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@article{eckert-maksic_automerization_2006, @article{andersson_1990,
title = {Automerization reaction of cyclobutadiene and its barrier height: An ab initio benchmark multireference average-quadratic coupled cluster study}, title = {Second-Order Perturbation Theory with a {{CASSCF}} Reference Function},
volume = {125}, author = {Andersson, Kerstin. and Malmqvist, Per Aake. and Roos, Bjoern O. and Sadlej, Andrzej J. and Wolinski, Krzysztof.},
issn = {0021-9606}, year = {1990},
url = {https://aip.scitation.org/doi/10.1063/1.2222366}, month = jul,
doi = {10.1063/1.2222366}, volume = {94},
shorttitle = {Automerization reaction of cyclobutadiene and its barrier height}, pages = {5483--5488},
pages = {064310}, publisher = {{American Chemical Society}},
number = {6}, issn = {0022-3654},
journaltitle = {The Journal of Chemical Physics}, doi = {10.1021/j100377a012},
shortjournal = {J. Chem. Phys.}, file = {/Users/monino/Zotero/storage/5LW6PKJ9/Andersson et al. - 1990 - Second-order perturbation theory with a CASSCF ref.pdf;/Users/monino/Zotero/storage/VXS655QG/j100377a012.html},
author = {Eckert-Maksić, Mirjana and Vazdar, Mario and Barbatti, Mario and Lischka, Hans and Maksić, Zvonimir B.}, journal = {J. Phys. Chem.},
urldate = {2021-03-25}, number = {14}
date = {2006-08-11},
note = {Publisher: American Institute of Physics},
file = {Snapshot:/Users/monino/Zotero/storage/3SREAKR9/1.html:text/html}
} }
@online{noauthor_aromaticity_nodate, @article{angeli_2001a,
title = {Aromaticity and Antiaromaticity: Electronic and Structural Aspects {\textbar} Wiley}, title = {Introduction of N-Electron Valence States for Multireference Perturbation Theory},
url = {https://www.wiley.com/en-us/Aromaticity+and+Antiaromaticity%3A+Electronic+and+Structural+Aspects-p-9780471593829}, author = {Angeli, C. and Cimiraglia, R. and Evangelisti, S. and Leininger, T. and Malrieu, J.-P.},
shorttitle = {Aromaticity and Antiaromaticity}, year = {2001},
abstract = {Designed to assist chemists in integrating the results of calculations on molecules and ions into their general body of chemical knowledge. Contains recent contributions from theoretical and computational chemistry to the development of the concept of aromaticity (antiaromaticity) and its expansion into new areas such as organometallic and cluster compounds and three-dimensional structures. Updates the modern status of aromaticity and covers basic principles and experimental applications.}, month = jun,
titleaddon = {Wiley.com}, volume = {114},
urldate = {2021-03-25}, pages = {10252--10264},
langid = {english}, publisher = {{American Institute of Physics}},
file = {Snapshot:/Users/monino/Zotero/storage/HGW4QMJY/Aromaticity+and+Antiaromaticity+Electronic+and+Structural+Aspects-p-9780471593829.html:text/html} issn = {0021-9606},
doi = {10.1063/1.1361246},
file = {/Users/monino/Zotero/storage/LXLLFJXM/Angeli et al. - 2001 - Introduction of n-electron valence states for mult.pdf},
journal = {J. Chem. Phys.},
number = {23}
} }
@article{baeyer_ueber_1885, @article{angeli_2001b,
title = {Ueber Polyacetylenverbindungen}, title = {N-Electron Valence State Perturbation Theory: A Fast Implementation of the Strongly Contracted Variant},
volume = {18}, shorttitle = {N-Electron Valence State Perturbation Theory},
rights = {Copyright © 1885 {WILEY}‐{VCH} Verlag {GmbH} \& Co. {KGaA}, Weinheim}, author = {Angeli, Celestino and Cimiraglia, Renzo and Malrieu, Jean-Paul},
issn = {1099-0682}, year = {2001},
url = {https://chemistry-europe.onlinelibrary.wiley.com/doi/abs/10.1002/cber.18850180296}, month = dec,
doi = {https://doi.org/10.1002/cber.18850180296}, volume = {350},
pages = {2269--2281}, pages = {297--305},
number = {2}, issn = {0009-2614},
journaltitle = {Berichte der deutschen chemischen Gesellschaft}, doi = {10.1016/S0009-2614(01)01303-3},
author = {Baeyer, Adolf}, abstract = {In this work we reconsider the strongly contracted variant of the n-electron valence state perturbation theory (SC NEV-PT) which uses Dyall's Hamiltonian to define the zero-order energies (SC NEV-PT(D)). We develop a formalism in which the key quantities used for the second-order perturbation correction to the energy are written in terms of the matrix elements of suitable operators evaluated on the zero-order wavefunction, without the explicit knowledge of the perturbation functions. The new formalism strongly improves the computation performances. As test cases we present two preliminary studies: (a) on N2 where the convergence of the spectroscopic properties as a function of the basis set and CAS-CI space is discussed and (b) on Cr2 where it is shown that the SC NEV-PT(D) method is able to provide the correct profile for the potential energy curve.},
