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file = {/Users/monino/Zotero/storage/EHYRIT8T/Adamo et Barone - 1999 - Toward reliable density functional methods without.pdf}
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}
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@article{aidas_2014,
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||||
title = {The {{Dalton}} Quantum Chemistry Program System},
|
||||
author = {Aidas, Kestutis and Angeli, Celestino and Bak, Keld L. and Bakken, Vebj{\o}rn and Bast, Radovan and Boman, Linus and Christiansen, Ove and Cimiraglia, Renzo and Coriani, Sonia and Dahle, P{\aa}l and Dalskov, Erik K. and Ekstr{\"o}m, Ulf and Enevoldsen, Thomas and Eriksen, Janus J. and Ettenhuber, Patrick and Fern{\'a}ndez, Berta and Ferrighi, Lara and Fliegl, Heike and Frediani, Luca and Hald, Kasper and Halkier, Asger and H{\"a}ttig, Christof and Heiberg, Hanne and Helgaker, Trygve and Hennum, Alf Christian and Hettema, Hinne and Hjerten{\ae}s, Eirik and H{\o}st, Stinne and H{\o}yvik, Ida-Marie and Iozzi, Maria Francesca and Jans{\'i}k, Branislav and Jensen, Hans J{\o}rgen Aa. and Jonsson, Dan and J{\o}rgensen, Poul and Kauczor, Joanna and Kirpekar, Sheela and Kj{\ae}rgaard, Thomas and Klopper, Wim and Knecht, Stefan and Kobayashi, Rika and Koch, Henrik and Kongsted, Jacob and Krapp, Andreas and Kristensen, Kasper and Ligabue, Andrea and Lutn{\ae}s, Ola B. and Melo, Juan I. and Mikkelsen, Kurt V. and Myhre, Rolf H. and Neiss, Christian and Nielsen, Christian B. and Norman, Patrick and Olsen, Jeppe and Olsen, J{\'o}gvan Magnus H. and Osted, Anders and Packer, Martin J. and Pawlowski, Filip and Pedersen, Thomas B. and Provasi, Patricio F. and Reine, Simen and Rinkevicius, Zilvinas and Ruden, Torgeir A. and Ruud, Kenneth and Rybkin, Vladimir V. and Sa{\l}ek, Pawel and Samson, Claire C. M. and {de Mer{\'a}s}, Alfredo S{\'a}nchez and Saue, Trond and Sauer, Stephan P. A. and Schimmelpfennig, Bernd and Sneskov, Kristian and Steindal, Arnfinn H. and {Sylvester-Hvid}, Kristian O. and Taylor, Peter R. and Teale, Andrew M. and Tellgren, Erik I. and Tew, David P. and Thorvaldsen, Andreas J. and Th{\o}gersen, Lea and Vahtras, Olav and Watson, Mark A. and Wilson, David J. D. and Ziolkowski, Marcin and {\AA}gren, Hans},
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year = {2014},
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||||
journal = {WIREs Comput. Mol. Sci.},
|
||||
volume = {4},
|
||||
number = {3},
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||||
pages = {269--284},
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issn = {1759-0884},
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doi = {10.1002/wcms.1172},
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abstract = {Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree\textendash Fock, Kohn\textendash Sham, multiconfigurational self-consistent-field, M\o ller\textendash Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms. This article is categorized under: Software {$>$} Quantum Chemistry},
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annotation = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/wcms.1172},
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file = {/Users/monino/Zotero/storage/MK4NYEM5/Aidas et al. - 2014 - The Dalton quantum chemistry program system.pdf;/Users/monino/Zotero/storage/T88T8WXM/wcms.html}
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}
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@article{andersson_1990,
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title = {Second-Order Perturbation Theory with a {{CASSCF}} Reference Function},
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author = {Andersson, Kerstin. and Malmqvist, Per Aake. and Roos, Bjoern O. and Sadlej, Andrzej J. and Wolinski, Krzysztof.},
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@ -191,6 +206,20 @@
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file = {/Users/monino/Zotero/storage/7E3MQEQM/Casanova et Krylov - 2020 - Spin-flip methods in quantum chemistry.pdf}
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}
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@incollection{casida_1995,
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title = {Time-{{Dependent Density Functional Response Theory}} for {{Molecules}}},
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booktitle = {Recent {{Advances}} in {{Density Functional Methods}}},
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author = {Casida, Mark E.},
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year = {1995},
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month = nov,
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series = {Recent {{Advances}} in {{Computational Chemistry}}},
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volume = {Volume 1},
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pages = {155--192},
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publisher = {{WORLD SCIENTIFIC}},
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||||
doi = {10.1142/9789812830586_0005},
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isbn = {978-981-02-2442-4}
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}
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@article{christiansen_1995,
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title = {Response Functions in the {{CC3}} Iterative Triple Excitation Model},
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author = {Christiansen, Ove and Koch, Henrik and Jo/rgensen, Poul},
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@ -205,6 +234,52 @@
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doi = {10.1063/1.470315}
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}
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@article{christiansen_1995a,
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title = {The Second-Order Approximate Coupled Cluster Singles and Doubles Model {{CC2}}},
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author = {Christiansen, Ove and Koch, Henrik and J{\o}rgensen, Poul},
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year = {1995},
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month = sep,
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journal = {Chemical Physics Letters},
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volume = {243},
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number = {5},
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pages = {409--418},
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issn = {0009-2614},
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doi = {10.1016/0009-2614(95)00841-Q},
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abstract = {An approximate coupled cluster singles and doubles model is presented, denoted CC2. The CC2 total energy is of second-order M\o ller-Plesset perturbation theory (MP2) quality. The CC2 linear response function is derived. Unlike MP2, excitation energies and transition moments can be obtained in CC2. A hierarchy of coupled cluster models, CCS, CC2, CCSD, CC3, CCSDT etc., is presented where CC2 and CC3 are approximate coupled cluster models defined by similar approximations. Higher levels give increased accuracy at increased computational effort. The scaling of CCS, CC2, CCSD, CC3 and CCSDT is N4, N5, N6, N7 and N8, respectively where N is th the number of orbitals. Calculations on Be, N2 and C2H4 are performed and results compared with those obtained in the second-order polarization propagator approach SOPPA.},
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langid = {english},
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||||
file = {/Users/monino/Zotero/storage/GCQ3GY6R/Christiansen et al. - 1995 - The second-order approximate coupled cluster singl.pdf;/Users/monino/Zotero/storage/53PI8AQM/000926149500841Q.html}
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}
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@article{christiansen_1995b,
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title = {Response Functions in the {{CC3}} Iterative Triple Excitation Model},
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author = {Christiansen, Ove and Koch, Henrik and Jo/rgensen, Poul},
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year = {1995},
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month = nov,
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journal = {J. Chem. Phys.},
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volume = {103},
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number = {17},
