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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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year = {1990},
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month = jul,
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journal = {J. Phys. Chem.},
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volume = {94},
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number = {14},
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||||
pages = {5483--5488},
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publisher = {{American Chemical Society}},
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||||
issn = {0022-3654},
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||||
doi = {10.1021/j100377a012},
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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},
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journal = {J. Phys. Chem.},
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||||
number = {14}
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||||
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}
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}
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@article{angeli_2001,
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title = {N-Electron Valence State Perturbation Theory: A Fast Implementation of the Strongly Contracted Variant},
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shorttitle = {N-Electron Valence State Perturbation Theory},
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author = {Angeli, Celestino and Cimiraglia, Renzo and Malrieu, Jean-Paul},
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year = {2001},
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month = dec,
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journal = {Chemical Physics Letters},
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volume = {350},
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number = {3},
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pages = {297--305},
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issn = {0009-2614},
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doi = {10.1016/S0009-2614(01)01303-3},
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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.},
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langid = {english},
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||||
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}
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}
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@article{angeli_2001a,
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@ -19,31 +36,14 @@
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author = {Angeli, C. and Cimiraglia, R. and Evangelisti, S. and Leininger, T. and Malrieu, J.-P.},
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year = {2001},
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month = jun,
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journal = {J. Chem. Phys.},
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||||
volume = {114},
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number = {23},
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pages = {10252--10264},
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publisher = {{American Institute of Physics}},
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issn = {0021-9606},
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||||
doi = {10.1063/1.1361246},
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file = {/Users/monino/Zotero/storage/LXLLFJXM/Angeli et al. - 2001 - Introduction of n-electron valence states for mult.pdf},
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journal = {J. Chem. Phys.},
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number = {23}
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}
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@article{angeli_2001b,
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title = {N-Electron Valence State Perturbation Theory: A Fast Implementation of the Strongly Contracted Variant},
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shorttitle = {N-Electron Valence State Perturbation Theory},
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author = {Angeli, Celestino and Cimiraglia, Renzo and Malrieu, Jean-Paul},
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year = {2001},
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month = dec,
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volume = {350},
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||||
pages = {297--305},
|
||||
issn = {0009-2614},
|
||||
doi = {10.1016/S0009-2614(01)01303-3},
|
||||
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.},
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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},
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journal = {Chemical Physics Letters},
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language = {en},
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||||
number = {3}
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||||
file = {/Users/monino/Zotero/storage/LXLLFJXM/Angeli et al. - 2001 - Introduction of n-electron valence states for mult.pdf}
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}
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@article{angeli_2002,
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@ -52,36 +52,48 @@
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author = {Angeli, Celestino and Cimiraglia, Renzo and Malrieu, Jean-Paul},
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year = {2002},
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month = nov,
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journal = {J. Chem. Phys.},
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volume = {117},
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number = {20},
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pages = {9138--9153},
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publisher = {{American Institute of Physics}},
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issn = {0021-9606},
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doi = {10.1063/1.1515317},
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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},
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journal = {J. Chem. Phys.},
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number = {20}
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}
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@book{AromaticityAntiaromaticityElectronic,
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title = {Aromaticity and {{Antiaromaticity}}: {{Electronic}} and {{Structural Aspects}} | {{Wiley}}},
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shorttitle = {Aromaticity and {{Antiaromaticity}}},
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||||
file = {/Users/monino/Zotero/storage/HGW4QMJY/Aromaticity+and+Antiaromaticity+Electronic+and+Structural+Aspects-p-9780471593829.html}
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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}
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}
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@article{baeyer_1885,
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title = {Ueber {{Polyacetylenverbindungen}}},
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author = {Baeyer, Adolf},
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year = {1885},
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journal = {Berichte Dtsch. Chem. Ges.},
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volume = {18},
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number = {2},
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pages = {2269--2281},
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issn = {1099-0682},
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doi = {10.1002/cber.18850180296},
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annotation = {\_eprint: https://chemistry-europe.onlinelibrary.wiley.com/doi/pdf/10.1002/cber.18850180296},
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copyright = {Copyright \textcopyright{} 1885 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim},
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file = {/Users/monino/Zotero/storage/T9A8FP8V/Baeyer - 1885 - Ueber Polyacetylenverbindungen.pdf;/Users/monino/Zotero/storage/B56CA56Z/cber.html},
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journal = {Berichte Dtsch. Chem. Ges.},
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language = {en},
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number = {2}
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langid = {english},
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annotation = {\_eprint: https://chemistry-europe.onlinelibrary.wiley.com/doi/pdf/10.1002/cber.18850180296},
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file = {/Users/monino/Zotero/storage/T9A8FP8V/Baeyer - 1885 - Ueber Polyacetylenverbindungen.pdf;/Users/monino/Zotero/storage/B56CA56Z/cber.html}
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}
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@article{balkova_1994,
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title = {A Multireference Coupled-cluster Study of the Ground State and Lowest Excited States of Cyclobutadiene},
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author = {Balkov{\'a}, A. and Bartlett, Rodney J.},
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year = {1994},
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month = aug,
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journal = {J. Chem. Phys.},
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volume = {101},
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number = {10},
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pages = {8972},
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publisher = {{American Institute of PhysicsAIP}},
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issn = {0021-9606},
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doi = {10.1063/1.468025},
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abstract = {The electronic structure of the ground state and several low-lying excited states of cyclobutadiene are studied using the new state-universal multireference coupled-cluster method with single and double excitations (MR-CCSD) augmented by a noniterative inclusion of the triple excitations [MR-CCSD(T)]. Two possible ground state configurations are examined, namely the square and the distorted rectangular geometries, and the multireference coupled-cluster energy barrier for the interconversion between the two rectangular ground state structures is estimated to be 6.6 kcal mol-1 compared with the best theoretical value, 6.4 kcal mol-1 obtained using the highly accurate coupled-cluster method with full inclusion of the triple excitations (CCSDT). The ordering of electronic states for the square geometry is determined, with the ground state singlet being located 6.9 kcal mol-1 below the lowest triplet electronic state. We also examine the potential energy surface for the interconversion between the two equivalent second-order Jahn\textendash Teller rhombic structures for the first excited singlet state. When comparing the MRCC energies with the results provided by various single- and multireference correlation methods, the critical importance of including both the dynamic and nondynamic correlation for a qualitatively correct description of the electronic structure of cyclobutadiene is emphasized. We also address the invariance properties of the present MRCC methods with respect to the alternative selections of reference orbital spaces.},
