8}, + pages = {6401-6405}, + title = {Infinitesimal differential diffusion quantum Monte Carlo study of CuH spectroscopic constants}, + url = {https://doi.org/10.1063/1.464838}, + volume = {98}, + year = {1993}, + bdsk-url-1 = {https://doi.org/10.1063/1.464838}} @article{Applencourt_2014, -author = {Peter Belohorec and Stuart M. Rothstein and Jan Vrbik}, -title = {Infinitesimal differential diffusion quantum Monte Carlo study of CuH spectroscopic constants}, -journal = {The Journal of Chemical Physics}, -volume = {98}, -number = {8}, -pages = {6401-6405}, -year = {1993}, -doi = {10.1063/1.464838}, -URL = { - https://doi.org/10.1063/1.464838 -}, -eprint = { - https://doi.org/10.1063/1.464838 -} -} - - - - + author = {Peter Belohorec and Stuart M. 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Caffarel}, + date-added = {2017-10-07 12:17:36 +0000}, + date-modified = {2017-10-07 12:17:36 +0000}, + doi = {10.5281/zenodo.200970}, + month = {Dec}, + note = {\url{https://github.com/LCPQ/quantum_package}}, + publisher = {Zenodo}, + title = {Quantum Package v1.0}, + url = {https://github.com/LCPQ/quantum_package}, + year = {2016}, + bdsk-url-1 = {https://github.com/LCPQ/quantum_package}, + bdsk-url-2 = {http://dx.doi.org/10.5281/zenodo.200970}} @article{Haghighi_Mood_2017, - Author = {Haghighi Mood, Kaveh and L{\"u}chow, Arne}, - Doi = {10.1021/acs.jpca.7b05798}, - Issn = {1520-5215}, - Journal = {The Journal of Physical Chemistry A}, - Month = {Aug}, - Number = {32}, - Pages = {6165--6171}, - Publisher = {American Chemical Society (ACS)}, - Title = {Full Wave Function Optimization with Quantum Monte Carlo and Its Effect on the Dissociation Energy of FeS}, - Url = {http://dx.doi.org/10.1021/acs.jpca.7b05798}, - Volume = {121}, - Year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/acs.jpca.7b05798}} + author = {Haghighi Mood, Kaveh and L{\"u}chow, Arne}, + doi = {10.1021/acs.jpca.7b05798}, + issn = {1520-5215}, + journal = {The Journal of Physical Chemistry A}, + month = {Aug}, + number = {32}, + pages = {6165--6171}, + publisher = {American Chemical Society (ACS)}, + title = {Full Wave Function Optimization with Quantum Monte Carlo and Its Effect on the Dissociation Energy of FeS}, + url = {http://dx.doi.org/10.1021/acs.jpca.7b05798}, + volume = {121}, + year = {2017}, + bdsk-url-1 = {http://dx.doi.org/10.1021/acs.jpca.7b05798}} @article{Dzubak_2017, - Author = {Dzubak, Allison L. and Krogel, Jaron T. and Reboredo, Fernando A.}, - Doi = {10.1063/1.4991414}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Jul}, - Number = {2}, - Pages = {024102}, - Publisher = {AIP Publishing}, - Title = {Quantitative estimation of localization errors of 3d transition metal pseudopotentials in diffusion Monte Carlo}, - Url = {http://dx.doi.org/10.1063/1.4991414}, - Volume = {147}, - Year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4991414}} + author = {Dzubak, Allison L. and Krogel, Jaron T. and Reboredo, Fernando A.}, + doi = {10.1063/1.4991414}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Jul}, + number = {2}, + pages = {024102}, + publisher = {AIP Publishing}, + title = {Quantitative estimation of localization errors of 3d transition metal pseudopotentials in diffusion Monte Carlo}, + url = {http://dx.doi.org/10.1063/1.4991414}, + volume = {147}, + year = {2017}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4991414}} @article{Doblhoff_Dier_2016, - Author = {Doblhoff-Dier, Katharina and Meyer, J{\"o}rg and Hoggan, Philip E. and Kroes, Geert-Jan and Wagner, Lucas K.}, - Doi = {10.1021/acs.jctc.6b00160}, - Issn = {1549-9626}, - Journal = {Journal of Chemical Theory and Computation}, - Month = {Jun}, - Number = {6}, - Pages = {2583--2597}, - Publisher = {American Chemical Society (ACS)}, - Title = {Diffusion Monte Carlo for Accurate Dissociation Energies of 3d Transition Metal Containing Molecules}, - Url = {http://dx.doi.org/10.1021/acs.jctc.6b00160}, - Volume = {12}, - Year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/acs.jctc.6b00160}} + author = {Doblhoff-Dier, Katharina and Meyer, J{\"o}rg and Hoggan, Philip E. and Kroes, Geert-Jan and Wagner, Lucas K.}, + doi = {10.1021/acs.jctc.6b00160}, + issn = {1549-9626}, + journal = {Journal of Chemical Theory and Computation}, + month = {Jun}, + number = {6}, + pages = {2583--2597}, + publisher = {American Chemical Society (ACS)}, + title = {Diffusion Monte Carlo for Accurate Dissociation Energies of 3d Transition Metal Containing Molecules}, + url = {http://dx.doi.org/10.1021/acs.jctc.6b00160}, + volume = {12}, + year = {2016}, + bdsk-url-1 = {http://dx.doi.org/10.1021/acs.jctc.6b00160}} @article{Dubeck__2016, - Author = {Dubeck{\'y}, Mat{\'u}{\v s} and Mit\'a\v{s}, Lubos and Jure{\v c}ka, Petr}, - Doi = {10.1021/acs.chemrev.5b00577}, - Issn = {1520-6890}, - Journal = {Chemical Reviews}, - Month = {May}, - Number = {9}, - Pages = {5188--5215}, - Publisher = {American Chemical Society (ACS)}, - Title = {Noncovalent Interactions by Quantum Monte Carlo}, - Url = {http://dx.doi.org/10.1021/acs.chemrev.5b00577}, - Volume = {116}, - Year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/acs.chemrev.5b00577}} + author = {Dubeck{\'y}, Mat{\'u}{\v s} and Mit\'a\v{s}, Lubos and Jure{\v c}ka, Petr}, + doi = {10.1021/acs.chemrev.5b00577}, + issn = {1520-6890}, + journal = {Chemical Reviews}, + month = {May}, + number = {9}, + pages = {5188--5215}, + publisher = {American Chemical Society (ACS)}, + title = {Noncovalent Interactions by Quantum Monte Carlo}, + url = {http://dx.doi.org/10.1021/acs.chemrev.5b00577}, + volume = {116}, + year = {2016}, + bdsk-url-1 = {http://dx.doi.org/10.1021/acs.chemrev.5b00577}} @article{Melton_2016, - Author = {Melton, Cody A. and Zhu, Minyi and Guo, Shi and Ambrosetti, Alberto and Pederiva, Francesco and Mit\'a\v{s}, Lubos}, - Doi = {10.1103/physreva.93.042502}, - Issn = {2469-9934}, - Journal = {Physical Review A}, - Month = {Apr}, - Number = {4}, - Publisher = {American Physical Society (APS)}, - Title = {Spin-orbit interactions in electronic structure quantum Monte Carlo methods}, - Url = {http://dx.doi.org/10.1103/PhysRevA.93.042502}, - Volume = {93}, - Year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.93.042502}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/physreva.93.042502}} + author = {Melton, Cody A. and Zhu, Minyi and Guo, Shi and Ambrosetti, Alberto and Pederiva, Francesco and Mit\'a\v{s}, Lubos}, + doi = {10.1103/physreva.93.042502}, + issn = {2469-9934}, + journal = {Physical Review A}, + month = {Apr}, + number = {4}, + publisher = {American Physical Society (APS)}, + title = {Spin-orbit interactions in electronic structure quantum Monte Carlo methods}, + url = {http://dx.doi.org/10.1103/PhysRevA.93.042502}, + volume = {93}, + year = {2016}, + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevA.93.042502}, + bdsk-url-2 = {http://dx.doi.org/10.1103/physreva.93.042502}} @article{Luchow_2015, - Author = {L{\"u}chow, Arne and Sturm, Alexander and Schulte, Christoph and Haghighi Mood, Kaveh}, - Doi = {10.1063/1.4909554}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Feb}, - Number = {8}, - Pages = {084111}, - Publisher = {AIP Publishing}, - Title = {Generic expansion of the Jastrow correlation factor in polynomials satisfying symmetry and cusp conditions}, - Url = {http://dx.doi.org/10.1063/1.4909554}, - Volume = {142}, - Year = {2015}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4909554}} + author = {L{\"u}chow, Arne and Sturm, Alexander and Schulte, Christoph and Haghighi Mood, Kaveh}, + doi = {10.1063/1.4909554}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Feb}, + number = {8}, + pages = {084111}, + publisher = {AIP Publishing}, + title = {Generic expansion of the Jastrow correlation factor in polynomials satisfying symmetry and cusp conditions}, + url = {http://dx.doi.org/10.1063/1.4909554}, + volume = {142}, + year = {2015}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4909554}} @article{Kannengiesser_2014, - Author = {Kannengie{\ss}er, Raphaela and Klahm, Sebastian and Vinh Lam Nguyen, Ha and L{\"u}chow, Arne and Stahl, Wolfgang}, - Doi = {10.1063/1.4901980}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Nov}, - Number = {20}, - Pages = {204308}, - Publisher = {AIP Publishing}, - Title = {The effects of methyl internal rotation and 14N quadrupole coupling in the microwave spectra of two conformers of N,N-diethylacetamide}, - Url = {http://dx.doi.org/10.1063/1.4901980}, - Volume = {141}, - Year = {2014}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4901980}} + author = {Kannengie{\ss}er, Raphaela and Klahm, Sebastian and Vinh Lam Nguyen, Ha and L{\"u}chow, Arne and Stahl, Wolfgang}, + doi = {10.1063/1.4901980}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Nov}, + number = {20}, + pages = {204308}, + publisher = {AIP Publishing}, + title = {The effects of methyl internal rotation and 14N quadrupole coupling in the microwave spectra of two conformers of N,N-diethylacetamide}, + url = {http://dx.doi.org/10.1063/1.4901980}, + volume = {141}, + year = {2014}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4901980}} @article{Klahm_2014, - Author = {Klahm, Sebastian and L{\"u}chow, Arne}, - Doi = {10.1016/j.cplett.2014.03.044}, - Issn = {0009-2614}, - Journal = {Chemical Physics Letters}, - Month = {Apr}, - Pages = {7--9}, - Publisher = {Elsevier BV}, - Title = {Accurate rotational barrier calculations with diffusion quantum Monte Carlo}, - Url = {http://dx.doi.org/10.1016/j.cplett.2014.03.044}, - Volume = {600}, - Year = {2014}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.cplett.2014.03.044}} + author = {Klahm, Sebastian and L{\"u}chow, Arne}, + doi = {10.1016/j.cplett.2014.03.044}, + issn = {0009-2614}, + journal = {Chemical Physics Letters}, + month = {Apr}, + pages = {7--9}, + publisher = {Elsevier BV}, + title = {Accurate rotational barrier calculations with diffusion quantum Monte Carlo}, + url = {http://dx.doi.org/10.1016/j.cplett.2014.03.044}, + volume = {600}, + year = {2014}, + bdsk-url-1 = {http://dx.doi.org/10.1016/j.cplett.2014.03.044}} @article{Wagner_2013, - Author = {Wagner, Lucas K.}, - Doi = {10.1002/qua.24526}, - Issn = {0020-7608}, - Journal = {International Journal of Quantum Chemistry}, - Month = {Aug}, - Number = {2}, - Pages = {94--101}, - Publisher = {Wiley-Blackwell}, - Title = {Quantum Monte Carlo forAb Initiocalculations of energy-relevant materials}, - Url = {http://dx.doi.org/10.1002/qua.24526}, - Volume = {114}, - Year = {2013}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/qua.24526}} + author = {Wagner, Lucas K.}, + doi = {10.1002/qua.24526}, + issn = {0020-7608}, + journal = {International Journal of Quantum Chemistry}, + month = {Aug}, + number = {2}, + pages = {94--101}, + publisher = {Wiley-Blackwell}, + title = {Quantum Monte Carlo forAb Initiocalculations of energy-relevant materials}, + url = {http://dx.doi.org/10.1002/qua.24526}, + volume = {114}, + year = {2013}, + bdsk-url-1 = {http://dx.doi.org/10.1002/qua.24526}} @article{Li_2013, - Author = {Li, Yan-Ni and Wang, Shengguang and Wang, Tao and Gao, Rui and Geng, Chun-Yu and Li, Yong-Wang and Wang, Jianguo and Jiao, Haijun}, - Doi = {10.1002/cphc.201201043}, - Issn = {1439-4235}, - Journal = {ChemPhysChem}, - Month = {Mar}, - Number = {6}, - Pages = {1182--1189}, - Publisher = {Wiley-Blackwell}, - Title = {Energies and Spin States of FeS0/−, FeS20/−, Fe2S20/−, Fe3S40/−, and Fe4S40/−Clusters}, - Url = {http://dx.doi.org/10.1002/cphc.201201043}, - Volume = {14}, - Year = {2013}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/cphc.201201043}} + author = {Li, Yan-Ni and Wang, Shengguang and Wang, Tao and Gao, Rui and Geng, Chun-Yu and Li, Yong-Wang and Wang, Jianguo and Jiao, Haijun}, + doi = {10.1002/cphc.201201043}, + issn = {1439-4235}, + journal = {ChemPhysChem}, + month = {Mar}, + number = {6}, + pages = {1182--1189}, + publisher = {Wiley-Blackwell}, + title = {Energies and Spin States of FeS0/−, FeS20/−, Fe2S20/−, Fe3S40/−, and Fe4S40/−Clusters}, + url = {http://dx.doi.org/10.1002/cphc.201201043}, + volume = {14}, + year = {2013}, + bdsk-url-1 = {http://dx.doi.org/10.1002/cphc.201201043}} @article{Austin_2012, - Author = {Austin, Brian M. and Zubarev, Dmitry Yu. and Lester, William A.