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pages = {7429--7441},
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publisher = {{American Institute of Physics}},
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issn = {0021-9606},
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doi = {10.1063/1.470315}
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}
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@article{dreuw_2015,
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title = {The Algebraic Diagrammatic Construction Scheme for the Polarization Propagator for the Calculation of Excited States},
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author = {Dreuw, Andreas and Wormit, Michael},
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year = {2015},
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journal = {WIREs Comput. Mol. Sci.},
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volume = {5},
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||||
number = {1},
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pages = {82--95},
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issn = {1759-0884},
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doi = {10.1002/wcms.1206},
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abstract = {The algebraic diagrammatic construction (ADC) scheme for the polarization propagator provides a series of ab initio methods for the calculation of excited states based on perturbation theory. In recent years, the second-order ADC(2) scheme has attracted attention in the computational chemistry community because of its reliable accuracy and reasonable computational effort in the calculation of predominantly singly excited states. Owing to their size-consistency, ADC methods are suited for the investigation of large molecules. In addition, their Hermitian structure and the availability of the intermediate state representation (ISR) allow for straightforward computation of excited-state properties. Recently, an efficient implementation of ADC(3) has been reported, and its high accuracy for typical valence excited states of organic chromophores has been demonstrated. In this review, the origin of ADC-based excited-state methods in propagator theory is described, and an intuitive route for the derivation of algebraic expressions via the ISR is outlined and comparison to other excited-state methods is made. Existing computer codes and implemented ADC variants are reviewed, but most importantly the accuracy and limits of different ADC schemes are critically examined. WIREs Comput Mol Sci 2015, 5:82\textendash 95. doi: 10.1002/wcms.1206 This article is categorized under: Structure and Mechanism {$>$} Molecular Structures Electronic Structure Theory {$>$} Ab Initio Electronic Structure Methods Theoretical and Physical Chemistry {$>$} Spectroscopy},
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langid = {english},
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||||
annotation = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/wcms.1206},
|
||||
file = {/Users/monino/Zotero/storage/ULV7SRTF/Dreuw et Wormit - 2015 - The algebraic diagrammatic construction scheme for.pdf;/Users/monino/Zotero/storage/D7CSY4E5/wcms.html}
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||||
}
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@article{dunning_1989,
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||||
title = {Gaussian Basis Sets for Use in Correlated Molecular Calculations. {{I}}. {{The}} Atoms Boron through Neon and Hydrogen},
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author = {Dunning, Thom H.},
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@ -300,6 +375,38 @@
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file = {/Users/monino/Zotero/storage/I2Q5L62K/Garniron et al. - 2019 - Quantum Package 2.0 An Open-Source Determinant-Dr.pdf}
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||||
}
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@article{harbach_2014,
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title = {The Third-Order Algebraic Diagrammatic Construction Method ({{ADC}}(3)) for the Polarization Propagator for Closed-Shell Molecules: {{Efficient}} Implementation and Benchmarking},
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shorttitle = {The Third-Order Algebraic Diagrammatic Construction Method ({{ADC}}(3)) for the Polarization Propagator for Closed-Shell Molecules},
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author = {Harbach, Philipp H. P. and Wormit, Michael and Dreuw, Andreas},
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year = {2014},
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month = aug,
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journal = {J. Chem. Phys.},
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||||
volume = {141},
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number = {6},
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pages = {064113},
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publisher = {{American Institute of Physics}},
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issn = {0021-9606},
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doi = {10.1063/1.4892418},
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abstract = {The implementation of an efficient program of the algebraic diagrammatic construction method for the polarisation propagator in third-order perturbation theory (ADC(3)) for the computation of excited states is reported. The accuracies of ADC(2) and ADC(3) schemes have been investigated with respect to Thiel's recently established benchmark set for excitation energies and oscillator strengths. The calculation of 141 vertical excited singlet and 71 triplet states of 28 small to medium-sized organic molecules has revealed that ADC(3) exhibits mean error and standard deviation of 0.12 {$\pm$} 0.28 eV for singlet states and -0.18 {$\pm$} 0.16 eV for triplet states when the provided theoretical best estimates are used as benchmark. Accordingly, the ADC(2)-s and ADC(2)-x calculations revealed accuracies of 0.22 {$\pm$} 0.38 eV and -0.70 {$\pm$} 0.37 eV for singlets and 0.12 {$\pm$} 0.16 eV and -0.55 {$\pm$} 0.20 eV for triplets, respectively. For a comparison of CC3 and ADC(3), only non-CC3 benchmark values were considered, which comprise 84 singlet states and 19 triplet states. For these singlet states CC3 exhibits an accuracy of 0.23 {$\pm$} 0.21 eV and ADC(3) an accuracy of 0.08 {$\pm$} 0.27 eV, and accordingly for the triplet states of 0.12 {$\pm$} 0.10 eV and -0.10 {$\pm$} 0.13 eV, respectively. Hence, based on the quality of the existing benchmark set it is practically not possible to judge whether ADC(3) or CC3 is more accurate, however, ADC(3) has a much larger range of applicability due to its more favourable scaling of O(N6) with system size.},
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file = {/Users/monino/Zotero/storage/8SWPC4TT/Harbach et al. - 2014 - The third-order algebraic diagrammatic constructio.pdf}
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}
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@article{hattig_2000,
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title = {{{CC2}} Excitation Energy Calculations on Large Molecules Using the Resolution of the Identity Approximation},
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author = {H{\"a}ttig, Christof and Weigend, Florian},
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year = {2000},
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month = oct,
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||||
journal = {J. Chem. Phys.},
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||||
volume = {113},
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||||
number = {13},
|
||||
pages = {5154--5161},
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||||
publisher = {{American Institute of Physics}},
|
||||
issn = {0021-9606},
|
||||
doi = {10.1063/1.1290013},
|
||||
file = {/Users/monino/Zotero/storage/WHT8RF9H/Hättig et Weigend - 2000 - CC2 excitation energy calculations on large molecu.pdf}
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||||
}
|
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@article{hirata_2000,
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||||
title = {High-Order Determinantal Equation-of-Motion Coupled-Cluster Calculations for Electronic Excited States},
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||||
author = {Hirata, So and Nooijen, Marcel and Bartlett, Rodney J.},
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@ -362,6 +469,22 @@