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copyright = {\textcopyright{} 1994 American Institute of Physics.},
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langid = {english},
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file = {/Users/monino/Zotero/storage/6MCJDAMM/1.html}
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}
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@article{bally_1980,
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@ -89,14 +101,32 @@
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author = {Bally, Thomas and Masamune, Satoru},
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year = {1980},
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month = jan,
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journal = {Tetrahedron},
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volume = {36},
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number = {3},
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pages = {343--370},
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issn = {0040-4020},
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doi = {10.1016/0040-4020(80)87003-7},
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file = {/Users/monino/Zotero/storage/DXWL3L8N/Bally et Masamune - 1980 - Cyclobutadiene.pdf;/Users/monino/Zotero/storage/XQ98S2QN/0040402080870037.html},
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journal = {Tetrahedron},
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language = {en},
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number = {3}
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langid = {english},
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file = {/Users/monino/Zotero/storage/DXWL3L8N/Bally et Masamune - 1980 - Cyclobutadiene.pdf;/Users/monino/Zotero/storage/XQ98S2QN/0040402080870037.html}
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}
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@article{banerjee_2016,
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title = {A State-Specific Multi-Reference Coupled-Cluster Approach with a Cost-Effective Treatment of Connected Triples: Implementation to Geometry Optimisation},
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shorttitle = {A State-Specific Multi-Reference Coupled-Cluster Approach with a Cost-Effective Treatment of Connected Triples},
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author = {Banerjee, Debi and Mondal, Monosij and Chattopadhyay, Sudip and Mahapatra, Uttam Sinha},
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year = {2016},
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month = may,
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journal = {Mol. Phys.},
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volume = {114},
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number = {10},
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pages = {1591--1608},
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publisher = {{Taylor \& Francis}},
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issn = {0026-8976},
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doi = {10.1080/00268976.2016.1142126},
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abstract = {Recently, we have suggested an approximate state-specific multi-reference coupled-cluster (SS-MRCC) singles, doubles and triples method based on the CCSDT-1a+d approximation applied to the single-reference CC approach, in which the contribution of the connected triple excitations is iteratively treated. The method, abbreviated as SS-MRCCSDT-1a+d is intruder-free and fully size-extensive. It has been employed for geometry optimisations of various systems possessing quasi-degeneracy of varying degrees (like N2H2 and O3) by invoking numerical gradient scheme. The method is also applied to CH2 and square cyclobutadiene in their excited states. For all systems under study, the computed values are in good accordance with state-of-the-art theoretical estimates indicating that the method might be a promising candidate for an accurate treatment of geometrical parameters of states plagued by electronic degeneracy in a computationally tractable manner.},
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annotation = {\_eprint: https://doi.org/10.1080/00268976.2016.1142126},
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file = {/Users/monino/Zotero/storage/W9FBB4VK/00268976.2016.html}
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}
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@article{casanova_2020,
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@ -104,16 +134,16 @@
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author = {Casanova, David and Krylov, Anna I.},
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year = {2020},
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month = feb,
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journal = {Phys. Chem. Chem. Phys.},
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volume = {22},
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number = {8},
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pages = {4326--4342},
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publisher = {{The Royal Society of Chemistry}},
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issn = {1463-9084},
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doi = {10.1039/C9CP06507E},
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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.},
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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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journal = {Phys. Chem. Chem. Phys.},
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language = {en},
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number = {8}
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langid = {english},
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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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@article{christiansen_1995,
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@ -121,13 +151,13 @@
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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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journal = {J. Chem. Phys.},
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number = {17}
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||||
doi = {10.1063/1.470315}
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}
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@article{eckert-maksic_2006,
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@ -136,31 +166,47 @@
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author = {{Eckert-Maksi{\'c}}, Mirjana and Vazdar, Mario and Barbatti, Mario and Lischka, Hans and Maksi{\'c}, Zvonimir B.},
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year = {2006},
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month = aug,
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journal = {J. Chem. Phys.},
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volume = {125},
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number = {6},
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pages = {064310},
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publisher = {{American Institute of Physics}},
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issn = {0021-9606},
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doi = {10.1063/1.2222366},
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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.},
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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},
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journal = {J. Chem. Phys.},
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number = {6}
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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}
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||||
}
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@article{ermer_1983,
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title = {Three {{Arguments Supporting}} a {{Rectangular Structure}} for {{Tetra}}-Tert-Butylcyclobutadiene},
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title = {Three {{Arguments Supporting}} a {{Rectangular Structure}} for {{Tetra-tert-butylcyclobutadiene}}},
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author = {Ermer, Otto and Heilbronner, Edgar},
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year = {1983},
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journal = {Angew. Chem. Int. Ed. Engl.},
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volume = {22},
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||||
number = {5},
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pages = {402--403},
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issn = {1521-3773},
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doi = {10.1002/anie.198304021},
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annotation = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/anie.198304021},
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copyright = {Copyright \textcopyright{} 1983 by Verlag Chemie, GmbH, Germany},
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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}
|
||||
langid = {english},
|
||||
annotation = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/anie.198304021},
|
||||
file = {/Users/monino/Zotero/storage/T32BDQPQ/Ermer et Heilbronner - 1983 - Three Arguments Supporting a Rectangular Structure.pdf;/Users/monino/Zotero/storage/4BR2A634/anie.html}
|
||||
}
|
||||
|
||||
@article{fantuzzi_2016,
|
||||
title = {The {{Nature}} of the {{Singlet}} and {{Triplet States}} of {{Cyclobutadiene}} as {{Revealed}} by {{Quantum Interference}}},
|
||||
author = {Fantuzzi, Felipe and Cardozo, Thiago M. and Nascimento, Marco A. C.},
|
||||
year = {2016},
|
||||
journal = {ChemPhysChem},
|
||||
volume = {17},
|
||||
number = {2},
|
||||
pages = {288--295},
|
||||
issn = {1439-7641},
|
||||
doi = {10.1002/cphc.201500885},
|
||||