}, - Doi = {10.1021/cr2001564}, - Issn = {1520-6890}, - Journal = {Chemical Reviews}, - Month = {Jan}, - Number = {1}, - Pages = {263--288}, - Publisher = {American Chemical Society (ACS)}, - Title = {Quantum Monte Carlo and Related Approaches}, - Url = {http://dx.doi.org/10.1021/cr2001564}, - Volume = {112}, - Year = {2012}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/cr2001564}} + author = {Austin, Brian M. and Zubarev, Dmitry Yu. and Lester, William A.}, + doi = {10.1021/cr2001564}, + issn = {1520-6890}, + journal = {Chemical Reviews}, + month = {Jan}, + number = {1}, + pages = {263--288}, + publisher = {American Chemical Society (ACS)}, + title = {Quantum Monte Carlo and Related Approaches}, + url = {http://dx.doi.org/10.1021/cr2001564}, + volume = {112}, + year = {2012}, + bdsk-url-1 = {http://dx.doi.org/10.1021/cr2001564}} @article{Petz_2011, - Author = {Petz, Ren{\'e} and L{\"u}chow, Arne}, - Doi = {10.1002/cphc.201000942}, - Issn = {1439-4235}, - Journal = {ChemPhysChem}, - Month = {Mar}, - Number = {10}, - Pages = {2031--2034}, - Publisher = {Wiley-Blackwell}, - Title = {Energetics of Diatomic Transition Metal Sulfides ScS to FeS with Diffusion Quantum Monte Carlo}, - Url = {http://dx.doi.org/10.1002/cphc.201000942}, - Volume = {12}, - Year = {2011}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/cphc.201000942}} + author = {Petz, Ren{\'e} and L{\"u}chow, Arne}, + doi = {10.1002/cphc.201000942}, + issn = {1439-4235}, + journal = {ChemPhysChem}, + month = {Mar}, + number = {10}, + pages = {2031--2034}, + publisher = {Wiley-Blackwell}, + title = {Energetics of Diatomic Transition Metal Sulfides ScS to FeS with Diffusion Quantum Monte Carlo}, + url = {http://dx.doi.org/10.1002/cphc.201000942}, + volume = {12}, + year = {2011}, + bdsk-url-1 = {http://dx.doi.org/10.1002/cphc.201000942}} @article{Luchow_2011, - Author = {L{\"u}chow, Arne}, - Doi = {10.1002/wcms.40}, - Issn = {1759-0876}, - Journal = {Wiley Interdisciplinary Reviews: Computational Molecular Science}, - Month = {Apr}, - Number = {3}, - Pages = {388--402}, - Publisher = {Wiley-Blackwell}, - Title = {Quantum Monte Carlo methods}, - Url = {http://dx.doi.org/10.1002/wcms.40}, - Volume = {1}, - Year = {2011}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/wcms.40}} + author = {L{\"u}chow, Arne}, + doi = {10.1002/wcms.40}, + issn = {1759-0876}, + journal = {Wiley Interdisciplinary Reviews: Computational Molecular Science}, + month = {Apr}, + number = {3}, + pages = {388--402}, + publisher = {Wiley-Blackwell}, + title = {Quantum Monte Carlo methods}, + url = {http://dx.doi.org/10.1002/wcms.40}, + volume = {1}, + year = {2011}, + bdsk-url-1 = {http://dx.doi.org/10.1002/wcms.40}} @article{Wang_2011, - Author = {Wang, Li and Huang, Dao-ling and Zhen, Jun-feng and Zhang, Qun and Chen, Yang}, - Doi = {10.1088/1674-0068/24/01/1-3}, - Issn = {2327-2244}, - Journal = {Chinese Journal of Chemical Physics}, - Month = {Feb}, - Number = {1}, - Pages = {1--3}, - Publisher = {AIP Publishing}, - Title = {Experimental Determination of the Vibrational Constants of FeS(X5Δ) by Dispersed Fluorescence Spectroscopy}, - Url = {http://dx.doi.org/10.1088/1674-0068/24/01/1-3}, - Volume = {24}, - Year = {2011}, - Bdsk-Url-1 = {http://dx.doi.org/10.1088/1674-0068/24/01/1-3}} + author = {Wang, Li and Huang, Dao-ling and Zhen, Jun-feng and Zhang, Qun and Chen, Yang}, + doi = {10.1088/1674-0068/24/01/1-3}, + issn = {2327-2244}, + journal = {Chinese Journal of Chemical Physics}, + month = {Feb}, + number = {1}, + pages = {1--3}, + publisher = {AIP Publishing}, + title = {Experimental Determination of the Vibrational Constants of FeS(X5Δ) by Dispersed Fluorescence Spectroscopy}, + url = {http://dx.doi.org/10.1088/1674-0068/24/01/1-3}, + volume = {24}, + year = {2011}, + bdsk-url-1 = {http://dx.doi.org/10.1088/1674-0068/24/01/1-3}} @article{Casula_2010, - Author = {Casula, Michele and Moroni, Saverio and Sorella, Sandro and Filippi, Claudia}, - Doi = {10.1063/1.3380831}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Apr}, - Number = {15}, - Pages = {154113}, - Publisher = {AIP Publishing}, - Title = {Size-consistent variational approaches to nonlocal pseudopotentials: Standard and lattice regularized diffusion Monte Carlo methods revisited}, - Url = {http://dx.doi.org/10.1063/1.3380831}, - Volume = {132}, - Year = {2010}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.3380831}} + author = {Casula, Michele and Moroni, Saverio and Sorella, Sandro and Filippi, Claudia}, + doi = {10.1063/1.3380831}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Apr}, + number = {15}, + pages = {154113}, + publisher = {AIP Publishing}, + title = {Size-consistent variational approaches to nonlocal pseudopotentials: Standard and lattice regularized diffusion Monte Carlo methods revisited}, + url = {http://dx.doi.org/10.1063/1.3380831}, + volume = {132}, + year = {2010}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.3380831}} @article{Nemec_2010, - Author = {Nemec, Norbert and Towler, Michael D. and Needs, R. J.}, - Doi = {10.1063/1.3288054}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Jan}, - Number = {3}, - Pages = {034111}, - Publisher = {AIP Publishing}, - Title = {Benchmark all-electron ab initio quantum Monte Carlo calculations for small molecules}, - Url = {http://dx.doi.org/10.1063/1.3288054}, - Volume = {132}, - Year = {2010}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.3288054}} + author = {Nemec, Norbert and Towler, Michael D. and Needs, R. J.}, + doi = {10.1063/1.3288054}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Jan}, + number = {3}, + pages = {034111}, + publisher = {AIP Publishing}, + title = {Benchmark all-electron ab initio quantum Monte Carlo calculations for small molecules}, + url = {http://dx.doi.org/10.1063/1.3288054}, + volume = {132}, + year = {2010}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.3288054}} @article{Casula_2009, - Author = {Casula, Michele and Marchi, Mariapia and Azadi, Sam and Sorella, Sandro}, - Doi = {10.1016/j.cplett.2009.07.005}, - Issn = {0009-2614}, - Journal = {Chemical Physics Letters}, - Month = {Aug}, - Number = {4-6}, - Pages = {255--258}, - Publisher = {Elsevier BV}, - Title = {A consistent description of the iron dimer spectrum with a correlated single-determinant wave function}, - Url = {http://dx.doi.org/10.1016/j.cplett.2009.07.005}, - Volume = {477}, - Year = {2009}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.cplett.2009.07.005}} + author = {Casula, Michele and Marchi, Mariapia and Azadi, Sam and Sorella, Sandro}, + doi = {10.1016/j.cplett.2009.07.005}, + issn = {0009-2614}, + journal = {Chemical Physics Letters}, + month = {Aug}, + number = {4-6}, + pages = {255--258}, + publisher = {Elsevier BV}, + title = {A consistent description of the iron dimer spectrum with a correlated single-determinant wave function}, + url = {http://dx.doi.org/10.1016/j.cplett.2009.07.005}, + volume = {477}, + year = {2009}, + bdsk-url-1 = {http://dx.doi.org/10.1016/j.cplett.2009.07.005}} @article{Liang_2009, - Author = {Liang, Binyong and Wang, Xuefeng and Andrews, Lester}, - Doi = {10.1021/jp900994c}, - Issn = {1520-5215}, - Journal = {The Journal of Physical Chemistry A}, - Month = {May}, - Number = {18}, - Pages = {5375--5384}, - Publisher = {American Chemical Society (ACS)}, - Title = {Infrared Spectra and Density Functional Theory Calculations of Group 8 Transition Metal Sulfide Molecules}, - Url = {http://dx.doi.org/10.1021/jp900994c}, - Volume = {113}, - Year = {2009}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/jp900994c}} + author = {Liang, Binyong and Wang, Xuefeng and Andrews, Lester}, + doi = {10.1021/jp900994c}, + issn = {1520-5215}, + journal = {The Journal of Physical Chemistry A}, + month = {May}, + number = {18}, + pages = {5375--5384}, + publisher = {American Chemical Society (ACS)}, + title = {Infrared Spectra and Density Functional Theory Calculations of Group 8 Transition Metal Sulfide Molecules}, + url = {http://dx.doi.org/10.1021/jp900994c}, + volume = {113}, + year = {2009}, + bdsk-url-1 = {http://dx.doi.org/10.1021/jp900994c}} @article{Burkatzki_2008, - Author = {Burkatzki, M. and Filippi, Claudia and Dolg, M.}, - Doi = {10.1063/1.2987872}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Oct}, - Number = {16}, - Pages = {164115}, - Publisher = {AIP Publishing}, - Title = {Energy-consistent small-core pseudopotentials for 3d-transition metals adapted to quantum Monte Carlo calculations}, - Url = {http://dx.doi.org/10.1063/1.2987872}, - Volume = {129}, - Year = {2008}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2987872}} + author = {Burkatzki, M. and Filippi, Claudia and Dolg, M.}, + doi = {10.1063/1.2987872}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Oct}, + number = {16}, + pages = {164115}, + publisher = {AIP Publishing}, + title = {Energy-consistent small-core pseudopotentials for 3d-transition metals adapted to quantum Monte Carlo calculations}, + url = {http://dx.doi.org/10.1063/1.2987872}, + volume = {129}, + year = {2008}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.2987872}} @article{Bande_2008, - Author = {Bande, Annika and L{\"u}chow, Arne}, - Doi = {10.1039/b803571g}, - Issn = {1463-9084}, - Journal = {Physical Chemistry Chemical Physics}, - Number = {23}, - Pages = {3371}, - Publisher = {Royal Society of Chemistry (RSC)}, - Title = {Vanadium oxide compounds with quantum Monte Carlo}, - Url = {http://dx.doi.org/10.1039/b803571g}, - Volume = {10}, - Year = {2008}, - Bdsk-Url-1 = {http://dx.doi.org/10.1039/b803571g}} + author = {Bande, Annika and L{\"u}chow, Arne}, + doi = {10.1039/b803571g}, + issn = {1463-9084}, + journal = {Physical Chemistry Chemical Physics}, + number = {23}, + pages = {3371}, + publisher = {Royal Society of Chemistry (RSC)}, + title = {Vanadium oxide compounds with quantum Monte Carlo}, + url = {http://dx.doi.org/10.1039/b803571g}, + volume = {10}, + year = {2008}, + bdsk-url-1 = {http://dx.doi.org/10.1039/b803571g}} @article{Burkatzki_2007, - Author = {Burkatzki, M. and Filippi, C. and Dolg, M.}, - Doi = {10.1063/1.2741534}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Jun}, - Number = {23}, - Pages = {234105}, - Publisher = {AIP Publishing}, - Title = {Energy-consistent pseudopotentials for quantum Monte Carlo calculations}, - Url = {http://dx.doi.org/10.1063/1.2741534}, - Volume = {126}, - Year = {2007}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2741534}} + author = {Burkatzki, M. and Filippi, C. and Dolg, M.}, + doi = {10.1063/1.2741534}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Jun}, + number = {23}, + pages = {234105}, + publisher = {AIP Publishing}, + title = {Energy-consistent pseudopotentials for quantum Monte Carlo calculations}, + url = {http://dx.doi.org/10.1063/1.2741534}, + volume = {126}, + year = {2007}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.2741534}} @article{Clima_2007, - Author = {Clima, Sergiu and Hendrickx, Marc F.A.