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||||
file = {/Users/monino/Zotero/storage/TEHKUF6P/Kállay et Gauss - 2004 - Calculation of excited-state properties using gene.pdf}
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||||
}
|
||||
|
||||
@article{kallay_2005,
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||||
title = {Approximate Treatment of Higher Excitations in Coupled-Cluster Theory},
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||||
author = {K{\'a}llay, Mih{\'a}ly and Gauss, J{\"u}rgen},
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year = {2005},
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||||
month = dec,
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||||
journal = {J. Chem. Phys.},
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||||
volume = {123},
|
||||
number = {21},
|
||||
pages = {214105},
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||||
publisher = {{American Institute of Physics}},
|
||||
issn = {0021-9606},
|
||||
doi = {10.1063/1.2121589},
|
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abstract = {The possibilities for the approximate treatment of higher excitations in coupled-cluster (CC) theory are discussed. Potential routes for the generalization of corresponding approximations to lower-level CC methods are analyzed for higher excitations. A general string-based algorithm is presented for the evaluation of the special contractions appearing in the equations specific to those approximate CC models. It is demonstrated that several iterative and noniterative approximations to higher excitations can be efficiently implemented with the aid of our algorithm and that the coding effort is mostly reduced to the generation of the corresponding formulas. The performance of the proposed and implemented methods for total energies is assessed with special regard to quadruple and pentuple excitations. The applicability of our approach is illustrated by benchmark calculations for the butadiene molecule. Our results demonstrate that the proposed algorithm enables us to consider the effect of quadruple excitations for molecular systems consisting of up to 10\textendash 12 atoms.},
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file = {/Users/monino/Zotero/storage/IYZ6TDUF/Kállay et Gauss - 2005 - Approximate treatment of higher excitations in cou.pdf}
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}
|
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@article{karadakov_2008,
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||||
title = {Ground- and {{Excited-State Aromaticity}} and {{Antiaromaticity}} in {{Benzene}} and {{Cyclobutadiene}}},
|
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author = {Karadakov, Peter B.},
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||||
@ -378,6 +501,22 @@
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||||
file = {/Users/monino/Zotero/storage/7UMPEAYT/Karadakov - 2008 - Ground- and Excited-State Aromaticity and Antiarom.pdf;/Users/monino/Zotero/storage/7ULNL76P/jp8037335.html}
|
||||
}
|
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||||
@article{koch_1995,
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||||
title = {Excitation Energies of {{BH}}, {{CH2}} and {{Ne}} in Full Configuration Interaction and the Hierarchy {{CCS}}, {{CC2}}, {{CCSD}} and {{CC3}} of Coupled Cluster Models},
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author = {Koch, Henrik and Christiansen, Ove and J{\o}rgensen, Poul and Olsen, Jeppe},
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year = {1995},
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month = sep,
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journal = {Chemical Physics Letters},
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||||
volume = {244},
|
||||
number = {1},
|
||||
pages = {75--82},
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||||
issn = {0009-2614},
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||||
doi = {10.1016/0009-2614(95)00914-P},
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abstract = {Excitation energies in the coupled cluster model hierarchy CCS, CC2, CCSD and CC3 have been calculated for Ne, BH and CH2 and compared with full configuration interaction (FCI) results. Single replacement dominated excitations are improved at each level in this hierarchy, with a decrease in the error compared to FCI of about a factor of three at each level. This decrease is in accordance with the fact that the single replacement dominated excitations in CCS, CC2, CCSD and CC3 are correct through respectively first, second and third order in the fluctuation potential. The improvement from CC2 to CCSD is due to the fact that CCSD gives a full coupled cluster treatment in the singles, doubles space. Double replacement dominated excitations can only be described at the CCSD and CC3 levels, and are correct through first and second order, respectively. The CC3 double replacement dominated excitations have similar quality as the single replacement dominated excitations in CC2. The scaling of CCS, CC2, CCSD and CC3 is N4, N5, N6 and N7, respectively, where N is the number of orbitals.},
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langid = {english},
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||||
file = {/Users/monino/Zotero/storage/NVUINP9Y/Koch et al. - 1995 - Excitation energies of BH, CH2 and Ne in full conf.pdf;/Users/monino/Zotero/storage/YNY2X43N/000926149500914P.html}
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}
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@article{koch_1997,
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title = {The {{CC3}} Model: {{An}} Iterative Coupled Cluster Approach Including Connected Triples},
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shorttitle = {The {{CC3}} Model},
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@ -442,6 +581,22 @@
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file = {/Users/monino/Zotero/storage/L3VLAU8A/Kucharski et Bartlett - 1991 - Recursive intermediate factorization and complete .pdf}
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}
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@article{kucharski_1991a,
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title = {Recursive Intermediate Factorization and Complete Computational Linearization of the Coupled-Cluster Single, Double, Triple, and Quadruple Excitation Equations},
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author = {Kucharski, Stanislaw A. and Bartlett, Rodney J.},
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year = {1991},
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month = jul,
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journal = {Theoret. Chim. Acta},
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volume = {80},
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number = {4},
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pages = {387--405},
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issn = {1432-2234},
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||||
doi = {10.1007/BF01117419},
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abstract = {The nonlinear CCSDTQ equations are written in a fully linearized form, via the introduction of computationally convenient intermediates. An efficient formulation of the coupled cluster method is proposed. Due to a recursive method for the calculation of intermediates, all computational steps involve the multiplication of an intermediate with aT vertex. This property makes it possible to express the CC equations exclusively in terms of matrix products which can be directly transformed into a highly vectorized program.},
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langid = {english},
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file = {/Users/monino/Zotero/storage/HWEYZCLA/Kucharski et Bartlett - 1991 - Recursive intermediate factorization and complete .pdf}
|
||||
}
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@article{lee_1988a,
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title = {Development of the {{Colle-Salvetti}} Correlation-Energy Formula into a Functional of the Electron Density},
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author = {Lee, Chengteh and Yang, Weitao and Parr, Robert G.},
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@ -570,6 +725,40 @@
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||||
file = {/Users/monino/Zotero/storage/686RRDFK/Manohar et Krylov - 2008 - A noniterative perturbative triples correction for.pdf}