abstract = {The generalized product function energy partitioning (GPF-EP) method is applied to the description of the cyclobutadiene molecule. The GPF wave function was built to reproduce generalized valence bond (GVB) and spin-coupled (SC) wave functions. The influence of quasiclassical and quantum interference contributions to each chemical bond of the system are analyzed along the automerization reaction coordinate for the lowest singlet and triplet states. The results show that the interference effect on the {$\pi$} space reduces the electronic energy of the singlet cyclobutadiene relative to the second-order Jahn\textendash Teller distortion, which takes the molecule from a D4h to a D2h structure. Our results also suggest that the {$\pi$} space of the 1B1g state of the square cyclobutadiene is composed of a weak four center\textendash four electron bond, whereas the 3A2g state has a four center\textendash two electron {$\pi$} bond. Finally, we also show that, although strain effects are nonnegligible, the thermodynamics of the main decomposition pathway of cyclobutadiene in the gas phase is dominated by the {$\pi$} space interference.},
|
||||
langid = {english},
|
||||
annotation = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/cphc.201500885},
|
||||
file = {/Users/monino/Zotero/storage/NTSYBUS7/Fantuzzi et al. - 2016 - The Nature of the Singlet and Triplet States of Cy.pdf;/Users/monino/Zotero/storage/C7HBJB3Y/cphc.html}
|
||||
}
|
||||
|
||||
@article{hirata_2000,
|
||||
@ -168,15 +214,15 @@
|
||||
author = {Hirata, So and Nooijen, Marcel and Bartlett, Rodney J.},
|
||||
year = {2000},
|
||||
month = aug,
|
||||
journal = {Chemical Physics Letters},
|
||||
volume = {326},
|
||||
number = {3},
|
||||
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}
|
||||
langid = {english},
|
||||
file = {/Users/monino/Zotero/storage/ZZI4JPPT/Hirata et al. - 2000 - High-order determinantal equation-of-motion couple.pdf}
|
||||
}
|
||||
|
||||
@article{hirata_2004,
|
||||
@ -184,30 +230,30 @@
|
||||
author = {Hirata, So},
|
||||
year = {2004},
|
||||
month = jul,
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {121},
|
||||
number = {1},
|
||||
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}
|
||||
file = {/Users/monino/Zotero/storage/3HCJINRI/Hirata - 2004 - Higher-order equation-of-motion coupled-cluster me.pdf}
|
||||
}
|
||||
|
||||
@article{irngartinger_1983,
|
||||
title = {Bonding {{Electron Density Distribution}} in {{Tetra}}-Tert-Butylcyclobutadiene\textemdash{} {{A Molecule}} with an {{Obviously Non}}-{{Square Four}}-{{Membered}} Ring},
|
||||
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},
|
||||
journal = {Angew. Chem. Int. Ed. Engl.},
|
||||
volume = {22},
|
||||
number = {5},
|
||||
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}
|
||||
langid = {english},
|
||||
annotation = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/anie.198304031},
|
||||
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}
|
||||
}
|
||||
|
||||
@article{kallay_2004,
|
||||
@ -215,14 +261,30 @@
|
||||
author = {K{\'a}llay, Mih{\'a}ly and Gauss, J{\"u}rgen},
|
||||
year = {2004},
|
||||
month = nov,
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {121},
|
||||
number = {19},
|
||||
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}
|
||||
file = {/Users/monino/Zotero/storage/TEHKUF6P/Kállay et Gauss - 2004 - Calculation of excited-state properties using gene.pdf}
|
||||
}
|
||||
|
||||
@article{karadakov_2008,
|
||||
title = {Ground- and {{Excited-State Aromaticity}} and {{Antiaromaticity}} in {{Benzene}} and {{Cyclobutadiene}}},
|
||||
author = {Karadakov, Peter B.},
|
||||
year = {2008},
|
||||
month = aug,
|
||||
journal = {J. Phys. Chem. A},
|
||||
volume = {112},
|
||||
number = {31},
|
||||
pages = {7303--7309},
|
||||
publisher = {{American Chemical Society}},
|
||||
issn = {1089-5639},
|
||||
doi = {10.1021/jp8037335},
|
||||
abstract = {The aromaticity and antiaromaticity of the ground state (S0), lowest triplet state (T1), and first singlet excited state (S1) of benzene, and the ground states (S0), lowest triplet states (T1), and the first and second singlet excited states (S1 and S2) of square and rectangular cyclobutadiene are assessed using various magnetic criteria including nucleus-independent chemical shifts (NICS), proton shieldings, and magnetic susceptibilities calculated using complete-active-space self-consistent field (CASSCF) wave functions constructed from gauge-including atomic orbitals (GIAOs). These magnetic criteria strongly suggest that, in contrast to the well-known aromaticity of the S0 state of benzene, the T1 and S1 states of this molecule are antiaromatic. In square cyclobutadiene, which is shown to be considerably more antiaromatic than rectangular cyclobutadiene, the magnetic properties of the T1 and S1 states allow these to be classified as aromatic. According to the computed magnetic criteria, the T1 state of rectangular cyclobutadiene is still aromatic, but the S1 state is antiaromatic, just as the S2 state of square cyclobutadiene; the S2 state of rectangular cyclobutadiene is nonaromatic. The results demonstrate that the well-known ``triplet aromaticity'' of cyclic conjugated hydrocarbons represents a particular case of a broader concept of excited-state aromaticity and antiaromaticity. It is shown that while electronic excitation may lead to increased nuclear shieldings in certain low-lying electronic states, in general its main effect can be expected to be nuclear deshielding, which can be substantial for heavier nuclei.},
|
||||
file = {/Users/monino/Zotero/storage/7UMPEAYT/Karadakov - 2008 - Ground- and Excited-State Aromaticity and Antiarom.pdf;/Users/monino/Zotero/storage/7ULNL76P/jp8037335.html}
|
||||
}
|
||||
|
||||
@article{koch_1997,
|
||||
@ -231,14 +293,30 @@
|
||||
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,
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {106},
|
||||
number = {5},
|
||||
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}
|
||||
file = {/Users/monino/Zotero/storage/BEW2ATM3/Koch et al. - 1997 - The CC3 model An iterative coupled cluster approa.pdf}
|
||||
}
|
||||
|
||||
@article{kostenko_2017,
|
||||
title = {Spectroscopic {{Observation}} of the {{Triplet Diradical State}} of a {{Cyclobutadiene}}},
|
||||
author = {Kostenko, Arseni and Tumanskii, Boris and Kobayashi, Yuzuru and Nakamoto, Masaaki and Sekiguchi, Akira and Apeloig, Yitzhak},
|
||||
year = {2017},
|
||||
journal = {Angew. Chem. Int. Ed.},
|
||||
volume = {56},
|
||||
number = {34},
|
||||
pages = {10183--10187},
|
||||
issn = {1521-3773},
|
||||
doi = {10.1002/anie.201705228},
|
||||
abstract = {Tetrakis(trimethylsilyl)cyclobuta-1,3-diene (1) was subjected to a temperature-dependent EPR study to allow the first spectroscopic observation of a triplet diradical state of a cyclobutadiene (2). From the temperature dependent EPR absorption area we derive a singlet\textrightarrow triplet (1\textrightarrow 2) energy gap, EST, of 13.9 kcal mol-1, in agreement with calculated values. The zero-field splitting parameters D=0.171 cm-1, E=0 cm-1 are accurately reproduced by DFT calculations. The triplet diradical 2 is thermally accessible at moderate temperatures. It is not an intermediate in the thermal cycloreversion of cyclobutadiene to two acetylene molecules.},
|
||||
langid = {english},
|
||||
annotation = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/anie.201705228},
|
||||
file = {/Users/monino/Zotero/storage/IKNKPNI3/anie.html}
|
||||
}
|
||||
|
||||
@article{kreile_1986,
|
||||
@ -246,15 +324,15 @@
|
||||
author = {Kreile, J{\"u}rgen and M{\"u}nzel, Norbert and Schweig, Armin and Specht, Harald},
|
||||
year = {1986},
|
||||
month = feb,
|
||||
journal = {Chemical Physics Letters},
|
||||
volume = {124},
|
||||
number = {2},
|
||||
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}
|
||||
langid = {english},
|
||||
file = {/Users/monino/Zotero/storage/2EQ8LH4G/Kreile et al. - 1986 - Uv photoelectron spectrum of cyclobutadiene. free .pdf;/Users/monino/Zotero/storage/QHJZT5VV/0009261486851338.html}
|
||||
}
|
||||
|
||||
@article{kucharski_1991,
|
||||
@ -262,15 +340,153 @@
|
||||
author = {Kucharski, Stanislaw A. and Bartlett, Rodney J.},
|
||||
year = {1991},
|
||||
month = jul,
|
||||
journal = {Theoret. Chim. Acta},
|
||||
volume = {80},
|
||||
number = {4},
|
||||
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}
|
||||
langid = {english},
|
||||
file = {/Users/monino/Zotero/storage/L3VLAU8A/Kucharski et Bartlett - 1991 - Recursive intermediate factorization and complete .pdf}
|
||||
}
|
||||
|
||||
@article{lefrancois_2015,
|
||||
title = {Adapting Algebraic Diagrammatic Construction Schemes for the Polarization Propagator to Problems with Multi-Reference Electronic Ground States Exploiting the Spin-Flip Ansatz},
|
||||
author = {Lefrancois, Daniel and Wormit, Michael and Dreuw, Andreas},
|
||||
year = {2015},
|
||||
month = sep,
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {143},
|
||||
number = {12},
|
||||
pages = {124107},
|
||||
publisher = {{American Institute of Physics}},
|
||||
issn = {0021-9606},
|
||||
doi = {10.1063/1.4931653},
|
||||
abstract = {For the investigation of molecular systems with electronic ground states exhibiting multi-reference character, a spin-flip (SF) version of the algebraic diagrammatic construction (ADC) scheme for the polarization propagator up to third order perturbation theory (SF-ADC(3)) is derived via the intermediate state representation and implemented into our existing ADC computer program adcman. The accuracy of these new SF-ADC(n) approaches is tested on typical situations, in which the ground state acquires multi-reference character, like bond breaking of H2 and HF, the torsional motion of ethylene, and the excited states of rectangular and square-planar cyclobutadiene. Overall, the results of SF-ADC(n) reveal an accurate description of these systems in comparison with standard multi-reference methods. Thus, the spin-flip versions of ADC are easy-to-use methods for the calculation of ``few-reference'' systems, which possess a stable single-reference triplet ground state.},
|
||||
file = {/Users/monino/Zotero/storage/2WIVTU65/Lefrancois et al. - 2015 - Adapting algebraic diagrammatic construction schem.pdf}
|
||||
}
|
||||
|
||||
@article{levchenko_2004,
|
||||
title = {Equation-of-Motion Spin-Flip Coupled-Cluster Model with Single and Double Substitutions: {{Theory}} and Application to Cyclobutadiene},
|
||||
shorttitle = {Equation-of-Motion Spin-Flip Coupled-Cluster Model with Single and Double Substitutions},
|
||||
author = {Levchenko, Sergey V. and Krylov, Anna I.},
|
||||
year = {2004},
|
||||
month = jan,
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {120},
|
||||
number = {1},
|
||||
pages = {175--185},
|
||||
publisher = {{American Institute of Physics}},
|
||||
issn = {0021-9606},
|
||||
doi = {10.1063/1.1630018},
|
||||
file = {/Users/monino/Zotero/storage/FDUTSFT8/Levchenko et Krylov - 2004 - Equation-of-motion spin-flip coupled-cluster model.pdf}
|
||||
}
|
||||
|
||||
@article{li_2009,
|
||||
title = {Accounting for the Exact Degeneracy and Quasidegeneracy in the Automerization of Cyclobutadiene via Multireference Coupled-Cluster Methods},
|
||||
author = {Li, Xiangzhu and Paldus, Josef},
|
||||
year = {2009},
|
||||
month = sep,
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {131},
|
||||
number = {11},
|
||||
pages = {114103},
|
||||
publisher = {{American Institute of Physics}},
|
||||
issn = {0021-9606},
|
||||
doi = {10.1063/1.3225203},
|
||||