urldate = {2021-03-25}, file = {/Users/monino/Zotero/storage/MU8H53BC/Angeli et al. - 2001 - N-electron valence state perturbation theory a fa.pdf;/Users/monino/Zotero/storage/KW4GRB2F/S0009261401013033.html},
date = {1885}, journal = {Chemical Physics Letters},
langid = {english}, language = {en},
note = {\_eprint: https://chemistry-europe.onlinelibrary.wiley.com/doi/pdf/10.1002/cber.18850180296}, number = {3}
file = {Snapshot:/Users/monino/Zotero/storage/NBII27D5/cber.html:text/html;Version soumise:/Users/monino/Zotero/storage/WM8EG65P/Baeyer - 1885 - Ueber Polyacetylenverbindungen.pdf:application/pdf}
} }
@article{reeves_further_1969, @article{angeli_2002,
title = {Further experiments pertaining to the ground state of cyclobutadiene}, title = {N-Electron Valence State Perturbation Theory: {{A}} Spinless Formulation and an Efficient Implementation of the Strongly Contracted and of the Partially Contracted Variants},
pages = {3}, shorttitle = {N-Electron Valence State Perturbation Theory},
journaltitle = {Journal of the American Chemical Society}, author = {Angeli, Celestino and Cimiraglia, Renzo and Malrieu, Jean-Paul},
author = {Reeves, P C and Henery, J and Pettit, R}, year = {2002},
date = {1969}, month = nov,
langid = {english}, volume = {117},
file = {Reeves et al. - 1969 - Further experiments pertaining to the ground state.pdf:/Users/monino/Zotero/storage/D2DINS7E/Reeves et al. - 1969 - Further experiments pertaining to the ground state.pdf:application/pdf} pages = {9138--9153},
publisher = {{American Institute of Physics}},
issn = {0021-9606},
doi = {10.1063/1.1515317},
file = {/Users/monino/Zotero/storage/HHFA46GF/Angeli et al. - 2002 - n-electron valence state perturbation theory A sp.pdf;/Users/monino/Zotero/storage/CPKUV9TE/1.html},
journal = {J. Chem. Phys.},
number = {20}
} }
@article{irngartinger_bonding_1983, @book{AromaticityAntiaromaticityElectronic,
title = {Bonding Electron Density Distribution in Tetra-tert-butylcyclobutadiene— A Molecule with an Obviously Non-Square Four-Membered ring}, title = {Aromaticity and {{Antiaromaticity}}: {{Electronic}} and {{Structural Aspects}} | {{Wiley}}},
volume = {22}, shorttitle = {Aromaticity and {{Antiaromaticity}}},
rights = {Copyright © 1983 by Verlag Chemie, {GmbH}, Germany}, file = {/Users/monino/Zotero/storage/HGW4QMJY/Aromaticity+and+Antiaromaticity+Electronic+and+Structural+Aspects-p-9780471593829.html}
issn = {1521-3773},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.198304031},
doi = {https://doi.org/10.1002/anie.198304031},
pages = {403--404},
number = {5},
journaltitle = {Angewandte Chemie International Edition in English},
author = {Irngartinger, Hermann and Nixdorf, Matthias},
urldate = {2021-03-25},
date = {1983},
langid = {english},
note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/anie.198304031},
file = {Full Text PDF:/Users/monino/Zotero/storage/7GLS7QBG/Irngartinger et Nixdorf - 1983 - Bonding Electron Density Distribution in Tetra-ter.pdf:application/pdf}
} }
@article{ermer_three_1983, @article{baeyer_1885,
title = {Three Arguments Supporting a Rectangular Structure for Tetra-tert-butylcyclobutadiene}, title = {Ueber {{Polyacetylenverbindungen}}},
volume = {22}, author = {Baeyer, Adolf},
rights = {Copyright © 1983 by Verlag Chemie, {GmbH}, Germany}, year = {1885},
issn = {1521-3773}, volume = {18},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.198304021}, pages = {2269--2281},
doi = {https://doi.org/10.1002/anie.198304021}, issn = {1099-0682},
pages = {402--403}, doi = {10.1002/cber.18850180296},
number = {5}, annotation = {\_eprint: https://chemistry-europe.onlinelibrary.wiley.com/doi/pdf/10.1002/cber.18850180296},
journaltitle = {Angewandte Chemie International Edition in English}, copyright = {Copyright \textcopyright{} 1885 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim},