}, - Doi = {10.1016/j.cplett.2007.01.073}, - Issn = {0009-2614}, - Journal = {Chemical Physics Letters}, - Month = {Mar}, - Number = {4-6}, - Pages = {341--345}, - Publisher = {Elsevier BV}, - Title = {Photoelectron spectra of FeS− explained by a CASPT2 ab initio study}, - Url = {http://dx.doi.org/10.1016/j.cplett.2007.01.073}, - Volume = {436}, - Year = {2007}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.cplett.2007.01.073}} + author = {Clima, Sergiu and Hendrickx, Marc F.A.}, + doi = {10.1016/j.cplett.2007.01.073}, + issn = {0009-2614}, + journal = {Chemical Physics Letters}, + month = {Mar}, + number = {4-6}, + pages = {341--345}, + publisher = {Elsevier BV}, + title = {Photoelectron spectra of FeS− explained by a CASPT2 ab initio study}, + url = {http://dx.doi.org/10.1016/j.cplett.2007.01.073}, + volume = {436}, + year = {2007}, + bdsk-url-1 = {http://dx.doi.org/10.1016/j.cplett.2007.01.073}} @article{Toulouse_2007, - Author = {Toulouse, Julien and Umrigar, C. J.}, - Doi = {10.1063/1.2437215}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Feb}, - Number = {8}, - Pages = {084102}, - Publisher = {AIP Publishing}, - Title = {Optimization of quantum Monte Carlo wave functions by energy minimization}, - Url = {http://dx.doi.org/10.1063/1.2437215}, - Volume = {126}, - Year = {2007}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2437215}} + author = {Toulouse, Julien and Umrigar, C. J.}, + doi = {10.1063/1.2437215}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Feb}, + number = {8}, + pages = {084102}, + publisher = {AIP Publishing}, + title = {Optimization of quantum Monte Carlo wave functions by energy minimization}, + url = {http://dx.doi.org/10.1063/1.2437215}, + volume = {126}, + year = {2007}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.2437215}} @article{Wu_2007, - Author = {Wu, Z. J. and Wang, M. Y. and Su, Z. M.}, - Doi = {10.1002/jcc.20603}, - Issn = {1096-987X}, - Journal = {Journal of Computational Chemistry}, - Month = {Feb}, - Number = {3}, - Pages = {703--714}, - Publisher = {Wiley-Blackwell}, - Title = {Electronic structures and chemical bonding in diatomic ScX to ZnX (X = S, Se, Te)}, - Url = {http://dx.doi.org/10.1002/jcc.20603}, - Volume = {28}, - Year = {2007}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/jcc.20603}} + author = {Wu, Z. J. and Wang, M. Y. and Su, Z. M.}, + doi = {10.1002/jcc.20603}, + issn = {1096-987X}, + journal = {Journal of Computational Chemistry}, + month = {Feb}, + number = {3}, + pages = {703--714}, + publisher = {Wiley-Blackwell}, + title = {Electronic structures and chemical bonding in diatomic ScX to ZnX (X = S, Se, Te)}, + url = {http://dx.doi.org/10.1002/jcc.20603}, + volume = {28}, + year = {2007}, + bdsk-url-1 = {http://dx.doi.org/10.1002/jcc.20603}} @article{Wagner_2007, - Author = {Wagner, Lucas K. and Mit\'a\v{s}, Lubos}, - Doi = {10.1063/1.2428294}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Jan}, - Number = {3}, - Pages = {034105}, - Publisher = {AIP Publishing}, - Title = {Energetics and dipole moment of transition metal monoxides by quantum Monte Carlo}, - Url = {http://dx.doi.org/10.1063/1.2428294}, - Volume = {126}, - Year = {2007}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2428294}} + author = {Wagner, Lucas K. and Mit\'a\v{s}, Lubos}, + doi = {10.1063/1.2428294}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Jan}, + number = {3}, + pages = {034105}, + publisher = {AIP Publishing}, + title = {Energetics and dipole moment of transition metal monoxides by quantum Monte Carlo}, + url = {http://dx.doi.org/10.1063/1.2428294}, + volume = {126}, + year = {2007}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.2428294}} @article{Casula_2006, - Author = {Casula, Michele}, - Doi = {10.1103/physrevb.74.161102}, - Issn = {1550-235X}, - Journal = {Physical Review B}, - Month = {Oct}, - Number = {16}, - Publisher = {American Physical Society (APS)}, - Title = {Beyond the locality approximation in the standard diffusion Monte Carlo method}, - Url = {http://dx.doi.org/10.1103/PhysRevB.74.161102}, - Volume = {74}, - Year = {2006}, - Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevB.74.161102}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/physrevb.74.161102}} + author = {Casula, Michele}, + doi = {10.1103/physrevb.74.161102}, + issn = {1550-235X}, + journal = {Physical Review B}, + month = {Oct}, + number = {16}, + publisher = {American Physical Society (APS)}, + title = {Beyond the locality approximation in the standard diffusion Monte Carlo method}, + url = {http://dx.doi.org/10.1103/PhysRevB.74.161102}, + volume = {74}, + year = {2006}, + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevB.74.161102}, + bdsk-url-2 = {http://dx.doi.org/10.1103/physrevb.74.161102}} @article{Schultz_2005, - Author = {Schultz, Nathan E. and Zhao, Yan and Truhlar, Donald G.}, - Doi = {10.1021/jp0539223}, - Issn = {1520-5215}, - Journal = {The Journal of Physical Chemistry A}, - Month = {Dec}, - Number = {49}, - Pages = {11127--11143}, - Publisher = {American Chemical Society (ACS)}, - Title = {Density Functionals for Inorganometallic and Organometallic Chemistry}, - Url = {http://dx.doi.org/10.1021/jp0539223}, - Volume = {109}, - Year = {2005}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/jp0539223}} + author = {Schultz, Nathan E. and Zhao, Yan and Truhlar, Donald G.}, + doi = {10.1021/jp0539223}, + issn = {1520-5215}, + journal = {The Journal of Physical Chemistry A}, + month = {Dec}, + number = {49}, + pages = {11127--11143}, + publisher = {American Chemical Society (ACS)}, + title = {Density Functionals for Inorganometallic and Organometallic Chemistry}, + url = {http://dx.doi.org/10.1021/jp0539223}, + volume = {109}, + year = {2005}, + bdsk-url-1 = {http://dx.doi.org/10.1021/jp0539223}} @article{Diedrich_2005, - Author = {Diedrich, Christian and L{\"u}chow, Arne and Grimme, Stefan}, - Doi = {10.1063/1.1846654}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Jan}, - Number = {2}, - Pages = {021101}, - Publisher = {AIP Publishing}, - Title = {Performance of diffusion Monte Carlo for the first dissociation energies of transition metal carbonyls}, - Url = {http://dx.doi.org/10.1063/1.1846654}, - Volume = {122}, - Year = {2005}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.1846654}} + author = {Diedrich, Christian and L{\"u}chow, Arne and Grimme, Stefan}, + doi = {10.1063/1.1846654}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Jan}, + number = {2}, + pages = {021101}, + publisher = {AIP Publishing}, + title = {Performance of diffusion Monte Carlo for the first dissociation energies of transition metal carbonyls}, + url = {http://dx.doi.org/10.1063/1.1846654}, + volume = {122}, + year = {2005}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.1846654}} @article{Takano_2004, - Author = {Takano, Shuro and Yamamoto, Satoshi and Saito, Shuji}, - Doi = {10.1016/j.jms.2004.01.003}, - Issn = {0022-2852}, - Journal = {Journal of Molecular Spectroscopy}, - Month = {Apr}, - Number = {2}, - Pages = {137--144}, - Publisher = {Elsevier BV}, - Title = {The microwave spectrum of the FeS radical}, - Url = {http://dx.doi.org/10.1016/j.jms.2004.01.003}, - Volume = {224}, - Year = {2004}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.jms.2004.01.003}} + author = {Takano, Shuro and Yamamoto, Satoshi and Saito, Shuji}, + doi = {10.1016/j.jms.2004.01.003}, + issn = {0022-2852}, + journal = {Journal of Molecular Spectroscopy}, + month = {Apr}, + number = {2}, + pages = {137--144}, + publisher = {Elsevier BV}, + title = {The microwave spectrum of the FeS radical}, + url = {http://dx.doi.org/10.1016/j.jms.2004.01.003}, + volume = {224}, + year = {2004}, + bdsk-url-1 = {http://dx.doi.org/10.1016/j.jms.2004.01.003}} @article{Wagner_2003, - Author = {Wagner, Lucas and Mit\'a\v{s}, Lubos}, - Doi = {10.1016/s0009-2614(03)00128-3}, - Issn = {0009-2614}, - Journal = {Chemical Physics Letters}, - Month = {Mar}, - Number = {3-4}, - Pages = {412--417}, - Publisher = {Elsevier BV}, - Title = {A quantum Monte Carlo study of electron correlation in transition metal oxygen molecules}, - Url = {http://dx.doi.org/10.1016/S0009-2614(03)00128-3}, - Volume = {370}, - Year = {2003}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/S0009-2614(03)00128-3}, - Bdsk-Url-2 = {http://dx.doi.org/10.1016/s0009-2614(03)00128-3}} + author = {Wagner, Lucas and Mit\'a\v{s}, Lubos}, + doi = {10.1016/s0009-2614(03)00128-3}, + issn = {0009-2614}, + journal = {Chemical Physics Letters}, + month = {Mar}, + number = {3-4}, + pages = {412--417}, + publisher = {Elsevier BV}, + title = {A quantum Monte Carlo study of electron correlation in transition metal oxygen molecules}, + url = {http://dx.doi.org/10.1016/S0009-2614(03)00128-3}, + volume = {370}, + year = {2003}, + bdsk-url-1 = {http://dx.doi.org/10.1016/S0009-2614(03)00128-3}, + bdsk-url-2 = {http://dx.doi.org/10.1016/s0009-2614(03)00128-3}} @article{Grossman_2002, - Author = {Grossman, Jeffrey C.}, - Doi = {10.1063/1.1487829}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Jul}, - Number = {4}, - Pages = {1434--1440}, - Publisher = {AIP Publishing}, - Title = {Benchmark quantum Monte Carlo calculations}, - Url = {http://dx.doi.org/10.1063/1.1487829}, - Volume = {117}, - Year = {2002}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.1487829}} + author = {Grossman, Jeffrey C.}, + doi = {10.1063/1.1487829}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Jul}, + number = {4}, + pages = {1434--1440}, + publisher = {AIP Publishing}, + title = {Benchmark quantum Monte Carlo calculations}, + url = {http://dx.doi.org/10.1063/1.1487829}, + volume = {117}, + year = {2002}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.1487829}} @article{Manten_2001, - Author = {Manten, Sebastian and L{\"u}chow, Arne}, - Doi = {10.1063/1.1394757}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Sep}, - Number = {12}, - Pages = {5362--5366}, - Publisher = {AIP Publishing}, - Title = {On the accuracy of the fixed-node diffusion quantum Monte Carlo method}, - Url = {http://dx.doi.org/10.1063/1.1394757}, - Volume = {115}, - Year = {2001}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.1394757}} + author = {Manten, Sebastian and L{\"u}chow, Arne}, + doi = {10.1063/1.1394757}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Sep}, + number = {12}, + pages = {5362--5366}, + publisher = {AIP Publishing}, + title = {On the accuracy of the fixed-node diffusion quantum Monte Carlo method}, + url = {http://dx.doi.org/10.1063/1.1394757}, + volume = {115}, + year = {2001}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.1394757}} @article{Noro_2000, - Author = {Noro, Takeshi and Sekiya, Masahiro and Koga, Toshikatsu and Matsuyama, Hisashi}, - Doi = {10.1007/s002140000126}, - Issn = {1432-2234}, - Journal = {Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta)}, - 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Author = {Bauschlicher, Charles W. and Ma\^{i}tre, Philippe}, - Doi = {10.1007/s002140050068}, - Issn = {0040-5744}, - Journal = {Theoretica Chimica Acta}, - Number = {2}, - Pages = {189}, - Publisher = {Springer Nature}, - Title = {Theoretical study of the first transition row oxides and sulfides}, - Url = {http://dx.doi.org/10.1007/s002140050068}, - Volume = {90}, - Year = {1995}, - Bdsk-Url-1 = {http://dx.doi.org/10.1007/s002140050068}} + author = {Bauschlicher, Charles W. and Ma\^{i}tre, Philippe}, + doi = {10.1007/s002140050068}, + issn = {0040-5744}, + journal = {Theoretica Chimica Acta}, + number = {2}, + pages = {189}, + publisher = {Springer Nature}, + title = {Theoretical study of the first transition row oxides and sulfides}, + url = {http://dx.doi.org/10.1007/s002140050068}, + volume = {90}, + year = {1995}, + bdsk-url-1 = {http://dx.doi.org/10.1007/s002140050068}} @article{Nakano_1993b, - Author = {Nakano, Haruyuki}, - Date-Modified = {2017-10-07 12:09:28 +0000}, - Doi = {10.1063/1.465674}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Nov}, - Number = {10}, - Pages = {7983--7992}, - Publisher = {AIP Publishing}, - Title = {Quasidegenerate perturbation theory with multiconfigurational self‐consistent‐field reference functions}, - Url = {http://dx.doi.org/10.1063/1.465674}, - Volume = {99}, - Year = {1993}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.465674}} + author = {Nakano, Haruyuki}, + date-modified = {2017-10-07 12:09:28 +0000}, + doi = {10.1063/1.465674}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Nov}, + number = {10}, + pages = {7983--7992}, + publisher = {AIP Publishing}, + title = {Quasidegenerate perturbation theory with multiconfigurational self‐consistent‐field reference functions}, + url = {http://dx.doi.org/10.1063/1.465674}, + volume = {99}, + year = {1993}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.465674}} @article{Schmidt_1993, - Author = {Schmidt, Michael W. and Baldridge, Kim K. and Boatz, Jerry A. and Elbert, Steven T. and Gordon, Mark S. and Jensen, Jan H. and Koseki, Shiro and Matsunaga, Nikita and Nguyen, Kiet A. and Su, Shujun and et al.