abstract = {The automerization of cyclobutadiene (CBD) is employed to test the performance of the reduced multireference (RMR) coupled-cluster (CC) method with singles and doubles (RMR CCSD) that employs a modest-size MR CISD wave function as an external source for the most important (primary) triples and quadruples in order to account for the nondynamic correlation effects in the presence of quasidegeneracy, as well as of its perturbatively corrected version accounting for the remaining (secondary) triples [RMR CCSD(T)]. The experimental results are compared with those obtained by the standard CCSD and CCSD(T) methods, by the state universal (SU) MR CCSD and its state selective or state specific (SS) version as formulated by Mukherjee et al. (SS MRCC or MkMRCC) and, wherever available, by the Brillouin\textendash Wigner MRCC [MR BWCCSD(T)] method. Both restricted Hartree-Fock (RHF) and multiconfigurational self-consistent field (MCSCF) molecular orbitals are employed. For a smaller STO-3G basis set we also make a comparison with the exact full configuration interaction (FCI) results. Both fundamental vibrational energies\textemdash as obtained via the integral averaging method (IAM) that can handle anomalous potentials and automatically accounts for anharmonicity\textendash{} and the CBD automerization barrier for the interconversion of the two rectangular structures are considered. It is shown that the RMR CCSD(T) potential has the smallest nonparallelism error relative to the FCI potential and the corresponding fundamental vibrational frequencies compare reasonably well with the experimental ones and are very close to those recently obtained by other authors. The effect of anharmonicity is assessed using the second-order perturbation theory (MP2). Finally, the invariance of the RMR CC methods with respect to orbital rotations is also examined.},
|
||||
file = {/Users/monino/Zotero/storage/72SLN6AI/Li et Paldus - 2009 - Accounting for the exact degeneracy and quasidegen.pdf}
|
||||
}
|
||||
|
||||
@article{lutz_2018,
|
||||
title = {Reference Dependence of the Two-Determinant Coupled-Cluster Method for Triplet and Open-Shell Singlet States of Biradical Molecules},
|
||||
author = {Lutz, Jesse J. and Nooijen, Marcel and Perera, Ajith and Bartlett, Rodney J.},
|
||||
year = {2018},
|
||||
month = apr,
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {148},
|
||||
number = {16},
|
||||
pages = {164102},
|
||||
publisher = {{American Institute of Physics}},
|
||||
issn = {0021-9606},
|
||||
doi = {10.1063/1.5025170},
|
||||
abstract = {We study the performance of the two-determinant (TD) coupled-cluster (CC) method which, unlike conventional ground-state single-reference (SR) CC methods, can, in principle, provide a naturally spin-adapted treatment of the lowest-lying open-shell singlet (OSS) and triplet electronic states. Various choices for the TD-CC reference orbitals are considered, including those generated by the multi-configurational self-consistent field method. Comparisons are made with the results of high-level SR-CC, equation-of-motion (EOM) CC, and multi-reference EOM calculations performed on a large test set of over 100 molecules with low-lying OSS states. It is shown that in cases where the EOMCC reference function is poorly described, TD-CC can provide a significantly better quantitative description of OSS total energies and OSS-triplet splittings.},
|
||||
file = {/Users/monino/Zotero/storage/WRSTKSLY/Lutz et al. - 2018 - Reference dependence of the two-determinant couple.pdf}
|
||||
}
|
||||
|
||||
@article{lyakh_2011,
|
||||
title = {The `Tailored' {{CCSD}}({{T}}) Description of the Automerization of Cyclobutadiene},
|
||||
author = {Lyakh, Dmitry I. and Lotrich, Victor F. and Bartlett, Rodney J.},
|
||||
year = {2011},
|
||||
month = jan,
|
||||
journal = {Chemical Physics Letters},
|
||||
volume = {501},
|
||||
number = {4},
|
||||
pages = {166--171},
|
||||
issn = {0009-2614},
|
||||
doi = {10.1016/j.cplett.2010.11.058},
|
||||
abstract = {An alternative route to extend the CCSD(T) approach to multireference problems is presented. The well-known defect of the CCSD(T) model in describing the non-dynamic electron correlation effects is remedied by `tailoring' the underlying coupled-cluster singles and doubles (CCSD) approach and applying the perturbative triples correction to it. The TCCSD(T) approach suggested in the paper has the same computational demands as the CCSD(T) method, though being mostly free from its drawbacks pertinent to multireference (quasidegenerate) situations. To test the approach we calculate the potential energy surface for the automerization of cyclobutadiene where the transition state exhibits a strong multireference character.},
|
||||
langid = {english},
|
||||
file = {/Users/monino/Zotero/storage/F6XZHQI8/S0009261410015393.html}
|
||||
}
|
||||
|
||||
@article{mahapatra_2010,
|
||||
title = {{Second-order state-specific multireference M\o ller Plesset perturbation theory: Application to energy surfaces of diimide, ethylene, butadiene, and cyclobutadiene}},
|
||||
shorttitle = {{Second-order state-specific multireference M\o ller Plesset perturbation theory}},
|
||||
author = {Mahapatra, Uttam Sinha and Chattopadhyay, Sudip and Chaudhuri, Rajat K.},
|
||||
year = {2010},
|
||||
journal = {J. Comput. Chem.},
|
||||
volume = {32},
|
||||
number = {2},
|
||||
pages = {325--337},
|
||||
issn = {1096-987X},
|
||||
doi = {10.1002/jcc.21624},
|
||||
abstract = {The complete active space spin-free state-specific multireference M\o ller-Plesset perturbation theory (SS-MRMPPT) based on the Rayleigh-Schr\"odinger expansion has proved to be very successful in describing electronic states of model and real molecular systems with predictive accuracy. The SS-MRMPPT method (which deals with one state while using a multiconfigurational reference wave function) is designed to avoid intruder effects along with a balanced description of both dynamic and static correlations in a size-extensive manner, which allows us to produce accurate potential energy surfaces (PESs) with a correct shape in bond-breaking processes. The SS-MRMPPT method is size consistent when localized orbitals on each fragment are used. The intruder state(s) almost inevitably interfere when computing the PESs involving the breaking of genuine chemical bonds. In such situations, the traditional effective Hamiltonian formalism often goes down, so that no physically acceptable solution can be obtained. In this work, we continue our analysis of the SS-MRMPPT method for systems and phenomena that cannot be described either with the conventional single-reference approach or effective Hamiltonian-based traditional MR methods. In this article, we investigate whether the encouraging results we have obtained at the SS-MRMPPT level in the study of cis-trans isomerization of diimide (N2H2), ethylene (C2H4), and 1,3-butadiene (C4H6) carry over to the study of chemical reactions. The energy surfaces of the double-bond flipping interconversion of the two equivalent ground and two lowest singlet state structures of cyclobutadiene have also been studied. All results have been discussed and assessed by comparing with other state-of-the-art calculations and corresponding experimental data whenever available. \textcopyright{} 2010 Wiley Periodicals, Inc. J Comput Chem, 2011},
|
||||
langid = {german},
|
||||
annotation = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.21624},
|
||||
file = {/Users/monino/Zotero/storage/UHJ8YMNH/Mahapatra et al. - 2011 - Second-order state-specific multireference Møller .pdf;/Users/monino/Zotero/storage/JXXGY7X8/jcc.html}
|
||||
}
|
||||
|
||||
@article{manohar_2008,
|
||||
title = {A Noniterative Perturbative Triples Correction for the Spin-Flipping and Spin-Conserving Equation-of-Motion Coupled-Cluster Methods with Single and Double Substitutions},
|
||||
author = {Manohar, Prashant U. and Krylov, Anna I.},
|
||||
year = {2008},
|
||||
month = nov,
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {129},
|
||||
number = {19},
|
||||
pages = {194105},
|
||||
publisher = {{American Institute of Physics}},
|
||||
issn = {0021-9606},
|
||||
doi = {10.1063/1.3013087},
|
||||
abstract = {A noniterative {$\mathsl{N}$} 7 N7 triples correction for the equation-of-motion coupled-cluster method with single and double substitutions (CCSD) is presented. The correction is derived by second-order perturbation treatment of the similarity-transformed CCSD Hamiltonian. The spin-conserving variant of the correction is identical to the triples correction of Piecuch and co-workers [Mol. Phys. 104, 2149 (2006)] derived within method-of-moments framework and is not size intensive. The spin-flip variant of the correction is size intensive. The performance of the correction is demonstrated by calculations of electronic excitation energies in methylene, nitrenium ion, cyclobutadiene, ortho-, meta-, and para-benzynes, 1,2,3-tridehydrobenzene, as well as C\textendash C bond breaking in ethane. In all cases except cyclobutadiene, the absolute values of the correction for energy differences were 0.1 eV or less. In cyclobutadiene, the absolute values of the correction were as large as 0.4 eV. In most cases, the correction reduced the errors against the benchmark values by about a factor of 2\textendash 3, the absolute errors being less than 0.04 eV.},
|
||||
file = {/Users/monino/Zotero/storage/686RRDFK/Manohar et Krylov - 2008 - A noniterative perturbative triples correction for.pdf}
|
||||
}
|
||||
|
||||
@book{minkin_1994,
|
||||
title = {Aromaticity and {{Antiaromaticity}}: {{Electronic}} and {{Structural Aspects}} | {{Wiley}}},
|
||||
shorttitle = {Aromaticity and {{Antiaromaticity}}},
|
||||
author = {Minkin, Vladimir I and Glukhovtsev, Mikhail N. and Simkin, Boris Ya.},
|
||||
year = {1994},
|
||||
file = {/Users/monino/Zotero/storage/HGW4QMJY/Aromaticity+and+Antiaromaticity+Electronic+and+Structural+Aspects-p-9780471593829.html}
|
||||
}
|
||||
|
||||
@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}}},
|
||||
author = {Qu, Zexing and Yang, Chen and Liu, Chungen},
|
||||
year = {2015},
|
||||
month = jan,
|
||||
journal = {J. Phys. Chem. A},
|
||||
volume = {119},
|
||||
number = {3},
|
||||
pages = {442--451},
|
||||
publisher = {{American Chemical Society}},
|
||||
issn = {1089-5639},
|
||||
doi = {10.1021/jp503220q},
|
||||
abstract = {Photoinduced chemical processes upon Franck\textendash Condon (FC) excitation in tetrakis(trimethylsilyl)-cyclobutadiene (TMS-CBD) have been investigated through the exploration of potential energy surface crossings among several low-lying excited states using the complete active space self-consistent field (CASSCF) method. Vertical excitation energies are also computed with the equation-of-motion coupled-cluster model with single and double excitations (EOM-CCSD) as well as the multireference M\o ller\textendash Plesset (MRMP) methods. Upon finding an excellent coincidence between the computational results and experimental observations, it is suggested that the Franck\textendash Condon excited state does not correspond to the first {$\pi$}\textendash{$\pi$}* single excitation state (S1, 11B1 state in terms of D2 symmetry), but to the second 1B1 state (S3), which is characterized as a {$\sigma$}\textendash{$\pi$}* single excitation state. Starting from the Franck\textendash Condon region, a series of conical intersections (CIs) are located along one isomerization channel and one dissociation channel. Through the isomerization channel, TMS-CBD is transformed to tetrakis(trimethylsilyl)-tetrahedrane (TMS-THD), and this isomerization process could take place by passing through a ``tetra form'' conical intersection. On the other hand, the dissociation channel yielding two bis(trimethylsilyl)-acetylene (TMS-Ac) molecules through further stretching of the longer C\textendash C bonds might be more competitive than the isomerization channel after excitation into S3 state. This mechanistic picture is in good agreement with recently reported experimental observations.},