author = {Ermer, Otto and Heilbronner, Edgar}, file = {/Users/monino/Zotero/storage/T9A8FP8V/Baeyer - 1885 - Ueber Polyacetylenverbindungen.pdf;/Users/monino/Zotero/storage/B56CA56Z/cber.html},
urldate = {2021-03-25}, journal = {Berichte Dtsch. Chem. Ges.},
date = {1983}, language = {en},
langid = {english}, number = {2}
note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/anie.198304021},
file = {Full Text PDF:/Users/monino/Zotero/storage/8VZ7BN4I/Ermer et Heilbronner - 1983 - Three Arguments Supporting a Rectangular Structure.pdf:application/pdf;Snapshot:/Users/monino/Zotero/storage/WN6RRMGU/anie.html:text/html}
} }
@article{kreile_uv_1986, @article{bally_1980,
title = {Uv photoelectron spectrum of cyclobutadiene. free cyclobutadiene stable up to high temperatures}, title = {Cyclobutadiene},
volume = {124}, author = {Bally, Thomas and Masamune, Satoru},
issn = {0009-2614}, year = {1980},
url = {https://www.sciencedirect.com/science/article/pii/0009261486851338}, month = jan,
doi = {10.1016/0009-2614(86)85133-8}, volume = {36},
abstract = {The Hel photoelectron spectrum of cyclobutadiene ({CB}) has been obtained under conditions which demonstrate that free {CB} is stable up to temperatures of several hundred °C. A new experimental argument for the rectangular geometry of {CB} is presented. Shake-up structures are unimportant for the interpretation of the {PE} spectrum of {CB}. {LNDO}/S {PERTCI}, {MNDO} {PERTCI} and previous experimental vertical ionization energy estimates accord with the experimental data.}, pages = {343--370},
pages = {140--146}, issn = {0040-4020},
number = {2}, doi = {10.1016/0040-4020(80)87003-7},
journaltitle = {Chemical Physics Letters}, file = {/Users/monino/Zotero/storage/DXWL3L8N/Bally et Masamune - 1980 - Cyclobutadiene.pdf;/Users/monino/Zotero/storage/XQ98S2QN/0040402080870037.html},
shortjournal = {Chemical Physics Letters}, journal = {Tetrahedron},
author = {Kreile, Jürgen and Münzel, Norbert and Schweig, Armin and Specht, Harald}, language = {en},
urldate = {2021-03-25}, number = {3}
date = {1986-02-14},
langid = {english}
} }
@article{bally_cyclobutadiene_1980, @article{casanova_2020,
title = {Cyclobutadiene}, title = {Spin-Flip Methods in Quantum Chemistry},
volume = {36}, author = {Casanova, David and Krylov, Anna I.},
issn = {0040-4020}, year = {2020},
url = {https://www.sciencedirect.com/science/article/pii/0040402080870037}, month = feb,
doi = {10.1016/0040-4020(80)87003-7}, volume = {22},
pages = {343--370}, pages = {4326--4342},
number = {3}, publisher = {{The Royal Society of Chemistry}},
journaltitle = {Tetrahedron}, issn = {1463-9084},
shortjournal = {Tetrahedron}, doi = {10.1039/C9CP06507E},
author = {Bally, Thomas and Masamune, Satoru}, abstract = {This Perspective discusses salient features of the spin-flip approach to strong correlation and describes different methods that sprung from this idea. The spin-flip treatment exploits the different physics of low-spin and high-spin states and is based on the observation that correlation is small for same-spin electrons. By using a well-behaved high-spin state as a reference, one can access problematic low-spin states by deploying the same formal tools as in the excited-state treatments (i.e., linear response, propagator, or equation-of-motion theories). The Perspective reviews applications of this strategy within wave function and density functional theory frameworks as well as the extensions for molecular properties and spectroscopy. The utility of spin-flip methods is illustrated by examples. Limitations and proposed future directions are also discussed.},
urldate = {2021-03-25}, file = {/Users/monino/Zotero/storage/7E3MQEQM/Casanova et Krylov - 2020 - Spin-flip methods in quantum chemistry.pdf},
date = {1980-01-01}, journal = {Phys. Chem. Chem. Phys.},
langid = {english} language = {en},
number = {8}
} }
@article{whitman_limits_1982, @article{christiansen_1995,
title = {Limits on the activation parameters for automerization of cyclobutadiene-1,2-d2}, title = {Response Functions in the {{CC3}} Iterative Triple Excitation Model},
volume = {104}, author = {Christiansen, Ove and Koch, Henrik and Jo/rgensen, Poul},
issn = {0002-7863}, year = {1995},
url = {https://doi.org/10.1021/ja00387a065}, month = nov,
doi = {10.1021/ja00387a065}, volume = {103},
pages = {6473--6474}, pages = {7429--7441},