}, - 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E. and Moskowitz, J. W.}, - Doi = {10.1063/1.458750}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Sep}, - Number = {6}, - Pages = {4172--4178}, - Publisher = {AIP Publishing}, - Title = {Correlated Monte Carlo wave functions for the atoms He through Ne}, - Url = {http://dx.doi.org/10.1063/1.458750}, - Volume = {93}, - Year = {1990}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.458750}} + author = {Schmidt, K. E. and Moskowitz, J. W.}, + doi = {10.1063/1.458750}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Sep}, + number = {6}, + pages = {4172--4178}, + publisher = {AIP Publishing}, + title = {Correlated Monte Carlo wave functions for the atoms He through Ne}, + url = {http://dx.doi.org/10.1063/1.458750}, + volume = {93}, + year = {1990}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.458750}} @article{Reynolds_1982, - Author = {Reynolds, Peter J. and Ceperley, David M. and Alder, Berni J. and Lester, William A.}, - Doi = {10.1063/1.443766}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Dec}, - Number = {11}, - Pages = {5593--5603}, - Publisher = {AIP Publishing}, - Title = {Fixed‐node quantum Monte Carlo for moleculesa) b)}, - Url = {http://dx.doi.org/10.1063/1.443766}, - Volume = {77}, - Year = {1982}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.443766}} + author = {Reynolds, Peter J. and Ceperley, David M. and Alder, Berni J. and Lester, William A.}, + doi = {10.1063/1.443766}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Dec}, + number = {11}, + pages = {5593--5603}, + publisher = {AIP Publishing}, + title = {Fixed‐node quantum Monte Carlo for moleculesa) b)}, + url = {http://dx.doi.org/10.1063/1.443766}, + volume = {77}, + year = {1982}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.443766}} @article{Marquart_1963, - Author = {Marquart, J. R. and Berkowitz, J.}, - Doi = {10.1063/1.1734242}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Jul}, - Number = {2}, - Pages = {283--285}, - Publisher = {AIP Publishing}, - Title = {Dissociation Energies of Some Metal Sulfides}, - Url = {http://dx.doi.org/10.1063/1.1734242}, - Volume = {39}, - Year = {1963}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.1734242}} + author = {Marquart, J. R. and Berkowitz, J.}, + doi = {10.1063/1.1734242}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Jul}, + number = {2}, + pages = {283--285}, + publisher = {AIP Publishing}, + title = {Dissociation Energies of Some Metal Sulfides}, + url = {http://dx.doi.org/10.1063/1.1734242}, + volume = {39}, + year = {1963}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.1734242}} @article{Giner_2017b, - Author = {Giner, E. and Angeli, C. and Scemama, A. and Malrieu, J.-P.}, - Date-Modified = {2017-10-07 12:40:53 +0000}, - Doi = {10.1016/j.comptc.2017.03.001}, - Issn = {2210-271X}, - Journal = {Computational and Theoretical Chemistry}, - Month = {Sep}, - Pages = {134--140}, - Publisher = {Elsevier BV}, - Title = {Orthogonal Valence Bond Hamiltonians incorporating dynamical correlation effects}, - Url = {http://dx.doi.org/10.1016/j.comptc.2017.03.001}, - Volume = {1116}, - Year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.comptc.2017.03.001}} + author = {Giner, E. and Angeli, C. and Scemama, A. and Malrieu, J.-P.}, + date-modified = {2017-10-07 12:40:53 +0000}, + doi = {10.1016/j.comptc.2017.03.001}, + issn = {2210-271X}, + journal = {Computational and Theoretical Chemistry}, + month = {Sep}, + pages = {134--140}, + publisher = {Elsevier BV}, + title = {Orthogonal Valence Bond Hamiltonians incorporating dynamical correlation effects}, + url = {http://dx.doi.org/10.1016/j.comptc.2017.03.001}, + volume = {1116}, + year = {2017}, + bdsk-url-1 = {http://dx.doi.org/10.1016/j.comptc.2017.03.001}} @article{Garniron_2017b, - Author = {Garniron, Yann and Scemama, Anthony and Loos, Pierre-Fran{\c c}ois and Caffarel, Michel}, - Date-Modified = {2017-10-07 12:41:01 +0000}, - Doi = {10.1063/1.4992127}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Jul}, - Number = {3}, - Pages = {034101}, - Publisher = {AIP Publishing}, - Title = {Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory}, - Url = {http://dx.doi.org/10.1063/1.4992127}, - Volume = {147}, - Year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4992127}} + author = {Garniron, Yann and Scemama, Anthony and Loos, Pierre-Fran{\c c}ois and Caffarel, Michel}, + date-modified = {2017-10-07 12:41:01 +0000}, + doi = {10.1063/1.4992127}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Jul}, + number = {3}, + pages = {034101}, + publisher = {AIP Publishing}, + title = {Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory}, + url = {http://dx.doi.org/10.1063/1.4992127}, + volume = {147}, + year = {2017}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4992127}} @article{Giner_2017a, - Author = {Giner, Emmanuel and Angeli, Celestino and Garniron, Yann and Scemama, Anthony and Malrieu, Jean-Paul}, - Date-Modified = {2017-10-07 12:40:49 +0000}, - Doi = {10.1063/1.4984616}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Jun}, - Number = {22}, - Pages = {224108}, - Publisher = {AIP Publishing}, - Title = {A Jeziorski-Monkhorst fully uncontracted multi-reference perturbative treatment. I. Principles, second-order versions, and tests on ground state potential energy curves}, - Url = {http://dx.doi.org/10.1063/1.4984616}, - Volume = {146}, - Year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4984616}} + author = {Giner, Emmanuel and Angeli, Celestino and Garniron, Yann and Scemama, Anthony and Malrieu, Jean-Paul}, + date-modified = {2017-10-07 12:40:49 +0000}, + doi = {10.1063/1.4984616}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Jun}, + number = {22}, + pages = {224108}, + publisher = {AIP Publishing}, + title = {A Jeziorski-Monkhorst fully uncontracted multi-reference perturbative treatment. I. Principles, second-order versions, and tests on ground state potential energy curves}, + url = {http://dx.doi.org/10.1063/1.4984616}, + volume = {146}, + year = {2017}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4984616}} @article{Garniron_2017a, - Author = {Garniron, Yann and Giner, Emmanuel and Malrieu, Jean-Paul and Scemama, Anthony}, - Date-Modified = {2017-10-07 12:40:58 +0000}, - Doi = {10.1063/1.4980034}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Apr}, - Number = {15}, - Pages = {154107}, - Publisher = {AIP Publishing}, - Title = {Alternative definition of excitation amplitudes in multi-reference state-specific coupled cluster}, - Url = {http://dx.doi.org/10.1063/1.4980034}, - Volume = {146}, - Year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4980034}} + author = {Garniron, Yann and Giner, Emmanuel and Malrieu, Jean-Paul and Scemama, Anthony}, + date-modified = {2017-10-07 12:40:58 +0000}, + doi = {10.1063/1.4980034}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Apr}, + number = {15}, + pages = {154107}, + publisher = {AIP Publishing}, + title = {Alternative definition of excitation amplitudes in multi-reference state-specific coupled cluster}, + url = {http://dx.doi.org/10.1063/1.4980034}, + volume = {146}, + year = {2017}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4980034}} @article{Scemama_2016, - Author = {Scemama, Anthony and Applencourt, Thomas and Giner, Emmanuel and Caffarel, Michel}, - Doi = {10.1002/jcc.24382}, - Issn = {0192-8651}, - Journal = {Journal of Computational Chemistry}, - Month = {Jun}, - Number = {20}, - Pages = {1866--1875}, - Publisher = {Wiley-Blackwell}, - Title = {Quantum Monte Carlo with very large multideterminant wavefunctions}, - Url = {http://dx.doi.org/10.1002/jcc.24382}, - Volume = {37}, - Year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/jcc.24382}} + author = {Scemama, Anthony and Applencourt, Thomas and Giner, Emmanuel and Caffarel, Michel}, + doi = {10.1002/jcc.24382}, + issn = {0192-8651}, + journal = {Journal of Computational Chemistry}, + month = {Jun}, + number = {20}, + pages = {1866--1875}, + publisher = {Wiley-Blackwell}, + title = {Quantum Monte Carlo with very large multideterminant wavefunctions}, + url = {http://dx.doi.org/10.1002/jcc.24382}, + volume = {37}, + year = {2016}, + bdsk-url-1 = {http://dx.doi.org/10.1002/jcc.24382}} @article{Caffarel_2016, - Author = {Caffarel, Michel and Applencourt, Thomas and Giner, Emmanuel and Scemama, Anthony}, - Doi = {10.1063/1.4947093}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Apr}, - Number = {15}, - Pages = {151103}, - Publisher = {AIP Publishing}, - Title = {Communication: Toward an improved control of the fixed-node error in quantum Monte Carlo: The case of the water molecule}, - Url = {http://dx.doi.org/10.1063/1.4947093}, - Volume = {144}, - Year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4947093}} + author = {Caffarel, Michel and Applencourt, Thomas and Giner, Emmanuel and Scemama, Anthony}, + doi = {10.1063/1.4947093}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Apr}, + number = {15}, + pages = {151103}, + publisher = {AIP Publishing}, + title = {Communication: Toward an improved control of the fixed-node error in quantum Monte Carlo: The case of the water molecule}, + url = {http://dx.doi.org/10.1063/1.4947093}, + volume = {144}, + year = {2016}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4947093}} @article{Giner_2016, - Author = {Giner, E. and David, G. and Scemama, A. and Malrieu, J. P.}, - Doi = {10.1063/1.4940781}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Feb}, - Number = {6}, - Pages = {064101}, - Publisher = {AIP Publishing}, - Title = {A simple approach to the state-specific MR-CC using the intermediate Hamiltonian formalism}, - Url = {http://dx.doi.org/10.1063/1.4940781}, - Volume = {144}, - Year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4940781}} + author = {Giner, E. and David, G. and Scemama, A. and Malrieu, J. P.