|
||||
file = {/Users/monino/Zotero/storage/Y3CT8YYT/Qu et al. - 2015 - Photoisomerization of Silyl-Substituted Cyclobutad.pdf;/Users/monino/Zotero/storage/W9Q4H9MA/jp503220q.html}
|
||||
}
|
||||
|
||||
@article{reeves_1969,
|
||||
@ -278,17 +494,17 @@
|
||||
author = {Reeves, P. C. and Henery, J. and Pettit, R.},
|
||||
year = {1969},
|
||||
month = oct,
|
||||
journal = {J. Am. Chem. Soc.},
|
||||
volume = {91},
|
||||
number = {21},
|
||||
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}
|
||||
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}
|
||||
}
|
||||
|
||||
@book{roos_1996,
|
||||
@incollection{roos_1996,
|
||||
title = {Multiconfigurational {{Perturbation Theory}}: {{Applications}} in {{Electronic Spectroscopy}}},
|
||||
shorttitle = {Multiconfigurational {{Perturbation Theory}}},
|
||||
booktitle = {Advances in {{Chemical Physics}}},
|
||||
@ -298,10 +514,91 @@
|
||||
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}
|
||||
isbn = {978-0-470-14152-6},
|
||||
langid = {english},
|
||||
annotation = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/9780470141526.ch5},
|
||||
file = {/Users/monino/Zotero/storage/KWDFZUBF/9780470141526.html}
|
||||
}
|
||||
|
||||
@article{schoonmaker_2018,
|
||||
title = {Quantum Mechanical Tunneling in the Automerization of Cyclobutadiene},
|
||||
author = {Schoonmaker, R. and Lancaster, T. and Clark, S. J.},
|
||||
year = {2018},
|
||||
month = mar,
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {148},
|
||||
number = {10},
|
||||
pages = {104109},
|
||||
publisher = {{American Institute of Physics}},
|
||||
issn = {0021-9606},
|
||||
doi = {10.1063/1.5019254},
|
||||
abstract = {Cyclobutadiene has a four-membered carbon ring with two double bonds, but this highly strained molecular configuration is almost square and, via a coordinated motion, the nuclei quantum mechanically tunnels through the high-energy square state to a configuration equivalent to the initial configuration under a 90\textdegree{} rotation. This results in a square ground state, comprising a superposition of two molecular configurations, that is driven by quantum tunneling. Using a quantum mechanical model, and an effective nuclear potential from density functional theory, we calculate the vibrational energy spectrum and the accompanying wavefunctions. We use the wavefunctions to identify the motions of the molecule and detail how different motions can enhance or suppress the tunneling rate. This is relevant for kinematics of tunneling-driven reactions, and we discuss these implications. We are also able to provide a qualitative account of how the molecule will respond to an external perturbation and how this may enhance or suppress infra-red-active vibrational transitions.},
|
||||
file = {/Users/monino/Zotero/storage/EEIUEQUN/Schoonmaker et al. - 2018 - Quantum mechanical tunneling in the automerization.pdf}
|
||||
}
|
||||
|
||||
@article{shen_2012,
|
||||
title = {Combining Active-Space Coupled-Cluster Methods with Moment Energy Corrections via the {{CC}}({{P}};{{Q}}) Methodology, with Benchmark Calculations for Biradical Transition States},
|
||||
author = {Shen, Jun and Piecuch, Piotr},
|
||||
year = {2012},
|
||||
month = apr,
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {136},
|
||||
number = {14},
|
||||
pages = {144104},
|
||||
publisher = {{American Institute of Physics}},
|
||||
issn = {0021-9606},
|
||||
doi = {10.1063/1.3700802},
|
||||
abstract = {We have recently suggested the CC(P;Q) methodology that can correct energies obtained in the active-space coupled-cluster (CC) or equation-of-motion (EOM) CC calculations, which recover much of the nondynamical and some dynamical electron correlation effects, for the higher-order, mostly dynamical, correlations missing in the active-space CC/EOMCC considerations. It is shown that one can greatly improve the description of biradical transition states, both in terms of the resulting energy barriers and total energies, by combining the CC approach with singles, doubles, and active-space triples, termed CCSDt, with the CC(P;Q)-style correction due to missing triple excitations defining the CC(t;3) approximation.},
|
||||
file = {/Users/monino/Zotero/storage/C6324F9Y/Shen et Piecuch - 2012 - Combining active-space coupled-cluster methods wit.pdf}
|
||||
}
|
||||
|
||||
@article{stoneburner_2017,
|
||||
title = {Systematic Design of Active Spaces for Multi-Reference Calculations of Singlet\textendash Triplet Gaps of Organic Diradicals, with Benchmarks against Doubly Electron-Attached Coupled-Cluster Data},
|
||||
author = {Stoneburner, Samuel J. and Shen, Jun and Ajala, Adeayo O. and Piecuch, Piotr and Truhlar, Donald G. and Gagliardi, Laura},
|
||||
year = {2017},
|
||||
month = oct,
|
||||
journal = {J. Chem. Phys.},
|
||||
volume = {147},
|
||||
number = {16},
|
||||
pages = {164120},
|
||||
publisher = {{American Institute of Physics}},
|
||||
issn = {0021-9606},
|
||||
doi = {10.1063/1.4998256},
|
||||
abstract = {Singlet-triplet gaps in diradical organic {$\pi$}-systems are of interest in many applications. In this study, we calculate them in a series of molecules, including cyclobutadiene and its derivatives and cyclopentadienyl cation, by using correlated participating orbitals within the complete active space (CAS) and restricted active space (RAS) self-consistent field frameworks, followed by second-order perturbation theory (CASPT2 and RASPT2). These calculations are evaluated by comparison with the results of doubly electron-attached (DEA) equation-of-motion (EOM) coupled-cluster (CC) calculations with up to 4-particle\textendash 2-hole (4p-2h) excitations. We find active spaces that can accurately reproduce the DEA-EOMCC(4p-2h) data while being small enough to be applicable to larger organic diradicals.},
|
||||
file = {/Users/monino/Zotero/storage/WXJDP8H3/Stoneburner et al. - 2017 - Systematic design of active spaces for multi-refer.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},
|
||||
author = {Varras, Panayiotis C. and Gritzapis, Panagiotis S.},
|
||||
year = {2018},
|
||||
month = nov,
|
||||
journal = {Chemical Physics Letters},
|
||||
volume = {711},
|
||||
pages = {166--172},
|
||||
issn = {0009-2614},
|
||||
doi = {10.1016/j.cplett.2018.09.028},
|
||||
abstract = {The application of the Restricted Active Space Self Consistent Field (RASSCF) quantum chemical method using an extended active space and including {$\sigma$}-{$\sigma$}, {$\pi$}-{$\sigma$} and {$\pi$}-{$\pi$} dynamical electron correlation shows that the transition state structure for the automerization reaction of cyclobutadiene is an isosceles trapezium. This transition state is obtained without any symmetry constraints. The calculated energy barrier height involving the zero point vibrational energy corrections is 9.62\,kcal{$\bullet$}mol-1 (0.417\,eV), with the corresponding rate constant being equal to 0.18\,\texttimes\,109\,s-1 (or 7.1\,\texttimes\,1010\,s-1 in case of using the vibrational energy splitting tunneling method).},
|
||||
langid = {english},
|
||||
file = {/Users/monino/Zotero/storage/X7QFY28N/S0009261418307590.html}
|
||||
}
|
||||
|
||||
@article{vitale_2020,
|
||||
title = {{{FCIQMC-Tailored Distinguishable Cluster Approach}}},
|
||||
author = {Vitale, Eugenio and Alavi, Ali and Kats, Daniel},
|
||||
year = {2020},
|
||||
month = sep,
|
||||
journal = {J. Chem. Theory Comput.},
|
||||
volume = {16},
|
||||
number = {9},
|
||||
pages = {5621--5634},
|
||||
publisher = {{American Chemical Society}},
|
||||
issn = {1549-9618},
|
||||
doi = {10.1021/acs.jctc.0c00470},
|
||||
abstract = {The tailored approach is applied to the distinguishable cluster method together with a stochastic FCI solver (FCIQMC). It is demonstrated that the new method is more accurate than the corresponding tailored coupled cluster and the pure distinguishable cluster methods. An F12 correction for tailored methods and FCIQMC is introduced, which drastically improves the basis set convergence. A new black-box approach to define the active space using the natural orbitals from the distinguishable cluster is evaluated and found to be a convenient alternative to the usual CASSCF approach.},
|
||||
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{whitman_1982,
|
||||
@ -309,14 +606,30 @@
|
||||
author = {Whitman, David W. and Carpenter, Barry K.},
|
||||
year = {1982},
|
||||
month = nov,
|
||||
journal = {J. Am. Chem. Soc.},
|
||||
volume = {104},
|
||||
number = {23},
|
||||
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}
|
||||
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}
|
||||
}
|
||||
|
||||
@article{xu_2015,
|
||||
title = {Multireference {{Second Order Perturbation Theory}} with a {{Simplified Treatment}} of {{Dynamical Correlation}}},
|
||||
author = {Xu, Enhua and Zhao, Dongbo and Li, Shuhua},
|
||||
year = {2015},
|
||||
month = oct,
|
||||
journal = {J. Chem. Theory Comput.},
|
||||
volume = {11},
|
||||
number = {10},
|
||||
pages = {4634--4643},
|
||||
publisher = {{American Chemical Society}},
|
||||
issn = {1549-9618},
|
||||
doi = {10.1021/acs.jctc.5b00495},
|
||||
abstract = {A multireference second order perturbation theory based on a complete active space configuration interaction (CASCI) function or density matrix renormalized group (DMRG) function has been proposed. This method may be considered as an approximation to the CAS/A approach with the same reference, in which the dynamical correlation is simplified with blocked correlated second order perturbation theory based on the generalized valence bond (GVB) reference (GVB-BCPT2). This method, denoted as CASCI-BCPT2/GVB or DMRG-BCPT2/GVB, is size consistent and has a similar computational cost as the conventional second order perturbation theory (MP2). We have applied it to investigate a number of problems of chemical interest. These problems include bond-breaking potential energy surfaces in four molecules, the spectroscopic constants of six diatomic molecules, the reaction barrier for the automerization of cyclobutadiene, and the energy difference between the monocyclic and bicyclic forms of 2,6-pyridyne. Our test applications demonstrate that CASCI-BCPT2/GVB can provide comparable results with CASPT2 (second order perturbation theory based on the complete active space self-consistent-field wave function) for systems under study. Furthermore, the DMRG-BCPT2/GVB method is applicable to treat strongly correlated systems with large active spaces, which are beyond the capability of CASPT2.},
|
||||
file = {/Users/monino/Zotero/storage/NMUPRMKE/Xu et al. - 2015 - Multireference Second Order Perturbation Theory wi.pdf;/Users/monino/Zotero/storage/A5RR8VJ5/acs.jctc.html}
|
||||
}
|
||||
|
||||
|
||||
|
||||
@ -221,14 +221,14 @@ The cyclobutadiene (CBD) molecule represents a playground for ground state and e
|
||||
\label{sec:intro}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
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.