number = {23}, publisher = {{American Institute of Physics}},
journaltitle = {Journal of the American Chemical Society}, issn = {0021-9606},
shortjournal = {J. Am. Chem. Soc.}, doi = {10.1063/1.470315},
author = {Whitman, David W. and Carpenter, Barry K.}, journal = {J. Chem. Phys.},
urldate = {2021-03-26}, number = {17}
date = {1982-11-01}, }
note = {Publisher: American Chemical Society},
file = {ACS Full Text Snapshot:/Users/monino/Zotero/storage/4U7ZD87S/ja00387a065.html:text/html} @article{eckert-maksic_2006,
} title = {Automerization Reaction of Cyclobutadiene and Its Barrier Height: {{An}} Ab Initio Benchmark Multireference Average-Quadratic Coupled Cluster Study},
shorttitle = {Automerization Reaction of Cyclobutadiene and Its Barrier Height},
author = {{Eckert-Maksi{\'c}}, Mirjana and Vazdar, Mario and Barbatti, Mario and Lischka, Hans and Maksi{\'c}, Zvonimir B.},
year = {2006},
month = aug,
volume = {125},
pages = {064310},
publisher = {{American Institute of Physics}},
issn = {0021-9606},
doi = {10.1063/1.2222366},
abstract = {The problem of the double bond flipping interconversion of the two equivalent ground state structures of cyclobutadiene (CBD) is addressed at the multireference average-quadratic coupled cluster level of theory, which is capable of optimizing the structural parameters of the ground, transition, and excited states on an equal footing. The barrier height involving both the electronic and zero-point vibrational energy contributions is 6.3kcalmol-16.3kcalmol-1{$<$}math display="inline" overflow="scroll" altimg="eq-00001.gif"{$><$}mrow{$><$}mn{$>$}6.3{$<$}/mn{$><$}mspace width="0.3em"{$><$}/mspace{$><$}mi{$>$}kcal{$<$}/mi{$><$}mspace width="0.2em"{$><$}/mspace{$><$}msup{$><$}mi{$>$}mol{$<$}/mi{$><$}mrow{$><$}mo{$>-<$}/mo{$><$}mn{$>$}1{$<$}/mn{$><$}/mrow{$><$}/msup{$><$}/mrow{$><$}/math{$>$}, which is higher than the best earlier theoretical estimate of 4.0kcalmol-14.0kcalmol-1{$<$}math display="inline" overflow="scroll" altimg="eq-00002.gif"{$><$}mrow{$><$}mn{$>$}4.0{$<$}/mn{$><$}mspace width="0.3em"{$><$}/mspace{$><$}mi{$>$}kcal{$<$}/mi{$><$}mspace width="0.2em"{$><$}/mspace{$><$}msup{$><$}mi{$>$}mol{$<$}/mi{$><$}mrow{$><$}mo{$>-<$}/mo{$><$}mn{$>$}1{$<$}/mn{$><$}/mrow{$><$}/msup{$><$}/mrow{$><$}/math{$>$}. This result is confirmed by including into the reference space the orbitals of the CC {$\sigma\sigma<$}math display="inline" overflow="scroll" altimg="eq-00003.gif"{$><$}mi{$>\sigma<$}/mi{$><$}/math{$>$} bonds beyond the standard {$\pi\pi<$}math display="inline" overflow="scroll" altimg="eq-00004.gif"{$><$}mi{$>\pi<$}/mi{$><$}/math{$>$} orbital space. It places the present value into the middle of the range of the measured data (1.6\textendash 10kcalmol-1)(1.6\textendash 10kcalmol-1){$<$}math display="inline" overflow="scroll" altimg="eq-00005.gif"{$><$}mrow{$><$}mo{$>$}({$<$}/mo{$><$}mn{$>$}1.6{$<$}/mn{$><$}mo{$>$}\textendash{$<$}/mo{$><$}mn{$>$}10{$<$}/mn{$><$}mspace width="0.3em"{$><$}/mspace{$><$}mi{$>$}kcal{$<$}/mi{$><$}mspace width="0.2em"{$><$}/mspace{$><$}msup{$><$}mi{$>$}mol{$<$}/mi{$><$}mrow{$><$}mo{$>-<$}/mo{$><$}mn{$>$}1{$<$}/mn{$><$}/mrow{$><$}/msup{$><$}mo{$>$}){$<$}/mo{$><$}/mrow{$><$}/math{$>$}. An adiabatic singlet-triplet energy gap of 7.4kcalmol-17.4kcalmol-1{$<$}math display="inline" overflow="scroll" altimg="eq-00006.gif"{$><$}mrow{$><$}mn{$>$}7.4{$<$}/mn{$><$}mspace width="0.3em"{$><$}/mspace{$><$}mi{$>$}kcal{$<$}/mi{$><$}mspace width="0.2em"{$><$}/mspace{$><$}msup{$><$}mi{$>$}mol{$<$}/mi{$><$}mrow{$><$}mo{$>-<$}/mo{$><$}mn{$>$}1{$<$}/mn{$><$}/mrow{$><$}/msup{$><$}/mrow{$><$}/math{$>$} between the transition state Btg1Btg1{$<$}math display="inline" overflow="scroll" altimg="eq-00007.gif"{$><$}mmultiscripts{$><$}mi{$>$}B{$<$}/mi{$><$}mrow{$><$}mi{$>$}t{$<$}/mi{$><$}mi{$>$}g{$<$}/mi{$><$}/mrow{$><$}none{$><$}/none{$><$}mprescripts{$><$}/mprescripts{$><$}none{$><$}/none{$><$}mn{$>$}1{$<$}/mn{$><$}/mmultiscripts{$><$}/math{$>$} and the first triplet A2g3A2g3{$<$}math display="inline" overflow="scroll" altimg="eq-00008.gif"{$><$}mmultiscripts{$><$}mi{$>$}A{$<$}/mi{$><$}mrow{$><$}mn{$>$}2{$<$}/mn{$><$}mi{$>$}g{$<$}/mi{$><$}/mrow{$><$}none{$><$}/none{$><$}mprescripts{$><$}/mprescripts{$><$}none{$><$}/none{$><$}mn{$>$}3{$<$}/mn{$><$}/mmultiscripts{$><$}/math{$>$} state is obtained. A low barrier height for the CBD automerization