}, + doi = {10.1063/1.4940781}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Feb}, + number = {6}, + pages = {064101}, + publisher = {AIP Publishing}, + title = {A simple approach to the state-specific MR-CC using the intermediate Hamiltonian formalism}, + url = {http://dx.doi.org/10.1063/1.4940781}, + volume = {144}, + year = {2016}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4940781}} @article{Giner_2015, - Author = {Giner, Emmanuel and Scemama, Anthony and Caffarel, Michel}, - Doi = {10.1063/1.4905528}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Jan}, - Number = {4}, - Pages = {044115}, - Publisher = {AIP Publishing}, - Title = {Fixed-node diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctions}, - Url = {http://dx.doi.org/10.1063/1.4905528}, - Volume = {142}, - Year = {2015}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4905528}} + author = {Giner, Emmanuel and Scemama, Anthony and Caffarel, Michel}, + doi = {10.1063/1.4905528}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Jan}, + number = {4}, + pages = {044115}, + publisher = {AIP Publishing}, + title = {Fixed-node diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctions}, + url = {http://dx.doi.org/10.1063/1.4905528}, + volume = {142}, + year = {2015}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4905528}} @article{Scemama_2014, - Author = {Scemama, A. and Applencourt, T. and Giner, E. and Caffarel, M.}, - Doi = {10.1063/1.4903985}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Dec}, - Number = {24}, - Pages = {244110}, - Publisher = {AIP Publishing}, - Title = {Accurate nonrelativistic ground-state energies of 3d transition metal atoms}, - Url = {http://dx.doi.org/10.1063/1.4903985}, - Volume = {141}, - Year = {2014}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4903985}} + author = {Scemama, A. and Applencourt, T. and Giner, E. and Caffarel, M.}, + doi = {10.1063/1.4903985}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Dec}, + number = {24}, + pages = {244110}, + publisher = {AIP Publishing}, + title = {Accurate nonrelativistic ground-state energies of 3d transition metal atoms}, + url = {http://dx.doi.org/10.1063/1.4903985}, + volume = {141}, + year = {2014}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4903985}} @article{Caffarel_2014, - Author = {Caffarel, Michel and Giner, Emmanuel and Scemama, Anthony and Ram{\'\i}rez-Sol{\'\i}s, Alejandro}, - Doi = {10.1021/ct5004252}, - Issn = {1549-9626}, - Journal = {Journal of Chemical Theory and Computation}, - Month = {Dec}, - Number = {12}, - Pages = {5286--5296}, - Publisher = {American Chemical Society (ACS)}, - Title = {Spin Density Distribution in Open-Shell Transition Metal Systems: A Comparative Post-Hartree--Fock, Density Functional Theory, and Quantum Monte Carlo Study of the CuCl2Molecule}, - Url = {http://dx.doi.org/10.1021/ct5004252}, - Volume = {10}, - Year = {2014}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/ct5004252}} + author = {Caffarel, Michel and Giner, Emmanuel and Scemama, Anthony and Ram{\'\i}rez-Sol{\'\i}s, Alejandro}, + doi = {10.1021/ct5004252}, + issn = {1549-9626}, + journal = {Journal of Chemical Theory and Computation}, + month = {Dec}, + number = {12}, + pages = {5286--5296}, + publisher = {American Chemical Society (ACS)}, + title = {Spin Density Distribution in Open-Shell Transition Metal Systems: A Comparative Post-Hartree--Fock, Density Functional Theory, and Quantum Monte Carlo Study of the CuCl2Molecule}, + url = {http://dx.doi.org/10.1021/ct5004252}, + volume = {10}, + year = {2014}, + bdsk-url-1 = {http://dx.doi.org/10.1021/ct5004252}} @article{Giner_2013, - Author = {Giner, Emmanuel and Scemama, Anthony and Caffarel, Michel}, - Doi = {10.1139/cjc-2013-0017}, - Issn = {1480-3291}, - Journal = {Canadian Journal of Chemistry}, - Month = {Sep}, - Number = {9}, - Pages = {879--885}, - Publisher = {Canadian Science Publishing}, - Title = {Using perturbatively selected configuration interaction in quantum Monte Carlo calculations}, - Url = {http://dx.doi.org/10.1139/cjc-2013-0017}, - Volume = {91}, - Year = {2013}, - Bdsk-Url-1 = {http://dx.doi.org/10.1139/cjc-2013-0017}} + author = {Giner, Emmanuel and Scemama, Anthony and Caffarel, Michel}, + doi = {10.1139/cjc-2013-0017}, + issn = {1480-3291}, + journal = {Canadian Journal of Chemistry}, + month = {Sep}, + number = {9}, + pages = {879--885}, + publisher = {Canadian Science Publishing}, + title = {Using perturbatively selected configuration interaction in quantum Monte Carlo calculations}, + url = {http://dx.doi.org/10.1139/cjc-2013-0017}, + volume = {91}, + year = {2013}, + bdsk-url-1 = {http://dx.doi.org/10.1139/cjc-2013-0017}} @article{Scemama_2013, - Author = {Scemama, Anthony and Caffarel, Michel and Oseret, Emmanuel and Jalby, William}, - Doi = {10.1002/jcc.23216}, - Issn = {0192-8651}, - Journal = {Journal of Computational Chemistry}, - Month = {Jan}, - Number = {11}, - Pages = {938--951}, - Publisher = {Wiley-Blackwell}, - Title = {Quantum Monte Carlo for large chemical systems: Implementing efficient strategies for petascale platforms and beyond}, - Url = {http://dx.doi.org/10.1002/jcc.23216}, - Volume = {34}, - Year = {2013}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/jcc.23216}} + author = {Scemama, Anthony and Caffarel, Michel and Oseret, Emmanuel and Jalby, William}, + doi = {10.1002/jcc.23216}, + issn = {0192-8651}, + journal = {Journal of Computational Chemistry}, + month = {Jan}, + number = {11}, + pages = {938--951}, + publisher = {Wiley-Blackwell}, + title = {Quantum Monte Carlo for large chemical systems: Implementing efficient strategies for petascale platforms and beyond}, + url = {http://dx.doi.org/10.1002/jcc.23216}, + volume = {34}, + year = {2013}, + bdsk-url-1 = {http://dx.doi.org/10.1002/jcc.23216}} @article{Scemama_2011, - Author = {Scemama, Anthony and Caffarel, Michel and Chaudret, Robin and Piquemal, Jean-Philip}, - Doi = {10.1021/ct1005938}, - Issn = {1549-9626}, - Journal = {Journal of Chemical Theory and Computation}, - Month = {Mar}, - Number = {3}, - Pages = {618--624}, - Publisher = {American Chemical Society (ACS)}, - Title = {Electron Pair Localization Function (EPLF) for Density Functional Theory andab InitioWave Function-Based Methods: A New Tool for Chemical Interpretation}, - Url = {http://dx.doi.org/10.1021/ct1005938}, - Volume = {7}, - Year = {2011}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/ct1005938}} + author = {Scemama, Anthony and Caffarel, Michel and Chaudret, Robin and Piquemal, Jean-Philip}, + doi = {10.1021/ct1005938}, + issn = {1549-9626}, + journal = {Journal of Chemical Theory and Computation}, + month = {Mar}, + number = {3}, + pages = {618--624}, + publisher = {American Chemical Society (ACS)}, + title = {Electron Pair Localization Function (EPLF) for Density Functional Theory andab InitioWave Function-Based Methods: A New Tool for Chemical Interpretation}, + url = {http://dx.doi.org/10.1021/ct1005938}, + volume = {7}, + year = {2011}, + bdsk-url-1 = {http://dx.doi.org/10.1021/ct1005938}} @article{Caffarel_2009, - Author = {Caffarel, Michel and Scemama, Anthony and Ram{\'\i}rez-Sol{\'\i}s, Alejandro}, - Doi = {10.1007/s00214-009-0713-y}, - Issn = {1432-2234}, - Journal = {Theoretical Chemistry Accounts}, - Month = {Dec}, - Number = {3-4}, - Pages = {275--287}, - Publisher = {Springer Nature}, - Title = {The lithium--thiophene interaction: a critical study using highly correlated electronic structure approaches of quantum chemistry}, - Url = {http://dx.doi.org/10.1007/s00214-009-0713-y}, - Volume = {126}, - Year = {2009}, - Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00214-009-0713-y}} + author = {Caffarel, Michel and Scemama, Anthony and Ram{\'\i}rez-Sol{\'\i}s, Alejandro}, + doi = {10.1007/s00214-009-0713-y}, + issn = {1432-2234}, + journal = {Theoretical Chemistry Accounts}, + month = {Dec}, + number = {3-4}, + pages = {275--287}, + publisher = {Springer Nature}, + title = {The lithium--thiophene interaction: a critical study using highly correlated electronic structure approaches of quantum chemistry}, + url = {http://dx.doi.org/10.1007/s00214-009-0713-y}, + volume = {126}, + year = {2009}, + bdsk-url-1 = {http://dx.doi.org/10.1007/s00214-009-0713-y}} @article{Berge_s_2008, - Author = {Berg{\`e}s, Jacqueline and Varmenot, Nicolas and Scemama, Anthony and Abedinzadeh, Zohreh and Bobrowski, Krzysztof}, - Doi = {10.1021/jp711944v}, - Issn = {1520-5215}, - Journal = {The Journal of Physical Chemistry A}, - Month = {Jul}, - Number = {30}, - Pages = {7015--7026}, - Publisher = {American Chemical Society (ACS)}, - Title = {Energies, Stability and Structure Properties of Radicals Derived from Organic Sulfides Containing an Acetyl Group after the*OH Attack: ab Initio and DFT Calculations vs Experiment}, - Url = {http://dx.doi.org/10.1021/jp711944v}, - Volume = {112}, - Year = {2008}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/jp711944v}} + author = {Berg{\`e}s, Jacqueline and Varmenot, Nicolas and Scemama, Anthony and Abedinzadeh, Zohreh and Bobrowski, Krzysztof}, + doi = {10.1021/jp711944v}, + issn = {1520-5215}, + journal = {The Journal of Physical Chemistry A}, + month = {Jul}, + number = {30}, + pages = {7015--7026}, + publisher = {American Chemical Society (ACS)}, + title = {Energies, Stability and Structure Properties of Radicals Derived from Organic Sulfides Containing an Acetyl Group after the*OH Attack: ab Initio and DFT Calculations vs Experiment}, + url = {http://dx.doi.org/10.1021/jp711944v}, + volume = {112}, + year = {2008}, + bdsk-url-1 = {http://dx.doi.org/10.1021/jp711944v}} @article{Caffarel_2007, - Author = {Caffarel, Michel and Hern{\'a}ndez-Lamoneda, Ram{\'o}n and Scemama, Anthony and Ram{\'\i}rez-Sol{\'\i}s, Alejandro}, - Doi = {10.1103/physrevlett.99.153001}, - Issn = {1079-7114}, - Journal = {Physical Review Letters}, - Month = {Oct}, - Number = {15}, - Publisher = {American Physical Society (APS)}, - Title = {Multireference Quantum Monte Carlo Study of theO4Molecule}, - Url = {http://dx.doi.org/10.1103/PhysRevLett.99.153001}, - Volume = {99}, - Year = {2007}, - Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.99.153001}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/physrevlett.99.153001}} + author = {Caffarel, Michel and Hern{\'a}ndez-Lamoneda, Ram{\'o}n and Scemama, Anthony and Ram{\'\i}rez-Sol{\'\i}s, Alejandro}, + doi = {10.1103/physrevlett.99.153001}, + issn = {1079-7114}, + journal = {Physical Review Letters}, + month = {Oct}, + number = {15}, + publisher = {American Physical Society (APS)}, + title = {Multireference Quantum Monte Carlo Study of theO4Molecule}, + url = {http://dx.doi.org/10.1103/PhysRevLett.99.153001}, + volume = {99}, + year = {2007}, + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevLett.99.153001}, + bdsk-url-2 = {http://dx.doi.org/10.1103/physrevlett.99.153001}} @article{Assaraf_2007, - Author = {Assaraf, Roland and Caffarel, Michel and Scemama, Anthony}, - Doi = {10.1103/physreve.75.035701}, - Issn = {1550-2376}, - Journal = {Physical Review E}, - Month = {Mar}, - Number = {3}, - Publisher = {American Physical Society (APS)}, - Title = {Improved Monte Carlo estimators for the one-body density}, - Url = {http://dx.doi.org/10.1103/PhysRevE.75.035701}, - Volume = {75}, - Year = {2007}, - Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevE.75.035701}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/physreve.75.035701}} + author = {Assaraf, Roland and Caffarel, Michel and Scemama, Anthony}, + doi = {10.1103/physreve.75.035701}, + issn = {1550-2376}, + journal = {Physical Review E}, + month = {Mar}, + number = {3}, + publisher = {American Physical Society (APS)}, + title = {Improved Monte Carlo estimators for the one-body density}, + url = {http://dx.doi.org/10.1103/PhysRevE.75.035701}, + volume = {75}, + year = {2007}, + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevE.75.035701}, + bdsk-url-2 = {http://dx.doi.org/10.1103/physreve.75.035701}} @article{Scemama_2006b, - Author = {Scemama, Anthony and Caffarel, Michel and Savin, Andreas}, - Date-Modified = {2017-10-07 12:40:29 +0000}, - Doi = {10.1002/jcc.20526}, - Issn = {1096-987X}, - Journal = {Journal of Computational Chemistry}, - Number = {1}, - Pages = {442--454}, - Publisher = {Wiley-Blackwell}, - Title = {Maximum probability domains from Quantum Monte Carlo calculations}, - Url = {http://dx.doi.org/10.1002/jcc.20526}, - Volume = {28}, - Year = {2006}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/jcc.20526}} + author = {Scemama, Anthony and Caffarel, Michel and Savin, Andreas}, + date-modified = {2017-10-07 12:40:29 +0000}, + doi = {10.1002/jcc.20526}, + issn = {1096-987X}, + journal = {Journal of Computational Chemistry}, + number = {1}, + pages = {442--454}, + publisher = {Wiley-Blackwell}, + title = {Maximum probability domains from Quantum Monte Carlo calculations}, + url = {http://dx.doi.org/10.1002/jcc.20526}, + volume = {28}, + year = {2006}, + bdsk-url-1 = {http://dx.doi.org/10.1002/jcc.20526}} @article{Scemama_2006a, - Author = {Scemama, Anthony and Leli{\`e}vre, Tony and Stoltz, Gabriel and Canc{\`e}s, Eric and Caffarel, Michel}, - Date-Modified = {2017-10-07 12:40:25 +0000}, - Doi = {10.1063/1.2354490}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Sep}, - Number = {11}, - Pages = {114105}, - Publisher = {AIP Publishing}, - Title = {An efficient sampling algorithm for variational Monte Carlo}, - Url = {http://dx.doi.org/10.1063/1.2354490}, - Volume = {125}, - Year = {2006}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2354490}} + author = {Scemama, Anthony and Leli{\`e}vre, Tony and Stoltz, Gabriel and Canc{\`e}s, Eric and Caffarel, Michel}, + date-modified = {2017-10-07 12:40:25 +0000}, + doi = {10.1063/1.2354490}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Sep}, + number = {11}, + pages = {114105}, + publisher = {AIP Publishing}, + title = {An efficient sampling algorithm for variational Monte Carlo}, + url = {http://dx.doi.org/10.1063/1.2354490}, + volume = {125}, + year = {2006}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.2354490}} @article{Scemama_2006c, - Author = {Scemama, Anthony and Filippi, Claudia}, - Date-Modified = {2017-10-07 12:40:34 +0000}, - Doi = {10.1103/physrevb.73.241101}, - Issn = {1550-235X}, - Journal = {Physical Review B}, - Month = {Jun}, - Number = {24}, - Publisher = {American Physical Society (APS)}, - Title = {Simple and efficient approach to the optimization of correlated wave functions}, - Url = {http://dx.doi.org/10.1103/PhysRevB.73.241101}, - Volume = {73}, - Year = {2006}, - Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevB.73.241101}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/physrevb.73.241101}} + author = {Scemama, Anthony and Filippi, Claudia}, + date-modified = {2017-10-07 12:40:34 +0000}, + doi = {10.1103/physrevb.73.241101}, + issn = {1550-235X}, + journal = {Physical Review B}, + month = {Jun}, + number = {24}, + publisher = {American Physical Society (APS)}, + title = {Simple and efficient approach to the optimization of correlated wave functions}, + url = {http://dx.doi.org/10.1103/PhysRevB.73.241101}, + volume = {73}, + year = {2006}, + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevB.73.241101}, + bdsk-url-2 = {http://dx.doi.org/10.1103/physrevb.73.241101}} @article{Scemama_2004, - Author = {Scemama, Anthony and Chaquin, Patrick and Caffarel, Michel}, - Doi = {10.1063/1.1765098}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Jul}, - Number = {4}, - Pages = {1725--1735}, - Publisher = {AIP Publishing}, - Title = {Electron pair localization function: A practical tool to visualize electron localization in molecules from quantum Monte Carlo data}, - Url = {http://dx.doi.org/10.1063/1.1765098}, - Volume = {121}, - Year = {2004}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.1765098} -} + author = {Scemama, Anthony and Chaquin, Patrick and Caffarel, Michel}, + doi = {10.1063/1.1765098}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Jul}, + number = {4}, + pages = {1725--1735}, + publisher = {AIP Publishing}, + title = {Electron pair localization function: A practical tool to visualize electron localization in molecules from quantum Monte Carlo data}, + url = {http://dx.doi.org/10.1063/1.1765098}, + volume = {121}, + year = {2004}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.1765098}} + @article{Assaraf_2000, - Author = {Assaraf, Roland and Caffarel, Michel and Khelif, Anatole}, - Doi = {10.1103/physreve.61.4566}, - Issn = {1095-3787}, - Journal = {Physical Review E}, - Month = {Apr}, - Number = {4}, - Pages = {4566--4575}, - Publisher = {American Physical Society (APS)}, - Title = {Diffusion Monte Carlo methods with a fixed number of walkers}, - Url = {http://dx.doi.org/10.1103/PhysRevE.61.4566}, - Volume = {61}, - Year = {2000}, - Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevE.61.4566}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/physreve.61.4566} -} + author = {Assaraf, Roland and Caffarel, Michel and Khelif, Anatole}, + doi = {10.1103/physreve.61.4566}, + issn = {1095-3787}, + journal = {Physical Review E}, + month = {Apr}, + number = {4}, + pages = {4566--4575}, + publisher = {American Physical Society (APS)}, + title = {Diffusion Monte Carlo methods with a fixed number of walkers}, + url = {http://dx.doi.org/10.1103/PhysRevE.61.4566}, + volume = {61}, + year = {2000}, + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevE.61.4566}, + bdsk-url-2 = {http://dx.doi.org/10.1103/physreve.61.4566}} + @article{Matthew_2017, - Author = {Matthew, Daniel J. and Tieu, Erick and Morse, Michael D.}, - Doi = {10.1063/1.4979679}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Apr}, - Number = {14}, - Pages = {144310}, - Publisher = {AIP Publishing}, - Title = {Determination of the bond dissociation energies of FeX and NiX (X = C, S, Se)}, - Url = {http://dx.doi.org/10.1063/1.4979679}, - Volume = {146}, - Year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4979679}} + author = {Matthew, Daniel J. and Tieu, Erick and Morse, Michael D.}, + doi = {10.1063/1.4979679}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Apr}, + number = {14}, + pages = {144310}, + publisher = {AIP Publishing}, + title = {Determination of the bond dissociation energies of FeX and NiX (X = C, S, Se)}, + url = {http://dx.doi.org/10.1063/1.4979679}, + volume = {146}, + year = {2017}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4979679}} @article{Xiao_2016, - Author = {Xiao, Suo and Li, Xiaopeng and Sun, Weiwei and Guan, Baoqin and Wang, Yong}, - Doi = {10.1016/j.cej.2016.05.068}, - Issn = {1385-8947}, - Journal = {Chemical Engineering Journal}, - Month = {Dec}, - Pages = {251--259}, - Publisher = {Elsevier BV}, - Title = {General and facile synthesis of metal sulfide nanostructures: In situ microwave synthesis and application as binder-free cathode for Li-ion batteries}, - Url = {http://dx.doi.org/10.1016/j.cej.2016.05.068}, - Volume = {306}, - Year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.cej.2016.05.068}} + author = {Xiao, Suo and Li, Xiaopeng and Sun, Weiwei and Guan, Baoqin and Wang, Yong}, + doi = {10.1016/j.cej.2016.05.068}, + issn = {1385-8947}, + journal = {Chemical Engineering Journal}, + month = {Dec}, + pages = {251--259}, + publisher = {Elsevier BV}, + title = {General and facile synthesis of metal sulfide nanostructures: In situ microwave synthesis and application as binder-free cathode for Li-ion batteries}, + url = {http://dx.doi.org/10.1016/j.cej.2016.05.068}, + volume = {306}, + year = {2016}, + bdsk-url-1 = {http://dx.doi.org/10.1016/j.cej.2016.05.068}} @article{Crack_2014, - Author = {Crack, Jason C. and Green, Jeffrey and Thomson, Andrew J. and Brun, Nick E. 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J.}, + doi = {10.1063/1.2908237}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {May}, + number = {17}, + pages = {174101}, + publisher = {AIP Publishing}, + title = {Full optimization of Jastrow--Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules}, + url = {http://dx.doi.org/10.1063/1.2908237}, + volume = {128}, + year = {2008}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.2908237}} @article{Umrigar_2007, - Author = {Umrigar, C. J. and Toulouse, Julien and Filippi, Claudia and Sorella, S. and Hennig, R. 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G.}, + doi = {10.1103/physrevlett.98.110201}, + issn = {1079-7114}, + journal = {Physical Review Letters}, + month = {Mar}, + number = {11}, + publisher = {American Physical Society (APS)}, + title = {Alleviation of the Fermion-Sign Problem by Optimization of Many-Body Wave Functions}, + url = {http://dx.doi.org/10.1103/PhysRevLett.98.110201}, + volume = {98}, + year = {2007}, + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevLett.98.110201}, + bdsk-url-2 = {http://dx.doi.org/10.1103/physrevlett.98.110201}} @article{Umrigar_2005, - Author = {Umrigar, C. 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J. and Filippi, Claudia}, + doi = {10.1103/physrevlett.94.150201}, + issn = {1079-7114}, + journal = {Physical Review Letters}, + month = {Apr}, + number = {15}, + publisher = {American Physical Society (APS)}, + title = {Energy and Variance Optimization of Many-Body Wave Functions}, + url = {http://dx.doi.org/10.1103/PhysRevLett.94.150201}, + volume = {94}, + year = {2005}, + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevLett.94.150201}, + bdsk-url-2 = {http://dx.doi.org/10.1103/physrevlett.94.150201}} @article{Tubman_2016, - Author = {Tubman, Norm M. and Lee, Joonho and Takeshita, Tyler Y. and Head-Gordon, Martin and Whaley, K. 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Birgitta}, + doi = {10.1063/1.4955109}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Jul}, + number = {4}, + pages = {044112}, + publisher = {AIP Publishing}, + title = {A deterministic alternative to the full configuration interaction quantum Monte Carlo method}, + url = {http://dx.doi.org/10.1063/1.4955109}, + volume = {145}, + year = {2016}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4955109}} @article{Per_2017, - Author = {Per, Manolo C. and Cleland, Deidre M.}, - Doi = {10.1063/1.4981527}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Apr}, - Number = {16}, - Pages = {164101}, - Publisher = {AIP Publishing}, - Title = {Energy-based truncation of multi-determinant wavefunctions in quantum Monte Carlo}, - Url = {http://dx.doi.org/10.1063/1.4981527}, - Volume = {146}, - Year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4981527}} + author = {Per, Manolo C. and Cleland, Deidre M.}, + doi = {10.1063/1.4981527}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Apr}, + number = {16}, + pages = {164101}, + publisher = {AIP Publishing}, + title = {Energy-based truncation of multi-determinant wavefunctions in quantum Monte Carlo}, + url = {http://dx.doi.org/10.1063/1.4981527}, + volume = {146}, + year = {2017}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4981527}} @article{Evangelista_2014, - Author = {Evangelista, Francesco A.