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}
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@article{mardirossian_2014,
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title = {{{$\omega$B97X-V}}: {{A}} 10-Parameter, Range-Separated Hybrid, Generalized Gradient Approximation Density Functional with Nonlocal Correlation, Designed by a Survival-of-the-Fittest Strategy},
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||||
shorttitle = {{{$\omega$B97X-V}}},
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author = {Mardirossian, Narbe and {Head-Gordon}, Martin},
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||||
year = {2014},
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||||
month = may,
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||||
journal = {Phys. Chem. Chem. Phys.},
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||||
volume = {16},
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||||
number = {21},
|
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pages = {9904--9924},
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publisher = {{The Royal Society of Chemistry}},
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issn = {1463-9084},
|
||||
doi = {10.1039/C3CP54374A},
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||||
abstract = {A 10-parameter, range-separated hybrid (RSH), generalized gradient approximation (GGA) density functional with nonlocal correlation (VV10) is presented. Instead of truncating the B97-type power series inhomogeneity correction factors (ICF) for the exchange, same-spin correlation, and opposite-spin correlation functionals uniformly, all 16 383 combinations of the linear parameters up to fourth order (m = 4) are considered. These functionals are individually fit to a training set and the resulting parameters are validated on a primary test set in order to identify the 3 optimal ICF expansions. Through this procedure, it is discovered that the functional that performs best on the training and primary test sets has 7 linear parameters, with 3 additional nonlinear parameters from range-separation and nonlocal correlation. The resulting density functional, {$\omega$}B97X-V, is further assessed on a secondary test set, the parallel-displaced coronene dimer, as well as several geometry datasets. Furthermore, the basis set dependence and integration grid sensitivity of {$\omega$}B97X-V are analyzed and documented in order to facilitate the use of the functional.},
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langid = {english},
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||||
file = {/Users/monino/Zotero/storage/GESCCCPT/Mardirossian et Head-Gordon - 2014 - ωB97X-V A 10-parameter, range-separated hybrid, g.pdf;/Users/monino/Zotero/storage/WG9ZZJ5X/c3cp54374a.html}
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||||
}
|
||||
|
||||
@article{matthews_2020,
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||||
title = {Analytic {{Gradients}} of {{Approximate Coupled Cluster Methods}} with {{Quadruple Excitations}}},
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author = {Matthews, Devin A.},
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year = {2020},
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||||
month = oct,
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||||
journal = {J. Chem. Theory Comput.},
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volume = {16},
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||||
number = {10},
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pages = {6195--6206},
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publisher = {{American Chemical Society}},
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issn = {1549-9618},
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||||
doi = {10.1021/acs.jctc.0c00522},
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abstract = {The analytic gradient theory for both iterative and noniterative coupled-cluster approximations that include connected quadruple excitations is presented. These methods include, in particular, CCSDT(Q), which is an analog of the well-known CCSD(T) method which starts from the full CCSDT method rather than CCSD. The resulting methods are implemented in the CFOUR program suite, and pilot applications are presented for the equilibrium geometries and harmonic vibrational frequencies of the simplest Criegee intermediate, CH2OO, as well as to the isomerization pathway between dimethylcarbene and propene. While all methods are seen to approximate the full CCSDTQ results well for ``well-behaved'' systems, the more difficult case of the Criegee intermediate shows that CCSDT(Q), as well as certain iterative approximations, display problematic behavior.},
|
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file = {/Users/monino/Zotero/storage/LCIZ3YB9/Matthews - 2020 - Analytic Gradients of Approximate Coupled Cluster .pdf;/Users/monino/Zotero/storage/ZZZQCDI4/acs.jctc.html}
|
||||
}
|
||||
|
||||
@book{minkin_1994,
|
||||
title = {Aromaticity and {{Antiaromaticity}}: {{Electronic}} and {{Structural Aspects}} | {{Wiley}}},
|
||||
shorttitle = {Aromaticity and {{Antiaromaticity}}},
|
||||
@ -578,6 +767,20 @@
|
||||
file = {/Users/monino/Zotero/storage/HGW4QMJY/Aromaticity+and+Antiaromaticity+Electronic+and+Structural+Aspects-p-9780471593829.html}
|
||||
}
|
||||
|
||||
@article{noga_1987,
|
||||
title = {The Full {{CCSDT}} Model for Molecular Electronic Structure},
|
||||
author = {Noga, Jozef and Bartlett, Rodney J.},
|
||||
year = {1987},
|
||||
month = jun,
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {86},
|
||||
number = {12},
|
||||
pages = {7041--7050},
|
||||
publisher = {{American Institute of Physics}},
|
||||
issn = {0021-9606},
|
||||
doi = {10.1063/1.452353}
|
||||
}
|
||||
|
||||
@article{peverati_2011,
|
||||
title = {Improving the {{Accuracy}} of {{Hybrid Meta-GGA Density Functionals}} by {{Range Separation}}},
|
||||
author = {Peverati, Roberto and Truhlar, Donald G.},
|
||||
@ -593,6 +796,21 @@
|
||||
file = {/Users/monino/Zotero/storage/PSFGYXNN/Peverati et Truhlar - 2011 - Improving the Accuracy of Hybrid Meta-GGA Density .pdf;/Users/monino/Zotero/storage/FB9CZB9Y/jz201170d.html}
|
||||
}
|
||||
|
||||
@article{purvis_1982,
|
||||
title = {A Full Coupled-cluster Singles and Doubles Model: {{The}} Inclusion of Disconnected Triples},
|
||||
shorttitle = {A Full Coupled-cluster Singles and Doubles Model},
|
||||
author = {Purvis, George D. and Bartlett, Rodney J.},
|
||||
year = {1982},
|
||||
month = feb,
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {76},
|
||||
number = {4},
|
||||
pages = {1910--1918},
|
||||
publisher = {{American Institute of Physics}},
|
||||
issn = {0021-9606},
|
||||
doi = {10.1063/1.443164}
|
||||
}
|
||||
|
||||
@article{qu_2015,
|
||||
title = {Photoisomerization of {{Silyl-Substituted Cyclobutadiene Induced}} by {$\sigma~\rightarrow$} {$\pi$}* {{Excitation}}: {{A Computational Study}}},
|
||||
shorttitle = {Photoisomerization of {{Silyl-Substituted Cyclobutadiene Induced}} by {$\sigma~\rightarrow$} {$\pi$}* {{Excitation}}},
|
||||
@ -642,6 +860,22 @@
|
||||
file = {/Users/monino/Zotero/storage/KWDFZUBF/9780470141526.html}
|
||||
}
|
||||
|
||||
@article{schirmer_1982,
|
||||
title = {Beyond the Random-Phase Approximation: {{A}} New Approximation Scheme for the Polarization Propagator},
|
||||
shorttitle = {Beyond the Random-Phase Approximation},
|
||||
author = {Schirmer, Jochen},
|
||||
year = {1982},
|
||||
month = nov,
|
||||
journal = {Phys. Rev. A},
|
||||
volume = {26},
|
||||
number = {5},
|
||||
pages = {2395--2416},
|
||||
publisher = {{American Physical Society}},
|
||||
doi = {10.1103/PhysRevA.26.2395},
|
||||
abstract = {Within the framework of the many-body Green's-function method we present a new approach to the polarization propagator for finite Fermi systems. This approach makes explicit use of the diagrammatic perturbation expansion for the polarization propagator, and reformulates the exact summation in terms of a simple algebraic scheme, referred to as the algebraic diagrammatic construction (ADC). The ADC defines in a natural way a set of approximation schemes (nth-order ADC schemes) which represent infinite partial summations exact up to nth order of perturbation theory. In contrast to the random-phase-approximation (RPA)-like schemes, the corresponding mathematical procedures are essentially Hermitian eigenvalue problems in limited configuration spaces of unperturbed excited configurations. Explicit equations for the first- and second-order ADC schemes are derived. These schemes are thoroughly discussed and compared with the Tamm-Dancoff approximation and RPA schemes.},