and a small {$\Delta$}E(A2g3,B1g1){$\Delta$}E(A2g3,B1g1){$<$}math display="inline" overflow="scroll" altimg="eq-00009.gif"{$><$}mrow{$><$}mi{$>\Delta<$}/mi{$><$}mi{$>$}E{$<$}/mi{$><$}mrow{$><$}mo{$>$}({$<$}/mo{$><$}mmultiscripts{$><$}mi{$>$}A{$<$}/mi{$><$}mrow{$><$}mn{$>$}2{$<$}/mn{$><$}mi{$>$}g{$<$}/mi{$><$}/mrow{$><$}none{$><$}/none{$><$}mprescripts{$><$}/mprescripts{$><$}none{$><$}/none{$><$}mn{$>$}3{$<$}/mn{$><$}/mmultiscripts{$><$}mo{$>$},{$<$}/mo{$><$}mmultiscripts{$><$}mi{$>$}B{$<$}/mi{$><$}mrow{$><$}mn{$>$}1{$<$}/mn{$><$}mi{$>$}g{$<$}/mi{$><$}/mrow{$><$}none{$><$}/none{$><$}mprescripts{$><$}/mprescripts{$><$}none{$><$}/none{$><$}mn{$>$}1{$<$}/mn{$><$}/mmultiscripts{$><$}mo{$>$}){$<$}/mo{$><$}/mrow{$><$}/mrow{$><$}/math{$>$} gap bear some relevance on the highly pronounced reactivity of CBD, which is briefly discussed.},
file = {/Users/monino/Zotero/storage/F5Y4YKWD/Eckert-Maksić et al. - 2006 - Automerization reaction of cyclobutadiene and its .pdf;/Users/monino/Zotero/storage/SSRES9DP/1.html},
journal = {J. Chem. Phys.},
number = {6}
}
@article{ermer_1983,
title = {Three {{Arguments Supporting}} a {{Rectangular Structure}} for {{Tetra}}-Tert-Butylcyclobutadiene},
author = {Ermer, Otto and Heilbronner, Edgar},
year = {1983},
volume = {22},
pages = {402--403},
issn = {1521-3773},
doi = {10.1002/anie.198304021},
annotation = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/anie.198304021},
copyright = {Copyright \textcopyright{} 1983 by Verlag Chemie, GmbH, Germany},
file = {/Users/monino/Zotero/storage/T32BDQPQ/Ermer et Heilbronner - 1983 - Three Arguments Supporting a Rectangular Structure.pdf;/Users/monino/Zotero/storage/4BR2A634/anie.html},
journal = {Angew. Chem. Int. Ed. Engl.},
language = {en},
number = {5}
}
@article{hirata_2000,
title = {High-Order Determinantal Equation-of-Motion Coupled-Cluster Calculations for Electronic Excited States},
author = {Hirata, So and Nooijen, Marcel and Bartlett, Rodney J.},
year = {2000},
month = aug,
volume = {326},
pages = {255--262},
issn = {0009-2614},
doi = {10.1016/S0009-2614(00)00772-7},
abstract = {A general-order equation-of-motion coupled-cluster (EOM-CC) method, which is capable of computing the excitation energies of molecules at any given pair of orders (m and n) of the cluster operator and the linear excitation operator, is developed by employing a determinantal algorithm. The EOM-CC(m,n) results of the vertical excitation energies are presented for CH+ with m and n varied independently in the range of 1{$\leqslant$}m,n{$\leqslant$}4 and for CH2 with 1{$\leqslant$}m=n{$\leqslant$}6. EOM-CCSDT [EOM-CC(3,3)] provides the excitation energies that are within 0.1 eV of the full configuration interaction results for dominant double replacement transitions.},
file = {/Users/monino/Zotero/storage/ZZI4JPPT/Hirata et al. - 2000 - High-order determinantal equation-of-motion couple.pdf},
journal = {Chemical Physics Letters},
language = {en},
number = {3}
}
@article{hirata_2004,
title = {Higher-Order Equation-of-Motion Coupled-Cluster Methods},
author = {Hirata, So},
year = {2004},
month = jul,
volume = {121},
pages = {51--59},
publisher = {{American Institute of Physics}},
issn = {0021-9606},
doi = {10.1063/1.1753556},
file = {/Users/monino/Zotero/storage/3HCJINRI/Hirata - 2004 - Higher-order equation-of-motion coupled-cluster me.pdf},
journal = {J. Chem. Phys.},
number = {1}
}
@article{irngartinger_1983,
title = {Bonding {{Electron Density Distribution}} in {{Tetra}}-Tert-Butylcyclobutadiene\textemdash{} {{A Molecule}} with an {{Obviously Non}}-{{Square Four}}-{{Membered}} Ring},
author = {Irngartinger, Hermann and Nixdorf, Matthias},
year = {1983},
volume = {22},
pages = {403--404},
issn = {1521-3773},
doi = {10.1002/anie.198304031},
annotation = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/anie.198304031},
copyright = {Copyright \textcopyright{} 1983 by Verlag Chemie, GmbH, Germany},
file = {/Users/monino/Zotero/storage/QZP8JWNP/Irngartinger et Nixdorf - 1983 - Bonding Electron Density Distribution in Tetra-ter.pdf;/Users/monino/Zotero/storage/X5NU6NTT/anie.html},
journal = {Angew. Chem. Int. Ed. Engl.},
language = {en},
number = {5}
}
@article{kallay_2004,
title = {Calculation of Excited-State Properties Using General Coupled-Cluster and Configuration-Interaction Models},