}, - Doi = {10.1063/1.4869192}, - Issn = {1089-7690}, - Journal = {The Journal of Chemical Physics}, - Month = {Mar}, - Number = {12}, - Pages = {124114}, - Publisher = {AIP Publishing}, - Title = {Adaptive multiconfigurational wave functions}, - Url = {http://dx.doi.org/10.1063/1.4869192}, - Volume = {140}, - Year = {2014}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4869192}} + author = {Evangelista, Francesco A.}, + doi = {10.1063/1.4869192}, + issn = {1089-7690}, + journal = {The Journal of Chemical Physics}, + month = {Mar}, + number = {12}, + pages = {124114}, + publisher = {AIP Publishing}, + title = {Adaptive multiconfigurational wave functions}, + url = {http://dx.doi.org/10.1063/1.4869192}, + volume = {140}, + year = {2014}, + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4869192}} @article{Liu_2016, - Author = {Liu, Wenjian and Hoffmann, Mark R.}, - Doi = {10.1021/acs.jctc.5b01099}, - Issn = {1549-9626}, - Journal = {Journal of Chemical Theory and Computation}, - Month = {Mar}, - Number = {3}, - Pages = {1169--1178}, - Publisher = {American Chemical Society (ACS)}, - Title = {iCI: Iterative CI toward full CI}, - Url = {http://dx.doi.org/10.1021/acs.jctc.5b01099}, - Volume = {12}, - Year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/acs.jctc.5b01099}} + author = {Liu, Wenjian and Hoffmann, Mark R.}, + doi = {10.1021/acs.jctc.5b01099}, + issn = {1549-9626}, + journal = {Journal of Chemical Theory and Computation}, + month = {Mar}, + number = {3}, + pages = {1169--1178}, + publisher = {American Chemical Society (ACS)}, + title = {iCI: Iterative CI toward full CI}, + url = {http://dx.doi.org/10.1021/acs.jctc.5b01099}, + volume = {12}, + year = {2016}, + bdsk-url-1 = {http://dx.doi.org/10.1021/acs.jctc.5b01099}} diff --git a/g.tex b/g.tex index 9b6f84f..523bc85 100644 --- a/g.tex +++ b/g.tex @@ -172,15 +172,15 @@ However, all the ideas presented in this work can be adapted without too much di Without entering into the mathematical details (which are presented below), the main ingredient of DMC in order to perform the matrix-vector multiplications probabilistically is the stochastic matrix (or transition probability matrix) that generates stepwise a series of states over which statistical averages are evaluated. The critical aspect of any Monte Carlo scheme is the amount of computational effort required to reach a given statistical error. -Two important avenues to decrease the error are the use of variance reduction techniques (for example, by introducing improved estimators \cite{Assaraf_1999}) or to improve the quality of the sampling (minimization of the correlation time between states). +Two important avenues to decrease the error are the use of variance reduction techniques (for example, by introducing improved estimators \cite{Assaraf_1999A}) or to improve the quality of the sampling (minimization of the correlation time between states). Another possibility, at the heart of the present work, is to integrate out exactly some parts of the dynamics, thus reducing the number of degrees of freedom and, hence, the amount of statistical fluctuations. -In a previous work,\cite{assaraf_99,caffarel_00} it has been shown that the probability for a walker to stay a certain amount of time in the same state obeys a Poisson law and that the \titou{on-state} dynamics can be integrated out to generate an effective dynamics connecting only different states with some renormalized estimators for the properties. +In previous works,\cite{Assaraf_1999B,Caffarel_2000} it has been shown that the probability for a walker to stay a certain amount of time in the same state obeys a Poisson law and that the \titou{on-state} dynamics can be integrated out to generate an effective dynamics connecting only different states with some renormalized estimators for the properties. Numerical applications have shown that the statistical errors can be very significantly decreased. Here, we extend this idea to the general case where a walker remains a certain amount of time within a finite domain no longer restricted to a single state. It is shown how to define an effective stochastic dynamics describing walkers moving from one domain to another. The equations of the effective dynamics are derived and a numerical application for a model (one-dimensional) problem is presented. -In particular, it shows that the statistical convergence of the energy can be greatly enhanced when domains associated with large average trapping times are cnosidered. +In particular, it shows that the statistical convergence of the energy can be greatly enhanced when domains associated with large average trapping times are considered. It should be noted that the use of domains in quantum Monte Carlo is not new. In their pioneering work, \cite{Kalos_1974} Kalos and collaborators introduced the so-called domain Green's function Monte Carlo approach in continuous space that they applied to a system of bosons with hard-sphere interaction. @@ -194,7 +194,7 @@ Section \ref{sec:DMC} presents the basic equations and notations of DMC. First, the path integral representation of the Green's function is given in Subsec.~\ref{sec:path}. The probabilistic framework allowing the Monte Carlo calculation of the Green's function is presented in Subsec.~\ref{sec:proba}. Section \ref{sec:DMC_domains} is devoted to the use of domains in DMC. -First, we recall in Subsec.~\ref{sec:single_domains} the case of a domain consisting of a single state. \cite{Assaraf_1999} +First, we recall in Subsec.~\ref{sec:single_domains} the case of a domain consisting of a single state. \cite{Assaraf_1999B} The general case is then treated in Subsec.~\ref{sec:general_domains}. In Subsec.~\ref{sec:Green}, both the time- and energy-dependent Green's function using domains is derived. Section \ref{sec:numerical} presents the application of the approach to the one-dimensional Hubbard model. @@ -215,14 +215,14 @@ As previously mentioned, DMC is a stochastic implementation of the power method \be T = \Id -\tau (H-E\Id), \ee -where $\Id$ is the identity operator, $\tau$ a small positive parameter playing the role of a time-step, $E$ some arbitrary reference energy, and $H$ the Hamiltonian operator. Starting from some initial vector, $\ket{\Psi_0}$, we have +where $\Id$ is the identity operator, $\tau$ a small positive parameter playing the role of a time step, $E$ some arbitrary reference energy, and $H$ the Hamiltonian operator. For any initial vector $\ket{\Psi_0}$ provided that $\braket{\Phi_0}{\Psi_0} \ne 0$ and for $\tau$ sufficiently small, we have \be +\label{eq:limTN} \lim_{N \to \infty} T^N \ket{\Psi_0} = \ket{\Phi_0}, \ee -where $\ket{\Phi_0}$ is the ground-state wave function. -The equality is up to a global phase factor playing no role in physical quantum averages. -This result is true for any $\ket{\Psi_0}$ provided that $\braket{\Phi_0}{\Psi_0} \ne 0$ and for $\tau$ sufficiently small. -At large but finite $N$, the vector $T^N \ket{\Psi_0}$ differs from $\ket{\Phi_0}$ only by an exponentially small correction, making easy to extrapolate the finite-$N$ results to $N \to \infty$. +where $\ket{\Phi_0}$ is the ground-state wave function, \ie, $H \ket{\Phi_0} = E_0 \ket{\Phi_0}$. +The equality in Eq.~\eqref{eq:limTN} holds up to a global phase factor playing no role in physical quantum averages. +At large but finite $N$, the vector $T^N \ket{\Psi_0}$ differs from $\ket{\Phi_0}$ only by an exponentially small correction, making it straightforward to extrapolate the finite-$N$ results to $N \to \infty$. Likewise, ground-state properties may be obtained at large $N$. For example, in the important case of the energy, one can rely on the following formula @@ -236,15 +236,16 @@ To proceed further we introduce the time-dependent Green's matrix $G^{(N)}$ defi \be G^{(N)}_{ij}=\mel{j}{T^N}{i}. \ee +\titou{where $\ket{i}$ and $\ket{j}$ are basis vectors.} The denomination ``time-dependent Green's matrix'' is used here since $G$ may be viewed as a short-time approximation of the (time-imaginary) evolution operator, $e^{-N\tau H}$ which is usually referred to as the imaginary-time dependent Green's function. -\titou{Introducing the set of $N-1$ intermediate states, $\{ i_k \}_{1 \le k \le N-1}$, in the $N$th product of $T$,} $G^{(N)}$ can be written in the following expanded form +\titou{Introducing the set of $N-1$ intermediate states, $\{ \ket{i_k} \}_{1 \le k \le N-1}$, in the $N$th product of $T$,} $G^{(N)}$ can be written in the following expanded form \be \label{eq:cn} G^{(N)}_{i_0 i_N} = \sum_{i_1} \sum_{i_2} ... \sum_{i_{N-1}} \prod_{k=0}^{N-1} T_{i_{k} i_{k+1}}, \ee -\titou{where $T_{i_{k} i_{k+1}} = ??$}. +\titou{where $T_{ij} =\mel{i}{T}{j}$}. Here, each index $i_k$ runs over all basis vectors. In quantum physics, Eq.~\eqref{eq:cn} is referred to as the path-integral representation of the Green's matrix (function). @@ -252,31 +253,32 @@ The series of states $\ket{i_0}, \ldots,\ket{i_N}$ is interpreted as a ``path'' Each path is associated with a weight $\prod_{k=0}^{N-1} T_{i_{k} i_{k+1}}$ and the path integral expression of $G$ can be recast in the more suggestive form as follows: \be \label{eq:G} - G^{(N)}_{i_0 i_N}= \sum_{\text{all paths $\ket{i_1},\ldots,\ket{i_{N-1}}$}} \prod_{k=0}^{N-1} T_{i_{k} i_{k+1}} + G^{(N)}_{i_0 i_N}= \sum_{\text{all paths $\ket{i_1},\ldots,\ket{i_{N-1}}$}} \prod_{k=0}^{N-1} T_{i_{k} i_{k+1}}. \ee + This expression allows a simple and vivid interpretation of the solution. -In the limit $N \to \infty$, the $i$th component of the ground state wave funciton (obtained as $\lim_{N \to \infty} G^{(N)}_{\titou{i_0 i_N}})$ is the weighted sum over all possible paths arriving at vector \titou{$\ket{i_N}$}. +In the limit $N \to \infty$, the $i$th component of the ground-state wave function (obtained as $\lim_{N \to \infty} G^{(N)}_{\titou{i_0 i_N}})$ is the weighted sum over all possible paths arriving at vector \titou{$\ket{i_N}$}. This result is independent of the initial vector $\ket{i_0}$, apart from some irrelevant global phase factor. When the size of the linear space is small the explicit calculation of the full sums involving $M^N$ terms (where $M$ is the size of the Hilbert space) can be performed. -We are in the realm of what one would call the ``deterministic'' power methods, such as the Lancz\`os or Davidson approaches. -If not, probabilistic techniques for generating only the paths contributing significantly to the sums are to be prefered. -This is the +In such a case, we are in the realm of what one would call the ``deterministic'' power methods, such as the Lancz\`os or Davidson approaches. +If not, probabilistic techniques for generating only the paths contributing significantly to the sums are to be preferred. +This is the central theme of the present work. %=======================================% \subsection{Probabilistic framework} \label{sec:proba} %=======================================% -In order to derive a probabilistic expression for the Green's matrix we introduce a so-called guiding vector, $\ket{\PsiG}$, having strictly positive components, \ie, $\PsiG_i > 0$, and apply a similarity transformation to the operators $G^{(N)}$ and $T$ +In order to derive a probabilistic expression for the Green's matrix we introduce a so-called guiding vector, $\ket{\PsiG}$, having strictly positive components, \ie, $\PsiG_i > 0$, in order to apply a similarity transformation to the operators $G^{(N)}$ and $T$ as follows: \begin{align} \label{eq:defT} - \bar{T}_{ij} & = \frac{\PsiG_j}{\PsiG_i} T_{ij} - \\ - \bar{G}^{(N)}_{ij}& = \frac{\PsiG_j}{\PsiG_i} G^{(N)}_{ij} + \bar{T}_{ij} & = \frac{\PsiG_j}{\PsiG_i} T_{ij}, + & + \bar{G}^{(N)}_{ij}& = \frac{\PsiG_j}{\PsiG_i} G^{(N)}_{ij}. \end{align} -Note that under the similarity transformation the path integral expression, Eq.