|
||||
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{minkin_1994} 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_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 autoisomerization barrier 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 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) \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.
|
||||
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.
|
||||
|
||||
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.
|
||||
|
||||
@ -598,11 +598,12 @@ Figure \ref{fig:D2h} shows the vertical energies of the studied excited states d
|
||||
|
||||
|
||||
\subsubsection{D4h geometry}
|
||||
\label{sec:D4h}
|
||||
Table \ref{tab:sf_D4h} shows vertical energies obtained with spin-flip methods and Table \ref{tab:D4h} vertical energies obtained with standard methods. As for the previous geometry we start with the SF-TD-DFT results with hybrid functionals. We can first notice that for the B3LYP and the PBE0 functionals we have a wrong ordering of the first triplet state $1\,{}^3A_{2g}$ and the ground state $\text{X}\,{}^1B_{1g}$. We retrieve the good ordering with the BH\&HLYP functional, so adding exact exchange to the functional allows us to have the right ordering between these two states. For the B3LYP and the PBE0 functionals we have that the energy differences for each states and for all bases are small with 0.004-0.007 eV for the triplet state $1\,{}^3A_{2g}$. We have 0.015-0.021 eV of energy difference for the $2\,{}^1A_{1g}$ state through all bases, we can notice that this state is around 0.13 eV (considering all bases) higher with the PBE0 functional. We can make the same observation for the $1\,{}^1B_{2g}$ state for the B3LYP and the PBE0 functionals, indeed we have small energy differences for all bases and the state is around 0.14-0.15 eV for the PBE0 functional. For the BH\&HLYP functional the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states are higher in energy than for the two other hybrid functionals with about 0.65-0.69 eV higher for the $2\,{}^1A_{1g}$ state and 0.75-0.77 eV for the $1\,{}^1B_{2g}$ state compared to the PBE0 functional. Then, we have the RSH functionals CAM-B3LYP, $\omega$B97X-V and LC-$\omega$PBE08. For these functionals the vertical energies are similar for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states with a maximum energy difference of 0.01-0.02 eV for the $2\,{}^1A_{1g}$ state and 0.005-0.009 eV for the $1\,{}^1B_{2g}$ state considering all bases. The maximum energy difference for the triplet state is larger with 0.047-0.057 eV for all bases. Note that the vertical energies obtained with the RSH functionals are close to the PBE0 ones except that we have the right ordering between the triplet state $1\,{}^3A_{2g}$ and the ground state $\text{X}\,{}^1B_{1g}$. The M06-2X results are closer to the BH\&HLYP ones but the M06-2X vertical energies are always higher than the BH\&HLYP ones. We can notice that the M06-2X energies for the $2\,{}^1A_{1g}$ state are close to the BH\&HLYP energies for the $1\,{}^1B_{2g}$ state. For these two states, when we compared the results obtained with the M06-2X and the BH\&HLYP functionals, we have an energy difference of 0.16-0.17 eV for the $2\,{}^1A_{1g}$ state and 0.17-0.18 eV for the $1\,{}^1B_{2g}$ state considering all bases. For the triplet state $1\,{}^3A_{2g}$ the energy differences are smaller with 0.03-0.04 eV for all bases. The M11 vertical energies are very close to the M06-2X ones for the triplet state with a maximum energy difference of 0.003 eV considering all bases, and are closer to the BH\&HLYP results for the two other states with 0.06-0.07 eV and 0.07-0.08 eV of energy difference for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states, respectively. Then we discuss the various ADC scheme results, note that we were not able to obtain the vertical energies with the AVQZ basis due to computational resources. For the ADC(2)-s scheme we can see that the energy difference for the triplet state are smaller than for the two other states, indeed we have an energy difference of 0.09 eV for the triplet state whereas we have 0.15 eV and 0.25 eV for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states, again when considering all bases. The energy difference for each state and through the bases are similar for the two other ADC schemes. We can notice a large variation of the vertical energies for the $2\,{}^1A_{1g}$ state between ADC(2)-s and ADC(2)-x with around 0.52-0.58 eV through all bases. The ADC(3) vertical energies are very similar to the ADC(2) ones for the $1\,{}^1B_{2g}$ state with an energy difference of 0.01-0.02 eV for all bases, whereas we have an energy difference of 0.04-0.11 eV and 0.17-0.22 eV for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states, respectively.
|
||||
|
||||
Now we look at Table \ref{tab:D4h} for vertical energies obtained with standard methods, we have first the various CC methods, for all the CC methods we were only able to reach the AVTZ basis.
|
||||
%For the CCSD method we cannot obtain the vertical energy for the $1\,{}^1B_{2g}$ state, we can notice a small energy variation through the bases for the triplet state with around 0.06 eV. The energy variation is larger for the $2\,{}^1A_{1g}$ state with 0.20 eV.
|
||||
Again, we have computed the vertical energies at the CCSDT and CCSDTQ level as well as their approximation the CC3 and CC4 methods, respectively. For the CC3 method we do not have the vertical energies for the triplet state $1\,{}^3A_{2g}$. Considering all bases for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states we have an energy difference of about 0.15 eV and 0.12 eV, respectively. The CCSDT energies are close to the CC3 ones for the $2\,{}^1A_{1g}$ state with an energy difference of around 0.03-0.06 eV considering all bases. For the $1\,{}^1B_{2g}$ state the energy difference between the CC3 and the CCSDT values is larger with 0.18-0.27 eV. We can make a similar observation between the CC4 and the CCSDTQ values, for the $2\,{}^1A_{1g}$ state we have an energy difference of about 0.01 eV and this time we have smaller energy difference for the $1\,{}^1B_{2g}$ with 0.01 eV. Then we discuss the multireference results and this time we were able to reach the AVQZ basis. Again we consider two different active spaces, four electrons in four orbitals and twelve electrons in twelve orbitals. If we compare the CASSCF(4,4) and CASPT2(4,4) values we can see large energy differences for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states, for the $2\,{}^1A_{1g}$ state we have an energy difference of about 0.67-0.74 eV and 1.65-1.81 eV for the $1\,{}^1B_{2g}$ state. The energy difference is smaller for the triplet state with 0.27-0.31 eV, we can notice that all the CASSCF(4,4) vertical energies are higher than the CASPT2(4,4) ones. Then we have the NEVPT2(4,4) methods (SC-NEVPT2(4,4) and PC-NEVPT2(4,4)) for which the vertical energies are quite similar, however we can notice that we have a different ordering of the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states with $1\,{}^1B_{2g}$ higher in energy than $2\,{}^1A_{1g}$ for the two NEVPT2(4,4) methods. Then we have the results for the same methods but with a larger active space. For the CASSCF(12,12) we have similar values for the triplet state with energy difference of about 0.06 eV for all bases but larger energy difference for the $2\,{}^1A_{1g}$ state with around 0.28-0.29 eV and 0.79-0.81 eV for the $1\,{}^1B_{2g}$ state. Note that from CASSCF(4,4) to CASSCF(12,12) every vertical energy is smaller. We can make the contrary observation for the CASPT2 method where from CASPT2(4,4) to CASPT2(12,12) every vertical energy is larger. For the CASPT2(12,12) method we have similar values for the triplet state and for the $2\,{}^1A_{1g}$ state, considering all bases, with an energy difference of around 0.05-0.06 eV and 0.02-0.05 eV respectively. The energy difference is larger for the $1\,{}^1B_{2g}$ state with about 0.27-0.29 eV. Next we have the NEVPT2 methods, the first observation that we can make is that by increasing the size of the active space we retrieve the right ordering of the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states. Again, every vertical energy is higher in the NEVPT2(12,12) case than for the NEVPT2(4,4) one.