author = {K{\'a}llay, Mih{\'a}ly and Gauss, J{\"u}rgen},
year = {2004},
month = nov,
volume = {121},
pages = {9257--9269},
publisher = {{American Institute of Physics}},
issn = {0021-9606},
doi = {10.1063/1.1805494},
file = {/Users/monino/Zotero/storage/TEHKUF6P/Kállay et Gauss - 2004 - Calculation of excited-state properties using gene.pdf},
journal = {J. Chem. Phys.},
number = {19}
}
@article{koch_1997,
title = {The {{CC3}} Model: {{An}} Iterative Coupled Cluster Approach Including Connected Triples},
shorttitle = {The {{CC3}} Model},
author = {Koch, Henrik and Christiansen, Ove and Jo/rgensen, Poul and {Sanchez de Mer{\'a}s}, Alfredo M. and Helgaker, Trygve},
year = {1997},
month = feb,
volume = {106},
pages = {1808--1818},
publisher = {{American Institute of Physics}},
issn = {0021-9606},
doi = {10.1063/1.473322},
file = {/Users/monino/Zotero/storage/BEW2ATM3/Koch et al. - 1997 - The CC3 model An iterative coupled cluster approa.pdf},
journal = {J. Chem. Phys.},
number = {5}
}
@article{kreile_1986,
title = {Uv Photoelectron Spectrum of Cyclobutadiene. Free Cyclobutadiene Stable up to High Temperatures},
author = {Kreile, J{\"u}rgen and M{\"u}nzel, Norbert and Schweig, Armin and Specht, Harald},
year = {1986},
month = feb,
volume = {124},
pages = {140--146},
issn = {0009-2614},
doi = {10.1016/0009-2614(86)85133-8},
abstract = {The Hel photoelectron spectrum of cyclobutadiene (CB) has been obtained under conditions which demonstrate that free CB is stable up to temperatures of several hundred \textdegree C. A new experimental argument for the rectangular geometry of CB is presented. Shake-up structures are unimportant for the interpretation of the PE spectrum of CB. LNDO/S PERTCI, MNDO PERTCI and previous experimental vertical ionization energy estimates accord with the experimental data.},
file = {/Users/monino/Zotero/storage/2EQ8LH4G/Kreile et al. - 1986 - Uv photoelectron spectrum of cyclobutadiene. free .pdf;/Users/monino/Zotero/storage/QHJZT5VV/0009261486851338.html},
journal = {Chemical Physics Letters},
language = {en},
number = {2}
}
@article{kucharski_1991,
title = {Recursive Intermediate Factorization and Complete Computational Linearization of the Coupled-Cluster Single, Double, Triple, and Quadruple Excitation Equations},
author = {Kucharski, Stanislaw A. and Bartlett, Rodney J.},
year = {1991},
month = jul,
volume = {80},
pages = {387--405},
issn = {1432-2234},
doi = {10.1007/BF01117419},
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.},
file = {/Users/monino/Zotero/storage/L3VLAU8A/Kucharski et Bartlett - 1991 - Recursive intermediate factorization and complete .pdf},
journal = {Theoret. Chim. Acta},
language = {en},
number = {4}
}
@article{reeves_1969,
title = {Further Experiments Pertaining to the Ground State of Cyclobutadiene},
author = {Reeves, P. C. and Henery, J. and Pettit, R.},
year = {1969},
month = oct,
volume = {91},
pages = {5888--5890},
publisher = {{American Chemical Society}},
issn = {0002-7863},
doi = {10.1021/ja01049a042},
file = {/Users/monino/Zotero/storage/T44XQHXX/Reeves et al. - 1969 - Further experiments pertaining to the ground state.pdf;/Users/monino/Zotero/storage/YFJV7DYC/ja01049a042.html},
journal = {J. Am. Chem. Soc.},
number = {21}
}
@book{roos_1996,
title = {Multiconfigurational {{Perturbation Theory}}: {{Applications}} in {{Electronic Spectroscopy}}},
shorttitle = {Multiconfigurational {{Perturbation Theory}}},
booktitle = {Advances in {{Chemical Physics}}},
author = {Roos, Bj{\"o}rn O. and Andersson, Kerstin and F{\"u}lscher, Markus P. and Malmqvist, Per-{\^a}ke and {Serrano-Andr{\'e}s}, Luis and Pierloot, Kristin and Merch{\'a}n, Manuela},
year = {1996},
pages = {219--331},
publisher = {{John Wiley \& Sons, Ltd}},
doi = {10.1002/9780470141526.ch5},
abstract = {This chapter contains sections titled: Introduction Multiconfigurational Perturbation Theory Applications in Spectroscopy Summary},
annotation = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/9780470141526.ch5},
copyright = {Copyright \textcopyright{} 1996 by John Wiley \& Sons, Inc.},
file = {/Users/monino/Zotero/storage/KWDFZUBF/9780470141526.html},
isbn = {978-0-470-14152-6}
}
@article{whitman_1982,
title = {Limits on the Activation Parameters for Automerization of Cyclobutadiene-1,2-D2},
author = {Whitman, David W. and Carpenter, Barry K.},
year = {1982},