|
||||
file = {/Users/monino/Zotero/storage/2M5FJF4N/Schirmer - 1982 - Beyond the random-phase approximation A new appro.pdf;/Users/monino/Zotero/storage/JJFVGMB7/PhysRevA.26.html}
|
||||
}
|
||||
|
||||
@article{schoonmaker_2018,
|
||||
title = {Quantum Mechanical Tunneling in the Automerization of Cyclobutadiene},
|
||||
author = {Schoonmaker, R. and Lancaster, T. and Clark, S. J.},
|
||||
@ -707,6 +941,38 @@
|
||||
file = {/Users/monino/Zotero/storage/WXJDP8H3/Stoneburner et al. - 2017 - Systematic design of active spaces for multi-refer.pdf}
|
||||
}
|
||||
|
||||
@article{trofimov_1997,
|
||||
title = {Polarization Propagator Study of Electronic Excitation in Key Heterocyclic Molecules {{I}}. {{Pyrrole}}},
|
||||
author = {Trofimov, A. B. and Schirmer, J.},
|
||||
year = {1997},
|
||||
month = jan,
|
||||
journal = {Chemical Physics},
|
||||
volume = {214},
|
||||
number = {2},
|
||||
pages = {153--170},
|
||||
issn = {0301-0104},
|
||||
doi = {10.1016/S0301-0104(96)00303-5},
|
||||
abstract = {The electronic excitation spectrum of pyrrole is studied using a polarization propagator method referred to as the second-order algebraic-diagrammatic construction (ADC(2)), along with a simple model for vibrational excitation accounting for all totally symmetric modes. The method describes the optical absorption profile of pyrrole with an expected accuracy of 0.2 \textendash{} 0.4 eV for the vertical excitation energies. The vibrational analysis provides for detailed additional spectroscopic information. In the singlet spectrum, besides the ns, np and nd (n = 3,4) Rydberg excitations, three {$\pi$}-{$\pi{_\ast}$} valence transitions, V{${'}$}(1A1), V(1B2) and V(1A1) can clearly be distinguished. No evidence is found for Rydberg-valence interaction near the equilibrium geometry. Substantial vibrational widths and distinct vibrational excitation patterns are predicted for the Rydberg series converging to the first and second ionization thresholds. Some new assignments of major spectral features are proposed. The long-wave absorption maximum in the 5.6 \textendash{} 6.6. eV region is explained exclusively by the presence of Rydberg transitions, while the most intense absorption in the short-wave band system (7.0 \textendash{} 8.3 ev) predominantly originates from the V(1B2) and V(1A1) valence transitions.},
|
||||
langid = {english},
|
||||
file = {/Users/monino/Zotero/storage/LDEZNDBL/Trofimov et Schirmer - 1997 - Polarization propagator study of electronic excita.pdf;/Users/monino/Zotero/storage/UQXY2Y9F/S0301010496003035.html}
|
||||
}
|
||||
|
||||
@article{trofimov_2002,
|
||||
title = {Electron Excitation Energies Using a Consistent Third-Order Propagator Approach: {{Comparison}} with Full Configuration Interaction and Coupled Cluster Results},
|
||||
shorttitle = {Electron Excitation Energies Using a Consistent Third-Order Propagator Approach},
|
||||
author = {Trofimov, A. B. and Stelter, G. and Schirmer, J.},
|
||||
year = {2002},
|
||||
month = oct,
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {117},
|
||||
number = {14},
|
||||
pages = {6402--6410},
|
||||
publisher = {{American Institute of Physics}},
|
||||
issn = {0021-9606},
|
||||
doi = {10.1063/1.1504708},
|
||||
file = {/Users/monino/Zotero/storage/R5C8YPQF/Trofimov et al. - 2002 - Electron excitation energies using a consistent th.pdf}
|
||||
}
|
||||
|
||||
@article{varras_2018,
|
||||
title = {The Transition State of the Automerization Reaction of Cyclobutadiene: {{A}} Theoretical Approach Using the {{Restricted Active Space Self Consistent Field}} Method},
|
||||
shorttitle = {The Transition State of the Automerization Reaction of Cyclobutadiene},
|
||||
@ -739,6 +1005,39 @@
|
||||
file = {/Users/monino/Zotero/storage/IWWZ436M/Vitale et al. - 2020 - FCIQMC-Tailored Distinguishable Cluster Approach.pdf;/Users/monino/Zotero/storage/XFRQ8TP9/acs.jctc.html}
|
||||
}
|
||||
|
||||
@article{weintraub_2009a,
|
||||
title = {Long-{{Range-Corrected Hybrids Based}} on a {{New Model Exchange Hole}}},
|
||||
author = {Weintraub, Elon and Henderson, Thomas M. and Scuseria, Gustavo E.},
|
||||
year = {2009},
|
||||
month = apr,
|
||||
journal = {J. Chem. Theory Comput.},
|
||||
volume = {5},
|
||||
number = {4},
|
||||
pages = {754--762},
|
||||
publisher = {{American Chemical Society}},
|
||||
issn = {1549-9618},
|
||||
doi = {10.1021/ct800530u},
|
||||
abstract = {By admixing a fraction of exact Hartree-Fock-type exchange with conventional semilocal functionals, global hybrids greatly improve the accuracy of Kohn-Sham density functional theory. However, because global hybrids exhibit incorrect asymptotic decay of the exchange-correlation potential, they can have large errors for diverse quantities such as reaction barrier heights, nonlinear optical properties, and Rydberg and charge-transfer excitation energies. These errors can be removed by using a long-range-corrected hybrid, which uses exact exchange in the long range. Evaluating the long-range-corrected exchange energy requires a model for the semilocal exchange hole, and such models are scarce. Recently, two of us introduced one such model (J. Chem. Phys. 2008, 128, 194105). This model obeys several exact constraints and was designed specifically for use in long-range-corrected hybrids. Here, we give sample results for three long-range-corrected hybrids based upon our exchange hole model and show how the model can easily be applied to any generalized gradient approximation (GGA) for the exchange energy to create a long-range-corrected GGA.},
|
||||
file = {/Users/monino/Zotero/storage/CYJT2QAT/Weintraub et al. - 2009 - Long-Range-Corrected Hybrids Based on a New Model .pdf;/Users/monino/Zotero/storage/4KXSKAKD/ct800530u.html}
|
||||
}
|
||||
|
||||
@article{werner_2012,
|
||||
title = {Molpro: A General-Purpose Quantum Chemistry Program Package},
|
||||
shorttitle = {Molpro},
|
||||
author = {Werner, Hans-Joachim and Knowles, Peter J. and Knizia, Gerald and Manby, Frederick R. and Sch{\"u}tz, Martin},
|
||||
year = {2012},
|
||||
journal = {WIREs Comput. Mol. Sci.},
|
||||
volume = {2},
|
||||
number = {2},
|
||||
pages = {242--253},
|
||||
issn = {1759-0884},
|
||||
doi = {10.1002/wcms.82},
|
||||
abstract = {Molpro (available at http://www.molpro.net) is a general-purpose quantum chemical program. The original focus was on high-accuracy wave function calculations for small molecules, but using local approximations combined with explicit correlation treatments, highly accurate coupled-cluster calculations are now possible for molecules with up to approximately 100 atoms. Recently, multireference correlation treatments were also made applicable to larger molecules. Furthermore, an efficient implementation of density functional theory is available. \textcopyright{} 2011 John Wiley \& Sons, Ltd. This article is categorized under: Software {$>$} Quantum Chemistry},
|
||||
langid = {english},
|
||||
annotation = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/wcms.82},
|
||||
file = {/Users/monino/Zotero/storage/YKQYRFTG/Werner et al. - 2012 - Molpro a general-purpose quantum chemistry progra.pdf;/Users/monino/Zotero/storage/49LMT8LJ/wcms.html}
|
||||
}
|
||||
|
||||
@article{whitman_1982,
|
||||
title = {Limits on the Activation Parameters for Automerization of Cyclobutadiene-1,2-D2},
|
||||
author = {Whitman, David W. and Carpenter, Barry K.},
|
||||
|
||||
@ -226,7 +226,7 @@ Indeed, synthetic work from Pettis and co-workers \cite{reeves_1969} gives a rec
|
||||
|
||||
At the ground state structrure ($D_{2h}$), the ${}^1A_g$ state has a weak multi-configurational character because of the well separated frontier orbitals and can be described by single-reference methods. But at the square ($D_{4h}$) geometry, the singlet state ${}^1B_{1g}$ has two singly occupied frontier orbitals that are degenerated so has a two-configurational character and single-reference methods are unreliable to describe it. The singlet ($D_{4h}$) is a transition state in the automerization reaction between the two rectangular structures (see Fig.\ref{fig:CBD}). The autoisomerization barrier (AB) for the CBD molecule is defined as the energy difference between the singlet ground state of the square ($D_{4h}$) structure and the singlet ground state of the rectangular ($D_{2h}$) geometry. The energy of this barrier was predicted, experimentally, in the range of 1.6-10 kcal.mol$^{-1}$ \cite{whitman_1982} and multi-reference calculations gave an energy barrier in the range of 6-7 kcal.mol$^{-1}$ \cite{eckert-maksic_2006}. All the specificities of the CBD molecule make it a real playground for excited-states methods.