~\eqref{eq:G}, relating $G^{(N)}$ and $T$ remains unchanged for the similarity-transformed operators, $\bar{G}^{(N)}$ and $\bar{T}$. +Note that, under this similarity transformation, the path integral expression relating $G^{(N)}$ and $T$ [see Eq.~\eqref{eq:G}] remains unchanged for $\bar{G}^{(N)}$ and $\bar{T}$. -Next, the matrix elements of $\bar{T}$ are expressed as those of a stochastic matrix multiplied by some residual weight, namely +Next, the matrix elements of $\bar{T}$ are expressed as those of a stochastic matrix multiplied by some residual weight, namely, \be \label{eq:defTij} \bar{T}_{ij}= p_{i \to j} w_{ij}. @@ -290,6 +292,7 @@ To build the transition probability density the following operator is introduced %As known, there is a natural way of associating a stochastic matrix to a matrix having a positive ground-state vector (here, a positive vector is defined here as %a vector with all components positive). \be +\label{eq:T+} T^+= \Id - \tau \qty( H^+ - \EL^+ \Id ), \ee where @@ -297,9 +300,9 @@ $H^+$ is the matrix obtained from $H$ by imposing the off-diagonal elements to b \be H^+_{ij}= \begin{cases} - \phantom{-}H_{ij}, & \text{if $i=j$}. + \phantom{-}H_{ij}, & \text{if $i=j$}, \\ - -\abs{H_{ij}}, & \text{if $i\neq j$}. + -\abs{H_{ij}}, & \text{if $i\neq j$}. \end{cases} \ee Here, $\EL^+ \Id$ is the diagonal matrix whose diagonal elements are defined as @@ -307,55 +310,46 @@ Here, $\EL^+ \Id$ is the diagonal matrix whose diagonal elements are defined as (\EL^+)_{i}= \frac{\sum_j H^+_{ij}\PsiG_j}{\PsiG_i}. \ee The vector $\EL^+$ is known as the local energy vector associated with $\PsiG$. - -Actually, the operator $H^+ - \EL^+ \Id$ in the definition of the operator $T^+$ has been chosen to admit by construction $\ket{\PsiG}$ as ground-state with zero eigenvalue -\be -\label{eq:defTplus} - \qty(H^+ - E_L^+ \Id) \ket{\PsiG} = 0, -\ee -leading to the relation +By construction, the operator $H^+ - \EL^+ \Id$ in the definition of the operator $T^+$ [see Eq.~\eqref{eq:T+}] has been chosen to admit $\ket{\PsiG}$ as a ground-state wave function with zero eigenvalue, \ie, $\qty(H^+ - E_L^+ \Id) \ket{\PsiG} = 0$, leading to the relation \be \label{eq:relT+} T^+ \ket{\PsiG} = \ket{\PsiG}. \ee -The stochastic matrix is now defined as +We are now in the position to define the stochastic matrix as \be \label{eq:pij} - p_{i \to j} = \frac{\PsiG_j}{\PsiG_i} T^+_{ij}. + p_{i \to j} + = \frac{\PsiG_j}{\PsiG_i} T^+_{ij} + = + \begin{cases} + 1 - \tau \qty[ H^+_{ii}- (\EL^+)_{i} ], & \text{if $i=j$}, + \\ + \tau \frac{\PsiG_{j}}{\PsiG_{i}} \abs{H_{ij}} \ge 0, & \text{if $i\neq j$}. + \end{cases} \ee -The diagonal matrix elements of the stochastic matrix write -\be - p_{i \to i} = 1 - \tau \qty[ H^+_{ii}- (\EL^+)_{i} ] -\ee -while, for $i \ne j$, -\be - p_{i \to j} = \tau \frac{\PsiG_{j}}{\PsiG_{i}} \abs{H_{ij}} \ge 0 -\ee -As seen, the off-diagonal terms, $p_{i \to j}$ are positive while the diagonal ones, $p_{i \to i}$, can be made positive if $\tau$ is chosen sufficiently small. -More precisely, the condition writes +As readily seen in Eq.~\eqref{eq:pij}, the off-diagonal terms of the stochastic matrix are positive, while the diagonal ones can be made positive if $\tau$ is chosen sufficiently small via the condition \be \label{eq:cond} - \tau \leq \frac{1}{\max_i\abs{H^+_{ii}-(\EL^+)_{i}}} + \tau^{-1} \geq \max_i\abs{H^+_{ii}-(\EL^+)_{i}}. \ee -The sum-over-states condition, Eq.~\eqref{eq:sumup}, follows from the fact that $|\PsiG\rangle$ is eigenvector of $T^+$, Eq.~\eqref{eq:relT+} +The sum-over-states condition [see Eq.~\eqref{eq:sumup}] \be - \sum_j p_{i \to j}= \frac{1}{\PsiG_{i}} \mel{i}{T^+}{\PsiG} = 1. + \sum_j p_{i \to j}= \frac{\mel{i}{T^+}{\PsiG}}{\PsiG_{i}} = 1. \ee -We have then verified that $p_{i \to j}$ is indeed a stochastic matrix. +follows from the fact that $\ket{\PsiG}$ is eigenvector of $T^+$ [see Eq.~\eqref{eq:relT+}]. +This ensures that $p_{i \to j}$ is indeed a stochastic matrix. -At first sight, the condition defining the maximum value of $\tau$ allowed, Eq.~\eqref{eq:cond}, may appear as rather tight -since for very large matrices it may impose an extremely small value for the time step. However, in practice during the simulation only a (tiny) -fraction of the linear space is sampled, and the maximum value of $\abs{H^+_{ii} - E^+_{Li}}$ for the sampled states turns out to be not too large, so reasonable values of $\tau$ -can be used without violating the positivity of the transition probability matrix. -Note that we can even escape from this condition by slightly generalizing the transition probability -matrix used as follows +At first sight, the condition defining the maximum value of $\tau$ allowed, Eq.~\eqref{eq:cond}, may appear rather tight since, for very large matrices, it may impose an extremely small value of the time step. +However, in practice, during the simulation only a (tiny) fraction of the linear space is sampled, and the maximum absolute value of $H^+_{ii}-(\EL^+)_{i}$ for the sampled states turns out to be \titou{not too large}. +Hence, reasonable values of $\tau$ can be selected without violating the positivity of the transition probability matrix. +\titou{Note that one can eschew this condition via a simple generalization of the transition probability matrix:} \be p_{i \to j} = \frac{ \frac{\PsiG_{j}}{\PsiG_{i}} \abs{\mel{i}{T^+}{j}} } { \sum_j \frac{\PsiG_{j}}{\PsiG_{i}} \abs{\mel{i}{T^+}{j}} } - = \frac{ \PsiG_{j} \abs{\mel{i}{T^+}{j}} } - { \sum_j \PsiG_{j} \abs{\mel{i}{T^+}{j}} } + = \frac{ \PsiG_{j} \abs*{T^+_{ij}} } + { \sum_j \PsiG_{j} \abs*{T^+_{ij}} }. \ee This new transition probability matrix with positive entries reduces to Eq.~\eqref{eq:pij} when $T^+_{ij}$ is positive. @@ -370,34 +364,33 @@ Using these notations the Green's matrix components can be rewritten as \ee \titou{where $i$ is identified to $i_N$.} -The product $\prod_{k=0}^{N-1} p_{i_{k} \to i_{k+1}}$ is the probability, denoted $\text{Prob}_{i_0 \to i_N}(i_1,...,i_{N-1})$, +The product $\prod_{k=0}^{N-1} p_{i_{k} \to i_{k+1}}$ is the probability, denoted $\text{Prob}_{i_0 \to i_N}(i_1,\ldots,i_{N-1})$, for the path starting at $\ket{i_0}$ and ending at $\ket{i_N}$ to occur. -Using the fact that $p_{i \to j} \ge 0$ and Eq.~\eqref{eq:sumup} we verify that $\text{Prob}_{i_0 \to i_N}$ is positive and obeys +Using Eq.~\eqref{eq:sumup} and the fact that $p_{i \to j} \ge 0$, one can easily verify that $\text{Prob}_{i_0 \to i_N}$ is positive and obeys \be - \sum_{i_1,\ldots,i_{N-1}} \text{Prob}_{i_0 \to i_N}(i_1,\ldots,i_{N-1}) = 1 + \sum_{i_1,\ldots,i_{N-1}} \text{Prob}_{i_0 \to i_N}(i_1,\ldots,i_{N-1}) = 1, \ee -as it should be. -The probabilistic average associated with this probability for the path, denoted here as, $ \expval{\cdots}$ is then defined as +as it should. +For a given path $i_1,\ldots,i_{N-1}$, the probabilistic average associated with this probability, denoted here as $\expval{\cdots}$, is then defined as \be +\label{eq:average} \expval{F} = \sum_{i_1,\ldots,i_{N-1}} F(i_0,\ldots,i_N) \text{Prob}_{i_0 \to i_N}(i_1,\ldots,i_{N-1}), -\label{average} \ee where $F$ is an arbitrary function. Finally, the path-integral expressed as a probabilistic average reads \be - \bar{G}^{(N)}_{ii_0}= \Big \langle \prod_{k=0}^{N-1} w_{i_{k}i_{k+1}} \Big \rangle + \bar{G}^{(N)}_{\titou{ii_0}}= \expval{ \prod_{k=0}^{N-1} w_{i_{k}i_{k+1}}} \label{cn_stoch} \ee -To calculate the probabilistic average, Eq.(\ref{average}), +To calculate the probabilistic average, Eq.~\eqref{eq:average}, an artificial (mathematical) ``particle'' called walker (or psi-particle) is introduced. During the Monte Carlo simulation the walker moves in configuration space by drawing new states with -probability $p(i_k \to i_{k+1})$, thus realizing the path of probability -${\rm Prob}(i_0 \to i_n)$. +probability $p_{i_k \to i_{k+1}}$, thus realizing the path of probability $\text{Prob}(i_0 \to i_n)$. The energy, Eq.~\eqref{eq:E0} is given as \be E_0 = \lim_{N \to \infty } \frac{ \expval{ \prod_{k=0}^{N-1} w_{i_{k}i_{k+1}} {(H\PsiT)}_{i_N}} } - { \expval{ \prod_{k=0}^{N-1} w_{i_{k}i_{k+1}} {\PsiT}_{i_N} }} + { \expval{ \prod_{k=0}^{N-1} w_{i_{k}i_{k+1}} {\PsiT}_{i_N} }}. \ee Note that, instead of using a single walker, it is possible to introduce a population of independent walkers and to calculate the averages over the population. In addition, thanks to the ergodic property of the stochastic matrix (see, for example, Ref.~\onlinecite{Caffarel_1988}) a unique path of infinite length from which sub-paths of length $N$ can be extracted may also be used. @@ -426,7 +419,7 @@ We shall not here insist on these practical details that can be found, for examp During the simulation, walkers move from state to state with the possibility of being trapped a certain number of times on the same state before exiting to a different state. This fact can be exploited in order to integrate out some part of the dynamics, thus leading to a reduction of the statistical -fluctuations. This idea was proposed some time ago\cite{assaraf_99,Assaraf_1999B,caffarel_00} and applied to the SU(N) one-dimensional Hubbard model. +fluctuations. This idea was proposed some time ago \cite{Assaraf_1999A,Assaraf_1999B,Caffarel_2000} and applied to the SU(N) one-dimensional Hubbard model. Let us consider a given state $|i\rangle$. The probability that the walker remains exactly $n$ times on $|i\rangle$ ($n$ from 1 to $\infty$) and then exits to a different state $j$ is @@ -462,7 +455,7 @@ The time-averaged contribution of the \titou{on-state} weight can be easily calc \be \bar{w}_i= \sum_{n=1}^{\infty} w^n_{ii} P_i(n)= \frac{T_{ii}}{T^+_{ii}} \frac{1-T^+_{ii}}{1-T_{ii}} \ee -Details of the implementation of the effective dynamics can be in found in Refs.~\onlinecite{assaraf_99} and \onlinecite{caffarel_00}. +Details of the implementation of the effective dynamics can be in found in Refs.~\onlinecite{Assaraf_1999B} and \onlinecite{Caffarel_2000}. %=======================================% \subsection{General domains} @@ -470,8 +463,8 @@ Details of the implementation of the effective dynamics can be in found in Refs. %=======================================% Let us now extend the results of the preceding section to a general domain. For that, -let us associate to each state $|i\rangle$ a set of states, called the domain of $|i\rangle$ and -denoted ${\cal D}_i$, consisting of the state $|i\rangle$ plus a certain number of states. No particular constraints on the type of domains +let us associate to each state $\ket{i}$ a set of states, called the domain of $\ket{i}$ and +denoted $\cD_i$, consisting of the state $\ket{i}$ plus a certain number of states. No particular constraints on the type of domains are imposed, for example domains associated with different states can be identical, or may have or not common states. The only important condition is that the set of all domains ensures the ergodicity property of the effective stochastic dynamics (that is, starting from any state there is a non-zero-probability to reach any other state in a finite number of steps). In practice, it is not difficult to impose such a condition.