month = nov,
volume = {104},
pages = {6473--6474},
publisher = {{American Chemical Society}},
issn = {0002-7863},
doi = {10.1021/ja00387a065},
file = {/Users/monino/Zotero/storage/9AK8SNDG/Whitman et Carpenter - 1982 - Limits on the activation parameters for automeriza.pdf;/Users/monino/Zotero/storage/WRSENMYS/ja00387a065.html},
journal = {J. Am. Chem. Soc.},
number = {23}
}

12
Manuscript/CBD.tex
View File

@ -221,20 +221,20 @@ Write an abstract
\label{sec:intro} \label{sec:intro}
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Despite the fact that excited states are involved in ubiquitious processes such as photochemistry, catalysis or in solar cell technology, none of the many methods existing is the reference in providing accurate excitation energies. Indeed, each method has its own flaws and there are so many chemical scenario that can occur, so it is still one of the biggest challenge in theoretical chemistry. Speaking of difficult task, cyclobutadiene (CBD) molecule has been a real challenge for experimental and theoretical chemists for many decades \cite{bally_cyclobutadiene_1980}. Due to his antiaromaticity \cite{noauthor_aromaticity_nodate} and his large angular strain \cite{baeyer_ueber_1885} the CBD molecule presents a high reactivity which made the synthesis of this molecule a particularly difficult exercise. Hückel molecular orbital theory gives a triplet state with square ($D_{4h}$) geometry for the ground state of the CBD,with the two singly occupied frontier orbitals that are degenerated by symmetry. This degeneracy is lifted by the Jahn-Teller effect, meaning by distortion of the molecule (lowering symmetry), and gives a singlet state with rectangular ($D_{2h}$) geometry for the ground state. Despite the fact that excited states are involved in ubiquitious processes such as photochemistry, catalysis or in solar cell technology, none of the many methods existing is the reference in providing accurate excitation energies. Indeed, each method has its own flaws and there are so many chemical scenario that can occur, so it is still one of the biggest challenge in theoretical chemistry. Speaking of difficult task, cyclobutadiene (CBD) molecule has been a real challenge for experimental and theoretical chemists for many decades \cite{bally_1980}. Due to his antiaromaticity \cite{AromaticityAntiaromaticityElectronic,} and his large angular strain \cite{baeyer_1885} the CBD molecule presents a high reactivity which made the synthesis of this molecule a particularly difficult exercise. Hückel molecular orbital theory gives a triplet state with square ($D_{4h}$) geometry for the ground state of the CBD,with the two singly occupied frontier orbitals that are degenerated by symmetry. This degeneracy is lifted by the Jahn-Teller effect, meaning by distortion of the molecule (lowering symmetry), and gives a singlet state with rectangular ($D_{2h}$) geometry for the ground state.
Indeed, synthetic work from Pettis and co-workers \cite{reeves_further_1969} gives a rectangular geometry to the singlet ground state of CBD and then was confirmed by experimental works \cite{irngartinger_bonding_1983,ermer_three_1983,kreile_uv_1986}. Indeed, synthetic work from Pettis and co-workers \cite{reeves_1969} gives a rectangular geometry to the singlet ground state of CBD and then was confirmed by experimental works \cite{irngartinger_1983,ermer_1983,kreile_1986}.
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 energy barrier for the automerization of the CBD was predicted, experimentally, in the range of 1.6-10 kcal.mol$^{-1}$ \cite{whitman_limits_1982} and multi-reference calculations gave an energy barrier in the range of 6-7 kcal.mol$^{-1}$ \cite{eckert-maksic_automerization_2006}. All the specificities of the CBD molecule make it a real playground for excited-states methods. 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 energy barrier for the automerization of the CBD 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 states $1{}^1B_{1g}$ 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) or equation-of-motion coupled-cluster with singles, doubles and triples (EOM-CCSDT). (\textcolor{red}{cite papier spin-flip}). 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 states $1{}^1B_{1g}$ 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}.