|
||||
|
||||
Excited states of the CBD molecule in both geometries are represented in Fig.\ref{fig:CBD}. Are represented ${}^1A_g$ and $1{}^3B_{1g}$ states for the rectangular geometry and ${}^1B_{1g}$and $1{}^3A_{2g}$ for the square one. Due to energy scaling doubly excited state $1{}^1B_{1g}$ and $2{}^1A_{1g}$ for the $D_{2h}$ and $D_{4h}$ structures, respectively, are not drawn. Doubly excited states are known to be challenging to represent for adiabatic time-dependent density functional theory (TD-DFT) and even for state-of-the-art methods like the approximate third-order coupled-cluster (CC3) \cite{christiansen_1995,koch_1997} or equation-of-motion coupled-cluster with singles, doubles and triples (EOM-CCSDT) \cite{kucharski_1991,kallay_2004,hirata_2000,hirata_2004}.
|
||||
Excited states of the CBD molecule in both geometries are represented in Fig.\ref{fig:CBD}. Are represented ${}^1A_g$ and $1{}^3B_{1g}$ states for the rectangular geometry and ${}^1B_{1g}$and $1{}^3A_{2g}$ for the square one. Due to energy scaling doubly excited state $1{}^1B_{1g}$ and $2{}^1A_{1g}$ for the $D_{2h}$ and $D_{4h}$ structures, respectively, are not drawn. Doubly excited states are known to be challenging to represent for adiabatic time-dependent density functional theory \cite{casida_1995} (TD-DFT) and even for state-of-the-art methods like the approximate third-order coupled-cluster (CC3) \cite{christiansen_1995,koch_1997} or equation-of-motion coupled-cluster with singles, doubles and triples (EOM-CCSDT) \cite{kucharski_1991,kallay_2004,hirata_2000,hirata_2004}.
|
||||
|
||||
In order to tackle the problems of multi-configurational character and double excitations several ways are explored. The most evident way that one can think about to describe multiconfigurational and double excitations are multiconfigurational methods. Among these methods, one can find complete active space self-consistent field (CASSCF) \cite{roos_1996}, the second perturbation-corrected variant (CASPT2) \cite{andersson_1990} and the second-order $n$-electron valence state perturbation theory (NEVPT2) \cite{angeli_2001,angeli_2001a,angeli_2002}. The exponential scaling of these methods with the size of the active space is the limitation to the application of these ones to big molecules.
|
||||
|
||||
@ -259,20 +259,20 @@ States energies and excitations energies calculations in the SCI framework are p
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Coupled-Cluster}
|
||||
\label{sec:CC}
|
||||
Different flavours of coupled-cluster (CC) calculations are performed using different codes. Indeed, CC theory provides a hierarchy of methods that provide increasingly accurate energies via the increase of the maximum excitation degree of the cluster operator. Without any truncation of the cluster operator one has the full CC (FCC) that is equivalent to the full configuration interaction (FCI) giving the exact energy and wave function of the system for a fixed atomic basis set. However, due to the computational exponential scaling with system size we have to use truncated CC methods. The CC with singles and doubles (CCSD), CC with singles, doubles and triples (CCSDT) calculations are achieved with \textcolor{red}{CFOUR}. The calculations in the context of CC response theory or ``approximate'' series (CC3,CC4) are performed with \textcolor{red}{DALTON}. The CC with singles, doubles, triples and quadruples (CCSDTQ) are done with the \textcolor{red}{CFOUR} code. The CC2, CC3 and CC4 methods can be seen as cheaper approximations of CCSD, CCSDT and CCSDTQ by skipping the most expensive terms and avoiding the storage of higher-excitations amplitudes.
|
||||
Different flavours of coupled-cluster (CC) calculations are performed using different codes. Indeed, CC theory provides a hierarchy of methods that provide increasingly accurate energies via the increase of the maximum excitation degree of the cluster operator. Without any truncation of the cluster operator one has the full CC (FCC) that is equivalent to the full configuration interaction (FCI) giving the exact energy and wave function of the system for a fixed atomic basis set. However, due to the computational exponential scaling with system size we have to use truncated CC methods. The CC with singles and doubles (CCSD), CC with singles, doubles and triples (CCSDT) calculations are achieved with \textcolor{red}{CFOUR}. The calculations in the context of CC response theory or ``approximate'' series (CC3,CC4) are performed with \textcolor{red}{DALTON} \cite{aidas_2014}. The CC with singles, doubles, triples and quadruples (CCSDTQ) are done with the \textcolor{red}{CFOUR} code. The CC2 \cite{christiansen_1995a,hattig_2000}, CC3 \cite{christiansen_1995b,koch_1995} and CC4 \cite{kallay_2005,matthews_2020} methods can be seen as cheaper approximations of CCSD \cite{purvis_1982}, CCSDT \cite{noga_1987} and CCSDTQ \cite{kucharski_1991a} by skipping the most expensive terms and avoiding the storage of higher-excitations amplitudes.
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Multiconfigurational methods}
|
||||
\label{sec:Multi}
|
||||
State-averaged complete-active-space self-consistent field (SA-CASSCF) calculations are performed with \textcolor{red}{MOLPRO}. On top of those, NEVPT2 calculations, both partially contracted (PC) and strongly contracted (SC) scheme are considered. The PC-NEVPT2 is theoretically more accurate to the strongly contracted version due to the larger number of pertubers and greater flexibility. CASPT2 is performed and extended multistate (XMS) CASPT2 for strong mixing between states with same spin and spatial symmetries is also performed.
|
||||
State-averaged complete-active-space self-consistent field (SA-CASSCF) calculations are performed with \textcolor{red}{MOLPRO} \cite{werner_2012}. On top of those, NEVPT2 calculations, both partially contracted (PC) and strongly contracted (SC) scheme are considered. The PC-NEVPT2 is theoretically more accurate to the strongly contracted version due to the larger number of pertubers and greater flexibility. CASPT2 is performed and extended multistate (XMS) CASPT2 for strong mixing between states with same spin and spatial symmetries is also performed.