|
||||
Again, we have computed the vertical energies at the CCSDT and CCSDTQ level as well as their approximation the CC3 and CC4 methods, respectively. Note that for CC we started from a restricted Hartree-Fock (RHF) reference and in that case the ground state is the $2\,{}^1A_{1g}$ state, then the $X\,{}^1B_{1g}$ state is the single deexcitation and the $1\,{}^1B_{2g}$ state is the double excitation from our ground state. For the CC3 method we do not have the vertical energies for the triplet state $1\,{}^3A_{2g}$. Considering all bases for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states we have an energy difference of about 0.15 eV and 0.12 eV, respectively. The CCSDT energies are close to the CC3 ones for the $2\,{}^1A_{1g}$ state with an energy difference of around 0.03-0.06 eV considering all bases. For the $1\,{}^1B_{2g}$ state the energy difference between the CC3 and the CCSDT values is larger with 0.18-0.27 eV. We can make a similar observation between the CC4 and the CCSDTQ values, for the $2\,{}^1A_{1g}$ state we have an energy difference of about 0.01 eV and this time we have smaller energy difference for the $1\,{}^1B_{2g}$ with 0.01 eV. Then we discuss the multireference results and this time we were able to reach the AVQZ basis. Again we consider two different active spaces, four electrons in four orbitals and twelve electrons in twelve orbitals. If we compare the CASSCF(4,4) and CASPT2(4,4) values we can see large energy differences for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states, for the $2\,{}^1A_{1g}$ state we have an energy difference of about 0.67-0.74 eV and 1.65-1.81 eV for the $1\,{}^1B_{2g}$ state. The energy difference is smaller for the triplet state with 0.27-0.31 eV, we can notice that all the CASSCF(4,4) vertical energies are higher than the CASPT2(4,4) ones. Then we have the NEVPT2(4,4) methods (SC-NEVPT2(4,4) and PC-NEVPT2(4,4)) for which the vertical energies are quite similar, however we can notice that we have a different ordering of the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states with $1\,{}^1B_{2g}$ higher in energy than $2\,{}^1A_{1g}$ for the two NEVPT2(4,4) methods. Then we have the results for the same methods but with a larger active space. For the CASSCF(12,12) we have similar values for the triplet state with energy difference of about 0.06 eV for all bases but larger energy difference for the $2\,{}^1A_{1g}$ state with around 0.28-0.29 eV and 0.79-0.81 eV for the $1\,{}^1B_{2g}$ state. Note that from CASSCF(4,4) to CASSCF(12,12) every vertical energy is smaller. We can make the contrary observation for the CASPT2 method where from CASPT2(4,4) to CASPT2(12,12) every vertical energy is larger. For the CASPT2(12,12) method we have similar values for the triplet state and for the $2\,{}^1A_{1g}$ state, considering all bases, with an energy difference of around 0.05-0.06 eV and 0.02-0.05 eV respectively. The energy difference is larger for the $1\,{}^1B_{2g}$ state with about 0.27-0.29 eV. Next we have the NEVPT2 methods, the first observation that we can make is that by increasing the size of the active space we retrieve the right ordering of the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states. Again, every vertical energy is higher in the NEVPT2(12,12) case than for the NEVPT2(4,4) one.
|
||||
|
||||
%%% TABLE VI %%%
|
||||
\begin{squeezetable}
|
||||
@ -769,7 +770,10 @@ For the $1\,{}^1B_{1g} $ state of the $(D_{2h})$ structure we see that all the x
|
||||
|
||||
Then, for the $2\,{}^1A_{g} $ state we obtain closer results of the SF-TD-DFT methods to the TBE than in the case of the $1\,{}^1B_{1g} $ state. Indeed, we have an energy difference of about 0.01-0.34 eV for the $2\,{}^1A_{g} $ state whereas we have 0.35-0.93 eV for the $1\,{}^1B_{1g} $ state. The ADC schemes give the same error to the TBE value than for the other singlet state with 0.02 eV for the ADC(2) scheme and 0.07 eV for the ADC(3) one. The ADC(2)-x scheme provides a larger error with 0.45 eV of energy difference. Here, the CC methods manifest more variations with 0.63 eV for the CC3 value and 0.28 eV for the CCSDT compared to the TBE values. The CC4 method provides a small error with less than 0.01 eV of energy difference. The multiconfigurational methods globally give smaller error than for the other singlet state with, for the two active spaces, 0.03-0.12 eV compared to the TBE value. We can notice that CC3 and CCSDT provide larger energy errors for the $2\,{}^1A_{g} $ state than for the $1\,{}^1B_{1g} $ state, this is due to the strong multiconfigurational character of the $2\,{}^1A_{g} $ state whereas the $1\,{}^1B_{1g} $ state has a very weak multiconfigurational character. It is interesting to see that SF-TD-DFT and SF-ADC methods give better results compared to the TBE than CC3 and even CCSDT meaning that spin-flip methods are able to describe double excited states. Note that multireference methods obviously give better results too for the $2\,{}^1A_{g} $ state.
|
||||
|
||||
Finally we look at the vertical energy errors for the $(D_{4h})$ structure. First, we consider the $1\,{}^3A_{2g} $ state, the SF-TD-DFT methods give errors of about 0.07-1.6 eV where the largest energy differences are provided by the Hybrid functionals. The ADC schemes give similar error with around 0.06-1.1 eV of energy difference. For the CC methods we have an energy error of 0.06 eV for CCSD and less than 0.01 eV for CCSDT. Then for the multireference methods with the four by four active space we have for CASSCF(4,4) 0.29 eV of error and 0.02 eV for CASPT2(4,4), again CASPT2 demonstrates its improvement compared to CASSCF. The other methods provide energy differences of about 0.12-0.13 eV. A larger active space shows again an improvement with 0.23 eV of error for CASSCF(12,12) and around 0.01-0.04 eV for the other multireference methods. CIPSI provides similar error with 0.02 eV. Then, we look at the $2\,{}^1A_{1g}$ state where the SF-TD-DFT shows large variations of error depending on the functionals, the energy error is about 0.10-1.03 eV. The ADC schemes give better errors with around 0.07-0.41 eV and where again the ADC(2)-x does not improve the ADC(2)-s energy but also gives worse results. For the CC methods we have energy errors of about 0.10-0.16 eV and CC4 provides really close energy to the TBE one with 0.01 eV of error. For the multireference methods we globally have an improvement of the energies from the four by four to the twelve by twelve active space with errors of 0.01-0.73 eV and 0.02-0.44 eV respectively with the largest errors coming from the CASSCF method. Lastly, we look at the $1\,{}^1B_{2g}$ state where we have globally larger errors. The SF-TD-DFT exhibits errors of 0.43-1.50 eV whereas ADC schemes give errors of 0.18-0.30 eV. CC3 and CCSDT provide energy differences of 0.50-0.69 eV and the CC4 shows again close energy to the CCSDTQ TBE energy with 0.01 eV of error. The multireference methods give energy differences of 0.38-1.39 eV and 0.11-0.60 eV for the four by four and twelve by twelve active space respectively. Here again we can make the same comment for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states. The first state has a strong multiconfigurational character but shows small errors through all methods and the latter has a weak multiconfigurational character but larger errors
|
||||
Finally we look at the vertical energy errors for the $D_{4h}$ structure. First, we consider the $1\,{}^3A_{2g} $ state, the SF-TD-DFT methods give errors of about 0.07-1.6 eV where the largest energy differences are provided by the hybrid functionals. The ADC schemes give similar error with around 0.06-1.1 eV of energy difference. For the CC methods we have an energy error of 0.06 eV for CCSD and less than 0.01 eV for CCSDT. Then for the multireference methods with the four by four active space we have for CASSCF(4,4) 0.29 eV of error and 0.02 eV for CASPT2(4,4), again CASPT2 demonstrates its improvement compared to CASSCF. The other methods provide energy differences of about 0.12-0.13 eV. A larger active space shows again an improvement with 0.23 eV of error for CASSCF(12,12) and around 0.01-0.04 eV for the other multireference methods. CIPSI provides similar error with 0.02 eV. Then, we look at the $2\,{}^1A_{1g}$ state where the SF-TD-DFT shows large variations of error depending on the functionals, the energy error is about 0.10-1.03 eV. The ADC schemes give better errors with around 0.07-0.41 eV and where again the ADC(2)-x does not improve the ADC(2)-s energy but also gives worse results. For the CC methods we have energy errors of about 0.10-0.16 eV and CC4 provides really close energy to the TBE one with 0.01 eV of error. For the multireference methods we globally have an improvement of the energies from the four by four to the twelve by twelve active space with errors of 0.01-0.73 eV and 0.02-0.44 eV respectively with the largest errors coming from the CASSCF method. Lastly, we look at the $1\,{}^1B_{2g}$ state where we have globally larger errors. The SF-TD-DFT exhibits errors of 0.43-1.50 eV whereas ADC schemes give errors of 0.18-0.30 eV. CC3 and CCSDT provide energy differences of 0.50-0.69 eV and the CC4 shows again close energy to the CCSDTQ TBE energy with 0.01 eV of error. The multireference methods give energy differences of 0.38-1.39 eV and 0.11-0.60 eV for the four by four and twelve by twelve active spaces respectively. We can notice that we have larger variations for the vertical energies of the square CBD than for the rectangular one. This can be explained by the fact that because of the degeneracy in the $D_{4h}$ structure it leads to strong multiconfigurational character states where single reference methods are unreliable. We can also see that for the CC methods we have a better description of the $2\,{}^1A_{1g}$ state than the $1\,{}^1B_{2g}$ state, this can be related, as previously said in Subsubsection \ref{sec:D4h}, to the fact that $1\,{}^1B_{2g}$ corresponds to a double excitation from the reference state. To obtain an improved description of the $1\,{}^1B_{2g}$ state we have to include quadruples.