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) (\textcolor{red}{voir papier reference energies for double excitations}), the second perturbation-corrected variant (CASPT2) (\textcolor{red}{voir papier reference energies for double excitations}) and the second-order $n$-electron valence state perturbation theory (NEVPT2). (\textcolor{red}{voir papier reference energies for double excitations}) 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. 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_2001b,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.
Another way to deal with double excitations is to use high level truncation of the equation-of-motion (EOM) formalism of coupled-cluster (CC) theory. However, to provide a correct description of doubly excited states one have to take into account contributions from the triple excitations in the CC expansion. Again, due to the scaling of CC methods with the number of basis functions the applicability of these methods is limited to small molecules. Another way to deal with double excitations is to use high level truncation of the equation-of-motion (EOM) formalism of coupled-cluster (CC) theory. However, to provide a correct description of doubly excited states one have to take into account contributions from the triple excitations in the CC expansion. Again, due to the scaling of CC methods with the number of basis functions the applicability of these methods is limited to small molecules.
An alternative to multiconfigurational and CC methods is the use of selected CI (SCI) methods for the computation of transition energies for singly and doubly excited states that are known to reach near full CI energies for small molecules. These methods allow to avoid an exponential increase of the size of the CI expansion by retaining the most energetically relevant determinants only, using a second-order energetic criterion to select perturbatively determinants in the FCI space. An alternative to multiconfigurational and CC methods is the use of selected CI (SCI) methods for the computation of transition energies for singly and doubly excited states that are known to reach near full CI energies for small molecules. These methods allow to avoid an exponential increase of the size of the CI expansion by retaining the most energetically relevant determinants only, using a second-order energetic criterion to select perturbatively determinants in the FCI space.
Finally, to describe doubly excited states, one can think of spin-flip formalism established by Krylov in 2001. To briefly introduce the spin-flip idea we can present it like: instead of taking the singlet ground state as reference, the reference configuration is taken as the lowest triplet state. So one can access the singlet ground state and the singlet doubly-excited state via a spin-flip deexcitation and excitation (respectively), the difference of these two excitation energies providing an estimate of the double excitation. Obviously spin-flip methods have their own flaws, especially the spin contamination (\textcolor{red}{voir papier spin-flip}) (i.e., an artificial mixing of electronic states of differents spin multiplicities) due to spin incompleteness of the spin-flip expansion and by spin contamination of the reference configuration. One can adress part of this problem by expansion of the excitation order but with an increase of the computational cost or by complementing the spin-incomplete configuration set with the missing configurations. Finally, to describe doubly excited states, one can think of spin-flip formalism established by Krylov in 2001. To briefly introduce the spin-flip idea we can present it like: instead of taking the singlet ground state as reference, the reference configuration is taken as the lowest triplet state. So one can access the singlet ground state and the singlet doubly-excited state via a spin-flip deexcitation and excitation (respectively), the difference of these two excitation energies providing an estimate of the double excitation. Obviously spin-flip methods have their own flaws, especially the spin contamination \cite{casanova_2020} (i.e., an artificial mixing of electronic states of differents spin multiplicities) due to spin incompleteness of the spin-flip expansion and by spin contamination of the reference configuration. One can adress part of this problem by expansion of the excitation order but with an increase of the computational cost or by complementing the spin-incomplete configuration set with the missing configurations.
In the present work we investigate ${}^1A_g$, $1{}^3B_{1g}$, $1{}^1B_{1g}$, $2{}^1A_{g}$ and ${}^1B_{1g}$, $1{}^3A_{2g}$, $2{}^1A_{1g}$,$1{}^1B_{2g}$ excited states for the $D_{2h}$ and $D_{4h}$, respectively, geometries. Computational details are reported in \ref{sec:compmet} for SCI (\ref{sec:SCI}), EOM-CC (\ref{sec:CC}), multiconfigurational (\ref{sec:Multi}) and spin-flip (\ref{sec:sf}) methods. Section \ref{sec:res} is devoted to the discussion of our results for excited states \ref{sec:states} and autoisomerization barrier \ref{sec:auto} of the CBD molecule. In the present work we investigate ${}^1A_g$, $1{}^3B_{1g}$, $1{}^1B_{1g}$, $2{}^1A_{g}$ and ${}^1B_{1g}$, $1{}^3A_{2g}$, $2{}^1A_{1g}$,$1{}^1B_{2g}$ excited states for the $D_{2h}$ and $D_{4h}$, respectively, geometries. Computational details are reported in \ref{sec:compmet} for SCI (\ref{sec:SCI}), EOM-CC (\ref{sec:CC}), multiconfigurational (\ref{sec:Multi}) and spin-flip (\ref{sec:sf}) methods. Section \ref{sec:res} is devoted to the discussion of our results for excited states \ref{sec:states} and autoisomerization barrier \ref{sec:auto} of the CBD molecule.