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Spin-Flip}
|
||||
\label{sec:sf}
|
||||
In both structures the CBD has a singlet ground state, for the spin-flip calculations we consider the lowest triplet state as reference. Spin-flip techniques are broadly accessible and here, among them, we explore equation-of-motion coupled-cluster singles and doubles (EOM-CCSD), configuration interaction singles (CIS), algebraic-diagrammatic construction (ADC) scheme and TD-DFT. The standard and extended spin-flip ADC(2) (SF-ADC(2)-s and SF-ADC(2)-x respectively) and SF-ADC(3) are performed using Q-CHEM 5.2.1 \cite{shao_2015}. Spin-flip TD-DFT calculations are also performed using Q-CHEM 5.2.1. The B3LYP \cite{becke_1988b,lee_1988a,becke_1993b}, PBE0 \cite{adamo_1999a,ernzerhof_1999} and BH\&HLYP hybrid GGA functionals are considered, they contain 20\%, 25\%, 50\% of exact exchange and are labeled, respectively, as SF-BLYP, SF-B3LYP, SF-PBE0, SF-BH\&HLYP. We also have done spin-flip TD-DFT calculations using range-separated hybrid (RSH) functionals as: CAM-B3LYP \cite{yanai_2004a}, LC-$\omega$PBE08 and $\omega$B97X-V. The main difference here between these RSH functionals is the amount of exact-exchange at long-range: 75$\%$ for CAM-B3LYP and 100$\%$ for LC-$\omega$PBE08 and $\omega$B97X-V. To complete the use of spin-flip TD-DFT we also considered the hybrid meta-GGA functional M06-2X \cite{zhao_2008} and the RSH meta-GGA functional M11 \cite{peverati_2011}.
|
||||
In both structures the CBD has a singlet ground state, for the spin-flip calculations we consider the lowest triplet state as reference. Spin-flip techniques are broadly accessible and here, among them, we explore algebraic-diagrammatic construction \cite{schirmer_1982} (ADC) using standard ADC(2)-s \cite{trofimov_1997,dreuw_2015} and extended ADC(2)-x \cite{dreuw_2015} schemes as well as the ADC(3) \cite{dreuw_2015,trofimov_2002,harbach_2014} scheme. We also use spin-flip within the TD-DFT \cite{casida_1995} framework. The standard and extended spin-flip ADC(2) (SF-ADC(2)-s and SF-ADC(2)-x respectively) and SF-ADC(3) are performed using Q-CHEM 5.2.1 \cite{shao_2015}. Spin-flip TD-DFT calculations are also performed using Q-CHEM 5.2.1. The B3LYP \cite{becke_1988b,lee_1988a,becke_1993b}, PBE0 \cite{adamo_1999a,ernzerhof_1999} and BH\&HLYP hybrid GGA functionals are considered, they contain 20\%, 25\%, 50\% of exact exchange and are labeled, respectively, as SF-BLYP, SF-B3LYP, SF-PBE0, SF-BH\&HLYP. We also have done spin-flip TD-DFT calculations using range-separated hybrid (RSH) functionals as: CAM-B3LYP \cite{yanai_2004a}, LC-$\omega$PBE08 \cite{weintraub_2009a} and $\omega$B97X-V \cite{mardirossian_2014}. The main difference here between these RSH functionals is the amount of exact-exchange at long-range: 75$\%$ for CAM-B3LYP and 100$\%$ for LC-$\omega$PBE08 and $\omega$B97X-V. To complete the use of spin-flip TD-DFT we also considered the hybrid meta-GGA functional M06-2X \cite{zhao_2008} and the RSH meta-GGA functional M11 \cite{peverati_2011}.
|
||||
%EOM-SF-CCSD and EOM-SF-CC(2,3) are also performed with Q-CHEM 5.2.1.
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
@ -310,7 +310,7 @@ Then if the CC4 values have not been obtained then we use the second scheme whic
|
||||
%================================================
|
||||
\subsection{Geometries}
|
||||
\label{sec:geometries}
|
||||
Two different sets of geometries obtained with different level of theory are considered for the ground state property and for the excited states of the CBD molecule. First, for the autoisomerization barrier because we consider an energy difference between two geometries it is needed to obtain these geometries at the same level of theory. Due to the fact that the square CBD is an open-shell molecule it is difficult to optimize the geometry so the most accurate method that we can use for both structures is the CASPT2(12,12) with the aug-cc-pVTZ (AVTZ) basis without frozen core. Then, for the excited states because we look at vertical energy transitions in one particular geometry we can use different methods for the different structures and use the most accurate method for each geometry. So in the case of the excited states of the CBD molecule we use CC3 without frozen core with the aug-cc-pVTZ basis for the rectangular ($D_{2h}$) geometry and we use RO-CCSD(T) with the aug-cc-pVTZ (AVTZ) basis again without frozen core for the square ($D_{4h}$) geometry. Table \ref{tab:geometries} shows the results on the geometry parameters obtained with the different methods.
|
||||
Two different sets of geometries obtained with different level of theory are considered for the ground state property and for the excited states of the CBD molecule. First, for the autoisomerization barrier because we consider an energy difference between two geometries it is needed to obtain these geometries at the same level of theory. Due to the fact that the square CBD is an open-shell molecule it is difficult to optimize the geometry so the most accurate method that we can use for both structures is the CASPT2(12,12) with the AVTZ basis without frozen core. Then, for the excited states because we look at vertical energy transitions in one particular geometry we can use different methods for the different structures and use the most accurate method for each geometry. So in the case of the excited states of the CBD molecule we use CC3 without frozen core with the AVTZ basis for the rectangular ($D_{2h}$) geometry and we use RO-CCSD(T) with the AVTZ basis again without frozen core for the square ($D_{4h}$) geometry. Table \ref{tab:geometries} shows the results on the geometry parameters obtained with the different methods.
|
||||
|
||||
%%% TABLE I %%%
|
||||
\begin{squeezetable}
|
||||
@ -585,7 +585,7 @@ CIPSI &6-31+G(d)& $1.486\pm 0.005$ & $3.348\pm 0.024$ & $4.084\pm 0.012$ \\
|
||||
\end{squeezetable}
|
||||
%%% %%% %%% %%%
|
||||
|
||||
Figure \ref{fig:D2h} shows the vertical energies of the studied excited states described in Tables \ref{tab:sf_tddft_D2h} and \ref{tab:D2h}. We see that the SF-TD-DFT vertical energies are rather close to the TBE one for the doubly excited state $2\,{}^1A_{g}$.Indeed, as presented later in subsection \ref{sec:TBE}, SF methods are able to describe effectively states with strong multiconfigurational character. The same observation can be done for the SF-ADC values but with much better results for the two other states. Again we can notice that the SF-ADC(2)-x and SF-ADC(3) schemes do not improve the values. For the multireference methods we see that using the smallest active space do not provide a good description of the $1\,{}^1B_{1g} $ state and in the case of CASSCF(4,4), as previously said, we even have $1\,{}^1B_{1g} $ state above the $2\,{}^1A_{g}$ state. For the CC methods taking into account the quadruple excitations is necessary to have a good description of the doubly excited state $2\,{}^1A_{g}$.