|
||||
|
||||
|
||||
%Here again we can make the same comment for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states of the square CBD than the $1\,{}^1B_{1g}$ and $2\,{}^1A_{g}$ states of the rectangular CBD. The first state ($2\,{}^1A_{1g}$) has a strong multiconfigurational character
|
||||
|
||||
|
||||
|
||||
@ -785,7 +789,7 @@ Finally we look at the vertical energy errors for the $(D_{4h})$ structure. Firs
|
||||
%\begin{tabular}{*{1}{*{8}{l}}}
|
||||
&\mc{3}{r}{$D_{2h}$ excitation energies (eV)} & \mc{3}{r}{$D_{4h}$ excitation energies (eV)} \\
|
||||
\cline{3-5} \cline{6-8}
|
||||
Method & AB & $1\,{}^3B_{1g} $ & $1\,{}^1B_{1g} $ & $2\,{}^1A_{g} $ & $1\,{}^3A_{2g} $ & $2\,{}^1A_{1g} $ & $1\,{}^1B_{2g} $ \\
|
||||
Method & AB & $1\,{}^3B_{1g} $~(98.7 \%) & $1\,{}^1B_{1g} $ (95.0 \%)& $2\,{}^1A_{g} $(0.84 \%) & $1\,{}^3A_{2g} $ & $2\,{}^1A_{1g} $ & $1\,{}^1B_{2g} $ \\
|
||||
\hline
|
||||
SF-TD-B3LYP & $10.41$ & $0.241$ & $-0.926$ & $-0.161$ & $-0.164$ & $-1.028$ & $-1.501$ \\
|
||||
SF-TD-PBE0 & $8.95$ & $0.220$ & $-0.829$ & $-0.068$ & $-0.163$ & $-0.903$ & $-1.357$ \\
|
||||
@ -794,26 +798,26 @@ SF-TD-M06-2X & $1.42$ & $0.000$ & $-0.354$ & $0.208$ & $-0.066$ & $-0.097$ & $-0
|
||||
SF-TD-CAM-B3LYP & $9.90$ & $0.280$ & $-0.807$ & $-0.011$ & $-0.134$ & $-0.920$ & $-1.370$ \\
|
||||
SF-TD-$\omega $B97X-V & $10.01$ & $0.335$ & $-0.774$ & $0.064$ & $-0.118$ & $-0.928$ & $-1.372$ \\
|
||||
SF-TD-M11 & $2.29$ & $0.097$ & $-0.474$ & $0.151$ & $-0.063$ & $-0.312$ & $-0.675$ \\
|
||||
SF-TD-LC-$\omega $PBE08 & $10.81$ & $0.435$ & $-0.710$ & $0.199$ & $-0.086$ & $-0.939$ & $-1.376$ \\
|
||||
SF-TD-LC-$\omega $PBE08 & $10.81$ & $0.435$ & $-0.710$ & $0.199$ & $-0.086$ & $-0.939$ & $-1.376$ \\[0.1cm]
|
||||
SF-ADC(2)-s & $-0.30$ & $0.069$ & $-0.026$ & $-0.018$ & $0.112$ & $0.112$ & $-0.190$ \\
|
||||
SF-ADC(2)-x & $1.44$ & $0.077$ & $-0.094$ & $-0.446$ & $0.068$ & $-0.409$ & $-0.303$ \\
|
||||
SF-ADC(3) & $0.65$ & $-0.043$ & $0.037$ & $0.075$ & $-0.065$ & $0.075$ & $-0.181$ \\
|
||||
SF-ADC(3) & $0.65$ & $-0.043$ & $0.037$ & $0.075$ & $-0.065$ & $0.075$ & $-0.181$ \\[0.1cm]
|
||||
CCSD & $0.95$ & & & & $-0.059$ & $0.100$ & \\
|
||||
CC3 & $-1.05$ & $-0.060$ (98.7 \%) & $-0.006$ (95.0 \%) & $0.628$ (0.84 \%) & & $0.162$ & $0.686$ \\
|
||||
CC3 & $-1.05$ & $-0.060$ & $-0.006$ & $0.628$ & & $0.162$ & $0.686$ \\
|
||||
CCSDT & $-0.25$ & $-0.051$ & $0.014$ & $0.280$ & $0.005$ & $0.131$ & $0.503$ \\
|
||||
CC4 & $-0.11$ & & $0.003$ & $-0.006$ & & $0.011$ & $-0.013$ \\
|
||||
CCSDTQ & $0.00$ & & $0.000$ & $0.000$ & $0.000$ & $0.000$ & $0.000$ \\
|
||||
CCSDTQ & $0.00$ & & $0.000$ & $0.000$ & $0.000$ & $0.000$ & $0.000$ \\[0.1cm]
|
||||
SA2-CASSCF(4,4) & & $0.208$ & $1.421$ & $0.292$ & $0.290$ & $0.734$ & $1.390$ \\
|
||||
CASPT2(4,4) & & $-0.050$ & $-0.202$ & $-0.077$ & $-0.016$ & $0.006$ & $-0.399$ \\
|
||||
XMS-CASPT2(4,4) & & & & $-0.035$ & & & \\
|
||||
SC-NEVPT2(4,4) & & $-0.083$ & $-0.703$ & $-0.041$ & $-0.120$ & $-0.072$ & $-0.979$ \\
|
||||
PC-NEVPT2(4,4) & & $-0.080$ & $-0.757$ & $-0.066$ & $-0.118$ & $-0.097$ & $-1.031$ \\
|
||||
MRCI(4,4) & & $0.106$ & $0.553$ & $0.121$ & $0.127$ & $0.324$ & $0.381$ \\
|
||||
MRCI(4,4) & & $0.106$ & $0.553$ & $0.121$ & $0.127$ & $0.324$ & $0.381$ \\[0.1cm]
|
||||
SA2-CASSCF(12,12) & $2.66$ & $0.224$ & $0.719$ & $0.068$ & $0.226$ & $0.443$ & $0.600$ \\
|
||||
CASPT2(12,12) & & $0.018$ & $0.058$ & $-0.106$ & $0.039$ & $0.038$ & $-0.108$ \\
|
||||
XMS-CASPT2(12,12) & & & & $-0.090$ & & & \\
|
||||
SC-NEVPT2(12,12) & $-0.65$ & $0.039$ & $0.063$ & $-0.063$ & $0.021$ & $0.046$ & $-0.142$ \\
|
||||
PC-NEVPT2(12,12) & & $0.000$ & $-0.062$ & $-0.093$ & $-0.013$ & $-0.024$ & $-0.278$ \\
|
||||
PC-NEVPT2(12,12) & & $0.000$ & $-0.062$ & $-0.093$ & $-0.013$ & $-0.024$ & $-0.278$ \\[0.1cm]
|
||||
%CIPSI & & $-0.001\pm 0.030$ & $0.017\pm 0.035$ & $-0.120\pm 0.090$ & $0.025\pm 0.029$ & $0.130\pm 0.050$ & \\
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\bf{TBE} & $\left[\bf{8.93}\right]$\fnm[1] & $\left[\bf{1.462}\right]$\fnm[2] & $\left[\bf{3.125}\right]$\fnm[3] & $\left[\bf{4.149}\right]$\fnm[3] & $\left[\bf{0.144}\right]$\fnm[4] & $\left[\bf{1.500}\right]$\fnm[3] & $\left[\bf{2.034}\right]$\fnm[3] \\
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\end{tabular}
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@ -843,12 +847,13 @@ In order to provide a benchmark of the AB and vertical energies we used coupled-
|
||||
|
||||
With SF-TD-DFT the quality of the results are, of course, dependent on the functional but for the doubly excited states we have solid results. In SF-ADC we have very good results compared to the TBEs even for the doubly excited states, nevertheless the ADC(2)-x scheme give almost systematically worse results than the ADC(2)-s ones and using the ADC(3) scheme does not always provide better values.
|
||||
|
||||
|
||||
The description of the excited states of the $D_{2h}$ structure give rise to good agreement between the single reference and multiconfigurational methods due to the large T1 percentage of the first two excited states. When this percentage is much smaller as in the case of the doubly excited state $2\,{}^1A_{g}$ the spin-flip methods show very good results within the ADC framework but even at the TD-DFT level spin-flip display good results compared to the TBE value. As said in the discussion, for the $D_{4h}$ geometry, the description of excited states is harder because of the strong multiconfigurational character where SF-TD-DFT can present more than 1 eV of error compared to the TBE. However, SF-ADC can show error of around 0.1-0.2 eV which can be better than the multiconfigurational methods results.
|
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|
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%%%%%%%%%%%%%%%%%%%%%%%%
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\acknowledgements{
|
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EM, AS, and PFL acknowledge funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant agreement No.~863481).}
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%%%%%%%%%%%%%%%%%%%%%%%%
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||||
|
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\nocite{*}
|
||||
\bibliography{CBD}
|
||||
\end{document}
|
||||
|
||||
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Reference in New Issue
Block a user