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Figure \ref{fig:D2h} shows the vertical energies of the studied excited states described in Tables \ref{tab:sf_tddft_D2h} and \ref{tab:D2h}. We see that the SF-TD-DFT vertical energies are rather close to the TBE one for the doubly excited state $2\,{}^1A_{g}$. Indeed, as presented later in subsection \ref{sec:TBE}, SF methods are able to describe effectively states with strong multiconfigurational character. The same observation can be done for the SF-ADC values but with much better results for the two other states. Again we can notice that the SF-ADC(2)-x and SF-ADC(3) schemes do not improve the values. For the multireference methods we see that using the smallest active space do not provide a good description of the $1\,{}^1B_{1g} $ state and in the case of CASSCF(4,4), as previously said, we even have $1\,{}^1B_{1g} $ state above the $2\,{}^1A_{g}$ state. For the CC methods taking into account the quadruple excitations is necessary to have a good description of the doubly excited state $2\,{}^1A_{g}$.
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%%% FIGURE III %%%
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\begin{figure*}
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@ -749,7 +749,7 @@ CIPSI & 6-31+G(d) & $0.2010\pm 0.0030$ & $1.602\pm 0.007$ & $2.13\pm 0.04$ \\
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\end{squeezetable}
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%%% %%% %%% %%%
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Figure \ref{fig:D4h} shows the vertical energies of the studied excited states described in Tables \ref{tab:sf_D4h} and \ref{tab:D4h}. We see that all methods exhibit larger variations of the vertical energies due to the high symmetry of the $D_{4h}$ structure. For the triplet state most of the methods used are able to give a vertical energy close to the TBE one, we can although see that CASSCF, with the two different active spaces, show larger energy error than most of the DFT functionals used. Then for the, strongly multiconfigurational character, $2\,{}^1A_{1g}$ state we have a good description by the CC and multireference methods with the largest active space, except for CASSCF. The SF-ADC(2) and SF-ADC(3) schemes are also able to provide a good description of the $2\,{}^1A_{1g}$ state and even for the $1\,{}^1B_{2g} $ we see that SF-ADC(2)-x give a worst result than SF-ADC(2). Multiconfigurational methods with the smallest active space do not demonstrate a good description of the two singlet excited states especially for the CASSCF method and for the the NEVPT2 methods that give the vertical energy of the $1\,{}^1B_{2g} $ state below the $2\,{}^1A_{1g}$ one. Note that CASPT2 improve a lot the description of all the states compared to CASSCF. The SF-TD-DFT are not able to describe the two singlet excited states.
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Figure \ref{fig:D4h} shows the vertical energies of the studied excited states described in Tables \ref{tab:sf_D4h} and \ref{tab:D4h}. We see that all methods exhibit larger variations of the vertical energies due to the high symmetry of the $D_{4h}$ structure. For the triplet state most of the methods used are able to give a vertical energy close to the TBE one, we can although see that CASSCF, with the two different active spaces, show larger energy error than most of the DFT functionals used. Then for the, strongly multiconfigurational character, $2\,{}^1A_{1g}$ state we have a good description by the CC and multireference methods with the largest active space, except for CASSCF. The SF-ADC(2) and SF-ADC(3) schemes are also able to provide a good description of the $2\,{}^1A_{1g}$ state and even for the $1\,{}^1B_{2g} $ we see that SF-ADC(2)-x give a worst result than SF-ADC(2). Multiconfigurational methods with the smallest active space do not demonstrate a good description of the two singlet excited states especially for the CASSCF method and for the the NEVPT2 methods that give the vertical energy of the $1\,{}^1B_{2g} $ state below the $2\,{}^1A_{1g}$ one. Note that CASPT2 improve a lot the description of all the states compared to CASSCF. The various TD-DFT functionals are not able to describe correctly the two singlet excited states.
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%%% FIGURE IV %%%
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\begin{figure*}
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@ -762,7 +762,7 @@ Figure \ref{fig:D4h} shows the vertical energies of the studied excited states d
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\subsubsection{TBE}
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\label{sec:TBE}
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Table \ref{tab:TBE} shows the energy differences, for the autoisomerization barrier (AB) and the different states considered, between the various methods treated and the Theoretical Best Estimate (TBE) at the AVTZ level for the AB and the states. First, we look at the AB energy difference. SF-TD-DFT shows large variations of the energy with errors of 1.42-10.81 \kcalmol compared to the TBE value. SF-ADC schemes provide smaller errors with 0.30-1.44 \kcalmol where we have that the SF-ADC(2)-x gives a worse error than the SF-ADC(2)-s method. CC methods also give small energy differences with 0.11-1.05 \kcalmol and where the CC4 provides an energy very close to the TBE one.
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Table \ref{tab:TBE} shows the energy differences, for the autoisomerization barrier (AB) and the different states considered, between the various methods treated and the Theoretical Best Estimate (TBE) at the AVTZ level for the AB and the states. The percentage \% T1 shown in parentheses for the excited states of the $D_{2h}$ geometry is a metric that gives the percentage of single excitation calculated at the CC3/AVTZ level and it allows us to characterize the transition. First, we look at the AB energy difference. SF-TD-DFT shows large variations of the energy with errors of 1.42-10.81 \kcalmol compared to the TBE value. SF-ADC schemes provide smaller errors with 0.30-1.44 \kcalmol where we have that the SF-ADC(2)-x gives a worse error than the SF-ADC(2)-s method. CC methods also give small energy differences with 0.11-1.05 \kcalmol and where the CC4 provides an energy very close to the TBE one.
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Then we look at the vertical energy errors for the $(D_{2h})$ structure. First we consider the $1\,{}^3B_{1g} $ state and we look at the SF-TD-DFT results. We see that increasing the amount of exact exchange in the functional give closer results to the TBE, indeed we have 0.24 and 0.22 eV of errors for the B3LYP and the PBE0 functionals, respectively whereas we have an error of 0.08 eV for the BH\&HLYP functional. For the other functionals we have errors of 0.10-0.43 eV, note that for this state the M06-2X functional gives the same result than the TBE. We can also notice that all the functionals considered overestimate the vertical energies. The ADC schemes give closer energies with errors of 0.04-0.08 eV, note that ADC(2)-x does not improve the result compared to ADC(2)-s and that ADC(3) understimate the vertical energy whereas ADC(2)-s and ADC(2)-x overestimate the vertical energy. The CC3 and CCSDT results provide energy errors of 0.05-0.06 eV respectively. Then we go through the multireference methods with the two different active spaces, four electrons in four orbitals and twelve electrons in twelve orbitals. For the smaller active space we have errors of 0.05-0.21 eV, the largest error comes from CASSCF(4,4) which is improved by CASPT2(4,4) that gives the smaller error. Then for the largest active space multireference methods provide energy errors of 0.02-0.22 eV with again the largest error coming from CASSCF(12,12) which is again improved by CASPT2(12,12) gives the smaller error.
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